perm filename ANALOG[RDG,DBL]5 blob
sn#595362 filedate 1981-06-22 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00067 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00009 00002 ∂25 Jan 1981 0633-PST Darden analogy seminar, electronically
C00011 00003 ∂Mailed to DARDEN@SUMEX 12:19 11-Feb
C00016 00004 ∂12 Feb 1981 0806-PST Darden
C00020 00005 ∂16 Feb 1981 1742-PST Darden Hello and Analogy Seminar
C00022 00006 ∂17 Feb 1981 0901-PST Darden Analogy Seminar, I, 2/17/81
C00032 00007 ∂23 Feb 1981 0643-PST Darden analogy.2
C00040 00008 ∂Mailed to DARDEN@SUMEX 18:13 25-Feb
C00046 00009 ∂26-Feb-81 0752 Darden@SUMEX-AIM analogies and other things
C00049 00010 ∂26-Feb-81 0804 Darden@SUMEX-AIM reply to queries
C00051 00011 ∂26-Feb-81 0945 Darden@SUMEX-AIM Analogy.3
C00059 00012 ∂26-Feb-81 1241 Buchanan@SUMEX-AIM Re: Analogy.3
C00060 00013 ∂28-Feb-81 1520 Darden@SUMEX-AIM Boyd and Winograd on natural kinds
C00063 00014 ∂Mailed to DARDEN @ SUMEX 11:41 4-March
C00071 00015 ∂Mailed to DARDEN @ SUMEX 12:02 4-March
C00085 00016 ∂05-Mar-81 0810 Darden@SUMEX-AIM analogy.4 MG's ''Metaphors and Models''
C00091 00017 ∂05-Mar-81 1005 Dietterich@SUMEX-AIM Re: analogy.4 MG's ''Metaphors and Models''
C00094 00018 ∂07-Mar-81 1938 Darden@SUMEX-AIM next analogy discussion
C00108 00019 ∂07-Mar-81 1950 Darden@SUMEX-AIM other points
C00112 00020 ∂11-Mar-81 0545 Darden@SUMEX-AIM non-analogy
C00115 00021 ∂Mailed to DARDEN @ SUMEX 16:21 13-March
C00126 00022 ∂13-Mar-81 2136 Darden@SUMEX-AIM (Response to message)
C00128 00023 ∂14-Mar-81 1108 CSD.GREINER at SU-SCORE My IJCAI Paper-To-Be
C00129 00024 ∂18-Mar-81 1824 Darden@SUMEX-AIM Russ's IJCAI paper
C00130 00025 ∂24-Mar-81 0736 Darden@SUMEX-AIM analogy.people file
C00133 00026 ∂27-Mar-81 2327 STT Analogy and alternate formulations
C00142 00027 ∂28-Mar-81 1409 Darden@SUMEX-AIM reply to Steve Tappel on problem reformulation and perspectives
C00145 00028 ∂29-Mar-81 0726 Darden@SUMEX-AIM theories in biology
C00150 00029 ∂01-Apr-81 1237 STT More on perspectives, Kling and Feynman
C00157 00030 ∂01-Apr-81 1810 Darden@SUMEX-AIM response to STT on methods for guessing hypotheses
C00159 00031 ∂02-Apr-81 1331 Buchanan@SUMEX-AIM new method
C00160 00032 ∂03-Apr-81 0452 Darden@SUMEX-AIM discovery of two-dimensional electorphoresis techniques
C00165 00033 ∂04-Apr-81 0726 Darden@SUMEX-AIM Maxam on DNA techniques
C00168 00034 ∂10-Apr-81 0550 Darden@SUMEX-AIM Analogy seminar.5
C00176 00035 ∂16-Apr-81 0659 Darden@SUMEX-AIM Discussions with Maxam
C00184 00036 ∂16-Apr-81 0733 Darden@SUMEX-AIM discussion with Winston and Gentner
C00190 00037 ∂17-Apr-81 0505 Darden@SUMEX-AIM properties and relations
C00195 00038 **** REREAD FROM HERE ON ****
C00196 00039 ∂19-Apr-81 1830 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Boyd on the meanings (referents) of theoretical terms.
C00202 00040 ∂19-Apr-81 2045 CSD.DIETTERICH@SU-SCORE Definitions of AI TERMS: Perspectives, Analogies, et al.
C00213 00041 ∂20-Apr-81 0605 Darden@SUMEX-AIM partial reply to Tom
C00218 00042 ∂22-Apr-81 0717 Darden@SUMEX-AIM hypothesis formation in gene regulation
C00229 00043 ∂23-Apr-81 0523 Darden@SUMEX-AIM gene regulation analogy
C00251 00044 ∂25-Apr-81 0900 Darden@SUMEX-AIM discussions with Herb Simon
C00260 00045 ∂25-Apr-81 0859 Darden@SUMEX-AIM Feigenbaum response
C00265 00046 ∂25-Apr-81 1312 STT definitions and examples for analogy and reformulation
C00290 00047 ∂25-Apr-81 1320 STT detailed example of analogy
C00312 00048 ∂01-May-81 0728 Darden@SUMEX-AIM plans on gene regulation
C00322 00049 ∂02-May-81 0652 Darden@SUMEX-AIM formation of a new concept
C00337 00050 ∂04-May-81 2218 Clancey at SUMEX-AIM The Titular Bishop of Titiopolis
C00345 00051 ∂05-May-81 0608 Darden@SUMEX-AIM response to Bill Clancey
C00352 00052 ∂05-May-81 1925 Darden@SUMEX-AIM fossils and categories
C00364 00053 ∂06-May-81 1114 Clancey at SUMEX-AIM Steno clarified
C00370 00054 ∂08-May-81 0917 Darden@SUMEX-AIM analogy.6
C00380 00055 ∂To Darden@SUMEX 17:47 20-May
C00388 00056 ∂20-May-81 1842 Darden@SUMEX-AIM teaching reasoning by analogy
C00391 00057 ∂20-May-81 1842 Darden@SUMEX-AIM Clancey on teaching reasoning by analogy
C00396 00058 ∂20-May-81 1832 Darden@SUMEX-AIM Russ on analogy
C00404 00059 ∂27-May-81 0756 Darden@SUMEX-AIM analogy.hesse
C00420 00060 ∂28-May-81 0540 Darden@SUMEX-AIM vacation
C00422 00061 ∂30-May-81 2005 STT Papers by Gentner on metaphor and analogy
C00431 00062 ∂TO STT 18:44 3-Jun Gi'me, gi'me, gi'me!
C00432 00063 ∂TO CSD.HOFSTADER@SCORE 15:46 8-Jun
C00435 00064 ∂ 3 Jun 1981 1636-PDT CSD.GREINER Re: here it is
C00437 00065 Unmailed article by Hofstadter - to appear in Scientific American
C00507 00066 ∂16 Jun 1981 1537-PDT CSD.HOFSTADTER analogies, etc.
C00514 00067 ∂To DARDEN@SUMEX 16:00 22-Jun
C00516 ENDMK
C⊗;
∂25 Jan 1981 0633-PST Darden analogy seminar, electronically
To: Bennett, Greiner, Cooper, Genesereth, Lenat
cc: Buchanan, Dietterich, STT@SAIL
Hi, folks, Tom Dietterich and I are both reading Metaphor and Thought,
edited by Andrew Ortony and probably still available in the Stanford
bookstore. Tom sent me a message about the Max Black article and it
occurred to me that we could all have a messge seminar electronically.
Are you interested? If so, I would suggest reading about one article
a week, briefly reacting to it and also typing in whatever new ideas
about analogy you have had during the week.
I am signing on about once a week so feel free to send me messages
at Darden at SUMEX. I feel like I hve retreated to a distant outpost,
so feel free to keep me posted on what is happening around there.
Bye, Lindley
-------
∂Mailed to DARDEN@SUMEX 12:19 11-Feb
Shoes, and ships and sealing wax...
Lindley -
Sorry to take so long to respond - your message found itself pushed deeper
and deeper into my stack of things to do, and only now surfaced. Yes, I
would be interested in participating in a long-distance seminar... I even
tried to find Ortony's book in the bookstore, unsuccessfully. Its list of
articles (or at least their titles) seemed really intriguing.
By the way, I'm now attending Hintikka's "Theory of Knowledge" class, and
finally getting a chance to peruse all sorts of basic philosophical
classics - by Russell, Quine, Husserl, as well as some spistemological
materpeices by the likes of Christie (yes, Agatha), and Sir Arthur
(Sherlock Holmes) Doyle. It is interesting seeing many familiar issues
(such as representation, and perception) addressed by people "on the
outside". [Just because they got there first doesn't mean they deserve
`insider' status...] Anyway, Hintikka is, of course, well versed in many
perspectives of these questions, and seems sorta familiar with some AI
approaches, and, apparently, fascinated by the prospects.
On other fronts, I just finished a surprisingly tiring week in bed -- a
funny bug which caused both a fever and a slew of painful ulcerations in
my mouth. It was terrible - not only couldn't I eat, but even talking
caused a great deal of pain, and even then came out like a drunken slur.
Fortunately that's all behind me. I can extoll the virtues of Xylocaine,
though. Makes me a believer of medical science...
Well, hope all is well with you. Keep me informed of your trials and
tribulations on the eastern coast.
- Russ -
PS During one of our discussions I mentioned it would be interesting if
DNA ever encoded a different interpreter -- so the same nucleotide base
sequence would be able to express distinct proteins. At that time I went
on to say that seemed an immensely difficult task -- and that it has
probably never happened and never will. Well, in the last few days, I
encountered descriptions of mitochondria from two totally independent
sources. I had never realized what an interesting substance it is. In
particular, it's RNA is different from that in the rest of the cell -- 3
of the 64 codons are translated DIFFERENTLY! So here's that case of
another interpreter! (Of course there is no evidence that any of the
mitochondria's DNA is ever transcribed by the nuclear RNA -- perhaps it
was to prevent this from ever happening that lead to this different
encoding -- ie to insure the continued isolation of the mitochondria...)
(You probably already knew this, and may even have mentioned it then; if
so, I ashamed to admit, it never sank in...)
∂12 Feb 1981 0806-PST Darden
To: GREINER
cc: BUCHANAN, DIETTERICH, STT@SAIL
HI, RUSS, GLAD TO HEAR FROM YOU. SORRY THAT YOU HAVE BEEN SICH; THIS MUST
BE PRIME SEASON FOR NASTY BUGS. THIS IS THE FIRST WEEK I HAVE FELT NEAR NORMAL
SINCE I GOT VIRAL PNEUMONIA DECEMBER 30.
SORYY YOU WEREN'T ABLE TO FIND THE ORTONY BOOK AT THE BOOKSTORE; THERE WERE
SEVERAL COPIES, I THINK IN THE LINGUISTIC SECTION, WHEN I BOUGHT MINE.
JIM, TOM AND STEVE ALL HAVE COPIES, SO XEROXING SEPARATE ARTICLES IS A
POSSIBILITY. I AM WAITING UNTIL MY Z19 TERMINAL COMES AND I FINGURE OUT
HOW TO GET INT TV-EDIT AND MAKE FILES TO SEND THE LONG MESSAGE ABOUT
GENERAL THOUGHTS ON ANALOGY AND SPECIFIC COMMENTS ON MAX BLACK'S ARTICLE.
TOM HAS BEEN THINKING LATELY BOUT HOW A SYSTEM COULD DEVELOP A VAUGE IDEA
ABOUT SOMETHING THAT HADN'T BEEN EXPLICITLY REPRESENTED AND THEN PROCEED
TO MAKE IT MORE DETAILED AND SPECIFIC. AS YOU KNOW, THE BOYD ARTICLE TALKS
ABOUT THE USE OF METAPHORS IN SCIENTIFIC THEORIES TO DO THIS.
KEEP ME POSTED ON INTERESTING IDEAS THAT COME OUT OF THE HINTIKKA
COURSE. YES, I KNOW ABOUT THE SLIGHTLY DIFFERENT GENETIC CODE IN
MITOCHONDRIA, BUT YOUR INTERPRETATION FROM AN AI PERSPECTIVE OF
HAVING DIFFERENT INTERPRETERS FOR THE SAME CODE IS AN
INTERESTING PERSPECTIVE FOR ME.
BRUCE IS SENDING ME AN INTERLISP MANUAL AND I AM GOING TO BE
TRYING TO LEARN LISP ALONG WITH EVERYTHING ELSE THIS SEMESTER, NAMELY
TEACHING HISTORY OF MODERN BIOLOGY (DARWIN NOW; GENETICS LATER); TEACHING
TWO SECTIONS OF INTRODUCTORY PHILOSOPHY OF SCIENCE (THE BEGINNINGS OF SCIENCE
IN THE PRESOCRATICS, PLATO AND ARISTOTLE NOW); READING THE ORTONY AND
SENDING ANALOGY THOUGHTS CROSS COUNTRY TO ALL OF YOU; READING ABOUT
CAI WORK IN TEACHING LOGIC; AND USUAL COMMITTEE STUFF. WHEW! WILL I MANAGE
IT ALL? WELL, WITH A TERMINAL AT HOME IT WILL BE EASIER.
KEEP IN TOUCH AND I WILL COPY YOU ON ANALOGY SEMINAR MESSAGES.
BYE, LINDLEY
-------
∂16 Feb 1981 1742-PST Darden Hello and Analogy Seminar
To: cooper
cc: Dietterich, STT@SAIL, Greiner, Buchanan
Hi, Greg, nice to hear from you. I am feeling much better and am
almost back to normal. I now have my own Z19 terminal at home;
unfortunately, the 1200 VADIC modem that I brought back from
SUMEX doesn't seem to be working properly, but I am borrowing
a friend's 300 baud one and am finally "on the air." I am not
sure why this is double space and will have to read the manual
to see what setting to change.
I enjoyed reading your thesis proposal and will read again and send
you comments, if any later. We have been sending occasional messages
about analogy, but haven't really started yet. I am going to try to
get into TV edit and type a long message about my current ideas
about analogy and the Black article in Ortony, Metaphor and Thought.
Russ said he had trouble finding a copy in the Stanford bookstore;
it can be ordered directly from Cambridge University Press, if
necessary. I will copy you on the messages.
Keep in touch., Bye Lindley
-------
∂17 Feb 1981 0901-PST Darden Analogy Seminar, I, 2/17/81
To: Dietterich, STT@SAIL, Greiner, Bennett, Cooper, Buchanan,
To: Lenat, Genesereth
cc: Darden
Hello everybody. I now have my own Z19 in my study in Greenbelt,
Maryland. There are two things that I wanted to do before starting
this seminar but haven't been able to do. First, I would like to
know how to set up a file with everyone's name in it and use that
for the To: in msg. Secondly, I had hoped to learn to use TV edit
before starting, but I spent the morning finding that it would
not respond to my ESC (command) signals. If anybody can help
with these details, please let me know. Anyway, I am tired of
waiting to start this, so I hope you will be able to read it
without good editing.
The basic question at issue if how do we (humans or computers)
come up with new ideas? A hypothesis to be examined is this: new ideas
arise by analogy with old ones. Although at the outset that hypothesis
sounds very restrictive as to the nature of new ideas, if one supposes
that more than one analogy can be operative, then one can get "new"
combinations of parts. This idea of using multiple analogies in
solving a complex problem is not one that I have read anywhere; I
found it operating in some of my historical cases.
One of our first questions is this: what is an analogy?
During the seminar last fall, one possible analysis emerged:
an analogy is a relation of matching some nodes in two heirarchy trees;
the nodes can be objects, propeties or relations, depending on what is
represented by the trees. The idea of using a generalization-
specialization tree allows more flexibility is matching than requiring
exact matches at the same specialization level.
One question we did not answer was how to find good analogies
That will probably depend on the context of the problem to be solved
by using the analogy, but may also involve the number of matches or
something else that is not context dependent.
Another key idea that we discussed last fall and that Tom and
I have discussed lately is that a new idea begins as a vague one (either
a short property list or general fuzziness). Analogies can be seen
as a way of coming up with the early, vague idea that will be sharpened
into a much more specific, new idea (say a new scientific theory) with
further specification. The additions or sharpening may come of the same
analogy, from other analogies, from "tinkering" with the vague idea
itself, or somewhere else.
Another idea that I have developed in my work is that interfield
connections between theories in two scientific fields can function much {
like an analogy. So, when I am discussing analogies, I am often thinking
about interfield connections as well. But if one is doing science and
one can find a related field with which to establish matching relations,
then that may well be more heuristically valuable than a mere analogy.
My evidence for that claim comes from historical cases in which interfield
connections were quite valuable.
On Max Black's article in Ortony, ed., Methphor and Thought,
"More About Metaphor" : Black's interaction view of metaphor (summarized
on pp.27-29) makes metaphor sound like a process: we choose a subject and
analogue (his primary and secondary subject, respectively) and use the
analogue to construct features of the subject. That more dynamic notion
than my earlier characterization of simply matching in already constructed
trees is probably useful. I don't think he is very clear about the nature of
the interaction that occurs between the subject and analogue: p.29, No. 5
I can understand that one uses properties of the analogue to construct new
properties of the subject but how does that induce "parallel"(??) changes
in the analogue? With analogies, it seems to me, the analogue is often
well understood, in fact, it is chosen because it is well understood, and
most of the influence goes in one direction. In my interfield theory cases,
it depends on how well developed a particular field is at the time of the
connection how much mutual interaction will occur. But for any given match
one field has a property which the other lacks and contruction occurs in
the field without that kind of property. For other properties, the other
field may be the one lacking that property so the influences goes the
other way. If we use p-1 in field-1 to construct p-1' in field 2, then it
seems to me that p-1 itself is not likely to change. But, perhaps, I am
just not understanding what Black means by "interaction.
Steve, I think you will particularly like the discussion on pp.32-
34 about the different ways of seeing a star: it is very much like your
problem-reformulation ideas.
I enjoyed trying to make sense of Black's last section on
whether metaphors are creative. It is a very tough problem to decide
what counts as a new or creative idea or theory. Also, if one takes
a realistic view of theories, then one much explain what is happening
when a new theory is proposed. Black's discussion of metaphors of
"creating" new views of things that we in some sense already there
is quite interesting: e.g. (p.39) "Did the slow-motion appearance
of a galloping horse exist before the invention of cinematography?"
His claim: "some metaphors enable us to see aspects of reality that
the metaphor's production helps to constitute." "some metaphors are...
'cognitive instruments,'indispensable for perceiving connections that,
once perceived, are then truly present...." It is fascinating to think
about the extent to which scientific theories do this. Also, it is int-
eresting to think about the extent to which models "create" such new
views of things, which in some sense are then "really" (sorry for the
use of that problematic work, Bruce) there. Could computer models of
things function to create new "views" (somehow I don't like that word)
of things?
Well, this is very long and I have a horror of a system crash
before I send it. My next message, if not a response to something from
one of you, will be on Boyd's article," What is Metaphor a Metaphor
For?"
Bye, Lindley
-------
∂23 Feb 1981 0643-PST Darden analogy.2
To: dietterich, STT@SAIL, Greiner, Bennett, Cooper, Buchanan
cc: Lenat, Genesereth, Darden
Hello everybody. I have a file that I created using TV-Edit called
<DARDEN>ANALOGY.2;1. Can you all call that from my directory?
Since I do not know the answer to that question, I am going to
try to send it to you using ctrl B in msg. If you don't receive
anything about analogy here, let me know what I should be doing.
A controversy about the role of analogies in scientific theories
has been an issue in philosophy of science. Are analogies "merely heuristic-
ally useful" in discovery but not an integral part of the theory, once
constructed or, alternatively, do they play a role in the knowledge-claims
made by a scientific theory?
For hard-nosed axiomatic types, analogies are not to be viewed as
an integral component of the finished theory. But for others, especially
realists such as Rom Harre'(E.g. in Principles of Scientific Thinking)or
Dick Boyd (in Ortony,"Metaphor and Theory Change:What is 'metaphor' a
Metaphor For?"), models, metaphors or analogies (I am using the words
synonymously here) become integral parts of a theory. Harre' believes that
theories aim at providing mechanisms which serve to account for observed
phenomena; models serve the function of providing the underlying mechanisms.
Boyd sees an aim of science as the "accommodation of language to the causal
structure of the world...this is the task of arranging our language so that
our linguistic categories 'cut the world at its joints'...."(p.358) In so far
as metaphors help us in discovering and discussing appropriate causal
structures, they function as integral components of our knowledge, according
to Boyd; however, he does suggest that a completed research program may
serve to fully explicate a metaphor. Boyd is concerned, as I am, with
understanding the processes by which we construct theories. One his most
important suggestions is that metaphors function in the early stages of
theory construction to express in a fuzzy way vague ideas about the nature
of theoretical entitites and mechanisms; "open-endedness" Boyd calls this
feature. I think he is correct in claiming that theory construction often
begains with vague ideas that are sharpened and articulated as theory
construction proceeds; and he is also right that this theory-articulation
is the task of the research community. Part of the measure of the "goodness"
of a metaphor will be the extent to which it suggests promising lines of
future work.(Much of the rest of Boyd's article goes on to discuss his
causal theory of reference: an important topic for a realist but not so
relevant to our discussions here.)
Boyd does not help us answer our question of what a metaphor is
but he does have some useful suggestions about the ways in which we should
allow metaphors to be vague at the outset (a very short property
list with a few specific properties or very general properties, e.g. the
gene must be sort of like an independent entity) and then sharpening the
similarities as we use the metaphors in theory construction.
I see the next step in using analogies to construct new theories
in an AI system to be finding a domain in which numerous analogies are
potentially useful, deciding on some way of providing the system with
large numbers of potential analogies from which to choose, developing
criteria for what kinds of matches in a generalization-specialization
tree will be chosen as constitutive of a potentially useful analogy....
and probably lots of other things I haven't thought about yet. Any
suggestions for a domain? I have been trying to design a project using the
DNA sequences, but direct comparisons rather than analogies are more
likely to be useful when discussing relations between sequences.
One possibility is the recent history of immunology with the clonal
selection theory and the mechanism of producing diversity with stable and
variable regions.{That is a vague idea at the moment.}
A question to Doug: how was analogy supposed to function in AM?
Do you think it functioned so seldom because generalization-specialization
obviated the need for using analogies? Do you think matching in a
generalization-specialization tree can replace the independent operation of
using analogies?
I hope that worked. I hope to hear from one of you soon. Bye, Lindley.
-------
-------
∂Mailed to DARDEN@SUMEX 18:13 25-Feb
Several points
Lindley -
1) A comment about (my recollection of) Boyd's article: Terry Winograd
made (what I thought to be) a similar point in his paper, "On primitives,
prototypes, and other semanitc anomalies". The issue was how to describe
an object, and the "standard" approach, (to which Terry was objecting,)
claimed the answer was to break the object down to its component, or
consituent parts, which are then (recursively) analysized and described.
Eventually one bottoms out, on the "atomic" primitives of this field.
Hence X was a bird if (it satisfied the "bird-liness" predicate,) X (i)
could fly, (ii) had feathers, ... The (psychologically motivated)
counterclaim is that this is NOT what people really do. We tend to have
prototypical entities stored away. ((As our canonical example of this)
under "bird" we would our standard example, Tweety. We then use this
Tweety for many purposes. In particular, we decide that X is a bird iff
it matches enough of the characteristics associated with Tweety.
The conclusion is that analogical connections are not only acceptable, but
sufficient as well -- we needn't go down to criterial subparts to decide
in which category to classify some object. With this background I thought
Boyd's point was analogous to Terry's -- Boyd was claiming that the use of
analogy was respectable, even in a scientific theory.
(Two notes: (i) Yes, this does have strong connections with Wittenstein
"Game" example. (ii) Many of KRL's problems stemmed from user's
confusions about these categorizing units -- that is, what does it mean to
say that Tweety "represents birdliness"? The Units Package inherited
these muddled semantics.)
2) Have you read MRG's "Metaphors and Models" paper, in the AAAI
proceedings? While everyone, (even Mike,) concedes it is hard to read,
and harder to understand, some of the ideas there seemed quite similar to
your interfield connection theory. (Mike addresses some of the
applications of significant analogies, especially those which were
necessary (ie "causally" generated,) as opposed to mere happenstance or
serendipy.)
3) Shall I send the course outline for Hintikka's class? I stopped
attending the class when it reached the point of "diminishing returns",
about a week ago. More precisely, while its interestingness remained
about the same, the importance of other things (eg IJCAI paper) recently
skyrocketed past it. I was also finding it frustrated -- while Hintikka
did seem intrigued with Cognitive Science in general, and AI in
particular, many of his views seem incompatible with these fields. One is
the dualistic approach he takes to issues of intentionality. He tends to
regard this as (closely related to) perception, based on the consequences
of this abstract thing called thoughts. Rather than consider neurological
explanations of such phenomena, he touts his possible-worlds-approach as
the answer, even with all the dilemmas to which this leads. (E.g. What
does it mean to say that "John thinks he sees X, but really ..."?)
His viewpoint is still interesting, just inapplicable, from my
perspective.
4) May I included you in my list of potential references?
5) My prefered mailing address is RDG@SAIL.
Does any of this makes sense?
- Russ -
∂26-Feb-81 0752 Darden@SUMEX-AIM analogies and other things
To: RDG@SAIL
cc: Buchanan@SUMEX-AIM, Dietterich@SUMEX-AIM, STT@SAIL,
cc: Bennett@SUMEX-AIM, Cooper@SUMEX-AIM, Lenat@SUMEX-AIM,
cc: Genesereth@SUMEX-AIM, Darden@SUMEX-AIM
Hi, Russ. It is nice to get a response to the analogy ideas. I suggest
that in the future you separate messages into comments on analogy and
send them to everyone else in the seminar and then do a separate message
to me about other things. Tom suggested that we set up an analogy file
and let everyone include the file name on their sndmsg list so we would
have a complete record of our analogy seminar. I don't know how to set
up that file, but if you or Tom or someone else does, then let's do it.
So, this is my response to the analogy comments in your message.
You suggest that Boyd is making a point similar to one made by
Winograd about our having some sort of essetial categories, such
as "birdness." Since I haven't read the Winograd article maybe I
don't understand, but I don't think Boyd is making that point. Also,
I don't see how putting birds into a bird category involves aanalogy;
similarities, yes. One of the most interesting of Boyd's ideas is
that analogies enable us to introduce new, yet still quite imprecise,
ideas in science. Does Winograd have anything to say about introducing
new categories?
I will look up Mike G's article on metaphors and models in AAAI.
One of the more interesting ideas that you and I discussed was your
interest in how the same thing could be looked at from different
perspectives, levels, or whatever. Have you thought more about that?
Are any of the analogy qustions relevant to those problems?
-------
∂26-Feb-81 0804 Darden@SUMEX-AIM reply to queries
To: RDG@SAIL
cc: Buchanan@SUMEX-AIM
Russ, this is a reply to the non-analogy portions of your message.
Yes, I would be interested in seeing the Hintakka course outline.
I am not suprised that you found much of his approach irrevelant;
unfortunately much of what happens in two fields, even when seemingly
related to the same topic, is difficult to connect specifically.
What is your IFCAI paper on?
Since I haven't seen any of your written work, there is not much
I could say if asked for a reference on you. If you would like to
send me some papers to look at, then I could be more helpful.
Keep me posted on things you are thinking about. By the way,
do you plan to be around the first couple of weeks in August?
Bye, Lindley.
-------
∂26-Feb-81 0945 Darden@SUMEX-AIM Analogy.3
To: dietterich@SUMEX-AIM, STT@SAIL, RDG@SAIL,
To: BENNETT@SUMEX-AIM, Cooper@SUMEX-AIM, Buchanan@SUMEX-AIM,
To: Lenat@SUMEX-AIM, Genesereth@SUMEX-AIM
Before discussing other articles on analogy, I want to capture
some recent thoughts. This week I went to a talk by Jim Reggia here at
Maryland on KMS or a Knowledge Management System that he has developed.
It is a framework for writing expert systems to be used by domain experts
directly. It includes components for creating a knowledge base, several
options as to type of inference method (Baysian, production rules, hypothsis
and test) and some other things. He has various people in the medical
school in Baltimore creating such systems in their areas of expertise.
It appears to me to be a fairly straight forward application of AI ideas
to making a higher-level "language"(not the best word here). My interest
in this activity is that once a number of these systems in the same format
get built, then they might be able to serve as some of the raw material for
use in searching for analogies. Say, in some domain using a hypothesis and
test framework one finds that none of the current hypotheses explains the
data. Then one could begin a search among other (similarly structured
or relevantly similar on some criteria) systems. Well, that is several
years away, but I thought I would mention it now while it is fresh in my
mind. I wonder if any of the MYCIN-like systems could provide a similar
stock of examples for an analogy search space?
I have read the articles in Metaphor and Thought by Kuhn and
Pylyshyn, which are responses to Boyd's article. They are both disappointing
though they suggest some ideas. Much of Kuhn's article is the same old Kuhn:
he disagrees with Boyd that we aim at "cutting nature at its joints," since
he believes that "another language might have located different joints, cut
up the world in another way." (p.414) A different paradigm creates
a different world.I much prefer Boyd's realism to Kuhn's relativism. More
interesting is his discussion of the role that a billiard ball model of
nuclei and electrons played in Bohr's thought (p.415). He makes the point
that Bohr knew that the model was not exact: that some of the properties of
ball did not carry over. Finding out the extent of the metaphor, Kuhn claims,
was an important aspect of the development of the quantum theory. I cer-
tainly agree that exploring the extent of a metaphor may be important
in theory construction. Kuhn goes on to claim that the model is still
essential to the theory. Can anyone explain this to me:"Without its
[the models's] aid, one cannot even today write down the Schrodinger
equation for a complex atom or molecule, for it is to the model, not
directly to nature, that the various terms in that equation refer." (p.415)
This question of the role that models, analogies or metaphors play in the
finished theory is an important one; but I don't have a clear
position on it yet.
Pylyshyn is a cognitive scientist. I found the article very difficult
to read since he obviously talks very differently from a philosopher.
Since I am not sure I accept a neoKantian, Piagetian view that we have
built in schemata with which we understand the world, I didn't accept
much of what he said. But I do see how a computer system is given
a set of categories into which more particular bits of knowledge must fit.
The problem of creativity for AI systems then becomes how they can
develop categories that they were not explicitly given at the outset.
(Tom, is this the problem you mentioned recently to me?) Perhaps a system
could create a new category by analogy with ones it already has or by
analogy with categories other systems (that it can somehow access and search)
One other interesting bit from Pylyshyn: he argues (p.435) that
thinking is literally (not analogically) computation, namely "rule-
governed transformations on intentially interpreted symbolic expressions..."
Though I am not sure what to make of this specific claim, I think that
ideas which we are at the outset suggested by analogy, once built into a
scientific theory that gets well-confirmed, do become our literal way of
seeing the world. That idea is a bit vague yet, but seems to me an
important one to make sense of. It involves the notion of legitimate
"theory-ladeness."
!!
Well, that is enough for today. Ihave some letters to write, an honors
thesis on functionalism to read, and prparation for class on the
contemporary theory of evolution.
Bye, Lindley.
-------
∂26-Feb-81 1241 Buchanan@SUMEX-AIM Re: Analogy.3
To: Darden@SUMEX-AIM, dietterich@SUMEX-AIM, STT@SAIL, RDG@SAIL,
To: BENNETT@SUMEX-AIM, Cooper@SUMEX-AIM, Lenat@SUMEX-AIM,
To: Genesereth@SUMEX-AIM
In response to the message sent 26 Feb 1981 0938-PST from Darden
the Kuhn quote is confusing because you are trying to put it into
a realist's framework. It makes sense to me, but there is no way
I can get it to make sense to you!
bgb
-------
∂28-Feb-81 1520 Darden@SUMEX-AIM Boyd and Winograd on natural kinds
To: RDG@SAIL
cc: Dietterich@SUMEX-AIM, STT@SAIL, Buchanan@SUMEX-AIM,
cc: Cooper@SUMEX-AIM, Bennett@SUMEX-AIM, Lenat@SUMEX-AIM,
cc: Genesereth@SUMEX-AIM
Hi, Russ. I reread your message about Winograd's ideas about how we
know natural kinds, i.e. through prototypes. I now can see a connection
to Boyd's point that we use analogies to begin constructing new natural
kind terms. Yes, you are right that both of them are proposing alternatives
to the view that we know natural kinds by taking them apart into their
primitive components (compositional reasoning, philosophers sometimes call
it). But the disanalogies between their positions seem great: in the early
stages of theory construction, according to Boyd, we have only a vague idea
about the nature of the theoretical entities; we certainly do not have a
clear prototype to use, hence the need for analogies to things already known.
If Winograd discusses how we come to have our prototypes and whether we
might sometimes revise them, then those topics would be more relevant to
the questions about theory construction that I would be interested in.
Thanks for the news release on evolution. Do you know if I can
access the news stories from SUMEX? I get angry and depressed about having
to fight these old 19th century battles again in this reactionary era.
My colleague here, Steve Brush (a historian of physics who has written
about the ideas of the age of the earth), is doing battle with the current
most prominent creationist position that maintains the earth is only about
6000 years old. He argues that that view would entail changing teaching
not only in biology but also geology and astronomy, etc., and would
thus substantially undermine science teaching in this country.
Bye, Lindley
-------
∂Mailed to DARDEN @ SUMEX 11:41 4-March
Analogy related points
1) WRT analogy between the articles by TW & Boyd:
Yes, your last message was correct: my only point was that both authors
were claiming that a strictly componential match was NOT the only
approach. Here seems a classic case of trying to extend an analogy too
far -- I hadn't meant to imply any similarities between (the content of)
those two papers beyond that.
To avoid further confusing Terry's points, I'll mail you a copy of that
paper, which appeared in the TINLAP-II ("Theoritical Issues in Natural
LAnguage Processing") proceedings. By the way, that issue contained
several articles which I thought were good, as well as some at the other
end of the spectrum. I remember there was an article by Pylyshyn there,
but forgot how I categorized it.
2) Yes, perspective does have a lot to do with analogy -- in fact, (from
one perspective) it could be regarded as the basic underlying
problem/question. Consider the "An airplane is like a bird" example. We
can take this to mean that one perspective of bird has many (or perhaps
all?) of the same properties that "airplane" has, when viewing airplanes
from that same perspective. In this case, we need to use the "X as a
flying thing" view. If we try to force the "X as a living organism"
perspective, (which we know to be appropriate for birds,) then we might
conclude that airplanes, by analogy, must make nests and live in trees.
Similarly "birds as small objects" loses big.
(An appendix below includes some first ideas at how one might begin to
implement such a system.)
3) To preserve our messages in a single place, include
"*<DARDEN>ANALOGY.BBD" in your recipient list. I believe this will stick
all messages at the end of that file. Once created, you might have to
twiddle the bits of its protection, to allow the rest of us access to
append onto that file. (Maybe not...) I had no trouble reading read your
various SUMEX files, at least those whose protection was set to 777752.
Russ
Comments of relation between Analogy and Perspective
[I concentrate on the canonical sentence "an X is (like) a Y".
Other forms of analogy can be handled analogously; maybe.]
One approach begins by classifying each property of an entity according to
the perspective to which it belongs. Hence "Height = 6 foot" is a
property of RDG, when RDG is viewed as a physical object, whereas
"Occupation = Student" pertains to RDG as a member of society, etc. To
make sense of "RDG is like a tree", we would have to first find one
perspective which covers both "RDG" and "tree". (This is, of course, a
very difficult task. Indeed, finding the "appropriate" perspective which
covers two entities may be no simpler than the analogy problem this
approach was designed to solve.) As trees do not seem to be social
creatures, we can consider the physical object viewpoint, and see that
both RDG and trees are tall; and (lacking other information) assume that
that was the point of this metaphor.
Certainly if we had "pre-loaded" all possible perspectives, we could
process analogies like "an X is like a Y" by first finding the
perspective, P, which is, in some sense, closest to both X and Y. Clearly
this is NOT what people do - we have an amazing ability for constructing
new, if strained, metaphors on the fly.
In this usage, perspectives seem similarly to classes -- as in the class
of flying objects, or of topics for communication, rather than regarding
some from the perspective of flying objects, or as a topic of
communication. There is an important difference, though: the standard
notions of "membership" does not apply to "perspective classes". For
example, we may view a centaur as being like a horse, even though we all
readily conceed no centaur belongs in the class of all horses. Loosely we
can say X belongs to perspective Y if some part of X is somehow isomorphic
to (standard examples of) Y.
(Note this does NOT directly match the KRL usage of perspective. Its
perspectives were things like "class of objects", or "prototypical
member". These were necessary to handle apparent ambiguities like:
What exactly is "Flight#33" if we know that (1) "Flight#33 is an element
of the class of all flights", and therefore has properties of a type
associated with individuals -- eg CityOfOrigin, DateOfFAA-Approval, ...
and also (2) "Flight#33 is a generic description of a whole group of
individual instances", (including the flight on April 7, and another one
piloted by Fred) and hence has properties associated with sets - such as
number of elements, etc. KRL would handle this case by dividing Flight#33
into two different "perspectives", of `Individual' and `Class', and
associate each type of slot with its appropriate perspective.)
∂Mailed to DARDEN @ SUMEX 12:02 4-March
Other Points
0. Last "Analogy related issues"
I wasn't sure whether the stuff I said was sufficiently general to warrant
its inclusion in the official ANALOGY dialog. Feel free to mail it
around, if you feel differently. (The same goes for any part of this
message which you feel has some general interest.)
1. Protection code:
I noticed most of your files were protected 777752. That might be a bit
too trusting of you. Most people (at least on SCORE) seem to use 775252;
and most mail files are 770404 [so I assume the 4 bit means appending is
allowed.]) By the way, that eight digit number is really a string of 3
pairs of octal numbers, which encode (i) what YOU the owner can do to the
file, (ii) what other people in your group can do to that file, and (iii)
what any random SUMEX users can do.
2. Schedule:
My only current Summer plans for the Summer are to attend the Cognitive
Science meeting, at UC Berkeley from 19-21 August, and to trek to
Vancouver for the IJCAI, from 24-28 August. (And possibly sit in on the
ACL meeting, at Stanford, from 29 June thru 1 July.) Will you be
meandering here beginning of August?
3. Reggia's system:
Did you know that EMYCIN was created to provide just this sort of general
facility, as was AGE. In my mind, these systems will never achieve the
generality their designers hope for. They all suffer the same fatal flaw:
their internal processors are static and unreachable. As such it is
difficult for the user (or the system itself) to even examine the program,
much less change it. So while these programs will do quite nicely on the
task for which they were designed, they are sadly inextensible. For
example, these systems offer the user access to the 3 or 4 processing
schemes which the designers considered appropriate. If one want to draw
conclusions a little bit differently, or store a slightly different type
of data, he (forgive my sexism) is forced to totally abandom that
representation structure and associated inference system.
Based on my discussion with Milt, KMS seems built along these lines -- one
"big switch" the user can turn to select one out of the N available
options.
Many of these problems would be solved if the system, built to reason
about and modify domain facts, was allowed to store facts about itself,
which it could then examine and, if necessary, alter. As these
modifications would directly affect the system, accordingly, the user
could twiddle the system to conform to his (more sexism) expectation, not
vice versa.
Doug and I wrote a paper which appeared in the AAAI proceeding which says
more on this theme. It describes a representation language langauge,
named RLL, which can use its knowledge about the domain of representation
to adapt itself to some user's specification. Much of the discussion in
this paper is addressed to various issues related to this point -- such as
why this is feasible (answer: sufficient bootstrapping), and whether the
system will be hideously slow, by having to simulate other systems
(answer: No, it can regain otherwise lost efficiency by "Cognitively
Economizing").
Many of these points will be reiterated in the soon-to-be-published
"Building Expert Systems" book, based on the collective experience many
Expert System Builder/Knowledge Engineers had in San Diego last summer.
There are also a small handful of recent memos which elaborate this idea.
(Milt volunteered to send Reggia copies of these.) While I do recommend
the AAAI paper, these memos are (i) rather verbose, (ii) poorly written,
and (iii) do not add much to the points made in the paper.
3. EURISKO
Doug and I are now working on EURISKO, a system which we hope will be able
to explore new and novel domains (in a single bound. Look, up in the ...)
Though still in the designing phase, we have thought through several
parts. (For example, I know understand the basic processing part, and
have begun to implement it.) As with RLL, EURISKO is capable of
"introspection" -- many of its actions will be devoted to improving its
own performance. Two subtasks towards this goal are automating the
discovery of heuristics, and deriving new representations. Analogy should
play a major role in both of these pursuits; and will, if we can figure
out how to do it.
Once EURISKO gets off the ground and has incorporated a sufficient number
of diverse Knowledge Bases (KBs), it could well employ a KB (or two) to
experiment with different forms of analogy -- testing them "empirically"
by seeing which types seem to give rise to interesting and usable new
connections, and in which domains. Certainly by this point we could
greatly benefit from collaboration with people such as yourself, who have
already given much thought to these matters. (Of course, we would
certainly enjoy the use of your expertise in many related tasks which
emerge before that as well.)
4. IJCAI paper
The IJCAI paper I was writing (note the tense) was an overview of this
system. A few days ago I realized the paper lacked "semantic content" --
it was full of "we will do this", and "it can be seen that"s, with no real
evidence to back up these claims. So I skunked the draft, at least for
the time being. If you would like, I would be glad to send you a copy of
it now, to acquaint you with our aspirations and hopes, if not our
mechanisms and/or results. (Do realize it is full of errors of every type
-- from typos thru gross misconceptions.)
5. Multiple KBs
For the analogy task you envision it is obviously important to make
connections between different KBs, designed and input by different
authors. There are many potential problems associated with this. Doug
and Mike spent some time addressing one major issue: how do you insure
agreement among users about the "real" semantics of their respective
domain facts. The most trivial manifestation of this problem is naming
conflicts. (Unfortunately,) deeper and more substantial difficulties can
occur. For example, there are many potential meanings of the disjunction,
"OR"; and no reason to assume two users happen to be using the same one.
[One of the examples in that AAAI paper (on RLL) dealt with this. The
"Meta-Description and Modifiability" paper Mike and Doug are writing deals
with this sort of problem, among others. (It was officially finished last
June, but is still only in draft form.)]
6. News service wires
To the best of my knowledge SAIL is the only computer in the world (or at
least only Research computer) which is hooked up to any NS. In
particular, I know SUMEX isn't. If you like, I would be glad to collect
the stories in which you are interested from my vantage here, and mail
them periodically to you there. All I need is a specification of the
words you wish scanned for. The NS program can accept any boolean
combination of words.
[Eg my entries include
(((DNA + (Molecular Genetics)) + (Interferon)))/AP/NYT
(((Intelligence * ((Monkey + (Gorilla + KoKo) + Simian)))))/AP/NYT
where + means OR (standard semantics, see above) and * stands for AND.
The /AP means on the Associated Wire, and /NYT is for the New York Times facility.]
I have a backlog of these, which I could forward if you wish.
6. References
I was trying to think of people outside Stanford who have had any recent,
(and hopefully favorable) contact with me. It isn't too important,
though. (To be honest: I needed to quickly conjure up a list for Rand,
and took the liberty of including your name in a second list of people who
"don't know me (or my work) too well, but will probably say nice things
about me". So it is not too likely you'll actually be contacted. If they
do, please feel free to beg out. [This is all due to a consulting job
with Rand I'll be starting soon.]
7. Horace Judson
Did you know he was offered (and will probably accept) a position at Johns
Hopkins, as a joint professor in Writing and the History of Science? Doug
& I had lunch with him a week ago, basically to answer his questions about
text-editors and formatters. I was a bit surprised at his views: ranging
from outright antagonism towards Kuhn and Velinkowsky, ambivalence towards
various socio-biologists, to both interest and admiration in various
neurological studies, such as Sperry (split brain).
In case the recent earthquake made the news there,
it did really happen.
I seemed to be the only fellow around who slept through it, though.
Let me know what's going on there.
Russ
∂05-Mar-81 0810 Darden@SUMEX-AIM analogy.4; MG's ''Metaphors and Models''
To: Dietterich@SUMEX-AIM, STT@SAIL, RDG@SAIL,
To: Bennett@SUMEX-AIM, buchanan@SUMEX-AIM, Lenat@SUMEX-AIM,
To: Genesereth@SUMEX-AIM, Clancey@SUMEX-AIM
Hi, Folks.
Russ suggested that I look at Mike's paper so
this is a brief discussion of Mike Genesereth's article on "Metaphors
and Models" in AAAI 80. This is a very interesting article and I am sorry
that I didn't discover it while I was still at Stanford. Is ANALOG im-
plemented somewhere? What does it do? Is the material discussed in this
paper a focus of your current work, Mike?
The idea of having a number of abstractions and then choosing one
approprite for a domain is much like the "hardware store" idea that
several of us played with one day: what primitive categories would we need
to do theory construction and can we find them by an examination of past
theories? What more has been done on finding types of abstractions besides
the heirarchy example mentioned? Is there one (or several) abstraction(s)
for causal models? I wonder if there isn't something quite basic about
two knowledge types: hierarchically structured (e.g. biological class-
ification) and interactive networks for causal interactions.
The beauty of the abstract hardware store is that we don't have to
find specific analogies and then do the abstracting of appropriate
properties since the abstractions are already available. The disadvantage
is that we lose the diversity and richness of specific analogues. But
Mike's suggestion that we could first search for an appropriate ab-
straction and if it isn't found then do more specific analogy matches
is a good way of combining the advantages of the two.
I also particularly liked Mike's suggestion that for a
particular task a single simulation structure may not be sufficient and
it may sometimes be possible to piece together several different ones.
I certainly found the use of different analogies in the construction
<?> nt analogies were
of theories in biology and I think some "creative" activities can
be viewed as "putting old things together in new ways."
Any ideas as to how one constructs the abstraction, given
a particular specific something (domain, structure, I'm not sure of the
proper terminology)? I found this statement intriguing, i.e.
fascinating but puzzling: "Abstractions are ways of capturing the
necessary interdependence of facts." How do we manage to find those
appropriate interdependences in a specific case?
What does the Hayes-Roth work do and can it really be used
to "induce new abstractions"? Tom, how did your work relate to this
problem (Mike cites Dietterich and Michalski, IJCAI, 79 in this
context.)? What current work is related to these issues? Does it
make use of analogies?
Well, I have to stop now in order to go out to lunch with
Ben Schneiderman from the CSD here at Md whom I met at a CAI workshop
last week but who says he is very sceptical about AI. I don't know
what he means but I suppose you all probably have experience with
sceptics of various sorts, probably like the philosophers of science
I encounter who think one can't say anthing about reasoning in
discovery. Oh, well, I'll see. Maybe he will be interested in
a CAI logic coure anyway.
Bye, Lindley.
-------
∂05-Mar-81 1005 Dietterich@SUMEX-AIM Re: analogy.4; MG's ''Metaphors and Models''
To: Darden@SUMEX-AIM, STT@SAIL, RDG@SAIL, Bennett@SUMEX-AIM,
To: buchanan@SUMEX-AIM, Lenat@SUMEX-AIM, Genesereth@SUMEX-AIM,
To: Clancey@SUMEX-AIM
In response to the message sent 5 Mar 1981 0804-PST from Darden
In response to your questions about discovering abstractions.
In AI abstraction usually refers to the process of forgetting details.
The work of HAyes-Roth and also my work with Michalski (and also Bruces
work on Meta-Dendral) all involve systems that take a set of descriptions
and decide which parts of the descriptions can be ignored. Thus,
Hayes-Roth's work might be given a description of two objects as:
big(x) & red(x) & causes(x, destruction of universe)
and
big(x) & red(x) & is(x, cure for cancer)
from which it will develop the "abstraction" of
big(x) & red(x)
This example shows how this AI work has been fairly trivial so far.
No new terms are introduced. The transformation is purely syntactic.
This syntactic technique can be a powerful tool, if you start with the
right representation to begin with. The problem of discovering an abstraction
of two bodies of knowledge that are represented in different ways is
an open problem.
--Tom
-------
∂07-Mar-81 1938 Darden@SUMEX-AIM next analogy discussion
To: csd.dietterich@SCORE, STT@SAIL, RDG@SAIL,
To: Bennett@SUMEX-AIM, Cooper@SUMEX-AIM
cc: Buchanan@SUMEX-AIM, Lenat@SUMEX-AIM, Genesereth@SUMEX-AIM,
cc: Clancey@SUMEX-AIM
This will be the file in which our analogy seminar discussions
are stored. Please include <DARDEN>ANALOGY.BBD on the To: of MSG from
now on.
Russ and I have exchanged a couple of messages about the Boyd
article and its relation to an article by Winograd and other matters.
I am going to edit his recent remarks about analogy and send them
to everyone else.
4-Mar-81 11:41:58-PST,4997;000000000001
Mail-from: ARPANET host SU-AI rcvd at 4-Mar-81 1141-PST
Date: 04 Mar 1981 1141-PST
From: Russell Greiner <RDG at SU-AI>
Subject: Analogy related points
To: darden at SUMEX-AIM
1) WRT analogy between the articles by TW & Boyd:
Yes, your last message was correct: my only point was that both authors
were claiming that a strictly componential match was NOT the only
approach. Here seems a classic case of trying to extend an analogy too
far -- I hadn't meant to imply any similarities between (the content of)
those two papers beyond that.
To avoid further confusing Terry's points, I'll mail you a copy of that
paper, which appeared in the TINLAP-II ("Theoritical Issues in Natural
LAnguage Processing") proceedings. By the way, that issue contained
several articles which I thought were good, as well as some at the other
end of the spectrum. I remember there was an article by Pylyshyn there,
but forgot how I categorized it.
2) Yes, perspective does have a lot to do with analogy -- in fact, (from
one perspective) it could be regarded as the basic underlying
problem/question. Consider the "An airplane is like a bird" example. We
can take this to mean that one perspective of bird has many (or perhaps
all?) of the same properties that "airplane" has, when viewing airplanes
from that same perspective. In this case, we need to use the "X as a
flying thing" view. If we try to force the "X as a living organism"
perspective, (which we know to be appropriate for birds,) then we might
conclude that airplanes, by analogy, must make nests and live in trees.
Similarly "birds as small objects" loses big.
(An appendix below includes some first ideas at how one might begin to
implement such a system.)
3) To preserve our messages in a single place, include
"*<DARDEN>ANALOGY.BBD" in your recipient list. I believe this will stick
all messages at the end of that file. Once created, you might have to
twiddle the bits of its protection, to allow the rest of us access to
append onto that file. (Maybe not...) I had no trouble reading read your
various SUMEX files, at least those whose protection was set to 777752.
Russ
Comments of relation between Analogy and Perspective
[I concentrate on the canonical sentence "an X is (like) a Y".
Other forms of analogy can be handled analogously; maybe.]
One approach begins by classifying each property of an entity according to
the perspective to which it belongs. Hence "Height = 6 foot" is a
property of RDG, when RDG is viewed as a physical object, whereas
"Occupation = Student" pertains to RDG as a member of society, etc. To
make sense of "RDG is like a tree", we would have to first find one
perspective which cers both "RDG" and "tree". (This is, of course, a
very difficult task. Indeed, finding the "appropriate" perspective which
covers two entities may be no simpler than the analogy problem this
approach was designed to solve.) As trees do not seem to be social
creatures, we can consider the physical object viewpoint, and see that
both RDG and trees are tall; and (lacking other information) assume that
that was the point of this metaphor.
Certainly if we had "pre-loaded" all possible perspectives, we could
process analogies like "an X is like a Y" by first finding the
perspective, P, which is, in some sense, closest to both X and Y. Clearly
this is NOT what people do - we have an amazing ability for constructing
new, if strained, metaphors on the fly.
In this usage, perspectives seem similarly to classes -- as in the class
of flying objects, or of topics for communication, rather than regarding
some from the perspective of flying objects, or as a topic of
communication. There is an important difference, though: the standard
notions of "membership" does not apply to "perspective classes". For
example, we may view a centaur as being like a horse, even though we all
readily conceed no centaur belongs in the class of all horses. Loosely we
can say X belongs to perspective Y if some part of X is somehow isomorphic
to (standard examples of) Y.
(Note this does NOT directly match the KRL usage of perspective. Its
perspectives were things like "class of objects", or "prototypical
member". These were necessary to handle apparent ambiguities like:
What exactly is "Flight#33" if we know that (1) "Flight#33 is an element
of the class of all flights", and therefore has properties of a type
associated with individuals -- eg CityOfOrigin, DateOfFAA-Approval, ...
and also (2) "Flight#33 is a generic description of a whole group of
individual instances", (including the flight on April 7, and another one
piloted by Fred) and hence has properties associated with sets - such as
number of elements, etc. KRL would handle this case by dividing Flight#33
into two different "perspectives", of `Individual' and `Class', and
associate each type of slot with its appropriate perspective.)
! 4-Mar-81 12:08:26-PST,8765;000000000001
Mail-from: ARPANET host SU-AI rcvd at 4-Mar-81 1208-PST
Date: 04 Mar 1981 1201-PST
From: Russell Greiner <RDG at SU-AI>
Subject: Other Points
To: darden at SUMEX-AIM
Last "Analogy related issues"
I wasn't sure whether the stuff I said was sufficiently general to warrant
its inclusion in the official ANALOGY dialog. Feel free to mail it
around, if you feel differently. (The same goes for any part of this
message which you feel has some general interest.)
EURISKO
Doug and I are now working on EURISKO, a system which we hope will be able
to explore new and novel domains (in a single bound. Look, up in the ...)
Though still in the designing phase, we have thought through several
parts. (For example, I now understand the basic processing part, and
have begun to implement it.) As with RLL, EURISKO is capable of
"introspection" -- many of its actions will be devoted to improving its
own performance. Two subtasks towards this goal are automating the
discovery of heuristics, and deriving new representations. Analogy should
play a major role in both of these pursuits; and will, if we can figure
out how to do it.
Once EURISKO gets off the ground and has incorporated a sufficient number
of diverse Knowledge Bases (KBs), it could well employ a KB (or two) to
experiment with different forms of analogy -- testing them "empirically"
by seeing which types seem to give rise to interesting and usable new
connections, and in which domains. Certainly by this point we could
greatly benefit from collaboration with people such as yourself, who have
already given much thought to these matters.
Multiple KBs
For the analogy task you envision it is obviously important to make
connections between different KBs, designed and input by different
authors. There are many potential problems associated with this. Doug
and Mike spent some time addressing one major issue: how do you insure
agreement among users about the "real" semantics of their respective
domain facts. The most trivial manifestation of this problem is naming
conflicts. (Unfortunately,) deeper and more substantial difficulties can
occur. For example, there are many potential meanings of the disjunction,
"OR"; and no reason to assume two users happen to be using the same one.
[One of the examples in that AAAI paper (on RLL) dealt with this. The
"Meta-Description and Modifiability" paper Mike and Doug are writing deals
with this sort of problem, among others. (It was officially finished last
June, but is still only in draft form.)]
Russ
LD: a brief reply to Russ's last comment: are there any existing
knowledge bases that we could begin now trying to do analogical
matching with?
-------
∂07-Mar-81 1950 Darden@SUMEX-AIM other points
To: RDG@SAIL
cc: Buchanan@SUMEX-AIM
Hi, Russ. As you know from being copied on the other message, I
created <darden>analogy.bbd and put in your messages and edited
them for general consumption.
I didn't know anything about levels of protection. How do
I change files from 77752 to 775252? None of the written documentation
I have from SUMEX tells me about all that.
I may come out in August and go on to IJCAI but I don't know
whether there is funding for that .
I agree with you about the kinds of limitations for systems like
Reggia's. I don't like having the choice of inference method chosen
since in the work I want to do, I wnat to build in the patterns of
reasoning myself. The Unit Editor looks more like soemthing I
could use if I decide to try to build a system to do theory
construction starting with a stage of the classcial theory of the
gene. (Did you hear any of the discussions about TRANSGEN?)
Yes, I would be interested in seeing your aborted IJCAI paper.
Can you send it on line?
Fine about using my name for a reference; I just thought I
could be more helpful with more info.
Yes, I would appreciate getting new stories of interest. Thanks
for offering to send them. I very much enjoyed the evolution article
no, enjoyed isn't the right word. The whole issue makes me quite
angry but I am interested in keeping up with the developments.
I like your DNA word list; what other choices for key words do
I have? Certainly genetics and evolution would be on my list.
Yes, I know that Judson is very opinionated; some subjects I
found I simply could not have a discussion about; I could only listen
to his views. He had told me the Hopkins job was a possibility;
I am pleased that it is definite.
EARTHQUAKE??? How big? Any damage?
Tonight is a cold March night. Crocus are blooming, along with
tiny yellow winter aconites and snowdrops; tulips and jonquils are
just beginning to come up out of the ground. Mostly it is 40 degrees
and either clear or raining, but tonight it is in the 20s with cold
wind.
I went to see an interesting French movie last week: Mon
Oncle d'Amerique. Several of us from the Philosophy Department went
and had an argument about whether it was a sociobiology movie,
or was built on Skinnerian behaviorism or showed strong influences
of French existentialism or maybe all three.
Keep in touch.
Bye, Lindley.
-------
∂11-Mar-81 0545 Darden@SUMEX-AIM non-analogy
Subject: non-analogy
To: csd.dietterich@SCORE, STT@SAIL, RDG@SAIL, Bennett@SUMEX-AIM,
To: Cooper@SUMEX-AIM, Buchanan@SUMEX-AIM, Lenat@SUMEX-AIM,
To: Genesereth@SUMEX-AIM, Clancey@SUMEX-AIM, csd.Grinberg@SCORE
Hi folks. I haven't had much time lately to read or think about
analogy so this is on another subject.
I was talking to a colleague of mine in the Philosophy Department
here, Ray Martin, about causality. He is quite familiar with the
philosophy literature on the subject and I mentioned that the
concept of causality and causal models is of interest to some
people in AI. He asked me for references to that literature.
The only paper I know on the topic is Chuck Rieger and Milt
Gringerg's "The Declarative Representation an Procedural
Simulation of Causality in Physical Mechanisms," March 1977.
Can any of you supply additional references? What are the major
issues and questions about causality of interest to people in AI?
Well, I can't talk longer now. I have to prepare for my classes
today on the question of the theory-ladeness of observation in science
(a topic dear to the heart of you relativists out there) and on my
work in the attics of Amsterdam trying to prove that Hugo de Vries
independently rediscovered Mendel's law of segregation (it can't be
proved with extant historical evidence). Interesting topics, but
I had rather spend the day reading Ortony and thinking about
theory construction.
Bye, Lindley.
-------
∂Mailed to DARDEN @ SUMEX 16:21 13-March
Misc responses
1) Protection:
I never cease to be amazed at how bad SUMEX's "HELP" facility is!
By trial and error I did find the PROTECTION command, which does part of the job.
Type
PROTECTION ANALOGY.BBD <6bit octal code>
to alter that file. (I assume wildcard entries ("*") will work here to
fix more than one file at a time.)
In general feel free to type <esc>s to get SUMEX to fill in characters, and
? which often indicates the sort of thing the command is now expecting.
Typing
DIRectory <filename(s)> ,
@@PROTection
@@
will tell you the protection for those files.
Ths still doesn't answer the question of how to insure that FUTURE files
have appropriate protection.
I'll ask around; and will let you know what I find out.
2) Limitations:
One of the problems will the rll idea is the difficulty I (and others)
have in communicating how it differs from other systems. In particular,
the Unit Editor shares the limitation I was referring to, wrt Reggia's
system -- neither system is capable of modifying its internal processing.
The Unit Editor provides but a few methods of inferencing (inheritance and
message passing facilities are the only ones I know of). Now suppose the
user wishes to create a new mode of inheritance, which allows him, for
example, to specify that the value of the GOODNESS slot should be
inherited using (something very similar to) the R mode. That is, this
value will usually be a restriction of the value of this unit's
prototype's GOODNESS slot. In this new mode, however, the user can
override this restriction. (We could make this example more realistic,
and sound less contrived, if we further embellish this mode by insisting
it issue a warning message when such a "psuedo-violation" occurs.)
Clearly one could simulate this effect using the Units Package -- it is,
after all, "Turing Equivalent". However the contortions required for this
would be phenomenal!
The only way to get the units package to do this (as opposed to merely
simulate its effect) is to actually twiddle its source LISP code -- a time
consuming and meticulous task. And even this is only a stop-gap solution.
This saming fixing up process will occur when the next user wishes to, for
example, run a certain program when such a violation occurs (rather than
print a message). Later on someone else will want to be able to let any
of a certain class of units be so violated, without comment; but he still
wants Units to scream and kick if ever another unit is affected.
Realize what is happening. As neither Mark nor Peter needed this
particular type of inheritance for their molecular genetics work, (or at
least both knew how to code around it, if need be,) this feature was never
added to Units. Unfortunately they made a further tacit assumption: that
no one else would ever need this, or any other facility not already
included in this package. That is, they providd NO way to alter the
insides of Units, period.
Now consider how RLL would handle this chore. First, RLL would have a
unit which represents this R mode of inheritance. This unit would house
all information needed to process such R-inherited slots. Creating a new
mode would require only editing a unit. Basically one would first copy
this mode-defining unit, "R", into "New-Mode". This newly created unit
would then be editted to specify what should happen when... [And yes, the
user would perform all of these steps - the copying, editing, etc - using
the same functions and commands he used to edit domain knowledge.]
The next user would also have access to these "internal" units (ie units
which control the internal processing). He would have the option of
altering (his version of) any of these, as necessary.
There are, of course, many non-technical issues related to this approach.
One is security. (Pretty much solved by letting each use keep his own
copy, ala MOLGEN's approach.) Another is understandability -- it's
important for me to be able to someone else's codes and conventions. This
is strongly related to the material in Doug & Mike's paper-to-be. A final
point is pedagogy -- how to keep from deluging the poor user with facts
about the versatility, (and apparent ill-definedness) of this full system.
(I've advocated the "Wizard of Oz" approach: Initially the user is only
told about the basic RLL agenda system, which he regards as an
inflexible interpreter, ala UNITS. After a few weeks, when he begins to
understand the system, he may complain about some characteristics of this
system, or worse, start to code around this perceived limitation. It is here
that the user is told about RLL's adaptability -- ie he could have changed
this all along, once he knew how. ["Just tap your heels together three
times, and say to yourself..."])
EURISKO is built along the same lines -- all of its components, such as
agenda processing mechanism, or rule interpreter, are explicitly encoded
in "bite-sized" chunks, which the user may, if he wishes, alter to suit
his purpose.
3) Transgen?
Sorry, I haven't even heard of it...
4) EURISKO paper:
I'll mail it to you over the net.
What it lacks in accuracy it makes up for in verbosity...
Please feel free to not read it, or to simply pick out relevant portions
for perusal.
5) News service
You get to scan for any boolean combination of words -- ie the NS function
could find any story with all of some set of words, or which contain any
of a set of words, or perhaps any story with all of these words, but none
of those, etc.
How about (EVOLUTION + GENETICS + CYTOLOGY + ((HISTORY + PHILOSOPHY) * SCIENCE))?
[The "+" represent disjunction, and "*" means AND.]
6) EARTHQUAKE
was about 4.5, and centered in Fremont (across the bay).
It caused no non-trivial damage anywhere.
(It was about a week ago, and has been followed by a slew of quakes
around this area, and around the world.
Who knows what's really happening under the mantle?..)
7) Movies
Went to see "Stardust Memories" a few weeks ago -- and didn't like it.
It's basically Woody Allen autobiographically sketching Woody Allen.
Well filmed, artistically produced and all that; I just didn't find
it's content all that interesting.
My friend Tom agreed with your comments on "Mon Oncle d'Amerique".
But I've not seen it.
8) Papers
(i) Those I've promised to send, are now in route. (ii) You've no doubt
also received (electronically) various miscellaneous News Service
articles. (I found those while cleaning up my directory; and decided to
further them along, before deleting my copies.)
9) Perspectives
I'm still not happy with my comments about perspectives...
I'd rather expected to be flooded with complaints about it,
which haven't (yet) come.
----
Nothing else to report. Hope all is well back east.
(Milt tells me your school's BB team won last night, by the way.)
Russ
∂13-Mar-81 2136 Darden@SUMEX-AIM (Response to message)
To: RDG@SU-AI
In response to your message sent 13 Mar 1981 1625-PST
Hi, Russ. Thanks for the messages. So sorry to hear about Delbruck.
Yes, the list of key words sounds fine for my interests in the news.
I have gotten very little feedback on the analogy messages so your
receipt of little on your message that I sent around is compatible.
Any idea why? I thought maybe the analogy messages were too long and
people didn't have much time to read them. Also, there may just not
be much interest in analogy since no one is currently building an
analogy system. I haven't received any message from Doug and Mike,
so I really don't know how interested they are.
What did the IJCAI message mean? Is there some way I can type the
file? what directory is it on? This is the first time I have received
anything other than a message.
Keep in touch. Nice to hear from you. Bye, Lindley.
-------
∂14-Mar-81 1108 CSD.GREINER at SU-SCORE My IJCAI Paper-To-Be
To: darden at SUMEX-AIM
cc: rdg at SU-AI
is now stored in "<GREINER>IJCAI.MSS" on SUMEX.
(I tried to mailed it to you, but used the wrong command.)
Let me know when you've read it (or printed it out) so I can
delete it to reclaim space.
(The original is still on SAIL.)
Russ
-------
∂18-Mar-81 1824 Darden@SUMEX-AIM Russ's IJCAI paper
To: RDG@SAIL
cc: Buchanan@SUMEX-AIM
Hi, Russ, I have copied your IJCAI paper and you can now reclaim
your file space at SUMEX. It looks quite interesting; I will
definitely enjoy learning more about EURISKO when I get a
chance to read it. This is now my spring break and I am
writing my paper for the Boston Colloquium for Philosophy of
Science which I willbe presenting April 14. It has been fun
learning to use TV-Edit but I really miss the ALTO and DOVER.
I hope to resume analogy messages as soon as the paper is done.
bye, Lindley.
-------
∂24-Mar-81 0736 Darden@SUMEX-AIM analogy.people file
To: Analogy seminar:
Hi folks, I haven't had many new thoughts about analogy lately
since I have been busy writing a paper of my own and swamped with
grading student papers. Bill has set up a file for sending msgs
about analogy to all of us as <Clancey>analogy.people, so if
anyone has had any thoughts about analogy or theory construction
lately, they can use that file to communicate with everybody:
just type ctrl B after the To: of sndmsg.
I have been trying to develop the idea that theory
construction starts with a vague idea that gains specificity
as more data is collected and as various interfield connections
are made. Could we construct an analogy finding system that
would import only parts of an analogue and then develop
additional properties in other ways? I have characterized
vague in two ways: the property list could have a few very
specific properties but be very short or one might not know
what ako heirarchy the thing or process is in. The idea of
the gene was vague in both of these ways at the beginning of
the field of genetics. I have been working on sets of questions
that one asks once one has postulated a new entity or process
that can guide removal of the vagueness and also types of
constraints that operate in theory construction. (Am I
discussing the "heuristics" of theory construction? I still
have problems with that word.)
Bye, Lindley
-------
∂27-Mar-81 2327 STT Analogy and alternate formulations
To: "@ANALOG.LST[1,STT]" at SU-AI
Here are some ideas about the importance of alternate formulations of a situation
or problem for suggesting helpful analogies.
I read R. P. Feynman's lectures "The Character of Physical Law" a few days ago.
One of the topics he discusses is how new (to us) physical laws
are discovered. He doesn't have anything to say about the role of analogy and
metaphor unfortunately, but he does talk about generalization and on pp. 47-55
gives a couple of interesting examples of different generalizations or
modifications suggested by different formulations of the same laws.
(If different formulations suggest different generalizations, presumably
different formulations suggest different analogies too.)
In Feynman's first example the starting law is Kepler's 2nd Law for the
motion of planets, that a planet sweeps out equal areas in equal times.
You can generalize from planets to any objects, and from just one to any number
of them, and propose the following general law:
the sum of areas swept out by a set of objects moving
relative to a fixed center is equal for equal times.
You have to weight the areas in the sum by the masses of the respective objects.
This new general law is none other than the law of conservation of angular
momentum.
Just how plausible a path can be made to this generalization, and whether the
generalization actually occurred historically, Feynman doesn't say (tsk tsk).
A different formulation of the 2nd Law can be obtained if you assume Newton's
law F = mA. It turns out then that a planet sweeps out equal areas in equal
times if and only if the force acting upon it is directed towards the center,
i.e. the sun. So that is an equivalent formulation of the 2nd Law: the only
force acting upon planets is sunwards. This formulation can be generalized in
analogous fashion (aha!) to the first, i.e., to any objects, not just the sun
and planets, to any number of them, and with a weighting by mass.
Exercise for the reader.
(Hint: Note that nothing so far has been said about the variation
of the force with distance. If you throw in Kepler's 3rd Law, its corresponding
alternate formulation says the force varies as inverse square of the distance.
Or see the next example.)
Again, Feynman doesn't discuss the historical question. I think the scheme is
too slick to be historical.
Feynman's second example gives three completely equivalent but qualitatively
quite different formulations for Newton's Law of Gravitation. (With some
discussion of how well each fits with relativistic and quantum-mechanical ideas.)
He goes on to say, on pp. 53-54, that
" They are equivalent scientifically. It is impossible to make a
decision, because there is no experimental way to distinguish
between them if all the consequences are the same. But psychologically
they are very different in two ways. First, philosophically you
like them or do not like them, and training is the only way to
beat that disease. Second, psychologically they are different
because they are completely unequivalent when you are trying to
guess new laws. "
" If [we] have a structure that is only partly accurate... We cannot
tell ahead of time , without some intuition, which is the best way
to write it so that we can find out the new situation. We must always
keep all the alternative ways of looking at a thing in our heads..."
The suggestion for theory-construction by analogy is that the theory-seeker
should keep several different formulations of the starting data, empirical
generalization or theory in mind, and look for analogies to each one. Which
analogies are suggested will depend heavily upon which formulation one uses.
This sounds a lot like what Russ was saying about perspectives some messages
ago. He gave the sample analogy "An airplane is like a bird."
If I may turn that example around, "A bird is like an airplane." Some
perspectives on birds, eg. that they have wings, that they fly, will suggest
this analogy and others, eg. that they sing, that they lay eggs, will not.
(Concordes "sing" shrilly, and bombers lay "eggs"? Forget it!)
Depending upon what it is that we want to understand about birds, we would be
well advised to use one perspective rather than another.
An important distinction between alternate perspectives and alternate
formulations appears to be that perspectives make an abstraction, while the
alternate formulations are logically equivalent to each other. But that
"logically equivalent" business only works in mathematics and physics and
suchlike domains anyway; alternate formulations of real-world objects could hardly
be anything but abstractions, and it's not to be expected they'll be completely
equivalent. So maybe in the end there is no distinction? I don't know.
In general Feynman isn't illuminating about the processes of discovering
new laws. On p. 156 he says: "In general we look for a new law by the following
process. First we guess it. Then..."
Ref:
Richard Feynman "The Character of Physical Law",
MIT Press Paperback Edition, 1967.
(From the Messenger Lectures given at Cornell, 1964.
Feynman is prof of theoretical physics at Cal Tech.)
Steve
∂28-Mar-81 1409 Darden@SUMEX-AIM reply to Steve Tappel on problem reformulation and perspectives
To: Analogy seminar:
cc: -- Messages from file:
I thought Steve's discussion of alternative perspectives vs. alternative
formulations was quite interesting from the point of view of some ideas
I have thought about analogy. Steve said that perspectives make an
abstraction; this idea seems to agree with Russ's notion that one can
construct numeous different perspectives of an object. Of course, the
problem for plugging an object into an analogy systems becomes how to
specify to perspectives. Steve continues by saying that reformulations,
in contrast to perspectives, are "logically equivalent." I think the
latter notion can be broadened to include isomorphic, namely, a re-
formation has a one-to-one match with the original. Analogies seem
more like the matching of two perspectives rather than like a complete
isomorphism. Remember the criticism of (who was it?) an AI paper that
we discussed in the seminar that used one area of math to construct
another very similar (isomorphic??) area: we said it seemed too close
to be just analogical. Isomorphisms seem too straight-forward to
be as interesting (creative?) as good analogies.
Sorry for the typos here: read "specify the perspectives" and
the first "isomorphic" should be "isomorphisms"
Bye, Lindley.
-------
∂29-Mar-81 0726 Darden@SUMEX-AIM theories in biology
To: Analogy seminar:, Brutlag@SUMEX-AIM, Maxam@SUMEX-AIM
I have just been reading a new paper of Ken Schaffner's ("Theory
Structure in the Biomedical Sciences," The Journalof Medicine and
Philosophy, 5 (1980)57-97) that has some interesting implications
for building systems to do theory construction in biology.
Schaffner argues that bio-medical theories (such as the operon
theory of gene regulation and Burnet's clonal selection theory
of antibody production) havethe form of "collections of overlapping
temporal models." What he is trying to do is capture the notion of
biological diversity: biological theories often contain several
mechanisms for carrying out a particular function. For example,
inducible enzymes may be explained by either induction or
derepression; the causes of mutation are many. This lack of
universality has bothered some philosophers who have universal
laws of physics as an ideal. But Schaffner argues that we should
expect to find diverse processes because of the evolutionary origin
of such processes.
When we think about building a system to do theory construction
by formulating all possible or some plausible mechanisms (maybe by
using analogies or interfield connections) and then eliminating all
but one that is the most compatible with the evidence, we must keep
in mind what level of generality we are working at. If we want a
particular hypothesisto explain a particular instance of enzyme
induction or mutation, for example, then we would expect to find
one mechanism operating. But ifwe are constructing a general
theory about the causes of enzyme induction, then we may need
to explicitly build in a means of coming up with several, all of
which may be found in particular systems.
Perhaps this idea is obvious to biologists, but I don't think
philosophers of science (and I don't know about AIists) have
explicitly concerned themselves with ways of generating theories
with multiple mechanisms. (Unfortunately, philosophers have had
very little to say about theory construction at all.)
Schaffner also wants to argue that these models may be "multilevel."
I don't think he has done a good job of characterizing what a level
is (in terms of part-whole aggregation); that is a tough problem that
I have been worring about for some time. (Greg, you might want to
look at the Schaffner paper since he is trying to deal with this
interlevel problem, which we talked about with respect to characterizing
the field of endocrinology. He hasn't gotten as far as our idea that
multi-levels result from the ability to black-box certain things for
certain purposes.)
Our plans for building a model of mutation to use in formulating
hypotheses in molecular evolution seem to fit rather nicely into
Schaffner's framework: we would have multiple models for how
mutation occurs and the task would be to figure out which one
applies to a partiuclar set of DNA sequences. Is anybody working
on this at all?
Bye, Lindley
-------
∂01-Apr-81 1237 STT More on perspectives, Kling and Feynman
To: "@ANALOG.LST[1,STT]" at SU-AI
In reply to Lindley's message: the fact that one can construct
numerous different perspectives of an object is consistent with the idea
that perspectives make an abstraction, but doesn't imply it, since one
can ALSO construct numerous different formulations of a situation,
NONE of which make an abstraction.
I am trying to sort out the distinctions between all these concepts
like perspective/abtraction/reformulation/analogy/isomorphism. If I get
anywhere I will send a message.
It was Kling whose analogies were criticized for being too close.
For instance, his system ZORBA analogized the following theorem of
group theory: "The intersection of two Abelian groups is an Abelian
group" with the following theorem of ring theory: "The intersection of two
commutative rings is a commutative ring." The proofs are almost isomorphic.
Actually Kling's system is intriguing in the following respect:
it does NOT construct a "ring" proof analogous in structure to a given
"group" proof, as one would expect.
Instead it merely observes which domain facts were used in the "group"
proof and selects analogous facts from the "ring" domain. These facts are
then used as input to a standard resolution theorem-prover. In other words
it is the use of analogy to focus on relevant facts in a domain, based
upon the facts that were relevant to an analogous problem. I don't recall
hearing that idea anywhere else. An example in science might be:
Suppose we wish to understand (the nature and origin of) the huge
canyons and other striking features of the Martian surface. An analogue
might be the cliffs, lakes and other striking features of Earthly mountain
ranges like the Sierra Nevada. There, we know, it was important to look for
rather subtle scars and remnants - scratches, piles of gravelly rocks.
These gave clues to the past shaping agents (glaciers).
Analogously, one would look for relatively small-scale curious features of
the Martial landscape which could be interpreted as scars or remnants of
some kind. (I recall people making close examinations of Mars-probe photos
looking for ripples, streamlines and similar indications of past floods.)
A further analogy: to understand how a painting was made, look at the
fine details of brushstroke.
In my last message I was somewhat unjust when I said "Feynman
isn't illuminating about the processes of discovering new laws." He
does make some interesting points in pp. 160-173 about how physicists
guess new laws.
He runs through several several methods for guessing which
physicists have used in the past - Maxwell putting together the known laws
and adding a term to make them consistent, Einstein examining the possible
symmetries of laws, Schrodinger guessing the equation, etc.
He claims that everybody knows these tricks now, and they are the first
thing people will try, so any outstanding problems must require a DIFFERENT
method to solve them. "I am sure that history does not repeat itself in
physics." (p. 163.)
If one accepts that analysis, the crucial phase in theory
construction or modification would be the invention of a new method for
guessing - not making the guesses themselves. The obvious question is, what
can we say about the process of inventing new methods? Here Feynman is
completely silent.
Suppose that by whatever means, a guess has been made. Feynman
claims, p. 171, that an experienced physicist can recognize correct guesses
immediately. "If you cannot see immediately that it is wrong, and it is simpler
than it was before, then it is right." I'm not convinced...
Refs:
Kling, Robert E. "A Paradigm for Reasoning by Analogy",
Artificial Intelligence 2 (1971) pp. 147-178.
Feynman, Richard P. "The Character of Physical Law",
MIT Press Paperback Edition, 1967.
∂01-Apr-81 1810 Darden@SUMEX-AIM response to STT on methods for guessing hypotheses
To: Analogy seminar:
I doubt that Feynman is right that scientists are all quite familiar
with the methods used in the past for guessing hypotheses and thus
new methods must be invented each time. His examples are just for
certain kinds of mathematical manipulations. Most scientists that
I have talked to are not at all articulate about any possible methods
to use for coming up with hypotheses. But even if Feynman were right,
then Steve is right when he says that just pushes the problem of
creativity back to finding new methods rather than finding new
hypotheses. My view is that we can look at past instances of
theory construction and find implicit patterns of reasoning used
but not articulated by the scientists and then use those methods
again. If we are concerned with the question of how to ceate new
methods, then I suppose my first attempt at answering that would be
to suggest we do that by analogy, just as we construct new hypotheses
by analogy. Does anyone have an example of a new method constructed
by analogy with an old one? Somehow I have a harder time thinking
of what new methods would be like.
-------
∂02-Apr-81 1331 Buchanan@SUMEX-AIM new method
To: Analogy seminar:
In DNA work, gel electrophoresis evolved as a technique from
one dimensional separation to two -- by analogy, I presume.
LD, would you pls elaborate?
bgb
-------
∂03-Apr-81 0452 Darden@SUMEX-AIM discovery of two-dimensional electorphoresis techniques
To: Maxam@SUMEX-AIM, Kedes@SUMEX-AIM, Friedland@SUMEX-AIM
cc: Analogy seminar:
Severalof us are having an electronic seminar on the topic of the
use of analogies in discoveries. Today I received a message from
Bruce asking for elaboration on the following: "In DNA work, gel
electrophoresis evolved as a techniques from one dimensional
separation to two--by analogy, I presume." I assume that Bruce is
talking about the wandering spot method that combines electrohoresis
and chromotography. Maxam discusses this method and a little of the
background to its development in his paper "Nucleotide Sequence of DNA,"
(manuscript, pp. I-23-24). There he says the following: "The new
direct DNA sequencing technique became known as two-dimenstional mobility shift
analysis or the wandering spot. It can be traced back to the cytosine
and thymine-distinguishing electrophoresis--homochromatography mobility shifts
exploited by Ling to sequence the long pyrimidine tracts of phage fd
(Ling, 1972a), and farther back to sequencing oligonucleotides by partial
exonuclease digestion and DEAE-cellulose chromatagraphy (Razzelland
Khorana, 1961; Holley, Madison, and Zamir, 1964). The latter approach gives
a one-dimensional array of nested segments, each (n) differing from the next
smaller one (n-1) by a single terminal nucleotide. When such partial
exonuclease products were later electrophoresed on DEAE-cellulose paper,
the interval between two successive segments (of chain length n and n-1)
was found to be often characteristic of th extra nucleotide....(Sanger,
Brownlee, and Barrell, 1965;Brownlee and Sanger, 1967)....The wandering
spot method, which evolved from these observations, sequences into a
DNA stradn from one end......Five accounts of this wendering spot or
two-dimensional mobility shift DNA sequencing technique appeared almost
simultaneiously in 1973."
This discussion doesn't tell us much about the reasoning in the
discovery but it doesn't sound like analogy. It sounds more like
applying two previously separate techniques in a single experiment
to get an added dimension of information. Is that correct? Do any
of the biologists know more about how this new technique was developed?
Do any of you have examples of discovery using analogy, either discovery
of new techniques or the proposal of new hypotheses?
Answers can be sent to the file <clancey>analogy.people to reach
Buchanan, Darden and the others in the analogy seminar.
Thanks, Regards, Lindley.
-------
∂04-Apr-81 0726 Darden@SUMEX-AIM Maxam on DNA techniques
Date: 4 Apr 1981 0724-PST
From: Darden@SUMEX-AIM
Subject: Maxam on DNA techniques
To: Analogy seminar:, Kedes@SUMEX-AIM, Brutlag@SUMEX-AIM,
To: Friedland@SUMEX-AIM
Allan Maxam sent me a message related to the DNA techniques question,
although he doesn't discuss the discovery of thosetechniques. I
am going to send it along to everyone else.
-- Messages from file: [SUMEX-AIM]<DARDEN>MESSAGE.TXT;1
-- Saturday, April 4, 1981 07:17:51 --
Date: 3 Apr 1981 1814-PST
From: Maxam
Subject: Re: discovery of two-dimensional electorphoresis techniques
To: Darden
cc: MAXAM
In response to your message sent 3 Apr 1981 0449-PST
Lindley,
The two-dimensional concept in DNA and RNA separation takes in
more than the wandering spot I mentioned. All instances except the so-called
"Southern-Cross" Blot seem to be either (1) Separate DNAs or RNAs in a
complex mixture first by one property (such as their sizes) in a first
dimension and then by some other property (such as their net charges, a
reflection of base composition) in a second dimension; or (2) separate
pieces of DNA (created for instance by some restriction enzyme X) in a first
cimension, and then break these into sub-pieces (with a different restriction
enzyme Y) and separate the latter in a second dimension. The former exploits
different pro properties of single pieces of nucleic acids, while the
latter stays with one property (size)., but creates distinct sub-pieces.
The wandering spot is an example of the two-property separation (see the
long paragraph in the middle of page I-25).
Who and what is the Analogy Seminar? See you soon.
Allan
-------
If anyone knows more about how the two dimensional idea originated,
I would be interested in hearing about it.
Lindley.
-------
∂10-Apr-81 0550 Darden@SUMEX-AIM Analogy seminar.5
Date: 10 Apr 1981 0548-PST
From: Darden@SUMEX-AIM
Subject: Analogy seminar.5
To: Analogy seminar:
This discussion is a continuation of an earlier one on perspectives.
The problem is to decide which properties or relations of a thing are
important to specify in order to analogize that thing to something else:
a"bird is like a plane" and "a bird is like a feather duster" require
different properties of a bird for matching. (That example is perhaps not
radical enough: one would like examples that require incompatible per-
spectives.)
The problem of how to recognize the important, appropriate, useful
properties is a very fundamental one. It is sometimes said that science
first goes through a natural history phase in which objects are found and
classified and then progresses to a theoretical phase. I disagree with this
view of the development of a science. In order to classify, a prior
decision must be made about which properties are the important ones.
Aristotle, for instance, breaks up the animal kingdom into groups according
to reproductive systems (egg-laying and non-egg-laying) and nutritive
fluilds (blooded and bloodless) because he viewed reproduction and nutrition
as the essential qualities of living things. This method of having a
theoretical view of essences and then building one's taxonomy on that
persisted for centuries. Of course, the difficulty is to justify a
judgment as to what the essential qualities are.
A change in the kinds of properties studied was an important
component in Laviosier's work in chemistry and Darwin's in biology.
The alchemists and phlogiston theorists had concentrated on qualitative
differences among substances--yellow is an important characteristic of gold.
Laviosier, probably as a result of influence of Newton, shifted the focus of
attention to quantitative weight relations. His study of weight changes
during combustion was the key to the postulation of oxygen. Then Dalton
was able to study combining weights of elements and infer relative
weights of atoms. The shift of perspecitive from qualitative properties
to quantitive weight relations was essential before Mendeleev could
classify the elements in the periodic table.
Another shift in perspecitve occurred in Darwin's work: a shift
from looking for the similarities among organisms (as those concerned with
essential qualities had done) to looking at the variations (which had
previously been the noise in the system). The amount of variation and
its cause became a key issue for the theory of natural selection.
Mendel's work was also dependent on seeing that variations were
important to study and that they might exhibit patterns in inheritance.
How do these shifts of perspecitve occur? Is there any "complete"
listing of properties and relations that would have included these very
different perspectives? If we are designing a search space for an
analogy building system to use, how do we decide what objects to include and
how do we decide which properties and relations will provide enough
flexibility so that different perspecitives of the object will be
available? Are the various different perspectives compatible or do we
sometimes have different perspectives that are as radically different
as figure-ground shifts? Is there a way of writing a very general
heuristic that would direct a system to construct radically different
perspectives? (That sounds very hard; it the old question of how you
avoid putting every thing in at the outset.)
Russ, you first started me thinking about the possibility of
looking at DNA sequences from different perspectives. Have you had
any new ideas about these issues? I just read a very interesting
paper by Harold Weintraub ("Recognition of Specific DNA Sequences
in Eukaryotic Chromosomes," Nucleic Acids Research 8 (1980)4745-4753)
that discusses the three dimensional coiling of DNA helixes within
nucleosomes and suggests that regulatory sites would be spaced at
about 80 basepair intervals. Thus a new perspective on the linear
sequence emerges when we consider another level of organization.
I suspect that a system that does hypothesis formation about molecular
evolution will have a somewhat different perspective of the sequences
than one that forms hypotheses about gene regulation.
Is anyone else thinking about alternative perspectives?
Bye, Lindley
-------
∂16-Apr-81 0659 Darden@SUMEX-AIM Discussions with Maxam
To: Friedland@SUMEX-AIM, Buchanan@SUMEX-AIM
cc: Darden@SUMEX-AIM, Maxam@SUMEX-AIM, Brutlag@SUMEX-AIM,
cc: Kedes@SUMEX-AIM, STT@SAIL, RDG@SAIL, Bennett@SUMEX-AIM,
cc: Lenat@SUMEX-AIM, Clayton@SUMEX-AIM, Bach@SUMEX-AIM
I had a great time visiting with Allan while I was in Boston and
i want to tell you all about some of my observations. It is an
interesting coincidence, Peter, that you sent a message about
the gene regulation issues just as Allan and I were discussing them
a continent away.
Allan is very interested, as we all know, in understanding the
control of genes and he is convinced that the linear sequence of
DNA must be the ultimate place of the encoding of the regulatory
machinery. That is good, since it is the linear sequences that we
have to work with. Allan has only a limited understanding of
AI and the kinds of expert systems that do scientific reasoning
that we want to build (so far as I can tell). He thinks of MOLGEN
primarily in terms of SEQ and his projections for what he wants
a program to do sort of sound like more sophisticated versions
of SEQ or other utility, algorithmic programs. He is very interested
in talking about the reasoning involved in doing hypothesis
formation for hypotheses about gene regulation, but I think he
verymuch wants to do that work himself, or possibly interact with
me and others who have ideas about how to do it. He seems to have
little interest in being involved in a long range plan of building
an expert system to do that. And, of course, that makes good sense;
Tom Dietterich and I last fall, while discussing the possiblities
of building a system to do hypothesis formation in gene regulation
realized that the system might not be allowed to function, since
as soon as the pattern matcher turned up promising looking data,
the biologists would want to formulate the hypotheses themselves.
So, my conclusion from talking to Allan is that Peter, you
should get together with Allan to talk about the kind of programs
he needs in order to analyze the sequences. He has some very
good ideas about where regulatory sequences might be located and
what they might look like and why we might lose them to
statistical noise if we don't build in certain possibilities and
what kinds of "deep-structure" relations among the atomic
groups in the bases do or do not make a difference. His
extensive knowledge about DNA-protein interactions is exactly
the right expertise to build into a sophisticated program to
look at the right places in the sequences. The MOLGEN
team could possibly incorporate all or some of that
knowledge in the pattern-matcher that is on the schedule
already, or we might want to write another proposal to
fund it, or you Peter, might want to do it yourself in your
copious free time.
Coupled with this work on writing a sophisticated pattern
matcher, Peter, Allan and I should get together and do some
systematic hypothesis formation. Bruce's suggestion of
constructing a "half-order theory" is a very good one;
I suggested to Allan that we sit down and outline the
requirements of any gene regulation theory (at a very
abstract level) and then begin to search for vague ideas
(abstract, generally specified types of hypotheses) that we
could instantiate in more particular hypotheses. Peter, I
would guess that your experience with devising skeletal plans
would be quite helpful in that stage. This abstract model
building that we would do would help us in deciding what
features to put into the program that will search through
the sequenes.
So, although we would not be building a full-blown Ai
expert system to do hypothesis formation, we would all get
experience with the reasoning involved in doing hypothesis
formation and with how to couple programs to analyze data to
that kind of reasoning.
Also, the knowledge that we gain about the sequences and
their interrelations and "deep-structure" would be very
valuable if we ever do build the system to do hypothesis
formation in molecular evolution. I have come to agree with
Doug that that area is probably the best now for doing an
AI expert system. Biologists will soon begin using the sequences
to do evolutionary trees ( has anyone started that already? why
isn't Dayhoff doing that in the way she did cytochrome C?) and
<<<RDG - I thought it was Dickerson!>>>
we could probably do a better job with the system we discussed.
If anyone is thinking about the molecular evolution problem,
Allan gave me a good paper that constructs a hypothetical
evolutionary tree using the immunoglobulin genes: H. Sakano, et.al.,
"Sequences at the somatic recombination sites of immunoglobulin
light-chain genes," Nature 280 (1979)288-294.
It would really be fun to begin this collabortion between
molecular biology, AI and philosopy of science. I hope we manage it.
Bye, Lindley.
-------
∂16-Apr-81 0733 Darden@SUMEX-AIM discussion with Winston and Gentner
To: Analogy seminar:
I have just gotten back from Boston and want to tell you all about
my discussions of analogy with Dedre (pronounced daydree or deedree,
I have trouble remembering since we mispronouned it last fall) Gentner
and Pat Winston.
Dedre, as you may remeber from her BBN paper, analyzes analogies as
matches among a relational network rather than as matching of properties.
She strongly argues a normative view that the "better, more
sophisticated" analogies have this relational mapping; she believes
that in early, naive, stages of analogy searching similar properties
are often matched but the good analogies get away from property
similarities to concentrate on overall relational similarities.
This view has influenced Pat who is continually working on his
analogy systems and revising the MIT paper describing it. He has
shifted from ideas of property matches to causal networks that
overlap or partially overlap. Pat and I agree (though I think
Dedre disagrees) that one can often use a partial analogy, i.e.,
the whole causal network doesn't have to be carried over from
the analogue; only one part of it may be relevant to the current
problem. Pat has a very unsophisticated (philosophically) notion
of cause (and seems totally unaware of any of the philosophical
literature on the topic--which may ultimately be good since
lots of distinctions at the outset may only be confusing--but
at some point he will have to clean up his notion). Anyway, at the
moment, the concept of causal interconnections is serving a very
important function in his analogy system. He recognizes, as we
all do, the difficulty of deciding how to represent the things
that one is going to match in an analogy system. By focusing
on what he is calling causal links in the system, he can get
a simple (relatively, some get rather spaghetti-like) causal network
model for a set of relations, e.g. the plot outline of Macbeth
(if that sounds far-fetched, remember he is using a loose notion
of cause: someone's being evil causes them to be a murderer).
When one has a new situation with some similarity among the nodes
to a previous system, then the causal network can be overlayed
as a way of reasoning by analogy. He told me about recent work
that attempts to translate parts of the causal network into
production rules (if x is evil, then x is a murderer), so instead
of having to access the analogous causal network to reason by
analogy, one only has to find the appropriae.
Well, if all this sounds less than crystal clear, it is
because I talked to him for about thirty minutes at a very rapid
pace. He found it astounding that I want to do reasoning by
analogy in real hypothesis formation in science since he has
had such trouble working out the toy domains he uses. But it
was fun to talk to someone who is actively doing an analogy
system and changing it constantly to incorporate new approaches.
Curiously, none of his graduate students work on analogy and
I didn't find anyone interested in philosophy of science;
Chomsky and philsophy of mind seem to dominate at MIT, in so
far as they are philosophical at all. Frankly, I find the
ways of thinking at Stanford much more sophisticated, though
perhaps a snap judgment after a few hours at MIT is not the
most informed of opinions.
I hve new editions of both Gentner's and Winston's papers
and I will do another analogy message after I read them if they
suggest new ideas.
Bye, Lindley.
P.s. sorry for the typos: "appropriae" should read "appropriate
rules."
-------
∂17-Apr-81 0505 Darden@SUMEX-AIM properties and relations
Mail-from: ARPANET host SU-SCORE rcvd at 16-Apr-81 0839-PST
Date: 16 Apr 1981 0837-PST
From: Tom Dietterich <CSD.DIETTERICH at SU-SCORE>
Subject: Re: discussion with Winston and Gentner
To: Darden at SUMEX-AIM
cc: CSD.DIETTERICH at SU-SCORE
In-Reply-To: Your message of 16-Apr-81 0728-PST
I have still not read Dedre's paper, but from our discussion last fall
it seems to me that she was saying the obvious thing about computer
systems: everything in a computer can be REDUCED to syntactic matching
of the contents of memory. Now if you want to think of memory as a relational
network, then you are matching relations. If you want to think of it as
a set of properties, then you are matching properties. In all cases,
analogy is going to be based on some hypothesized partial similarity
between the two things being analogized. It seems to me what Dedre is
advocating is that we deepen our notion of "similarity" to include
relations as well as features. In other words, we should compare
things in predicate calculus rather than merely propositional calculus.
Pat Winston is further advocating that causal relations are
particularly important ways in which two things can be similar. I agree
100% with that idea, and I agree with your observation that Winston's
notion of causality is quite naive.
I think it might be fruitful to investigate the concept of "similarity".
What features/relations/functions, etc. are being used to determine
how two things are similar? Can the history of science tell us
anything about what scientists have used? Here is a partial list of
everything I could think of:
1. Similar features (color, shape, size)
2. Similar relations (this covers a lot of things:
a. substructure: contains(a,b), has-as-parts(a, x, y)
b. time: precedes(a,b)
c. causal structure: causes(a,b), enables(a,b), etc. etc.
d. purpose: has-as-goal(x, y), serves-role-of(x, y)
e. mechanism: is-implemented-by(x, y),
acts-as-unit(set of ants, individual)
There are all kinds of procedural relations that we probably
could add here...Scientists will probably use whatever they
know about two things to posit an analogy--the analogy may
be based on similar surface features, or on a deeper insight into
the mechanisms responsible: e.g. the growth of knowledge is analogous to
biological evolution. This analogy is based on the underlying mechanism
of "random generate and test search" with pruning of poor ideas/organisms.
It leads naturally (sic) to Doug's proposal that Nature might be using
"plausible generate and test" instead! Here is a wierd interfield analogy
(I don't think it qualifies as a connection yet).
--Tom
⊗
ps. Please forward this to everyone on the list. From SCORE, I am
unable to access Clancey's mailing list file.
-------
I am using the Forward command on MSG for the first time. If you all
don't receive Tom's msg, please tell me what I should do.
Bye, Lindley
-------
**** REREAD FROM HERE ON ****
∂19-Apr-81 1830 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Boyd on the meanings (referents) of theoretical terms.
To: Analogy-seminar: ;
Well, I finally finished reading (and re-reading) Boyd's article in
Ortony. I found it to be really fascinating--especially his concept
of epistemic access which is very similar to what AI people have been
saying recently. Are there any other good articles I can read about
the causal theory of reference or about Realist philosophers in general?
He basically seems to be saying that the meaning of a linguistic
term T is the sum total of all of the knowledge we have about that
term. Although this sounds tautological, I think it is an important point.
He mentions some of the things we might know about a term:
1. How to measure it directly (operational definition).
2. How to measure it indirectly (measure its manifestations).
3. What its effects are (causal roles).
4. Theories in which it plays a role. (This is interesting. STT
mentioned this as a possible way of "defining" a term. This is a
kind of mental inversion of perspective that we were discussing
earlier.)
5. Definite description (necessary and sufficient conditions).
6. Procedures for modifying the theories in which the term plays a role.
If this is the case, then it is possible to develop new terms by
modifying these various kinds of knowledge. AM develops new terms
by modifying #5, definite descriptions (in LISP).
Other AI concept-learning programs are similarly limited in using
only necessary (or sufficient) conditions.
I have been thinking about a distinction between (1) theories in
which a term participates, and (2) theories serve to define a term
(e.g., by reducing it to other terms, reformulating it in other terms,
providing operational definitions or necessary and sufficient
definitions). I call (1) "ordinary theories" and (2) "term theories".
Most concept learning programs start with a set of terms
that have little or no term theories and proceed to develop ordinary
theories by expressing them as boolean (or other) combinations of
the original terms. The problem with this approach is that it
does not permit the introduction of new terms. Most AI programs make
use of the "closed world assumption" in many ways. The strongest
way--exemplified by Mitchell's version space algorithm--is to assume that
the only possible (ordinary) theories that exist are those that can be
expressed using combinations of the existing terms. This assumption
allows theory construction to be accomplished by simple syntactic
operations. This approach ignores the "new term problem" and the
"wandering term problem"--that is, the problem that the meaning of
terms changes over time.
An interesting project would be to attempt to approach these
problems by modifying both the "ordinary theories" and the "term theories".
Lakatos provides some ideas (in Proofs and Refutations) for using
ordinary theories to guide the modification of term theories.
Boyd raises the possibility that metaphors serve to provide a
partial "term theory" (in their role of filling holes in the language)
which scientists must then explicate further.
--Tom
-------
∂19-Apr-81 2045 CSD.DIETTERICH@SU-SCORE Definitions of AI TERMS: Perspectives, Analogies, et al.
To: Analogy-seminar: ;
cc: klc at SU-AI
In a message a while back, STT mentioned that he was thinking about
the distinctions among AI terms such as "perspective", "abstraction",
and "reformulation". I have given them a little thought, and I'd
like to share my attempts at defining them. This has also helped
me to see what I find dissatisfying about existing AI work on
analogy (Winston, Kling, Evans, Genesereth, etc.)
I am casting all of these definitions in terms of units and slots of
units. The definitions are a little impoverished. I expect each
definition could be deepened in many ways. The units&slots
representation is just used to anchor the discussion. The definitions
of abstraction, prototype, and exemplar are taken (roughly) from a
paper by Winograd ("On primitives, prototypes, and other semantic
anomalies", TINLAP-2, 1978).
A PERSPECTIVE is a meta-level unit that specifies which object level
slots should be examined by some process. Thus, when we want to view
Russ Greiner as a physical object, we can create a perspective that
says "examine these slots: length, width, mass, temperature, color,
density, chemical composition, physical structure". Notice, that when
I said "view Russ as a PHYSICAL OBJECT" I was referring to another
unit--the PHYSICAL OBJECT unit--and using that unit to tell me which
of Russ's slots were relevant to this perspective. I think an
important part of a perspective is that it is a GROUP of slots
(features, predicates, etc.) along with some procedures that tell me
how to interpret the contents of those slots. ("term theories" for the
slots). The slots sort of "hang together". They form a coherent way
of viewing Russ.
An ABSTRACTION is a unit, such as PHYSICAL OBJECT, that has a set of
generalized slots that attempt to capture characteristics that are
common to a class of things. Abstractions, in AI, almost always list
positive features that are held in common. They can be obtained from
fully described units by DROPPING irrelevant slots. If this is the
case, then an abstraction is a unit obtained by viewing a class of
objects from one perspective--using one set of slots. But it need not
be the case. Genesereth, for instance, says that an abstraction is a
(predicate logic) theory, and the instances of the abstraction are
models or partial models of that theory.
A PROTOTYPE is a unit that gives typical, expected values for its
slots. Exceptions are allowed. A prototype may even list typical
alternatives, such as RIGHT-HANDED (85%), LEFT-HANDED (15%).
"Prototype" carries the connotation that it can easily be instantiated
to give an individual member of the class. Thus, the prototype TABLE
could have a #-OF-LEGS slot and a HEIGHT slot TABLE[#-OF-LEGS= 3 or 4,
HEIGHT= 30-45 inches, etc.].
An EXEMPLAR is a chosen element of a class that is typical of all
elements in the class. A exemplar of TABLE is actually a table, whereas
the abstraction PHYSICAL OBJECT is not in itself a physical object.
REFORMULATION has three meanings: (1) a set of rules for recasting one
set of slots (perspective) in terms of another, (2) a unit obtained by
reformulation from another unit, and (3) the act of reformulating.
Thus, STT reformulates a circle (expressed as center + radius) as a
set of points, as a conic section, as a degenerate ellipse, etc. The
basic approach to reformulation is to use the set of rules to write a
formula that relates elements of both formulations and then solve for
the desired one.
ISOMORPHISM: a one-to-one mapping that completely preserves some
perspective (set of slots). Thus, we might preserve the physical
structure of a toy-block arch to map it isomorphically into
a real arch. The mapping does not necessarily preserve color, mass,
or chemical composition, however.
ANALOGY: A partial mapping between two units. The quality, or depth,
or usefulness, of an analogy depends upon the nature of this partial
mapping. If the partial mapping is an ISOMORPHISM, then the analogy
is our friend the pattern match. This is the kind of analogy that
Winston is using. (and Kling and Evans) Genesereth locates analogies
by looking for common ABSTRACTIONS. The abstraction indicates how to
map one slot of one object A to the analogous slot of object B. This
presumes that the abstractions are already known--an assumption that
won't work for "new" analogies. Mike is using them to recognize "old"
analogies. Winston mentions a third kind of analogy that combines
abstraction with isomorphism. He first abstracts A to get A', and B
to get B', and then conducts the pattern match. I think truly
interesting analogies are those that combine REFORMULATION with
pattern matching. We analogize A to B by finding reformulations of A
and B (call them A' and B') such that the reformulations are
isomorphic or share a common abstraction.
I think there are two basic "analogy problems". One is to discover a
useful analogy--to guide the reformulation, abstraction, and matching
processes to discover useful analogies. The other problem is to deepen
the analogy to determine what parts are "positive", "negative", and
"neutral".
The process of discovering useful analogies may be aided by attempting
to compare prototypical A's to B's. The process of deepening the analogy
may involve creating an abstraction that describes both A and B.
(Is an abstraction a "dead analogy", a "compiled analogy?").
Notice that abstraction --> prototype --> exemplar is a series of
ever more particular descriptions. We can develop analogies by
matching exemplars, matching prototypes, or matching abstractions.
We can also bring reformulation into the act and reformulate before and
after the matching.
Notice that if you are doing simple matching of exemplars without
reformulation, then the analogy is equivalent to viewing the
two exemplars from a single perspective. Winston extends this
perspective to call it a "transfer frame".
Also, notice that if the abstractions are based on simple dropping of
slots, then finding an analogy by finding a common abstraction is
equivalent to finding a single perspective.
I'd be interested to hear your reactions! Does any of this stuff make
sense?
--Tom
-------
∂20-Apr-81 0605 Darden@SUMEX-AIM partial reply to Tom
Date: 20 Apr 1981 0603-PST
From: Darden@SUMEX-AIM
Subject: partial reply to Tom
To: Analogy seminar:
Tom, I found your analogy discussions fascinating. I will have to think
about all of it for a while and wait until I have more time to respond
adequately. But a few brief comments. Your analysis of Boyd's article
was quite good and you located some of the lively, current issues in
philosophy of science. I will try to find you additional references
on the causal theory of reference. The idea of a term's meaning coming
from the theory in which it is used, rather than being given by an
antecedent defintition has been discussed by philosophers of science
for a while, even the later Hempel articles began to propose that view.
It can be traced back to Wittgenstein's idea that the context determines
the meaning: "the meaning is the use." It is very interesting to watch
you struggle, from an AI framework, to distinctions that philosophers
have come to via another route (some sort of indiciation of the correct
ness?). Another instance is your "term theories" vs. ? was it "object
theories." That is the old distinction between definitions and laws,
expect expressed from the perspective that the term may be defined by
the context. A problem that i think philosophers of science have never
solved is how discovered properties (e.g. atomic weight of atoms) at
first play a role in laws but later become part of the definition
of a term. Neither AI nor the older positivistic views of science
that see science as a static, fixed set of defintions and theories,
can accomodate conceptual change. You are struggling with some of the
most fundamental problems between a static view of knowledge and
a dynamic one. (And doing a rather good job too).
The only other references that come to mind immediately are
two by a colleague of mine, Dudley Shapere. In Part II of
"Notes Toward a Post-postivistic Interpretation of Science"
(in ed. Peter Achinstein and S. Barker, THE LEGACY OF LOGICAL
POSTIVISM, Johns Hopkins, 1969) Shapere discusses what it is for
a term to be interpreted realically: to say "A exists" implies
that (1) A can interact with other things that exist,(2) A may
have properties that are not yet manifesting themselves and (3)
A is soemthing about which can have different and competing
theories. In a newer paper, Shapere says some suggestive things
about conceptual change, though I don't think his ideas are
very well-worked out yet: "The Character of Scientific Change,"
in ed. T. Nickles, SCIENTIFIC DISCOVERY, LOGIC AND RATIONALITY,
Reidel, 1980. I don't think he has very much to say about
actual methods for introducing new terms. i found your suggestion
that we might be able to get new ones by altering any of the
knowledge by which we "define" terms fascinating to think about.
Well, I have to prepare for class and relunctantly must quit now.
I will reread your message and respond in more detail later.
Bye, Lindley.
-------
∂22-Apr-81 0717 Darden@SUMEX-AIM hypothesis formation in gene regulation
Date: 22 Apr 1981 0709-PST
From: Darden@SUMEX-AIM
Subject: hypothesis formation in gene regulation
To: Friedland@SUMEX-AIM, Maxam@SUMEX-AIM
cc: Analogy seminar:, Brutlag@SUMEX-AIM, Kedes@SUMEX-AIM,
cc: csd.Mostow@SCORE, Bach@SUMEX-AIM
Peter and Allan Maxam and I are going to be having discussions
about hypothesis formation (which you all know I am very interested
in ) in gene regulation (which you all may know that Peter and Allan
are very interested in). When analogies are relevant to our discussion,
I intend to send copies of the message to everybody in the analogy
seminar we are having. I am including various other people in this
first message; if you would like to continue to participate in theise
discussions, let me know; otherwise I won't clutter up your msgs with
copies.
I have various ideas about how to do systematic hypothesis formation.
One that has been of interest to a number of us is the use of analogies.
I have just been reading an interesting proposal and I would like to
have comments from anyone that has ideas about how to pursue this.
In Judson's THE EIGHTH DAY OF CREATION, THE MAKERS OF THE
REVOLUTION IN BIOLOGY, Sidney Brenner (pp. 220-221) speculates about
what will be necessary if molecular biology is to understand the
process of embryological development in terms of gene regulation by
suggesting a vague analogy to computer programs. I am going to quote
Brenner and then ask if you all have any more detailed ideas of how to
exploit this analogy.
"...in the next twenty-five years we are going to have to teach
biologists another language still. I don't know what it's called yet;
nobody knows. But what one is aiming at, I think, is the fundamental
problem of the theory of elaborate systems. Especially, elaborate systems
that arise under conditions of natural selection. And here there is a
grave problem of levels: it may be wrong to believe that all the logic
is at the molecular level. We may need to get beyond the clock mechanisms.
Yet still, if the changes are made at the nucleotides, then clearly we
can't understand anything until we understand all the levels of computation
that connect the change in the gene with the change in the development,
the growth--or the behavior. That's an immense task. I don't want to
say trite things--you know, we all criticized the biochemists for
saying that the cell is a bag of enzymes [LD:he shouldn't forget that the
enzyme theory of life was extremely important in the early founding of
biochemistry as a field. Oversimplifications at the beginning are
often necessary and quite fruitful.]; well, I mean you might as well
condemn us for saying the cell is a bag of repressors and operators.
"There is something to be thought about here that has not yet been
formulated successfully. John von Neumann wrote a very interesting essay
many years ago, in which he asked, How does one state a theory of
pattern vision? And he said, maybe the thing is that you can't give a
theory of pattern vision--but all you can do is to give a prescription for
making a device that will see patterns! [Does anybody know how this came out?
Was a theory devised after all?] In other words, where a science like physics
works in terms of laws, or a science like molecular biology, to now,
is stated in terms of mechanisms [an interesting contrast:laws vs.
mechanisms], maybe now what one has to begin to think of is algorithms.
Recipes. Procedures. [I am having trouble thinking about the relation
between mechanisms and procedures: what would it be to have a recipe
for building an embryo but not know the (underlying?) mechanisms. Well,
we could just have a cookbook (sounds like alchemy) that says dump in
this gene and a dash of salt and you will get a certain end product;
but this wouldn't give us an understanding of what is happening. Do
computer scientists think of procedural knowledge as providing
understanding? I'm not sure these are well'formed questions.]
[I'm leaving out a paragraph that argues that descriptive
knowledge is not procedural knowledge.]
"I believe that in biology, programmatic explanations will be
algorithmic explanations," Brenner said. "You will have to say, Next switch
on gene group number fifty-eight. And then one has that whole lot of
molecular biology--what is gene group fifty-eight and what does it do.
And one takes for granted that gene group fifty-eight performs its com-
putation. And then the simultaneous steps, the alternative steps, the
sequential steps. In great detail. So. I feel that this new molecular
biology has to go in this direction[this is important--if you have
been asleep so far wake up here!!!]--to explore the high-level logical
computations, the programs, the algorithms of development, in molecular
terms. We've got to try to carry the analysis to that level--and to
carry the molecular biology with it. But of course we're asking
the questions that people raised in the 1870s. Not the 1970s [He
is probably referring to Roux and Weismann and the whole problem of how
chromosomes control development: Weismann thought chromsomes fragment
during differentiation so that determinants for different parts of the
body get parceled out: lots of lovely heirarchical control that wasn't
confirmed by cytological observation.] But of course we're doing it with
modern tools and with everything we know. And one would like to be
able to fuse the two--to be able to move between the molecular hardware
and the logical software of how it's all organized, without feeling
they are different sciences."
Can we pursue this analogy between gene control and programs?
In programs, what are the control structures? What levels of heirarchical
control operate? Do you suppose genes are part of subroutines? What
would a program for development look like? The complexity seems
rather mind-boggling; what high-level, abstract, simplifications can
we make? How are parts of programs interrelated? Do you suppose genes
have demons? What other questions would a person who understands
the control structures in programs ask of the genes?
Hypothesis formation can be done in a number of ways. One idea
that wwe have been pursuing is that analogies can be useful. Doug Lenat
has already tried to exploit an analogy between the failure of attempts
to generate programs randomly and the need for heuristics and the random
mutation of DNA to suggest the need for heuristic in DNA for evolution.
Can we exploit Brenner's suggestion and get hypotheses (either very
abstract or more detailed) about gene regulation from analogies
to programs? Are there other analogies for regulation, control mechanisms,
or information transfer that anyone else thinks worth pursuing?
Looking forward to you comments. Bye, Lindley
-------
∂23-Apr-81 0523 Darden@SUMEX-AIM gene regulation analogy
Date: 23 Apr 1981 0517-PST
From: Darden@SUMEX-AIM
Subject: gene regulation analogy
To: Analogy seminar:, Maxam@SUMEX-AIM, Kedes@SUMEX-AIM
Mail-from: ARPANET host SU-SCORE rcvd at 22-Apr-81 1807-PST
Date: 22 Apr 1981 1807-PST
From: CSD.MOSTOW at SU-SCORE
Subject: Re: hypothesis formation in gene regulation
To: Darden at SUMEX-AIM
cc: friedland at SU-SCORE
In-Reply-To: Your message of 22-Apr-81 0709-PST
Just last night I happened to be thinking about the program/gene-regulation
analogy in anticipation of starting some introductory readings in molecular
biology. So the following can be viewed as ignorance-based inference.
A key question in gene regulation seems to be whether the language of gene
regulation is entirely expressed by the AGTC sequence or depends on 3-D
structure as well. An experiment that could settle this question would be
very useful. One of the problem constraints is really very strong: the DNA
in every cell of an organism is identical, yet different cells with the SAME
DNA develop in different ways and do different things. In a simple analogy,
the DNA is the program. If this program does different things in different
cells, the PROGRAM STATE must be different in those cells. We already know
about certain kinds of local state. For example, in the transcription
process state is represented by a molecular structure that attaches to the
DNA and zips along it, producing protein. (Forgive me if I get facts wrong.)
Does the 3-D configuration of DNA encode a more global state? If so, several
predictions are possible:
(1) Different configurations will be found in cells with different functions.
(If the configuration is always the same, it doesn't encode program state.)
(2) If different configurations of the same DNA are placed in identical
environments (the soup of stuff that floats around in cells), they will
produce different mixes of protein. I have no idea of whether this is
experimentally feasible.
(3) If the configuration of DNA can be changed somehow (electrically?
magnetically? but without interfering with other cell processes), its
protein-producing behavior will change. If the change is random, the
resulting behavior will reflect it: perhaps protein production will stop,
or abnormal proteins will be produced.
(4) Suppose 3-D structure is determined by the core of protein or whatever
the DNA is wrapped around. If a core corresponding to one type of cell
is replaced by a core corresponding to another, the restructured DNA should
produce behavior closer to the other type of cell, depending on how much
state is encoded in other ways, such as relative concentrations of different
molecular structures (operators and repressors?) in the two kinds of cells.
Various kinds of state could be encoded in 3-D configuration. The above
discussion considers cell type as a kind of global state. Cell phase is
another kind of stae: how do changes in configuration affect cell division
and cell growth processes? Lower level state involves intra-cell processes.
Here one might expect to find relatively local changes in configuration
associated with processes controlled by portions of a gene.
What if 3-D configuration of DNA is not part of program state? It may still
be an important part of the gene regulation language, even if configuration
is entirely determined by the AGTC sequence. Aren't there molecules that
are coded to attach to subsequences of DNA that lie next to each other when
wrapped around the core? Understanding the sequence may require the ability
to predict its 3-D structure. Can this structure be predicted solely from
the sequence, or does it also depend on the core?
The program analogy predicts that every process must somehow have its state
encoded, and that there must be operators capable of changing this state.
For example, suppose 3-D configuration is determined by the core the DNA is
wrapped around, and in turn determines cell type. Then one should be able
to construct a cell of a given type by injecting the right core into an
empty cell along with some DNA; the DNA should wrap around the core and
form the right configuration. Does anything like this happen during cell
differentiation?
If program state is not encoded in DNA 3-D configuration, one could imagine
it being encoded in DNA motion. (Well, maybe a knowledgeable person couldn't.)
Different frequencies of motion could encode state corresponding to different
cell processes, say; this assumes that the frequency would affect what local
reactions could occur, and that molecular mechanisms exist for maintaining
and changing frequencies. This seems far-fetched to me; I include it for
completeness.
At the lower levels of program state, the program analogy predicts something
in the role of program counter. (This corresponds to short-term memory in
a production system analogy.) At the lower levels, what determines which
reactions are allowed to take place, and controls their sequence? If not
3-D configuration, perhaps it's the concentration of different substances
in the cell environment. Perhaps processes are not entirely switched on and
off, but regulated to a higher or lower level of activity by a feedback loop.
This is certainly consistent with what I know of biological processes. If
you want to turn off a process that produces X, then have a low level of some
substance necessary for the production of X, and/or a high level of something
that destroys X. At equilibrium, the level of X will be low or zero. Get a
high or low level of the controlling substances by the same kind of feedback.
Ultimately the generation of such substances must be controlled by the program
-- isn't this what the transcription of DNA into protein does?
Another constraint is that the language of gene regulation arose by evolution.
It's not clear to me what features this origin should produce in the language.
The sort of changes necessary for a useful mutation should be expressible as
simple perturbations in the language; otherwise they would not tend to occur.
For example, the language should be such that mutations can occur at any level
in a hierarchy. The mutation of lengthened limbs should not have to be
represented separately for each limb. The hierarchy may be tangled: for
instance, bilateral asymmetry affects a whole side of the body, while
changes in height involve, say, the lower limbs. The levels of the hierarchy
correspond to different phases in development. Either mutations relating to
both legs affect processes that occur before the legs are separated, or they
affect two copies of the same process that occur after left-right separation.
Other constructs suggested by the program analogy are parameters and names.
Useful subroutines often take input parameters and return a result. If these
concepts apply to gene regulation, how would they show up? There would have
to be a way to specify a process to run and what parameters to run it with.
Suppose both the procedure call and the called subroutine are encoded as
ACTG sequences. (An alternative would be for them to be encoded as things
generated from those sequences, e.g., protein structures.) How can the
procedure name the subroutine? I'd expect to see the name coded as a
pattern that uniquely matches some subsequence in the subroutine, via some
series of transcription transformations. In the simplest case, this pattern
would just be an ACTG sequence -- a purely symbolic (unstructured) name. But
structured names are a possibility. Perhaps a subroutine name is represented
as a description (in some language) of what the subroutine does: "call any
procedure that produces X."
What does it mean to pass parameters to a subroutine? It means to invoke a
subroutine whose subsequent behavior depends on the values of the parameters.
Some of the reasons that make subroutines useful in programs may not apply to
DNA produced by evolution. One such reason is storage economy: it takes less
space to pass different parameters to a single general subroutine than to
"compile in line" a separate copy of the subroutine for each place it is called.
Perhaps this consideration is not important for DNA, or subroutine-sharing is
too complex to be produced by evolution.
If parameter-passing does occur, though, it may be in a very literal sense:
the calling procedure builds a structure containing a key that matches the
subroutine name, plus some pieces corresponding to the parameter values; this
structure wanders around till it finds the subroutine sequence and binds to it,
and the subroutine then does something to the structure, so that the result
depends on what parameters were passed.
Even if subroutine-calling doesn't occur, there must still be some mechanism
for control sequencing, so the remarks above about naming may still apply.
If subroutine-calling does occur, there should be some way to signal the
calling procedure when the subprocessing is completed. Actually, the issue
here is not one of sequential processing -- cell processes occur in parallel
-- but of synchronization in general. If there are sequences of DNA that
represent high-level control sequences, there should be some mechanism for
knowing when to proceed from one high-level step to the next.
The program analogy suggests some predictions about flow of control that may
help in designing experiments to learn more about the gene regulation code.
Suppose there is a way for one procedure, embedded in a DNA sequence, to name
another, and we want to learn the naming scheme. Presumably the way procedure
calling happens is that the calling procedure constructs (via a transcription-
like interpretation process) a molecular structure that wanders around till
it binds to the subroutine site. If so, we could gather valuable data by
tracing the movement of such structures, studying how they bind, and looking
for systematic relations between the binding key and sequences near the
original transcription site. Such relations would be candidates for naming
schemes.
Some of the predictions made above can be tested or further specified based
on reasoning. For example, is it really practical to call a procedure by
constructing a stucture with a key that matches it, and waiting for it to
bind? How long would it take? Would it be more feasible if there were more
than one target? More than one message (the structure sent from the calling
procedure to the subroutine)? If the subroutine were near the calling
procedure? (What are the implications of sending multiple messages? What
would keep a message from wandering around indefinitely and then finding
the subroutine site at an inappropriate time much later in the program
execution? Do messages decay, so as to release useful material (resources)?
More likely, are they garbage-collected by roving message-eaters? Is there
a feedback mechanism to halt message-sending once the message is received?)
Suppose there is a naming scheme as described above. How long must names be
in order to be unique? This depends on whether naming is localized. What is
the address space at a particular procedure? Should it be able to call any
procedure on any gene? On any chromosome? How many subroutines should it
be able to call? Is it biologically reasonable to use path names ("call
procedure X on gene Y in chromosome Z")? Given a particular set of
assumptions, one ought to be able to derive a lower bound on name size.
For instance, a name 10 symbols long (symbols = {A, G, T, C}) can name at
most 4↑10 ~ 1 million things. Such arguments should help give an idea of
what length matches to look for.
Given the sequential nature of DNA, one might expect to find it used for
linear sequencing. That is, if sequence X and Y are adjacent, and X is
a procedure call, one might expect Y to take effect when the processing
associated with X is complete. If so, one should find a path of information
propagation leading from X back to Y if one charts all the reactions leading
from X and to Y. Electron microscope movies would make this a lot easier.
The reason to expect such linear sequencing, by the way, is that it would
simplify placeholding -- the program counter (at the level of X and Y) would
be encoded as a structure attached to the sequence at X, and would be allowed
to move to Y upon receipt of a message indicating completion of X. An
alternative is for the name of Y to be encoded somewhere (e.g., in X) and
when X is done send a message to Y to invoke it.
A slightly different analogy is suggested by production systems. Here, a
production corresponds to an ACTG sequence. The production conditions are
represented by a set of activator messages that must be present, say as
structures bound to sites in the sequence. When this occurs, the actions
are executed by, say, transcribing a particular kind of protein. Perhaps
this process consumes the input structures so as to prevent immediate
re-execution; perhaps it is inhibited by some feedback process.
Do we know what controls transcription locally?
I apologize for my ignorance, which I plan to start correcting soon. The
above speculation is certainly unconfused by the facts. I hope wading
through it has not been entirely useless for you. - Jack
-------
Jack is certainly doing an interesting job of using the program/regulation
analogy. It is probably useful to have someone so little constrained by
the facts as part of a team to do hypothesis formation; facts will need
to be brought in at some places to prune and to indicate the difficulties
of doing some of the experiments, but wide-ranging and little constrained
analogy use is a good component to have.
-------
∂25-Apr-81 0900 Darden@SUMEX-AIM discussions with Herb Simon
Date: 24 Apr 1981 0550-PST
From: Darden@SUMEX-AIM
Subject: discussions with Herb Simon
To: Analogy seminar:
cc: Friedland@SUMEX-AIM, Maxam@SUMEX-AIM, Kedes@SUMEX-AIM
I had lunch with Herb Simon yesterday. Curiously, he isn't thinking about
analogy in theory construction at all.
He is a very impressive person; the range of things I heard him talk
about in a three hour period was astounding. He understands better than
anyone I have ever talked to what I am trying to do with the history of
science, namely use it to find the patterns of reasoning used to do
science. He has been reading a lot of nineteenth century chemistry
in connection with the BACON work and really understands the inductive
reasoning pattern of finding regularities in numerical data. (Allan an d
Larry, you may not know that BACON is a program at Carnegie-Mellon that
is rediscovereing empirical laws by using an inductive method of looking
for patterns in data--a very bottom-up approach, "data-driven) But he
has not yet learned that he must look at the incorrect views that were
proposed, as well as the ones that panned out. Our current set of
scientific concepts, laws and theories are the result of severe pruning
in the past. Nor has he realized that a good scientific reasoning
system would be able to generate the concepts and theories or propose
experiments that were possible at a given time but were not done because
no human happened to think of them. (This is an idea John McCarthy and
I have been playing with lately: could an experiment that showed
semiconservative gene replication have been done prior to the
discovery of the Watson-Crick double helix? Could chromosomes in
bacteria or viruses, for instance, have somehow been labelled so that
you could find the daughter cells contained some of the intact
chromsomes from the parent?)
Also, Simon does not know what an explanatory theory is, nor is
he worring sufficiently about how to introduce new theoretical terms,
though he claims that BACON has been able to come up with the concepts
of inertial mass (but it didn't propose impetus, which was the medieval
concept that preceded mass, so of course, I think he somehow put mass
in) and index of refraction. Simon has not yet realized that one must
have another source of ideas than the data alone nor that analogies
(and interfield connections) can be a source of those new ideas.
I think if the BACON type of data-driven, bottom up approach (but
more sophisticated than just looking for numerical relations--Simon
is too much of a mathematician and too tied to physics and chemistry
in his approach to science) were coupled to a top-down, specify the
abstract components of a theory (by using analogies, by using interfield
connections, by using tight constraints coming from knowledge within the
field, etc.) to get what Bruce calls a "half-order" theory, then we
would have a powerful theory construction system. That certainly
turned into a run-on sentence! Basic idea: data-driven component
(constrained somewhat by what we think we might find) plus a top-down
approach built by expectations of what the final theory should look like
or do (i.e. either structurally or functionally specified). Empirical
regularities come up from the bottom; new theoretical ideas come from the
top; when we can connect the two, we know we really have something.
A historical example is that classcial genetics demanded a gene that
could self-replicate (among other things) and various ideas about
replication were proposed, including Pauling's idea of complementary
copying (he was thinking of stereochemical conformation as the mechanism
I think, very much like the old lock and key idea). The data wasn't
available until the structure of DNA began to be elucidated, but
keeping the biological function in mind was a key component in Watson
and Crick's thinking and they immediately recognized the signifance of
compementary base pairing when the chemical and x-ray data came in.
Simon is thinking of applying BACON to classical genetics and has
been reading Mendel. I, as many of you know, have been wanting to
build a theory construction system that would have the reasoning
patterns from classical genetics that I have found (some of us called
it TRANSGEN last fall). I Simon gets BACON to the point of rediscovering
the 3:1 ratios and the 9:3:3:1 ratios, that will be a nice starting
point to add a top-down theory construction system to work with. Genes
were analogized to atoms: discreet entities with some specific functional
properties and interrelations (they cause characters, segregate and
independently assort). Analogies provide vague ideas with which to
begin formulating an explanatory theory. Lately, I have been thinking
about a vague idea as a frame, constructed by analogy with another frame,
with lots of the property slots still blank. Theory construction procedes
by filling in the slots, soemtimes using additional analogies from elsewhere
to fill in the slots. (A potentially useful AI-philosophy of science
interfield connection?)
Curiously, I didn't find anyone at MIT, including Winston, thinking
about applying analogies to theory construction, though he is working in
reasoning by analogy. And then I talk to Simon about scientific reasoning
and he hasn't connected analogical reasoning to what he is doing. Stanford
is clearly the most likely place for building a system for doing
creative theory construction by analogy.
-------
∂25-Apr-81 0859 Darden@SUMEX-AIM Feigenbaum response
Date: 25 Apr 1981 0427-PST
From: Darden@SUMEX-AIM
Subject: Feigenbaum response
To: Analogy seminar:
Date: 25 Apr 1981 0100-PST
From: Feigenbaum
Subject: comments on Darden's message
To: darden, buchanan, friedland, maxam, kedes
Date: 25 Apr 1981 0056-PST
From: Feigenbaum
Subject: copy of note re Lindley's note
To: feigenbaum
In response to your message sent 24 Apr 1981 0913-PST
Just a quick note as an addemdum to Lindley's long memo.
There does exist in AI a "complete" problem solving model (framework, if you
wish) that couples (i.e. totally integrates) bottom - up (data-driven) reasoning
with top-down (theory-driven) reasoning. It is the so-called "blackboard"
model, first developed in connection with the CMU speech understanding research;
later used in a big sonar-understanding system and also the CRYSALIS
program for crystallographic analysis (see the paper "Rule-Based Understanding
of Signals" by Penny Nii and me); and subsequently generalized and made
available in the AGE system. Because of its incremental, opportunistic
way of working either top-down, when that makes headway, or bottom-up, when
that makes headway, I have felt for some time that it is the most powerful
problem-solving framework so far developed for the AI armada.
Lindley is right: the programs that use this framework strive to connect
up inferential structures built down from to the top with structures
built up from the data, a linkup between the two being the essense of
a "plausible hypothesis". This sounds vague in a short note like this, but
is actually quite specific and readily doable using the AGE software package.
It is being used currently, for example, for programs that "understnd the
gist" of a story as the sentences and paragraphs (i.e. the linguistic data)
are read (by Walter Kintsch at the University of Colorado).
Incidentally, Lindley's comments about what Simon "doesn't understand" are
naive. Herb often takes either extreme or highly simplifed views for
effect in clarifying issues. His span of deep understanding is indeed
awesome, second to none, even that awesome-awesome Joshua Lederberg.
Ed Feigenbaum
-------
(please forward this to mailing list "Analogy Seminar")
-----------------------------------------------------------------------
-------
LD: I was, indeed, very impressed with the depth and breadth of
Simon's knowledge, but I really don't think he has yet seen the
importance of analogies in constructing explanatory theories.
-------
∂25-Apr-81 1312 STT definitions and examples for analogy and reformulation
To: "@ANALOG.LST[1,STT]" at SU-AI
Several days ago Tom put forward some definitions for terms that we have
been throwing around in this seminar. I think it will be quite helpful
in discussing analogy and related concepts if we have concrete definitions,
even oversimplified ones. We can at least use them as metaphors.
I mostly agree with Tom's definitions and wish to propose more concrete
versions, especially of the concept of "reformulation"
which I happen to be specially interested in.
Very briefly, one reformulates a description of (or theory about) some
objects as a description of some different objects, with a
relationship between the two sets of objects that makes the descriptions
equivalent. More about this later.
Before I get into a lot of formalistic details (which you might not
want to read) let me explain my basic approach.
Tom said "I think truly interesting analogies are those that combine
reformulation with pattern matching." I would like to generalize this point.
Reformulation can be combined with any of the following...
GENERALIZATION: Alternate formulations of the same concept will suggest
different generalizations. I gave an example of this in my March 27 message,
taken from Feynman's book "The Character of Physical Law".
The example is Kepler's Second Law which
states that a planet sweeps out equal areas in equal times. This
can be generalized to the law of conservation of angular momentum.
In an alternate formulation, Kepler's Second Law says that the planet's
only acceleration is sunwards. By a further reformulation, assuming F = mA,
the force acting upon the planet is directed towards the sun. (Newton
proves the equivalence in Propositions I and II, Section II, Book I of
his "Principia".) The new formulation could be generalized to a claim that
all objects attract each other. I don't know whether either generalization
occurred historically.
SPECIALIZATION: A typical simple way of specializing a concept is to
instantiate one or more of its parameters. Now since a new formulation
uses different parameters, it will suggest different specializations.
For example, suppose books are represented as (Author, Title) pairs.
We might specialize to books by John Steinbeck or books with the title
"Introduction to Molecular Genetics". Alternatively we could represent
books as (Publisher, Year, Subject) triples, and specialize to books
published in 1975 by Simon & Schuster, or books on enzyme kinetics.
This example sounds like database retrieval using alternate views.
ANALOGY: As Tom suggested, "We analogize A to B by finding reformulations
of A and B (call them A' and B') such that the reformulations are
isomorphic or share a common abstraction."
See detailed example in the next message.
REFORMULATION: If A is a reformulation of B, and B of C, then by my
definition A will be a reformulation of C. Combining reformulation with
itself we just get reformulation again.
PROBLEM SOLVING: Alternate formulations of a problem
will suggest different facts or methods to bring to bear in solving it.
As an everyday example, suppose you are trying to move a heavy chest
of drawers. If you continue to think of it as a HEAVY CHEST you are in
for a difficult job.
But if you think of it as a chest OF DRAWERS you will cleverly remove the
drawers and carry them one by one to your destination, then move the empty
framework.
This would be an instance of viewing an object as composite and reducing an
operation on the whole object to operations on its components, a particular
kind of problem reformulation.
The rest of this message gives definitions for generalization, analogy
and the rest in terms of a particular representation that I find
convenient. In these definitions I have factored out
the (allegedly) ubiquitous process of reformulation. The resulting
definitions are pretty simpleminded, and the idea is to enrich them by
combining them with reformulation. (Though the definition I give for
reformulation is pretty simpleminded too...)
I do not have good real-world or scientific examples and my representation
and definitions assume an easily formalizable domain like mathematics.
In the future I hope to generalize some of my reformulation ideas
to less formal domains. I would be
grateful for any suggestions or examples in this regard. Lindley's
historical examples of change of perspective in science are intriguing
(in her April 10 message Analogy seminar.5). Lindley: if you think of
more examples like those please send me a message.
**** REPRESENTATION ****
For defining analogy etc. we need some way to describe systems
of relationships between objects; an analogy will be some kind of partial
match between two systems. I represent these systems as "situations".
A situation is basically a predicate-calculus theory about some objects,
with drastic restrictions upon the form of statements, and some abbreviations.
The exact notation needn't be taken seriously of course.
A situation consists of:
I. A name.
II. A set of objects.
III. A set of statements about the objects. Statements are atomic only,
i.e., a statement is a single relation applied to some of the objects.
Statements are numbered for convenient reference.
IV. A set of dependencies, which I will explain after giving an example.
They are important in reformulation and analogy.
Here is a typical situation in plane geometry.
It describes two circles A and B that are tangent to each other
(forming a figure 8) and it also describes their centers and radii.
CirclesTangentOutside:
Objs A, B, qa, qb, ra, rb, d
Stmnts 1. CircleCR(A qa ra) ;A is a circle with center qa
2. CircleCR(B qb rb) ;and radius ra. B similarly.
3. Tangent(A B)
4. Outside(A B)
5. Distance(qa qb d) ;I.e. distance(qa qb) = d
6. Plus(ra rb d) ;I.e. ra+rb = d
Deps 1,2: 3,4 <=> 5,6
1: A <-> qa,ra
2: B <-> qb,rb
5: qa,qb -> d
6: ra,rb -> d
Please note that the objects here are variables; the situation describes
ANY pair of circles tangent to each other, not a particular pair.
Also, any situation can be viewed as a new relation, here the relation
CirclesTangentOutside(A B qa ra qb rb d) defined by the conjunction of
statements 1 thru 6.
There are two kinds of dependencies shown here. A formal predicate-calculus
semantics can be given but I won't bore you with that. Informally,
Logical dependencies:
The six statements of the situation are not all independent.
Given two circles, saying that they are tangent and outside is equivalent
to saying the distance between their centers is exactly the sum of their
radii. I write this as "1,2: 3,4 <=> 5,6".
We could delete statements 3 and 4 from the situation without changing its
meaning, or alternatively delete 5 and 6, but we may find it useful to keep
them all.
Functional dependencies:
The seven objects in the situation are not independent either.
A circle uniquely determines its center and radius, and vice-versa, thus
"1: A <-> qa,ra" and for the other circle "2: B <-> qb,rb".
The Circle relation imposes these functional dependencies among its parameters.
The Distance and Plus relations would usually be thought of as functions but
I prefer to stick to a uniform relational notation and write the dependencies
separately.
Causal dependencies?
In a richer representation for a "situation" one would want to talk about
causal dependencies within it. I haven't any idea how to represent those.
Logical dependencies are a poor substitute but sufficient for mathematical
domains.
Causal dependencies are presumably of great importance in real-world
analogies, especially in justifying arguments from analogy. Mary Hesse talks
about the issue in her 1966 book "Models and Analogies in Science".
Do any of you have later references on
causal structures in analogies? (Pat Winston's system - others?)
**** DEFINITIONS ****
Here are proposed structural definitions for analogy and other concepts
of interest.
In the definitions P, Q and S are situations as define above.
First, some basic concepts that need to be made clear.
ISOMORPHISM or MATCH:
P is isomorphic to Q if there is a one-to-one match of P's objects to Q's,
under which every statement of P becomes a statement of Q and vice versa.
P and Q are the same except for having different object names.
Any dependency true in P will be true in Q (for the corresponding objects
and statements) and vice-versa, so one result of finding a match is that
you can freely propagate dependencies.
SUBSITUATION or PART:
P is a subsituation or part of Q if P's objects and statements are subsets
of Q's. Any logical or functional dependency of Q is inherited by P
provided P contains all the objects and statements mentioned in the
dependency. (It's an interesting question whether causal dependencies
would be so inherited.)
EQUIVALENCE:
P and Q are equivalent if they have the same objects and the set
of statements in each implies the set of statements in the other.
Because of logical dependencies, a situation may have many equivalent
subsituations.
Like reformulation, equivalence can be factored out of the more
interesting concepts.
PROJECTION:
Projection is central to my definition of reformulation.
Intuitively a projection describes the same situation but ignores some its
objects. Formally,
P is a projection of S if P is a subsituation of S and P is equivalent
to S with existential quantification of the extra objects of S.
That may be incomprehensible so here's an example. Let this be S:
Objs p1 c1 p2 c2
Stmnts 1. ParentOf(p1 c1)
2. ParentOf(p2 c2)
3. Siblings(p1 p2)
We want to know what is the relationship between c1 and c2 when we don't
explicitly mention p1 and p2. The answer is FirstCousins(c1 c2).
Two people are first cousins if and only if there exist two other people,
their parents respectively, who are siblings.
We can't take the projection P = FirstCousins(c1 c2) directly because it
doesn't appear in situation S, but we can add it without losing equivalence
and then project. (Thus projection often combines with equivalence.)
The inverse operation to projection I call extension. P extends to S.
Now for the more interesting concepts. Remember that the equivalence
and reformulation components have been factored out.
GENERALIZATION:
P is a generalization of Q if it has all the same objects but lacks
some of the statements of Q. In other words, P is a subsituation of Q but
only with respect to statements. It's quite simpleminded: you generalize
by deleting statements.
SPECIALIZATION is the inverse of generalization, adding statements.
ABSTRACTION:
Abstraction = Projection + Generalization. One can ignore some of the
objects and/or delete some of the statements.
Actually, this just amounts to the same concept as subsituation, but we can
combine abstraction with equivalence and reformulation, remember.
ANALOGY:
P is analogous to Q if they have isomorphic abstractions.
That is, if there are abstractions P' of P and Q' of Q, such that P' and
Q' are isomorphic. Another way to say it is that parts of P and Q match,
or there is a partial match between P and Q.
This definition for analogy is the same as one of Winston's.
For a closer examination of the structure of an analogy we can use
Mary Hesse's trichotomy of positive, negative and neutral analogy.
See my next message for details and an example.
Tom suggests finding analogies by matching prototypes or exemplars in
addition to matching abstractions. I haven't thought about that but it
sounds like a good idea.
FORMULATION:
A formulation of a situation S is any projection P of S
such that S: x → y where x stands for all P's objects and y for all
other objects in S. Intuitively, P has all the information S has. Given
values of P's objects, all other objects are determined by them.
In relational database terminology, the objects of x are a "key" for S.
REFORMULATION:
P reformulates Q (and vice-versa) if P and Q are alternate formulations of
some wider situation S. Trivially, P reformulates itself or any projection
of itself, but
for interesting reformulations we expect the set of P's objects
and the set of Q's objects to be disjoint or nearly so.
Here's an example of finding a reformulation. Suppose P is Circle(c).
First we think of objects that are related in some way to c, such as
the area of c, a point on c, a line tangent to c, etc.
Those new objects which are functionally determined by c are used to
build up an extension S of P. Note that of the three I mentioned, only
the area is a function of c. After awhile we have something like this S:
Objs c, q, r, a, d, ...
Stmnts 1. Circle(c)
2. CenterOf(c q)
3. RadiusOf(c r)
4. AreaOf(c a)
5. Times(π r r a) ;I threw this in just for fun
6. Disk(d)
7. BoundaryOf(d c)
Deps 1,5: 3 <=> 4 ;More fun
2: c -> q
3: c -> r
4: c -> a
5: r <-> a
7: d <-> c
1,2,3: q,r -> c
1,2,3,5: q,a -> c
etc.
Now if we choose any subset of the new objects that functionally determines
c, and project onto it, we get a reformulation of Circle(c). The most
common reformulation chooses q and r yielding this reformulation Q:
Objs q, r
Stmnts 1. Point(q)
2. Length(r)
Any fact about a circle should be translatable into a corresponding fact
about a point and a length, and vice-versa.
The requirement that the objects of P and of Q determine each other can be
relaxed. Typically at least one of them determines the other. It depends
what you're going to do with the reformulation.
PERSPECTIVE:
Here is an interesting thought. Suppose we go along with Tom's definition
of a perspective as a meta-level unit that describes a coherent group of
slots to be examined in object-level units. (Or in my terminology, a
perspective would describe a coherent group of objects, related by the
situation to some particular object we're concerned about.)
Now if the objects we're supposed to examine are already explicit in the
situation, the perspective is asking us to take a particular projection.
The projection is "coherent" in some way, as opposed to a random choice
of a subset of objects.
If the objects we're supposed to examine are NOT already in the situation,
the perspective seems to be asking us to reformulate. Go find those objects,
then project onto them. This sounds like an idea I have been developing
for "reformulation schemas" which would provide top-down guidance for
finding appropriate reformulations. For example, if the current goal is
to find a curve that is constrained by some other objects, a good
reformulation schema might advise us to re-express the constraints in terms
of points and distances, since curves are commonly defined that way.
If there are meta-level units guiding projection and reformulation there
are presumably meta-level units to guide generalization, specialization,
abstraction and analogy too. Why not! Any ideas on what these might look
like?
∂25-Apr-81 1320 STT detailed example of analogy
To: "@ANALOG.LST[1,STT]" at SU-AI
This message is to show further structure of analogies and give an example
of finding and extending analogies by the use of reformulation.
It uses ideas from my last message but probably is readable independently.
**** MORE ON THE STRUCTURE OF ANALOGY ****
In the last message I defined analogy as isomorphism between abstractions
of P and Q, or equivalently as a partial match between P and Q.
We can use Mary Hesse's idea of positive, negative, and neutral analogy to
fill in more details.
I propose to mark each object, statement and dependency in P as being in
+, - or ? analogy to (some thing in) Q. Likewise each thing in Q, to P.
Matched objects and statements are certainly in positive analogy to their
counterparts in Q. It's not too hard to figure out the negative and neutral
analogies for objects and statements. But dependencies are peculiar and I've
not been able to invent formal criteria for them. Instead I just rate them
as seems intuitively right in each case.
Objects Statements Dependencies
Positive The object The corresponding Sufficient condition:
analogy is matched statement is true Q has the same
+ + + to one of Q. in Q. dependency, using
matching objects and
statements.
Negative (none) The corresponding (unknown)
analogy statement is not
- - - always true in Q.
Especially, if it
is never true in Q.
Neutral The object is Not all objects in (unknown)
analogy not matched the statement are
? ? ? to one of Q. matched.
When I say "the corresponding statement" I mean the result of substituting
the matching object for each parameter of the statement. If the parameters
aren't all matched, there's no corresponding statement (and we have a neutral
analogy.)
**** EXAMPLE OF DEVELOPMENT OF AN ANALOGY ****
Here is the example I want to work through:
How is a parabola analogous to a straight line?
(Think about it. Sorry to use mathematical examples all the time, but they're
a lot easier to formalize.)
We'll start with situations Parab1 and Line1, with initially no analogy
between them. Everything on each side is in neutral analogy to the other
side. Not that there's much on either side, as yet.
Parab1: Line1:
Objs b ?
? l
Stmnts 1. Parabola(b) ?
2. ? Line(l)
Deps
As per the discussion in the last message, we can replace either side
(situation) of the analogy by an equivalent or reformulated situation.
(I will rename the situation only when reformulation is used.)
Our first move is to notice that parabolas and straight lines are both
curves. Since Parabola(b) => Curve(b) we can add the statement Curve(b)
to Parab1 without losing equivalence, and similarly for Line1.
Curve(b) is isomorphic to Curve(l) and we get some positive analogies.
Parab1: Line1:
Objs b + l
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
Deps : 1 => 2 + : 1 => 2
The analogy so far says, b and l both may be abstractly described as curves.
If you think about it, that's not a very impressive analogy.
There are deeper analogies to be found, if we bring to bear some domain
knowledge about parabolas and lines.
One definition of a parabola is the intersection of a plane and a cone, with
the plane parallel to the edge of the cone. So we can extend Parab1 with two
more objects, a plane p and a cone c, with the bridging statement that b is
the intersection of p and c. There is a reformulation here: the cone and
plane determine a unique parabola (not vice-versa, but that's OK.)
<<Hmm - is that true? /\ )
At the moment, we are keeping both
formulations glommed together as a single situation.
(By the way, to make things work out nicely I'm assuming a double-ended cone,
two ordinary cones stuck together at their apex.
I think this is the usual setup in the theory of conic sections.)
Parab2: Line1:
Objs b + l
p c e ?
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. Intersection(p c b) ?
4. Plane(p) ?
5. Cone(c) ?
6. Edge(e c) ?
7. Line(e) ?
8. Parallel(p e) ?
Deps : 1 => 2 + : 1 => 2
: 1 <=> 3,4,5,6,8 ?
: 6 => 7 ?
For simplicity I am leaving out the functional dependencies.
At this point we notice that Line(e) on the left could match to Line(l).
It's a poor analogy, and I can think of two objections to it:
(1) Object l is already matched to b, we can't match it to e too.
There is a way to get around this, we could copy l as l', match l' to e,
and declare Equal(l l'). But it's a hack.
(2) The objects e and l have quite different roles in their respective
situations. Object e is rather remotely related to the main object b, as
a minor aspect of an alternate formulation of it. Whereas object l is the
main (and only) object in its situation. "Roles" is just a vague metaphor
here.
We wonder now if we can extend Line1 analogously to how we extended Parab1.
Let's see, which neutral analogies might be made positive by extending Line1?
Could we get an isomorph to Intersection(p c b), i.e., could the line l
be an intersection of two new objects? Rooting about in our domain
knowledge, we quickly retrieve that two planes intersect to form a line.
So situation Line1 is extended with two new objects (the planes).
Matching b to l, p to p1, and c to p2 we get more positive analogies.
The whole analogy now says b and l are both curves, formed by the
intersection of two things one of which is a plane.
Parab2: Line2:
Objs b p c + l p1 p2
e ?
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. Intersection(p c b) + Intersection(p1 p2 l)
4. Plane(p) + Plane(p1)
5. Cone(c) - Plane(p2)
6. Edge(e c) ?
7. Line(e) ?
8. Parallel(p e) ?
Deps : 1 => 2 + : 1 => 2
: 1 <=> 3,4,5,6,8 + : 1 <=> 3,4,5
: 6 => 7 ?
Getting ambitious, we wish that c were a plane or p2 were a cone, to eliminate
a negative analogy. Well, two planes intersecting always form a line
so we're not going to get a parabola that way.
However... a plane and a cone DO intersect in a line, when the plane happens to
be tangent to the surface of the cone! What luck!
We have managed to reformulate a line as a conic section of sorts.
Note that this rather bizarre reformulation probably would not be in our domain
knowledge. We have to invent it, guided by the developing analogy.
Thus analogy can suggest a new reformulation, as well as vice-versa.
The analogy continues.
We observe (deduce) that the intersection line l lies in the plane p1,
therefore is parallel to p1, analogous to line e and plane p on the
other side.
There's one little hitch. We want to match l with e, but we already matched l
with b. I guess we use the hack I mentioned before, introducing a new object
l' and declaring Equal(l l'). We now have
Parab2: Line3:
Objs b p c e + l p1 c2 l'
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. Intersection(p c b) + Intersection(p1 c2 l)
4. Plane(p) + Plane(p1)
5. Cone(c) + Cone(c2)
6. Edge(e c) + Edge(l' c2)
7. Line(e) + Line(l')
8. Parallel(p e) + Parallel(p2 l')
9. - Equal(l l')
10. - Inside(l' p2)
Deps : 1 => 2 + : 1 => 2
: 1 <=> 3,4,5,6,8 + : 1 <=> 3,4,5,6,10
: 6 => 7 + : 6 => 7
? 4: 10 => 8
All statements match those for the parabola, except Line(l), Equal(l' l), and
Inside(l' p1).
What can we do with this analogy?
We can drop the original formulations Parabola(b) and Line(l), eliminating
one negative analogy. We must still remember them in some sense or we
would forget the point of the whole thing.
With the Parabola(b) - Line(l) mismatch gone, notice that all statements
of Parab2 occur in Line3. Recall the definition of
generalization/specialization. Line3 is a specialization of Parab2!
(Up to object names.) What does this mean? It means that lines are in
fact degenerate parabolas.
At least, according to our intersection-of-plane-and-cone formulation of
parabolas, they are. We might think it pathological to consider lines as
parabolas, and revise our domain knowledge to say that the plane must not
be merely tangent to the cone. Then we would have to check our other
definitions and reformulations of the concept "parabola", to make sure
they don't admit the pathological case.
This amounts to changing our concept of "parabola" slightly.
**** ALTERNATIVE ANALOGIES ****
Using a different reformulation of a parabola, we can develop a different
analogy between parabolas and lines.
Let's go back to our first, weak analogy between a parabola and a line.
We had found that both are curves.
Parab1: Line1:
Objs b + l
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
Deps : 1 => 2 + : 1 => 2
In seeking to deepen the analogy we introduced an alternate formulation of a
parabola, as the intersection of a plane and a cone.
Suppose we try a different formulation instead.
A parabola is commonly defined as the set of points equidistant from a fixed
point and a fixed line, called the focus and directrix of the parabola
respectively. The relation ParabolaFD(b f d), which we presume has been
appropriately defined
elsewhere, relates a parabola b to its focus f and directrix d.
We extend Parab1 with ParabolaFD(b f d) and its implicants, and obtain
Parab5: Line1:
Objs b + l
f d p ?
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. ParabolaFD(b f d) ?
4. Point(f) ?
5. Line(d) ?
6. On(p b) ?
7. Distance(p f r) ?
8. Distance(p d r) ?
Deps : 1 => 2 + : 1 => 2
: 3 <=> 1 ?
: 3 <=> 4 ?
: 3 <=> 5 ?
3: 6 <=> 7,8 ?
(By the way, we get lines as degenerate parabolas again, when the focus
point happens to lie on the directrix line. Well, I'll ignore it.)
As before, we get a poor analogy by matching Line(d) with Line(l).
As before, we look in our domain knowledge about lines for material with which
we can extend the Line1 situation analogously to the Parab5 situation.
That is, facts about and/or alternate formulations of a line, which involve
any of the relations Parabola, ParabolaFD, Point, Line, On, or Distance.
There's quite a bit relating points, lines and distances. In particular there
are two ways to define a line in terms of points and distances between points:
A. Given any two points q1 and q2, we can draw a unique line through them.
A point is on the line if and only if it is collinear with
q1 and q2. Collinearity can be defined purely in terms of distances so
this is not circular.
Call this relation LineThrough(l q1 q2).
B. Given any two points q1 and q2, we also can draw a unique line passing
midway between them. A point is on this line if and only if it is
equidistant from q1 and q2.
Call this relation LineBetween(l q1 q2).
One of these extensions to Line(l) is going to give a better analogy than the
other. Trying (A) first, we get
Parab5 Line5
Objs b f d p rf rd + l q1 q2 p' r1 r2
? r3
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. ParabolaFD(b f d) - LineThrough(l q1 q2)
4. Point(f) + Point(q1)
5. Line(d) - Point(q2)
6. On(p b) + On(p' l)
7. Distance(p f rf) + Distance(p' q1 r1)
8. Distance(p d rd) + Distance(p' q2 r2)
? Distance(q1 q2 r3)
? PerfectSum(r1 r2 r3)
9. Equal(rf rd) -
Deps : 1 => 2 + : 1 => 2
: 3 <=> 1 + : 3 <=> 1
: 3 <=> 4 + : 3 <=> 4
: 3 <=> 5 + : 3 <=> 5
3: 6 <=> 7,8,9 + 3: 6 <=> 7,8,9,10
This analogy says, both a parabola and a line are curves
determined by two objects, one of which is a point.
In both cases, a point is on the curve if and only if a certain
distance relationship holds.
Unfortunately the distance relationships are only about half-matched.
Trying (B), we get
Parab5 Line6
Objs b f d p r + l q1 q2 p' r'
Stmnts 1. Parabola(b) - Line(l)
2. Curve(b) + Curve(l)
3. ParabolaFD(b f d) - LineThrough(l q1 q2)
4. Point(f) + Point(q1)
5. Line(d) - Point(q2)
6. On(p b) + On(p' l)
7. Distance(p f r) + Distance(p' q1 r')
8. Distance(p d r) + Distance(p' q2 r')
Deps : 1 => 2 + : 1 => 2
: 3 <=> 1 + : 3 <=> 1
: 3 <=> 4 + : 3 <=> 4
: 3 <=> 5 + : 3 <=> 5
3: 6 <=> 7,8 + 3: 6 <=> 7,8
In this analogy the distance relationships for parabola and line are isomorphic!
Much better. A point is on the parabola or line whenever it is equidistant from
the two determining objects.
The only difference is that for a parabola these objects are a point and a line,
while for a line they are two points.
What can we do with this analogy?
This analogy might suggest the generalization of taking ANY two geometric
objects - points, lines, circles, parabolas, etc. - and seeing what curve is
traced by a point constrained to be equidistant from the two objects.
The result is:
Determining objects Resulting curve
point, point line
point, line parabola
line, line line
point, circle ellipse if the point is inside the circle,
hyperbola if it's outside,
line segment if it's exactly on the circle.
line, circle parabola
circle, circle ellipse or hyperbola
point, parabola beats me
line, parabola ...
...
The generalization is fruitful for a while, then starts producing garbage.
On that note I will end.
∂01-May-81 0728 Darden@SUMEX-AIM plans on gene regulation
Date: 1 May 1981 0556-PDT
From: Darden@SUMEX-AIM
Subject: plans on gene regulation
To: Friedland@SUMEX-AIM
cc: Analogy seminar:, csd.mostow@SCORE, Maxam@SUMEX-AIM,
cc: Kedes@SUMEX-AIM
Hi, Peter. Allan and I had a long phone conversation yesterday. We
are both trying to learn enough about each other's interests to form
some idea of what a joint project would be like. Allan, as we know,
wants to understand gene regulation and he is interested in the
reasoning that goes into hypothesis formation and model building.
I, as you know, have some ideas about how to do hypothesis formation
and would like to systematically apply them in a domain. Thus,
Allan and I are coming to realize that he and I may be able to try
doing some systematic hypothesis construction about gene regulation.
But I don't have a very clear picture of what you want to do. What
AI component do you see as your goal? As I mentioned in an earlier
msg, a more sophisticated pattern matcher than the one for SEQ might
be one component. I see that Jack is talking about that at a recent
MOLGEN meeting. Have you two been discussing it? Do you have
specific ideas about gene regulation, either from work with the
sequences or by analogy or???? Another possibility is to pursue
the analogy between control structures in AI systems (or computer
programs more generally) and control of genes. Have you thought
about Jack's msg on this or other possible analogies? Do you think
it is a possibly fruitful analogy? Have you had other ideas about
how to make models of gene regulation or how to use the sequences
or how to use other material in UE?
Let me tell you a bit more about Allan's and my ideas. Allan
said that a small control piece of DNA has recently been found
in SV40; it is looking like a fairly important discovery. The
sequence of SV40 has been known now for 3 years. Question: could
we have used the sequence information to give us clues that that
particular piece of the DNA was an important one? In other words,
we would take a very recent piece of reasoning (rather than my
more distant historical case examples), analyze the pattern of
reasoning there, and ask if we can generalize the pattern and
use it elsewhere to find important locations in the sequences.
Allan is using very close (closer than interfield connections,
I will have to find a new term, he is trying to find a pattern
of reasoning for the field, since it doesn't yet have one)...
let me start this sentence over, I am thinking in the middle and
messing up the grammar. Allan is using very closely related
examples to try to devise a reasoning pattern. That is a very
constrained was of doing it and may prove quite fruitful, if
we have any good examples yet to work from. There is always
the danger that one's model organism is the quirk and the results
may not be generalizable.
My idea would be to do several kinds of things in order to do
hypothsis formation. Allan's very constrained way of looking
at quite closely related examples would be one component. But
was should also do some more wide-ranging things, namely looking
for more far-flung interfield connections and analogies that wuld
allow us to build models, preferably several differnt ones. I order
to do this model building we need to set up what kinds of things
the model has to account for, both at a very general abstract level
(what, eventually, will a good model of gene regulation have to
explain?) and then much more tightly, what data do we have right now
to be explained by a more local model? Then, we have to specify in
the abstract what components the finished model must have (is this
like the "half-order theory"). I am here thinking of something like
Jacob's idea that if one had coordinate control of the operon, then
there must be a signal with a transmitter and a receiver. This abstract
specification of the model led Jacob and Monod to predict the existence
of the operator and to look for mutants of it, which they found. Obviously
analogies can be useful in this stage of model building, and the wider
one's range of past experiences (or those of a team), the wider the
range of analogies we can consider. (This is the real stumbling
block to building an AI system to reason by analogy; one needs a stock
of possible analogies to draw from and AI systems don't have them and
can't yet use other systems as sources either.) Peter, do you have
ideas about model building in general or specific models in particular
in mind? Did your work in devising skeletal plans for experiment
planning give you any insight into how to come up with general
models?
In addition to doing constrained and far-flung model building, we
would also have the pattern analysis of the sequences as another end
from which to approach the problem (the data-driven rather than model
driven component). Also, the model building would aim at providing
predictions testable with the sequences.
This is all beginning to sound similar to things I have said in
earlier msgs, so it is probably time to stop and get some feedback.
Interfield collaboration is often quite difficult. If we actually
manage to do something that is important for molecular biology,
AI and philosophy of science simultaneously, it will be really
something. It sounds a bit wild and I think that Allan is quite right
that we should actually DO at least a small part of a project to
demonstrate feasibility of the combination of these approaches before
we can hope to convince a funding agency to support it.
It would be good if we could all get together somewhere soon. Let's
keep talking about it.
Bye, Lindley
P.S. Excuse the typos; I hope it was readable anyway. Since I ended
up saying so much about analogy here, I am going to circulate this
msg more widely than just to the people who actually want to work
on gene regulation.
-------
∂02-May-81 0652 Darden@SUMEX-AIM formation of a new concept
Date: 2 May 1981 0651-PDT
From: Darden@SUMEX-AIM
Subject: formation of a new concept
To: Analogy seminar:
I have discovered an excellent example of the development of a new
concept: the development of the concept of the virus. The structure of the
reasoning that was involved in arriving at this new concept is similar to
reasoning by analogy and to reasoning using interfield connections. But
it is more complicated. In the reasoning by analogy that we have been
disgramming (e.g. a recent msg from Steve in which he had two columes
with positive and negative analogous relations between a line and a
parallelogram) we have had one thing and an analogue with property lists.
The task is to match or not match properties and then to try to construct
properties for one based on properties of the other, but modified somehow.
Similarily in the interfield connection between genes and chromosomes that
I have discussed extensively, we can map similar properties known
independently (e.g. genes occur in pairs and chromosomes occur in pairs) and
then map from known ones on one side to blanks on the other.
genes chromosomes
occur in pairs <-------------> occur in pairs
predict:linkage <-------------- fewer chromosomes than genes
indpendent asst. -------------> pred:random assortment of homologous
chromosomes in meiosis
The construction of the new concept of a virus extends this
framework to have three property lists rather than two. It is a bit
like using two different analogies in order to construct something in the
middle. I have been wanting a good example of a problem that required two
different analogies to get two different parts of the solution, but I haven't
found a good one. The construction of the virus concept occurs by
constructing a new property list in the middle between the property
lists for microorganism and chemical substance. Eventually one gets
a whole new field bridging biology and chemistry, namely virology.
At first one has "paradoxical" data, i.e. that can't be fitted into the
microbiology framework or the chemical framework. Resolving the paradox
results in the new concept (goodness!it sounds a bit Hegelian)
Here are the lists:
microorganisms viruses chemical substances
(cellular, organized) (?) (fluid, unorganized)
1.microscopic (light) submicroscopic submicroscopic
2.not filterable filterable filterable
3.reproduce reproduce don't reproduce
4.grow in culture don't grow in cul. don't grow
5some infectious some infectious not inf.;some toxic
About 1900 this list of properties attributed to "filterable
infectious agents"(viruses) was viewed as paradoxical: were they living
organisms having an organized cellular structure or chemical substances?
The conservative stance was to say they were one or the other and make
slight modifications in the original concepts. The typical response for
those with a bacteriology background was to say that viruses were organisms
that were just smaller than previously known ones and therefore sub-
microscopic and filterable; the right culture conditions just hadn't been
found yet. Thus the conservative response was to retain the microorganism
concept and slightly modify properties 1 and 2 and blame current limitations
of techniques for the failure of 4 to apply. Since reproduction had been
seen as an essence of life since Aristotle's time, one could argue this
modification had tradition in its favor. The second conservative response
from the chemical side was to say that the evidence for reproduction
namely, the ability to continue to be infectious even after dilution,was
weak; instead the virus is a toxin that could be effective in very small
doses. The radical response was to say one had a new things that wasn't
a microorganism capable of independent reproduction but wasn't just a
chemical substance either. All three types of positions were maintained
historically, with the largest number of responses on the conservative
modification of a microorganism side (maybe because that was the most
reasonable or maybe for the sociological reason that more people working
on viruses came from bacteriology than from biochemistry).
The people who advocated the radical position of creating a new
kind of concept had trouble doing so. Beijerinck, in 1899, after studying
the properties of tobacco mosaic disease, proposed it was casued by a
"contagious living fluid." But he said that the idea of self-supporting
molecules was hard to conceive, if not "contrary to nature." The idea of
a self-reproducing molecule was almost unthinkable in 1900! Beijerinck
proposed something a little less radical by comparing viruses to
"chromoplasts" (I guess he means chloroplasts) which "grow only within
cellular protoplasm, even though they have an independent existence and
function separately." Thus, by analogy, he suggested that viruses could
passively incorporate themselves into the reproduction of a cell rather
than being totally independently self-reproducing. It is fascinating to
read his work and see him groping toward a new idea and finding it hard to
even think it, especially since the idea of DNA replication is so much
a part of the way we think now.
Stanley's crystallization of the tmv virus in the 30s added another
property from the chemical side and Stanley discussed viruses as
"autocatalytic proteins." The new concept was talking hold: a chemical that
could cause production of more of itself was what Beijerinck had trouble
conceiving.
The defining properties of viruses changed with empirical work.
"Submicroscopic" and "filterable" were seen to be very technique limited,
not fundamental natural properties. Interestingly, what at first was seen
as possibly just a technical limitation, namely the inability to find the
right culture medium for growing viruses, came to be seen as a
fundamental property, namely viruses are not capable of independent
reproduction outside other cells. Finally, the discovery that viruses
are made of nucleic acid (either DNA or RNA) as well as protein, and the
development of the electron microscope that allowed one to see virus
morphology provided the properties by which viruses are now classified.
Once one had a firmly established new concept, then its property list
could be modified with new work. The original establishment of the new
concept was the hard part and it occurred by pulling properties from
two older lists that were thought to belong to incompatible classes.
The vaguely specified concept of a "filterable infectious agent" changed
the essentials of its property list almost completely. In AI terms,
the abstraction would have changed. Also note that the concept of virus
required a new branch to have to be added in the isa hierarchy.
I have been puzzling over what kinds of units I set up
when I gave the list of typical properties for microorganisms and
chemical substances. I suppose they are abstractions, in the sense that
Tom Dietterich specified in an earlier msg on definition of terms.
They are at some high level in the isa hierarchies that would have lots
of instances; these particular properties were the perspective selected
because they were the paradoxically grouped ones turning up in the data
about viruses. Some would probably be in any "fundamental" abstraction,
e.g. the ability of miscroorganisms to reproduce; but others are very
local to the present problem, e.g. not filterable. I think the question
of perspective, i.e. what goes into the property lists that get matched
or not matched, is a key problem in understanding how to construct
good analogies. This focus on perspective is something Russ focused on
a while back and Tom suggested that we might be able to set up slots
to specify different perspectives. We ought to think about this some more.
The virus concept was for early twentieth century biologists
what the wavicle was for physicists. But somehow I find it much easier to
live with self-reproducing molecules than wavicles, probably because the
double helix is so beautifully simply conceptualizable and wavicles aren't.
There are a couple of other scientific examples that put parts
of two previusly different frameworks together to get something new.
Darwin's use of both the analogy to artificial selection and to Malthus's
idea of population outstripping food supply is a case I want to work out
sometime. Also, Francis Everitt told me that Maxwell used analogies
both to heat and to water in the development of electromagnetic theory,
resulting in somewhat paradoxical properties, but I don't know the details
there.
HYPOTHESIS FOR THE WEEK:
Creativity is putting old things together in new ways.
Bye, Lindley
-------
∂04-May-81 2218 Clancey at SUMEX-AIM The Titular Bishop of Titiopolis
Date: 4 May 1981 2212-PDT
From: Clancey at SUMEX-AIM
Subject: The Titular Bishop of Titiopolis
To: Analogy seminar:
We've discussed the importance of analogies for theory formation, but we
haven't discussed how a scientific paradigm serves as a perspective for
reformulating old analogies (now seen to be impoverished).
Gould's column in Natural History this month provides a good example.
In the 17th century, people observed "odd things in rocks" like things that
resembled sharks' teeth, clams, alphabet letters, and "paintings" of
recognizable scenes like Christ on the cross. They reasoned that "Nature is
wonderful," that "God creates with striking similarity in different realms,
in order to display the order of his thoughts and the glorious harmony of
his world."
So something in a rock that looks like a shark's tooth was formed with the
rock, a miraculous occurrence no different from the coincidence that God made
a world with 7 planets and 7 notes in a musical scale. So there is
similarity to be found in the world, and this is part of the scheme of
creation.
Our Titualar Bishop, Steno, made his contribution to geology in the following
way. He decided that what was problematic about finding sharks' teeth and
crystals in rocks, and finding strata in basins (an important connection),
is that they are cases of "solids enclosed within a solid body." How did
they get there? Steno reasoned that "a general theory of the origin of
solids within solids could provide a guide for understanding the earth's
history." (Gould does not say why Steno was motivated to have such an
understanding.)
Steno made two great taxonomic insights: 1) solids within solids constitute
a fundamental class of objects, and 2) these solids can be sorted according
to the different causes that fashioned them. Steno "was an adherent of
the new mechanical philosophy that insisted on physical causes for
phenomena and viewed internal similarity as a sure sign of common
manufacture." Thus, Steno reformulated this category of phenomena,
specializing it according to cause, a broad kind of analysis that he
brought over from another field.
Steno used two principles for his new taxonomy. The principle of molding
was that "we can tell which solid hardened first by noting the impress of
one object on the other." (Thus, the shark's tooth was formed before the
rock, calcite intrusion after the rock.) The principle of similarity is
that a product which resembles something we know how is made must be
similar in its manner and place of production. (Thus, sedimentary rocks
are so identified because they resemble strata of sediment laid down by
rivers.) From these two principles, come a remarkable set of conclusions
about "how seas and land have changed places, how mountains have emerged
from the waters," etc.
To summarize, Steno's genuis was to ask how a clam in a rock, a letter in
a rock, and a crucifixion in a rock were different. He took an original
analogy and reabstracted it as "cases of a solid within a solid" (instead of
the original term "tongue stones," thus getting away from the fixation on
shark's teeth themselves, and including all of the phenomena that needed to
be explained). He then applied the perspective of physical causation to
specialize the category. So he was able to recognize fossils for what
they were.
I am struck by the analogy between how the mechanical perspective influenced
Steno, and how the information processing perspective is influencing my own
work. Rather than simply saying that human expertise consists of certain
kinds of structures and processes for reasoning, cognitive scientists are
asking "Why those structures?" "Why those processes?" We want to form
an explanatory theory at the "hardware" level--spreading hierarchical
activiation of associations, hierarchical short term memory, goal stack,
inherited process abort conditions--these are fragments of the theory being
constructed that will explain why people adopt certain strategies for
searching memory and solving problems, and why they fail in certain ways.
I find that I am learning how to do this work by forming analogies between
my problem and the kind of analysis undertaken for other problems (thus work
in subtraction affects work in medical diagnosis).
Lindley, why have you not discussed very much the importance of intrafield
analogies which cause questions to be asked in the first place? Is it
because the paradigms are so broad and relatively fixed, that they shed
little light on advances within a paradigm, which are more influenced by
interfield analogy? That is, are you more concerned with solutions to
problems as opposed to what makes something problematical? Or is question-
asking the easy part?
Bill
-------
∂05-May-81 0608 Darden@SUMEX-AIM response to Bill Clancey
Date: 5 May 1981 0604-PDT
From: Darden@SUMEX-AIM
Subject: response to Bill Clancey
To: Analogy seminar:
cc: Friedland@SUMEX-AIM, csd.mostow@SCORE, Maxam@SUMEX-AIM
Hi, Bill. This will be a short msg to respond to a few specific
questions in your very interesting analogy discussion and then I will
make a longer, edited msg on Steno and the problem of fossils which
is a terrific case for lots of things.
I had a little trouble understanding your use of the word analogy
until I translated "introfield analogies which cause questions to
be asked in the first place" into similarities that serve to constitute
(perhaps temporarily) an inductive class. I don't yet have a clear notion
of the difference between analogy and similarity. Sometimes I think we
are dealing with a continuum, analogies have fewer common properties than
things which are similar. But at other times I want something more
"fundamental." Similarities would pick out things that should belong
together in some kind of "natural" classification (an elusive concept
in taxonomy for centuries) and analogies would not be "fundamental."
But I can never make enough sense of the quoted words to formulate
this latter view clearly. Maybe Gentner's idea of restricting analogies
to relations (causal? structural?) between things and not having
similar properties of the things count might help. In my paper on
"Theory construction in Genetics" I am trying to distinguish analogies
from interfield connections that postulate some kind of "physical
relation"(i.e. a real connection in the world between things that
can be tested scientifically) but I'm not sure how well I succeed there.
There has to be some distinction between the things that we think are
similar and require a scientific explanation to account for the similarity
(whether interfield or intrafield) and a "mere" analogy. This problem
becomes particularly pressing when one sees the radical regroupings
that have occurred in the history of science among what things were
taken to be similar and requiring a single theory to explain them.
The fossils case is terrific for seeing this problem as I will disucss
in a later msg.
I don't like Kuhn's term paradigm for dozens of reasons but I do think
the idea that what we see as similar is influenced by broad conceptual frameworks is a correct idea. I don't hve any general analysis yet of how
those frameworks are formed or how they change, but I consider those
very important problems in understanding the reasoning in scientific
change.
I would indeed like to know why scientists come to view particular
things as problematic at certain times, but I don't yet know how to
give general answers to that question. I have lots of particular answers
coming from particular cases, but no inductive similarities yet.
The reason I have been concentrating on analogy and interfield connections
is because that seems like a promising answer to one of my many questions
about scientific reasoning, namely where do new ideas come from in theory
construction. I simply don't believe I have enough evidence from the
history of science to make very broad sweeping claims, a la Kuhn, about
all of the components of reasoning (or lack thereof) in scientific
change. I anyone has ideas about why scientists come to regroup things
and demand a new theory I would find that very interesting.
Bill, I tried to follow what connections you are making. One area
is "the Information processing perspective." Is the other cognitive
psychology? What is the statement of the interfield connection--
maybe, all thinking is computing. (comparable to genes are in or
on chromosomes) Pylsyshyn (in the Ortony book) said :"the notion of
computation stands in the same relation to cognition as geometry does
to mechanics: It is not a metaphor but part of a literal description of
cognitive activity." Does this make sense to anybody?
What are "inherited process abort conditions"?
I will stop this msg now and go on to talk about the fossils case.
Bye, Lindley.
-------
∂05-May-81 1925 Darden@SUMEX-AIM fossils and categories
To: Analogy seminar:
The interpretation of what we now call fossils is one of the
most interesting classificatory problems in the history of science.
There is a terrific book on the subject that I highly recommend
called THE MEANING OF FOSSILS by Martin Rudwick (who, coincidently
recently resigned his position at the Free University of Amsterdam in
protest against political interference of Marxist students in what
is taught in the classroom; I am currently working on creating a
position for him here at Maryland).
Steno is one among many of the very interesting characters in the
fossils story. The field of paleontology emerged with difficulty out
of a number of different traditions for interpreting "fossils," which
literally meant "things dug up." Not only were objects classified in
very different ways than we do today, their interpretations were based on
radically different world-views. It took some time before our way of
viewing fossils emerged; even the problem of determining which things were
the remains of previoulsy living things was a problem that took a while
to emerge.
There were three different kinds of problems associated
with fossils: form, matter and position. The Aristotelian world view
that analyzed any individual thing as composed of form and matter
allowed one to ask: how did the form of shell get into a rock? Although
Aristotle himself thought forms never existed apart from the matter they
informed, some of his followers proposed that the forms of shells could
get into rocks to make them look like shells. In other words, the
explanation for the curious positions of shells on mountain tops was
that somehow the form got there and influenced the shape of the rock matter.
The shell-shaped rocks were not viewed as having previously been shells.
The NeoPlatonists, influenced by magical traditions, thought
that the microscosm of earth mirrored the macroscosm of the universe.
Celestial influeces affected the earth, making star-shaped stones and
other curious things, and one needed to understand these influences
in order to control these forces for the benefit (or evil in black
magic) of humans. The Christian notion that fossils were wonderous
creations came later and Noah's flood gave one possible explanation for
positions.
Gesner's ON FOSSIL OBJECTS of 1565 is an early attempt at
providing a classification that includes fossils.
The basic classificatory principle was to group objects dug up according
to their resemblances to objects in other realms of nature. His
categories included (1) resemblance to geometrical figures (a Platonic
influence according to Rudwick), (2) those resembling heavenly bodies
(some look star-like) and (3) those related to terrestrial objects
(heaven and earth were radically different in the Greek world view)
including (a) those resembling works of man and (b) those
resembling various kinds of known plants and animals. Particularly
problematic were things like belemnites (shells,shaped like a bullet, of
an extinct squid-like creature) that resembled no known living thing.
Thus, placing things in the latter category depended on allowing the
possibility of extinction, as well as the state of biological knowledge
of the time.
Steno's "Prodromus to a Dissertation Concerning a Solid
Naturally Contained in a Solid," is a book that cuts across numerous
of our contemporary scientific fields. Since Bill asked about the origin
of Steno's problems, I will quote him at length from the introduction:
"The first question was, whether the Glossopetrae Melitenses [tongue-
stones of Malta] were once the teeth of sharks [which they resembled in
form ]; this, it was at once apparent, is identical with the general
question whether bodies which are similar to marine bodies, and which are
found far from the sea were once produced in the sea [a question about
whether an inductive class exists and what its causes might be]. But
since there are found also on land other bodies resembling those which
grow in fresh waters, in the air, and in other fluids [crystals--the
similarities between living things and crystals has long been noted--
their reproduction is so striking], if we grant to the earth the power
of producing these bodies, we cannot deny to it the possibility of
bringing forth the rest. It was necessary, therefore, to extend the
investigation to all those bodies which we elsewhere see growing in
a fluid. But many other bodies also, are found among the rocks, possessed
of a certain form; and if one should say that they were produced by the
force of the place, one must confess that all the rest were produced
by the same force [some kind of strong unity of science thesis?].
And so I saw the matter finally brought to the point that any given
solid naturally contained within a solid must be examined in order
to ascertain whether it was produced in the same place in which it
is found; that is, the character not only of the place where it is
found, but also of the place where it was produced, must be
investigated. But no one, in truth, will easily determine the place
of production who does not know the manner of production, and all
discussion concerning the manner of production is idle unless we gain
some certain knowledge concerning the nature of matter. From this it is
clear how many questions must be solved in order that a single
question may be set at rest."
Goodness! How research programs can get out of hand!
The fossils story goes on but this msg has enough (maybe too
much) historical content already. I refer interested readers to Rudwick's
book.
The struggles to know what things are "fundamentally" similar
and are produced by similar causes have been long and hard in the history
of science. I haven't yet seen generalizable patterns of reasoning as
to how irrelevant, spurious resemblances are to be distinguished from
fundmental, law-like ones except by trial and error: one forms categories,
on some basis or other, and tries to fit things into them. If the things
don't fit well, then the categories have to be revised. The virus case
was a good example of category revision. I don't know all the details of
the revision of categories for fossils, but it was hard to come to the
idea that some species might be extinct, an idea that was a prerequisite
for our modern notion of fossils. Lamarck proposed that species could
evolve into other species in order to avoid having to postulate extinction.
Hypothesis for the week: a basic intellectual activity is
looking for similarities, finding differences that don't fit the
pattern, and revising the pattern. (I'm not sure exactly how reasoning
by analogy fits into that.) New ideas result either from finding a new
pattern of similarities or from resolving an anomaly that doesn't fit an
old pattern.
Bye, Lindley
-------
∂06-May-81 1114 Clancey at SUMEX-AIM Steno clarified
To: Analogy seminar:
Lindley,
My msg about Steno was to help me understand the different parts
analogies play in theory formation. I think I was hypothesizing three
purposes of analogy: observation, methodology (questions to ask), and
interfield connections (theory formation).
Your message made clear that the category of "odd things in rocks"
is based on similarities that are superficial, lacking the process or
structural connections that appear in an analogy. So in common sense terms,
we might say that the "clam in the rock" is analogous to "Christ painted on
a rock." But in this discussion
we are being more precise by saying those observations "constitute an
inductive class based on (surface) similarity." I will have to think more
about this, but I think there is a basis for this distinction.
The second part of my msg was about intrafield METHODOLOGICAL
analogies. These are the analogies which "cause questions to be asked."
I pointed out that Steno was proceeding according to the method of
sorting a category on the basis of physical cause (I still don't know
where he got this idea; haven't read your fossil msg yet). Similarly,
I find that in cognitive science people are studying the problems and
methodologies of other researchers, and attempting to apply those
methodologies to their own work. This is how work in reading, subtraction,
medical diagnosis, and the like influence are influencing one another.
(And I don't just mean something as simple as using EMYCIN in different
domains. This is a matter of understanding what kinds of questions are
being raised and what constitutes an explanatory theory.) My point was
that analogy is playing a big part in helping me learn how to do science.
I think there are two basic things that I am trying to learn: 1) how to
describe a program on a theoretical level (what are useful descriptive
terms for characterizing the kinds of data structures and processes in
a program), and 2) thinking of the program as a computational model of
human reasoning, what should be problematical to me (what questions should
I be asking myself about human memory and information processing that
would place my model on a deeper, more primitive foundation)?
In short, as a scientist groping to define his field, I am
interested in methodological questions, such as how methodologies
get established and change.
Regarding interfield connections between computer science and
psychology (or info proc psych and cog psych or whatever), I don't think
this is the same thing as the other interfield connections you have
been making. I think what Pylyshyn is saying is that computation is not
a way of thinking about thinking--thinking IS computation. The mind is
analogous to a computer, but the PROCESS of thinking is computational
(no analogy, just "literal description"). By using the analogy between
mind and computer we might develop a single theory of computation, perhaps
analogous to the way geometry stands to its different applications.
[The meaning of "inherited process abort conditions": think of
a stack of processes (tasks, goals), each of which can say "pop the
stack and return to me" at any time. These are the "abort conditions"
which are inherited, or persist, as the stack grows (think of them as
demons, if you wish). This idea is useful for modeling how people
stop trying to reach a goal before it is accomplished and return to
some higher goal, perhaps to reconsider their approach or plan of
attack for achieving the higher goal.]
Bill
-------
∂08-May-81 0917 Darden@SUMEX-AIM analogy.6
Date: 8 May 1981 0908-PDT
From: Darden@SUMEX-AIM
Subject: analogy.6
To: Analogy seminar:
I am reading various articles on analogy. I will soon
send a msg on Mary Hesse's Models and Analogies and
Dedre Gentner's critiques of Hesse. I think last fall we all should
have read the Hesse book to give us common examples and a framework for
talking. I would suggest that anyone who has time to do so should read
that material in the next week or so. Bruce has a copy of the Hesse book
if Chuck ever gave it back to him and Bruce and Steve have copies of
Gentner's papers.
The rest of this msg will provide quotations: comments by
Minsky on analogy and comments by Robert Oppenheimer about the use of
analogy in science. There is nothing strikingly new in this material but
it will serve to show that the topic we are trying to understand is
important and some of the things we have been saying are things others
agree with.
In a New York Times Magazine article, "Creating Computers That
Think" (Dec.7, 1980, which Steve sent me), Minsky said:"When somebody says
what's the difference between a machine that knows to pick up a block and
put it on top of another block and a machine that really understands what
it is doing, I say that the one that understands it has many ways to look
at the situation. It can look at the block as something that is about to
fall off of another block or is pretty because it's up high or is valuable
because because you could climb up higher on it. It's this network of
analogies and metaphors between different things that is important."
We obviously need to keep working on the problem of how to devise
different perspectives of the same thing.
Robert Oppenheimer in "Analogy in Science"(American Psychologist,
v.1 (1956)127-135) discusses the role of analogies in creativity in science.
"analogy is...an indispensable and inevitable tool for scientific progress
...I mean a special kind of similarity which is the similarity of structure,
the similarity of form, a similarity of constellation between two sets of
structures, two sets of particulars, that are manifestly very different
but have structural parallels. It has to do with relation and inter-
connection....We come to new things in science with what equipment we have,
which is how we have learned to think, and above all how we have learned
to think about the relatedness of things."
He discusses the analogies between water waves, light waves and
the waves of "atomic mechanics, of wave mechanics." They all share the
properties (are these structural properties in some sense??)of
interference, linearity, superposition,diffraction. In each case one
tried to form a new theory by taking over more of the properties of the old
one but then some had to be given up. "At each point the first
scientists have tried to make a theory like the earlier theories, light
like sound, as a material wave; matter waves like light waves, like a
real, physical wave; and in each case it has been of found one had to
widen the framework a little, and find the disanalogy which enabled one
to preserve what was right about the analogy."(p.131)
He discusses several other examples that I will not discuss:
the analogy between radioactive decay and emission of light which we
owe to Fermi; the analogy between electromagnetic forces and nuclear
forces.
A final section is on relations between sciences. He is making
exactly the same distinction I do (in "Theory Construction in Genetics")
between analogies and interfield connections. Oppenheimer says: "When
I turn to the question of analogies between sciences I talk of
something very different. There is first of all the fact that there are
situations that are not analogies at all. There are congruences when,
in two different sciences, by different techniques, different language,
different concepts, it turns out that the same subject has been explored
from two sides. And when it turns out that there is a mapping of one
description on the other, usually one description contains more elements
than the other, is richer; the other may then be more economical and more
convenient. Examples: The chemical theory of valence and atomic physics....
And relations between classical genetics and the discovery of the genetic
substances DNA,RNA."(p.133)
I need to think about this suggestion that one field provides a
more economical way of talking (e.g. "gene") while the other provides
richer information (DNA sequences). These differences may be
important when we are thinking about what is gained or lost by mapping
from one field to another.
Also the idea that there may be some disanalogy (negative
analogy in Hesse's terms) that means one must "widen" one's framework may
apply somehow to interfield connections. The widening that occurred in
coming to think of light waves without a medium and whatever it is one
thinks of atomic waves (I personally don't know enough to think about them)
are part of coming up with "radically" new ideas. The widening of
framework that occurred with the construction of the concept of a virus
was quite similar. In these cases we are severing connections between
properties that we had thought were essentially correlated: waves and
a medium; reproduction and independent microorganism. As Oppenheimer
indicates, this new way of thinking is not proposed at first; in the
beginning one tries to carry over all the old properties; but the data
force the elimination of some.
Hypothesis for the week: we think new thoughts by severing what
were previously thought to be essential correlations. [Does this make any
sense?]
Bye, Lindley
-------
∂To Darden@SUMEX 17:47 20-May
Heuristic:Algorithm :: Analogy:Inheritance
Thought for the day -
Heuristic:Algorithm :: Analogy:Inheritance
That is, inheritance is sorta a degenerate form of analogy, in which we
are "guaranteed" an acceptable, justifiable match. Analogy covers a great
deal more ground, by permitted less well justified reasons. Consider
"inheritizing" (by analogy to "analogizing") Fred to Boy. This means that
we can deduce that Fred will "inherit" (the value of) his species, and
gender from Boy.
The analogy "Fred is like Mary" may or may not allow the value for any
particular slotname (eg species or gender) to be copied. In this case, of
course, Fred:Species did correspond to Mary:Species, whereas one should
not have been able to conclude Fred's gender from Mary's. (IE it was only
from the "as a person" perspective that these two were analogous; not from
the "as a student", or ... viewpoints.)
Anyway, let's now look at this from the RLL/EURISKO angle. (Note I
resisted the temptation to use "perspective".) What does it mean for
units U and V to represent analogous objects? Perhaps that there is some
slot, S, such that U:S and V:S are the same value. When S is "Isa", we
get that degenerate inheritance-like relation -- eg Fred:Isa = Person =
Mary:Isa; and we expect every inheritable slot with a value stored on
TypicalPerson to be inherited by both Mary and Fred; and hence that these
two units should posses a great deal of similarity.
Of course there is a strong dependence of this slot, S. If S is, say,
GPA, not very much can be concluded -- only that both students are,
apparently, equally studious. One can deduce almost nothing from the fact
that two units have the same number of slots.
Anyway, let's further examine this (= U:S V:S) comparison. Equality seems
too stringent a requirement -- let's now weaken it to simply some relation
R. We will declare U and V somehow analogous if there is some slot S and
relation R such that R( U:S, V:S ).
This R might be a weakened form of EQ, such as SameElements, or
SomeElementInCommon, or even SameNumberOfElements. Or it might be more
obscure, like AddUpTo7, or even Analogous (leading to an obvious,
unavoidable recursion).
To be reasonable, we should have some logic for the slots, and the
relations. As we saw above, we should have higher expectations for some
slots than for others. Finding two units with similar names (eg
R=ManyLettersInCommon, and S = MyName) seems unlikely to yield anything
terribly deep or interesting. (Note this is NOT a property inherent to
syntactic slots -- we've great expectations for MyWorth, or MyCreator...)
The next step is to consider classes of slots. Recalling my comments on
perspectives from a while ago, we can implicitly define an equivalence
class, relative to a perspective, using a set of N slots, Si, and a single
2N-ary relation, R. Now two units, U and V, are considered analogous if
R( U:S1 V:S1 U:S2 V:S2 ... U:SN V:SN ) holds.
So now we've begged the question of analogy to finding the appropriate
Si's, and relation R. [Now for the hand waving.] One method of
determining appropriate slots might involve intersecting the slots
defining for both units with those which are constitutive for this
perspective. (EG Height intrinsically pertains to physical objects, and
GPA to students, whereas there is no "natural" connection between Height
and student, or GPA and physical objects. So how did I deduce that? its
easy if there is already a class which corresponds to this perspective --
just examine the slots which are defined for all instances of this class.
(In RLL, this is the value of Typicalx:NewPossibleSlots.) Lacking such a
pre-existing class, who knows?)
As to that R: the full generality of that 2N-ary relation seems overkill.
Chances are the slots were defined in some clean, "semi-decomposably"
manner, such that were can make do conparing just U:Si and V:Si - ie in
pairs. This R is then the conjunction of these N Ri's.
So now what? Probably more loud shouting about dependencies, and
underlying explanations -- which I'll spare the hapless reader. Perhaps
someone will have a more concrete extension to this idea?
As you might have guessed, neither Doug nor I have any real conclusions to
state -- this letter is meant to describe a mode of attack; and to end my
too-lengthly silence.
Russ
[I don't have easy access to the Analogy Bulletin Board. If you think
this letter is fitting, could you forward it there? Thanks.]
∂20-May-81 1842 Darden@SUMEX-AIM teaching reasoning by analogy
To: Analogy seminar:
As some of you know, I am mildly interested in developing an ICAI course to
do logic teaching at Maryland. It doesn't look practical, given our limitiations
on equipment, to try to bring the big Suppe system here. I'm been talking
to Jack Minker here who has some sort of theorem prover (I'm supposed to
get a demonstration this week) and he has ordered a language called
Prologue which is a predicate calculus language for a Z80 (the kind of thing
we are most likely to be able to afford for students to use).
Anyway, one of my vague ideas (the beginning of something creative??) this
week was to try to bring together teaching reasoning by analogy with teaching
how to solve logic problems. It would be a sort of fun way of trying out
some ideas about analogy in a very constrained domain and might even result
in something good for teaching. Exemplars are obviously important in
learning to solve problems. I don't know how far I will get with all this,
but it seems worth thinking about a bit.
I sent a msg earlier this week to Bill Clancey about this idea and he
responded with a very interesting msg about the kinds of reasoning by
analogy that might be important in teaching. I am going to forward that
msg to the seminar. I will be interested in any other ideas, pro or con,
that people have about this.
Bye, Lindley.
-------
∂20-May-81 1842 Darden@SUMEX-AIM Clancey on teaching reasoning by analogy
To: Analogy seminar:
∂20 May 1981 1001-PDT Clancey Re: fossils, etc.
To: Darden
cc: Buchanan
In response to your message sent 19 May 1981 0843-PDT
Lindley,
I am fairly certain that no one has incorporated AI representations
of analogies into a CAI program that teaches by analogy. The closest we have
come is to relate subject material by generalization/spec'ztn links, and then
explain new material by referring to previously mentioned examples of the
generalization (Goldstein did this in his WUMPUS program at MIT). I think
the Basic Instructional Program (BIP), which Avron worked on in the early,
mid-70's, could have profitably taught programming by analogy. It has a
network of problems organized by the general "tasks" each requires (like
"sort a list") and the "skills" or "techniques" that each task requires
(like "use an iterative statement with a WHILE clause). This could form the
basis, I think, for relating problems by analogy.
In talking about teaching through analogy, I think about several
kinds of analogy: forming analogies between problems on the basis of deep,
structural properties which suggest application of the same problem-solving
methods (relating programs by the tasks they require in BIP), forming
analogies between problem-solving methods (relating techniques), and
teaching the concept of a task or technique by analogy to non-programming
concepts (a "2 dimensional array" is analogous to the chairs in a classroom).
Anyone thinking about using a theorem prover for a CAI system should
be thoroughly familiar with the very complex, well-tested system being used
by Suppes at IMSSS. Adele Goldberg's thesis (mid 70's) showed that to use
a theorem prover for teaching, one must adapt it to use reasoning patterns
that people use, partly making the program less sophisticated, and partly
drawing out certain steps so they include intermediate organizational and
strategic concepts that people find useful. (My thesis made the same point
with regard to using MYCIN for teaching.) You also want to be able to
detect and understand systematic errors that students make in their proofs.
In GUIDON2, I will attempt to teach rules by relating them to
generalizations, involving a mapping of both premise and action to more
abstract concepts. For teaching the causal story that explains why a rule
is correct, it is sometimes useful to use non-medical analogies. For
example, one explains that the spleen acts like a filter (something like
a sponge in appearance) which catches diplococcus cells, preventing
infection. If the spleen is removed, or the spleen is disabled (by sickle
cells clogging the filter and killing it), infection by diplococcus becomes
more likely. I just use text strings to record these explanations.
Bye for now.
Bill
-------
-------
∂20-May-81 1832 Darden@SUMEX-AIM Russ on analogy
To: Analogy seminar:
Mail-from: ARPANET host SU-AI rcvd at 20-May-81 1745-PDT
Date: 20 May 1981 1747-PDT
From: Russell Greiner <RDG at SU-AI>
Subject: Heuristic:Algorithm :: Analogy:Inheritance
To: darden at SUMEX-AIM
Thought for the day -
Heuristic:Algorithm :: Analogy:Inheritance
That is, inheritance is sorta a degenerate form of analogy, in which we
are "guaranteed" an acceptable, justifiable match. Analogy covers a great
deal more ground, by permitted less well justified reasons. Consider
"inheritizing" (by analogy to "analogizing") Fred to Boy. This means that
we can deduce that Fred will "inherit" (the value of) his species, and
gender from Boy.
The analogy "Fred is like Mary" may or may not allow the value for any
particular slotname (eg species or gender) to be copied. In this case, of
course, Fred:Species did correspond to Mary:Species, whereas one should
not have been able to conclude Fred's gender from Mary's. (IE it was only
from the "as a person" perspective that these two were analogous; not from
the "as a student", or ... viewpoints.)
Anyway, let's now look at this from the RLL/EURISKO angle. (Note I
resisted the temptation to use "perspective".) What does it mean for
units U and V to represent analogous objects? Perhaps that there is some
slot, S, such that U:S and V:S are the same value. When S is "Isa", we
get that degenerate inheritance-like relation -- eg Fred:Isa = Person =
Mary:Isa; and we expect every inheritable slot with a value stored on
TypicalPerson to be inherited by both Mary and Fred; and hence that these
two units should posses a great deal of similarity.
Of course there is a strong dependence of this slot, S. If S is, say,
GPA, not very much can be concluded -- only that both students are,
apparently, equally studious. One can deduce almost nothing from the fact
that two units have the same number of slots.
Anyway, let's further examine this (= U:S V:S) comparison. Equality seems
too stringent a requirement -- let's now weaken it to simply some relation
R. We will declare U and V somehow analogous if there is some slot S and
relation R such that R( U:S, V:S ).
This R might be a weakened form of EQ, such as SameElements, or
SomeElementInCommon, or even SameNumberOfElements. Or it might be more
obscure, like AddUpTo7, or even Analogous (leading to an obvious,
unavoidable recursion).
To be reasonable, we should have some logic for the slots, and the
relations. As we saw above, we should have higher expectations for some
slots than for others. Finding two units with similar names (eg
R=ManyLettersInCommon, and S = MyName) seems unlikely to yield anything
terribly deep or interesting. (Note this is NOT a property inherent to
syntactic slots -- we've great expectations for MyWorth, or MyCreator...)
The next step is to consider classes of slots. Recalling my comments on
perspectives from a while ago, we can implicitly define an equivalence
class, relative to a perspective, using a set of N slots, Si, and a single
2N-ary relation, R. Now two units, U and V, are considered analogous if
R( U:S1 V:S1 U:S2 V:S2 ... U:SN V:SN ) holds.
So now we've begged the question of analogy to finding the appropriate
Si's, and relation R. [Now for the hand waving.] One method of
determining appropriate slots might involve intersecting the slots
defining for both units with those which are constitutive for this
perspective. (EG Height intrinsically pertains to physical objects, and
GPA to students, whereas there is no "natural" connection between Height
and student, or GPA and physical objects. So how did I deduce that? its
easy if there is already a class which corresponds to this perspective --
just examine the slots which are defined for all instances of this class.
(In RLL, this is the value of Typicalx:NewPossibleSlots.) Lacking such a
pre-existing class, who knows?)
As to that R: the full generality of that 2N-ary relation seems overkill.
Chances are the slots were defined in some clean, "semi-decomposably"
manner, such that were can make do conparing just U:Si and V:Si - ie in
pairs. This R is then the conjunction of these N Ri's.
So now what? Probably more loud shouting about dependencies, and
underlying explanations -- which I'll spare the hapless reader. Perhaps
someone will have a more concrete extension to this idea?
As you might have guessed, neither Doug nor I have any real conclusions to
state -- this letter is meant to describe a mode of attack; and to end my
too-lengthly silence.
Russ
[I don't have easy access to the Analogy Bulletin Board. If you think
this letter is fitting, could you forward it there? Thanks.]
-------
∂27-May-81 0756 Darden@SUMEX-AIM analogy.hesse
To: Analogy seminar:
This is a msg about some of the issues discussed in Mary Hesse's
MODELS AND ANALOGIES IN SCIENCE, which I have recently been rereading.
The ideas that I remembered from previous reading was the very useful notion
of positive, negative and neutral analogy, and the idea that exploiting
of the neutral analogy (i.e. that part that hasn't been matched yet)
was a good method of constructing a new theory, or a new part
of a theory. Similarity is the primitive relation for determining positive
analogy. As Gentner points out, that relation is hard to analyze and we
are much better off if we can use "identity" instead. Thus, if two things
to be analogized can be seen as having identical abstractions (formulated
by leaving out the negative analogy), we have a more manageable analysis
of analogy. I'm not sure what happens to the neutral analogy in the
abstraction. Tom recently discussed Mike G.'s analysis of analogy (via
abstractions) as being an analysis of dead analogies, i.e. already
completely formulated with no neutral analogy left. Maybe in an analogy
to be used in theory construction there is only a partial match
between abstractions and there is still neutral analogy left to be
exploited.
A problem that we have been wrestling with since our early discussions
about analogy is this: why would we expect that a neutral feature should
map into the analogue?
Steve Tappel recently sent me a msg that expressed this worry
and I am now going to quote his msg and show how Hesse tries to answer
this worry:
"Perhaps for the analogy seminar you could propose a trial set of a few
analogies, from Hesse or Gentner or that you have been considering yourself,
and see what people can propose in the way of representations and rules
for constructing and using those analogies. I like Gentner's idea of having
only exact matches rather than matching "similar" relations. I guess what's
really mysterious to me about analogies is why they work. And what general
constraints can one put on the structure of an analogy because of the
requirement that it have a reasonable chance of "working"? I guess this is
just another way of asking what constitutes a good analogy apart from its
actual usefulness, which one can't measure while constructing the analogy."
Hesse has an answer to why we would expect to be able to transfer
from the analogue to the subject. Consider her example:
properties of sound properties of light
causal echoes reflection
relations loudness brightness
pitch color
detected by ear detected by eye
propagated in air propagated in "ether"
<----similarity relations--->
I couldn't draw a vertical arrow, but the vertical relations are
causal relations. She has a weak concept of a causal relation: "at least
a tendency to co-occurrence." (p.77)
Hesse's insistence that the properties to be matched have causal
relations plays the same role as Gentner's insistence that good analogies
match identical structures rather than identical properties and Winston's
adoption of Gentner's idea and his application of it to the matching of
causal networks or parts of causal networks. They are all looking for ways
to insure that the properties or relations can be transferred from the
analogue to the subject.
But two conflicting demands are coming into play: insuring that
properties or causal connections transfer from the analogue to the subject
vs. having sufficiently open-ended and dissimilar relations between the
subject and analogue that the analogy can be used to construct something
"new." I found that latter demand very hard to state. Let me illustrate by
using Hesse's example. On the one hand, she insists that being wave-like
entails a medium in which it is propagated. Constructing a theory of light
waves by analogy with sound waves quite reasonably involved postulating
the aether as the medium of propagation: a typical use of neutral analogy
for introducing a new concept. And if we lived in a simple world with
only a limited number of kinds of causal connections then we would be
able to count on such transfers via neutral analogy to work. (Maybe
someone should devise a simple world where a limited number of types
exist and analogies can always be exploited fruitfully.)
Curiously, Hesse doesn't discuss the breakdown of the expectation
that the aether should exist. Oppenheimer (see Analogy.6) saw more clearly
than Hesse that we come to new situations with prior expectations but our
expectations are not always fulfilled: the neutral analogy may not be
exploitable in the way we thought was demanded by necessary causal
connections. Creating something new may involve severing connections
previously thought to be essential: electro-magnetic waves with no
medium, the waves of wave-mechanics, the virus as a reproducing molecule,
(what other examples do we have of new concepts that involve severing
old connections?). We come to see that the analogue connections must
be severed because the theory we construct by analogy with those
connections isn't confirmed by the data (e.g. aether theories, attempts
to find independent microorganisms as agents in viral diseases).
To recapitulate: suppose we have a problem in one field and we
wish to construct a theory to solve it. We try to find an analogy
(my analysis of this step is that we abstract the (a?) general form of the
problem, match to other problems with the same general form, import
the form of the solution, and particularize for our problem--see my
"Reasoning in Scientific Change") and we use the analogy in constructing
a theory. Then there are two possible outcomes:either the theory
is confirmed and we had found a fruitful analogy or the theory isn't
confirmed. Maybe there are other analogies to things already known
that can be used to construct yet another theory. Or, alternatively,
maybe the disconfirmation showed that prior expectations were just wrong:
something "new" (previously hard to think) has to be constructed.
The "new" thing may involve omitting from a list of properties one or
several properties that were previously thought to be essentially related
to the others, may involve severing causal connections previously
thought to be necessary, may involve putting old properties together in
new ways,may involve postulating new types of causal relations.
Note:essentail properties vs. necessary causal connections.
Gentner's criticizes Hesse for concentrating too
much on similar properties and instead advocates matching identical
structures (However, Hesse's insistence that the properties be causally
related [the vertical relations] mitigates this criticism.)
Winston has moved from looking at property matches to
matching causal networks or parts of causal networks. What we are
seeing in this AI work is a similar move to the one made in the history of
philosophy. Aristotle and Bacon saw the aim of science as the finding of
the essential forms of things; loosely,as finding the essential properties
for classes. Somehow (and I don't know the history well-enough here) by
the late 17th century, the task had become to find necessary and
sufficient causes. Despite Hume's critique of the concept of necessary
causal connections, Mill's methods were aimed at finding causal connections.
In the 20th c. we are left with vague talk about cluster concepts and
struggles with understanding the concept of cause,given knowledge about
complicated networky interconnections.
If the world consisted of classes with essential properties and
events connected in one-to-one causal relations and [this next requirement
I'm a bit unclear about] some similarity of classes and causal raltions
existed (i.e. there are types, each is not unique) then we could count
on finding good analogies. But our real world is much less neat and
we stumble around trying to find useful similarities.
I worry a bit that the units and slots form of reprensentation
and the hierarchies with inheritance that accompany it will constrain us
a bit too much into looking for essential properties. It seems less
amenable to finding structural and causal relations. Tom's msg of
April 22 gave us a very useful set of concepts for thinking about
an analogy system using a units and slots representation. Objects
with essential properties seem to be the underlying ontology behind:
ABSTRACTION--a unit that has a set of generalized slots that attempt
to capture characteristics that are common to a class of things
Similarly defined are perspective, prototype, exemplar and reformulation.
The one that seems more related to a structural or causal analysis is
ISOMORPHISM: a one-to-one mapping that completely preserves some
perspective, e.g.toy-block arch to real arch.
Several desirable characteristics of system that will use
analogies to do theory construction emerge from this discussion:
We want to be able to deal with property matches as well as matches of
structural or causal relations. We want to have analogies that work
and give us fruitful neutral analogy to use in theory construction and
we also want to have analogies that fail and force us to create something
new. Although I have been talking here about a total analogy succeeding
or failing, actually some parts may succeed while others fail.
Mary Hesse's book has more material worth discussing but
I will save that for another time.
Bye, Lindley
-------
∂28-May-81 0540 Darden@SUMEX-AIM vacation
Date: 28 May 1981 0540-PDT
From: Darden@SUMEX-AIM
Subject: vacation
To: Analogy seminar:
Hi, I'm letting all my correspondents know that I will be away from
May 28 through June 9, and thus not responding promptly to msgs.
I look forward to having lots of interesting mail containing EXCITING
NEW IDEAS from the three groups that I talk to: the analogy seminar,
the gene regulation group and the NASA group (of one) working on expert
systems.
I'll be in Mississippi with my father and brother, enjoying the things
I like about the South and being reminded of all the things I dislike.
This trip will include a trip to the Gulf coast to swim and eat shrimp.
Ya'll keep in touch.
Bye, Lindley
-------
∂30-May-81 2005 STT Papers by Gentner on metaphor and analogy
To: "@ANALOG.LST[1,STT]" at SU-AI
Lindley has sent me a collection of recent papers by Dedre Gentner on
metaphor and analogy which may interest members of the analogy seminar.
The most pertinent is her BBN Report "The Structure of Analogical
Models in Science" which attempts a structural characterization of
good scientific analogy. I think it is an excellent paper, not least
because Gentner is rather specific about the structural properties
that a good scientific analogy should (in her view) have. In other
papers she presents experimental studies on the interpretation of
metaphorical statements by children and adults. See Lindley's
message Analogy.hesse of May 27 for more about some of Gentner's ideas.
Below are abstracts of the Gentner papers. Anybody who
wants copies, fill in the order blank immediately below, or reasonable
facsimile thereof, and send it to STT@SAIL. I will have copies made
and distribute them.
-------------------------------------------------------------------------
| Yes! I'll take this opportunity to receive my FREE copy of one or |
| more of Dedre Gentner's papers! |
| Please send me "The Structure of Analogical Models in Science": ___ |
| Please send me the following papers (specify): |
| __________________________________________________________________ |
| Send it/them to me at: ____________________________________________ |
| (Default: your box at Margaret Jacks Hall.) |
-------------------------------------------------------------------------
ABSTRACTS OF PAPERS
Dedre Gentner "The Structure of Analogical Models in Science"
BBN Report No. 4451, July 1980. 79 pages.
(Gentner's abstract)
Analogical models can be powerful aids to reasoning, as when light is
explained in terms of water waves; or they can be misleading, as when
chemical processes are thought of in terms of life processes such as
putrefaction. This paper proposes a structural characterization of good
science analogy using a theoretical approach in which complex metaphors
and analogies are treated as structure-mappings between domains. To
delineate good from poor science analogy, a series of comparisons is
made. First, metaphor and analogy are contrasted with literal similarity;
then, explanatory-predictive analogy is contrasted with expressive
metaphor; finally, within science, good explanatory analogy is
contrasted with poor explanatory analogy. Analogies of historical
importance are analyzed and empirical findings are discussed.
Dedre Gentner "Are Scientific Analogies Metaphors?"
BBN Report No. 4604. 45 pages plus figures. To appear in
D.S. Miall (Ed.), METAPHOR: PROBLEMS AND PERSPECTIVES.
Brighton, Sussex: Harvester Press, Ltd.
Nearly identical with "The Structure of Analogical Models in Science"
except that most of the experimental portions have been excised.
Dedre Gentner "Studies of Metaphor and Complex Analogies"
Paper presented at the A.P.A. Symposium on Metaphor as Process,
Montreal, September 1980. 26 pages plus figures.
"This research is aimed at discovering the proper psychological
characterization of complex metaphorical and analogical comparisons.
The basic theoretical framework is a structure-mapping theory of
metaphor and analogy."
"A central claim is that high-level relational information is more
likely to be preserved than information about the objects themselves.
Objects and their attributes can be arbitrarily different between
the two domains; it is the relational structure that overlaps in
metaphorical likeness."
Gentner reports the results of experiments with adult and child
subjects, who were asked to interpret metaphorical comparisons such as
"Blood vessels are like aqueducts", "Science is like a glacier",
"Billboards are like warts". She concludes that her structure-mapping
hypothesis is supported, and finds "a developmental trend towards more
relational interpretations of metaphors".
Dedre Gentner "Children's Performance on a Spatial Analogies Task"
CHILD DEVELOPMENT, 1977, 48, 1034-1039.
(Gentner's abstract)
Young children performed as well as or better than adults on tasks
requiring use of spatial analogies. The tasks involved body-parts
analogies, such as, "If this [pictured] mountain had a knee, where
would it be?" The entities referred to were physical objects familiar
to young children, and this question format clearly called for analogical
responding. Thus, sources of confusion were minimized. In a pilot
study, it was shown that preschool children could apply such body-parts
analogies to pictures as consistently as adults. The mappings were
then made more difficult by varying the orientation of the pictured
objects or by adding misleading pictorial details to the pictured
objects. Adults peformed somewhat less consistently than pre-schoolers
and first graders when misleading details were present; there were no
age differences when orientation was varied. These results suggest that
analogical ability is present at a very early age.
∂TO STT 18:44 3-Jun Gi'me, gi'me, gi'me!
Steve -
I'd like a copies of
Dedre Gentner "The Structure of Analogical Models in Science"
BBN Report No. 4451, July 1980. 79 pages.
Dedre Gentner "Studies of Metaphor and Complex Analogies"
Paper presented at the A.P.A. Symposium on Metaphor as Process,
Montreal, September 1980. 26 pages plus figures.
Let me know if you need (or even, would just like) help xeroxing...
(I assume that that is how you intend to get the papers to replicate.)
Russ
∂TO CSD.HOFSTADER@SCORE 15:46 8-Jun
on things sorta like analogies
Doug -
I just finished reading (and enjoying) the proto-article you sent.
It was quite relevant -- I'm now in the standard "what to do for a thesis"
quandry, and several of the issues related to the idea of analogy loom as
strong candidates for thesis topic.
If you have some time, perhaps we could get together and discuss some
ideas -- I'd be curious to get your comments and conjectures, as well
as to test out mine on a not-totally-AI audience.
The basic theme relates to the
ubiquity of analogy and its relation to abstraction;
-- noting that these mapping can be found in everything
from regular language usage to law to common sense reasoning.
(Some of the ideas come from Mike Genesereth's paper "Metaphor and Models",
[my subtitle: "What's the Meta in Metaphor, For?"].)
I also had a few specific comments on your paper, which I'd enjoy discussing.
Russ
-----
1. Prototypes, familiar resemblences - see TW's paper on Primitives ,...
[Wittgenstein]
2. English full of these analogies -
First is Lakoff, with his theory of metaphor
[time is money]
Then idea of extending word usage - not even in asimilie --
eg given bachelor, what is a bachelor bear?
[consider issue of saying that bear is married - to a person, or same species?
how is this resolved - given its ambiguity, which is closer?]
3. Anne's talk on law - cattle includes geese...
4. Categorizing - McC's arms in the room, not people
5. encoding - as in Chaitkin -- to decide which relation is apt, find one which
is simplest - people do... (with correct metric)
6.Roles - see Indonesia's plays - confusing mass of circles
∂ 3 Jun 1981 1636-PDT CSD.GREINER Re: here it is
To: CSD.HOFSTADTER
cc: CSD.GREINER
Thanks...
(long winded introduction to a question:)
Did you meet Professor Lindley Darden when she was here first term this year?
She's a Philosopher of Science, who was visiting Bruce Buchanan.
Together they taught a course on Theory Formation, trying to formalize
and understand this and other similar "magical" processes.
Her major research interest is concerned with "Interfield Connections" --
which is intimately related to the notion of analogy.
Anyway, she has since returned to UofMaryland.
Several of us HPPers have maintained contact with her, using
SUMEX and the ARPAnet. Many of the messages have been on the theme
of analogy -- in a bulletin board type of arrangement.
(Feel free to probe the file ANALOG[rdg,dbl] on SAIL, to see the
past messages.)
(and now the question:) Would you mind if I send around this article
to these Analogy people? Would you like to be added to that list?
Russ
-------
---------------
Unmailed article by Hofstadter - to appear in Scientific American
∂3 Jun 1981 1551-PDT CSD.HOFSTADTER here it is
To: CSD.Greiner
Roles and Analogies in Real and Artificial Worlds
by Douglas R. Hofstadter
In our research in artificial intelligence, my graduate students
Gray Clossman and Marsha Meredith and I have been looking at typical
human thought processes in everyday life as well as in more restricted
domains, and everywhere we look, we seem to find that inside the internal
representations of concepts, there are substructures that have a kind of
independence of the structures of which they are part. Such a substructure
is modular -- that is, it is "exportable" from its native context to alien
contexts. It is an autonomous structure in its own right, and we call
these things ROLES. A role, then, is a natural "module of description"
of something -- a sort of "bite-sized chunk" that seems to feel comfortable
moving out of its first home and finding homes in other spots, some of them
rather unlikely at first glance.
One intriguing example from everyday life is the "First Lady" role.
Most Americans use this term more flexibly than they probably realize. They
would probably say, if asked, that the term means "wife of the President",
and not think much more about it. But if in some context they were asked
about the First Lady of Canada, what would almost surely pop into mind is
the name of Margaret Trudeau. Now they might tend to reject this suggestion
as soon as it occurred to them -- but for us the important thing is that
her name would occur at all. First of all, people know her as the EX-WIFE
of Trudeau, not his wife. Secondly, Trudeau is not the President of Canada
(there is none), but its Prime Minister. So -- how is "ex-wife of Prime
Minister" the same as "wife of President"?
Before you answer, "Well, 'wife' and 'ex-wife' are related concepts,
as are 'Prime Minister' and 'President'", consider who might be the current
First Lady of Great Britain. Whose name came to mind? Margaret Thatcher?
Queen Elizabeth? They are ladies, but do they really play the role of "First
Lady"? Did it occur to you that it might be Dennis Thatcher or Prince
Philip? At first these suggestions seem laughable, yet they are at the same
time quite compelling -- particularly the first (Dennis Thatcher). In fact,
I once clipped out a newspaper article that portrayed Dennis Thatcher as
England's First Lady. And we have found in informal conversations that many
people come to feel happy with the idea after a while.
What kind of sense does this make? How can a MAN be a LADY? Well,
language is a slippery thing. It is much slipperier than dictionary
definitions would have you believe. Its slipperiness comes from the
underlying slipperiness of concepts, and in particular of these elusive
things we are calling roles.
Here, of course, you could argue that the "First Lady" role goes over
naturally into "husband of Prime Minister", simply because what "First Lady"
REALLY means is "spouse of Head of State". But this will not do either.
In Haiti, until recently the title of First Lady belonged to the widow
!
- 2 -
of the former President XXXXXXXXX ("Papa Doc") Duvalier. She is also
the mother of the current President, Jean-Claude ("Baby Doc") Duvalier.
Not long ago there occurred a bitter power struggle between her and her
daughter-in-law, the wife of "Baby Doc", for the title of "First Lady".
In the end, the younger woman won out but the older one was given the
lifetime title of "First Lady of the Revolution". Now, do you wish to
amend your suggestion to say "spouse (or ex-spouse) of (present or former)
head of state"? You know perfectly well that we will be able to bring up
other exceptions. For example, one could imagine a meeting of the Poobah
Club at which the Grand Poobah's wife was introduced as the First Lady of the
Club. Now the Grand Poobah is hardly a chief of state. So, you amend your
definition to say "spouse (or ex-spouse) of the head of an organization".
But suppose... Actually, I'll let YOU go on inventing exceptional cases.
For any rule you propose, there is bound to be some conceivable way to slip
by it.
And worse yet, something terrible is happening to the concept. All
the time, as it is growing more and more general, flexible, and powerful,
it is also growing more and more cumbersome and strange. Furthermore --
and this is the REALLY central point -- something crucial is being lost,
namely, the notion that "wife of the President" is the most NATURAL meaning,
for Americans. If one knew only the generalized definition, one would get
the impression that Sam Pfeffenhauser, the ex-father-in-law of the corner
drugstore's temporary boss is just as good an example of the "First Lady"
concept as is Nancy Reagan. Something is wrong when this happens. The
definition should not only be GENERAL, it should also incorporate some
indication of what the SPIRIT of the idea is.
Computers have a hard time getting the spirit of things; they prefer
to know things to the letter. And so people spend an awful lot of time,
while talking to computers, writing extremely long and detailed descriptions
of ideas that they could get across in ONE GOOD EXAMPLE to anyone with half
a brain. And if not in one example, then in two or three at most. So the
question is, how to get a computer to understand what "First Lady" means?
We want, then, to examine the idea of "roles" in some detail.
In order to illustrate how the notion of "role" can be modeled in
more formal domains than international political protocol, I switch now
to one of my favorite domains -- the natural numbers. I shall pose some
little puzzles that Gray and I have been thinking about, and which I hope
are intriguing to readers. Each of them has no single "correct" answer,
but rather a set of possible answers with varying degrees of plausibility
or defensibility. What we are interested in is devising a computer program
that is able to see the rationale behind each possible answer, and thus to
be able to come up with the same set of "feelings" as a typical person would
about what is a good and what is a bad answer.
The domain of natural numbers might sound at first like a rather
hard-edged, precise little mathematical world, but actually it is a domain
in which problems requiring extremely subtle subjective judgments can be
formulated. We imagine our program to have very little detailed arithmetical
!
- 3 -
knowledge about the integers. It does not, for instance, recognize 9 as
a square; in fact, it does not even know about multiplication. It does not
know that 6 is even and 7 odd. What, then, does it know? It knows how to
count up or down -- it has a knowledge of successorship. Thus, it recognizes
that the sequence of numerals "1 2 3 4 5" represents an upward counting
process. It also can apply the notion of counting to structures it is
looking at, as in "4 4 4 4 4", which it would recognize as a group of five
copies of the numeral "4". It knows that 9 is bigger than 4, although it
has no idea HOW MUCH bigger. You can think of our hypothetical computer
program as having the arithmetical sophistication of a five-year-old and an
avid curiosity about number patterns. Without further ado, then, here is
the first problem.
Consider the structure we'll call "A": 1 2 3 4 5 5 4 3 2 1.
Now consider the structure called "B": 1 2 3 4 4 3 2 1.
The question is: "What is to B as 4 is to A?"
Or, in the language of roles, "What plays the role in B
that 4 plays in A?"
Note that by asking it this way, we leave it to the puzzle solver to decide
what role 4 actually does play in A. It would be analogous to asking
"Who is the Nancy Reagan of England?", leaving it to the listener to figure
out what conceptual role Nancy Reagan fills, and then to try to export that
role to England, letting it slip and stretch in whatever ways are necessary
at that time. I have found that many people are quite happy with Dennis
Thatcher as "the Nancy Reagan of England", but balk at calling him the
"First Lady of England". A curious point, which we will come back to later,
is this: if the role is left implicit, nonverbalized, it has more fluidity
in the way it transfers than if it is "frozen" in an English phrase.
This is actually the way most analogies crop up. Seldom does someone
say to you explicitly, "What is the counterpart of Central Park in San
Francisco?" Usually it happens through a more implicit channel. When you
are visiting San Francisco for the first time, you are driven through Golden
Gate Park, and somehow it REMINDS you of Central Park. After the fact, you
can point out some similarities (both are long and thin rectangles, both
contain lakes and curvy roads, and so on). In fact, as it happens, both
were designed by Frederick Law Olmstead, but you may not know that. Most
analogies arise as a result of unconscious filterings and arrangings of
perceptions, not as consciously sought solutions to cooked-up puzzles.
Incidentally, when I first thought of writing about roles and analogies,
I had in mind both the First Lady example and the numerical examples. As
I developed my thoughts, I realized that I was unconsciously developing a
parallel in my mind between the First Lady example and the number puzzles.
I call it a "meta-analogy", since it is an analogy between analogies. In
this meta-analogy, I see structure A as corresponding to the United States,
structure B to Great Britain, 4 to Nancy Reagan, and the unknown object to
the unknown person.
!
- 4 -
Let us now look at some possible answers to the first "formal" problem.
The most likely answer is 3. The justification seems to be, "4 precedes
the central pair (55) in A, and the corresponding central pair in B is
44, which is preceded by 3." Well and good. Then how about in C?
C: 1 2 3 4 5 6 6 6 6 5 4 3 2 1
The central pair of C is 66, which is flanked on both sides by 6's. So is
6 to C what 4 is to A? Probably most people would prefer 5, although it is
perfectly LOGICAL to insist on 6. The preference for 5 comes, nonetheless,
from a very sensible instinct to generalize the "central pair" notion
(itself a ROLE, to be sure) to "central plateau" (or whatever you want to
call it). In people there are competing urges -- one, to stay with the
original concept, and two, to flex and bend when it "feels right", when it
would seem rigid and stodgy to insist on previous conventions over simple
and "natural" extensions. But it is these words, "natural", "flexible",
"rigid", "feel right", and so on, that are so extraordinarily hard to put
into programs.
Now let's investigate some other ways to make the role of that 4 slip.
Consider this structure:
D: 1 1 2 2 3 3 4 4 5 4 4 3 3 2 2 1 1
Here is a curious kind of reversal -- now there is no central pair, but
everything else is in pairs. Some people might still pick 4, as it is
next to the center. But what about 44 -- a pair rather than a single
number? It seems that, as long as "pair" and "singleton" are switching
places, we might as well go all the way, and give an answer that reflects
that perceptual turnabout. In fact, it would seem rigid and unimaginative
to insist on sticking with single numbers when it is so obvious that the
easiest way to perceive D is in terms of pairs:
D: (11) (22) (33) (44) 5 (44) (33) (22) (11)
Not just 4, but every part of A has a role, and there are corresponding
roles in D. As you can see, inside each role the concepts of pair and
singleton have been switched.
Incidentally, this is as good a time as any to point out some features
of my "meta-analogy" between these problems and the First Lady problem.
If you think of the President as "the highest, most central figure in the
land", and his wife as "the one standing next to him", you'll see that this
characterization carries over almost literally to the numerical problems.
In structure A, the highest, most central figure -- the "President" -- is 5
(or possibly the pair of 5's), and his "wife", standing next to him, is 4.
In structure B, the President is 4 (or the pair of 4's), and his wife is 3.
In structure C, the President is 6 (or else the group of 6's), and his
wife is 5. Now in D, the President is for once unambiguous (5), but to
compensate, there is a choice as to his wife. If you think of pairs as
males and singletons as females, then D presents us with a case where the
"sexes" are reversed, exactly as in the case of England's "First Lady"
problem. The most reasonable answer seems to be the "spouse" -- in this
case, the "husband" -- of 5, namely the pair 44.
!
- 5 -
Consider now a pair of curious cases:
E: 1 2 3 4 5 6 7 8
F: 8 7 6 5 4 3 2 1
What can we make of these? A very rigid person might cling to the idea
captured in the phrase "number to the left of the central pair", despite
the fact that nothing at all distinguishes the central pair in either of
these examples. Such a person would give the rather inane answers of 3 for
E and 6 for F. Such a person would do better, as Lewis Carroll once said,
to take up football instead of analogies. But what would be a wiser view
of, say, E? How to map E onto A? The mapping is doomed to be imperfect,
so how can we do best? We might think of E as mapping onto the left half
of A. This would involve a tacit judgment that it is all right to abandon
the attempt to map E onto ALL of A, in return for the ease of mapping E onto
a "natural" portion of A. This is a pretty subtle step to take, I would
say. It would suggest 7 as the answer. Then what about F? Do we prefer 2
or 7? It depends on whether we choose to map F onto the left half or the
right half of A. Mapping F onto the left half of A involves mapping a purely
descending sequence onto a purely ascending sequence. But either choice
requires a willingness to let go of qualities that had seemed important --
an ability to bend gracefully under pressure. Fluid analogies are not a
game for uptight minds!
These kinds of situations are difficult because they involve, in
essence, a pulling-apart of 4's role in A into two rival facets, each
of which claims to be the more essential in defining the role. In the
mapping of A onto F, one of the rival facets sees 4's role in A as "one
less than the President", while the other facet sees 4's role as "the
next-to-the-rightmost numeral in a chain of successors". Thus one facet
is primarily concerned with magnitude, the other primarily with position.
The facet you find more convincing will determine your answer to F.
This kind of split happened, pretty much, when you tried to decide
on Queen Elizabeth versus Margaret Thatcher -- or their husbands. Which is
more important -- for someone to be a ceremonial FIGUREHEAD, or a political
HEAD OF STATE, for their wife (or husband) to be called the "First Lady"?
In the United States, these features happily coincide in one person -- the
President -- but in Britain, they do not. So consider the following target
structures:
G: 5 4 3 2 1 1 2 3 4 5
H: 1 2 3 4 6 5 5 6 4 3 2 1
In G, what is most central is simultaneously lowest, and what is highest is
simultaneously most peripheral! (G can be pictured as a valley, contrasting
with A's mountain peak.) We have a "figurehead" (the 5's flanking the
structure at either end), and we have a "chief of state" (the two central
1's). Which one's spouse would better fill the "First Lady" role? Or, to
!
- 6 -
remind you of where this all came from, what in G plays the role of 4 in A?
I personally would opt for 2 because it stands next to the central group.
To me, centrality seems more important here than magnitude does, just as
political power seems more substantive than ceremonial show. Corresponding
to this, I prefer Dennis Thatcher to Prince Philip, as Great Britain's First
Lady.
So what happens when we tackle H? There are three "reasonable"
possibilities (in the sense of appealing to the proverbial "reasonable
man"): 6 (flanking the central pair of 5's); 5 (being the next-to-largest
number); and 4 (flanking the central "crater" 6556). This makes life a
little difficult. Once again, there is no Gloriously Right Answer; but
there are certainly reasons that seem good and reasons that seem shaky.
For instance, if someone had the audacity to say, "The answer is 4, because
4 is the fourth term of H, just as it is the fourth term of A", we would
be flabbergasted. What possible fundamental significance could there be
to such a mundane and arbitrary characterization as "fourth element of"?
It seems to cling to an extremely superficial view of A, the way a little
child might insist that a red Volkswagen bug and a red Cadillac are more
similar than two VW bugs of different colors. To see 4 as no more than
the fourth element of A is to miss all of A's interest. It is to see A
as shown below:
* * * 4 * * * * * *
It seems that a GOOD answer must take A's structure into account in a full,
rich, yet simple way. This means that all of A must be perceived in terms
of interacting, mutually intertwined conceptual structures -- roles that
are mutually dependent, in the way that "family", "husband", "wife",
"mother", "father", "son", "daughter", "brother", "sister", and so on
are all interdependent concepts.
The word "ROLE" makes us think of the theater. In a play, the various
roles all mingle together in SCENES. A scene is a larger-scale structure
than an individual role; it is a place where several roles coexist and
interact. In our analogy problems, one way to go about trying to seek a
satisfying answer might be to try to perceive the two structures involved
as if they were two enactments of a single scene, simply portrayed by
two different directors using different actors, and so on. Thus, the core
roles would exist and be filled in both presentations, but at the same time
each presentation would have minor aspects, or roles, unique to it. For
instance, the adaptation of the Greek legend of Orpheus and Eurydice into
a contemporary context of Carnaval time in Rio de Janeiro is the basis
for the movie "Black Orpheus". Many original features cannot be DIRECTLY
exported, but with poetic modification, they can be -- and director Marcel
Camus meets the challenge with great flair. In the movie, there are, of
course, many minor parts -- extras -- that add Brazilian flavor, yet they
do not impair the analogy at all; in fact they enrich it. This is the kind
of thing that appeals deeply to human sensibilities, both intellectually and
emotionally.
!
- 7 -
Now that you've seen some tricky variations, I would like to return to
our first puzzle and point out some of its hidden subtlety. First of all,
the "central pair" notion, which functions as the keystone of structure A,
is actually just a kind of by-product, an accidental artifact of the
structure of A. How would you describe the structure of A without quoting
it digit by digit? You'd probably say it rises from 1 to 5, then descends
from 5 to 1, making two halves that are mirror images. But such a description
refers only to the two halves, not to the fact that at their meeting point
these halves form a pair of 5's. Yet perceptually, a shift takes place when
you see A. To the mind's eye, it appears something like this:
1 2 3 4 5 5 4 3 2 1
---
Somehow, a new conceptual entity has been born in the center. It is, as
I said above, the KEYSTONE of A (notice that this depends upon, or implies,
a mapping of A onto an arch).
Why don't we perceive the pair of 3's, say, as a unit as well? Probably
simply because they don't touch. And consider this structure:
1 2 3 4 5 1 2 3 4 5
The central pair "51" doesn't pop out as being salient or important, does
it? In A, though, the combination of adjacency and equality, especially
when supplemented by centrality, somehow makes the two central 5's merge into
a unit in the perceiver's mind, albeit usually not in a highly conscious
manner. If this perceptual shift did not happen, then the answer of 5 in C,
based largely on "equating" the plateaus in A and C, would be considerably
less compelling.
In the first puzzle, both A and B had obvious central plateaus (or
Presidents, if you prefer). This suggested a good starting point for an
overall mapping of A onto B: central plateau onto central plateau, start
onto start, finish onto finish, and so on. But if we tried to complete this
mapping, we would obviously run into trouble.
A: 1 2 3 4 5 5 4 3 2 1
\ | | | | /
\ | | | | /
B: 1 2 3 4 4 3 2 1
We MUST have 1 in A mapping onto 1 in B, mustn't we? And the centers have
to match up, too, don't they? But where between 1 and 5 does the analogy
break down? It seems that some sort of mapping of 4 onto 3, as shown above,
is pretty satisfying to many people. But press them one step more, and they
will shrug, grin, and give up.
!
- 8 -
Similarly, though you can ask for "the Nancy Reagan of England", it
makes less sense to ask, "Who is the Maureen Reagan of England?" (remember
that Maureen Reagan is Nancy Reagan's step-daughter). Suppose that the
Thatchers had a biological daughter. Could she be the counterpart to
Maureen Reagan? Suppose that Margaret Thatcher had a step-daughter. Would
she be the counterpart? Or suppose that Margaret Thatcher had no daughter,
but Dennis Thatcher had twin step-daughters. Then would these twins taken
together constitute the counterpart of Maureen Reagan? Just as we rebelled
earlier, asking, "How can a man be a lady?", we would now rebel and ask,
"How can two persons fill a role defined by one person?" Of course, we've
already dealt with just such a case in example D, where the pair of 4's in
D played the role of a single 4 in A.
Issues like this, needless to say, arise all the time in the pursuit
of good analogies, and facing such mismatches directly leads occasionally
to productive insights. One could go on and press for even more detailed
correspondences between entities in Britain and in the United States. What
is the British counterpart of Watergate? Who plays the part of Richard
Nixon? Of John Mitchell? Senator Sam Irvin? Senator Daniel Inouye?
G. Gordon Liddy? John Sirica? John Dean? Officer XXXXXXXXXwicz?
Alexander Butterfield? The less salient an object is inside a larger
structure, the harder it is to characterize it in an exportable way.
But what makes something salient? Usually it is its proximity, in some
sense, to a "distinguished" element of the same structure. For instance, in
the following structure:
1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 4 3 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1
the central 4 is probably the most distinguished individual numeral. Then,
depending on how you perceive the sequence, different features will jump out
at you. For instance, do you see it as "letters" or as "words" (larger-scale
chunks of the sequence)? Try thinking about it both ways, and see what is
salient to you from those different perspectives. When I see it at the
"word" level, the central group "3334333" seems just a shade less salient
than the 9, and after that, perhaps, the two flanking groups of 1's. The
two groups of 3's by themselves come next. Only then do the groups of 2's
get recognized! On the other hand, when I perceive it at the "letter" level,
what is salient is quite different. For instance, after the central 4,
probably the next most salient numbers to me are the first and last 1's,
as they are very easy to describe, then maybe the first and last 2's. After
that, the two 3's flanking the central 9 -- but at that point it starts to
get a little harder to pinpoint various items without resorting to uninspired
descriptions such as "the fourth term".
A distinguished term is something we can get at by an elegant and crisp
description. A nearly-distinguished term is something we can get at by
first pointing to a distinguished term, then describing a short "jog" that
leads to it from there. Just as in giving someone directions, some places
are more salient, some are less so. Some buildings in New York City are
inherently difficult to direct someone to, while others are inherently easy.
In the same way, some roles in a complex conceptual structure are highly
distinguished and easily exporta`∧e, while others are very hard to describe
and although they may have certain idiosyncratic qualities in their local
context, nothing makes them stand out globally.
!
- 9 -
As you move farther and farther away from its central roles, any
analogy becomes more and more strained. "Who is the Jackie Phlump of
England?" is a meaningless question, meaningless even to Jackie Phlump's
best friend, because Jackie's role just is too small and idiosyncratic
within the structure of the United States. It is not exportable. The
fact that Jackie is the manager of Snagwallow's hotdog stand in Gooseburg
doesn't help much, because one then has to figure out the identities of the
English Gooseburg and the English Snagwallow, not to mention the English
equivalent of the good old American institution of the hotdog stand.
Finally, I can illustrate this point in the context of the high-level
"meta-analogy" by asking the following strange question: "Are there two
natural-number structures X and Y such that, when you map structure X onto
structure Y, thinking of X as Great Britain and Y as the United States, two
pieces of X can be found that obviously play the roles of the two houses
of Parliament while the two corresponding pieces of Y play the roles of the
two houses of Congress?" It seems that that would attempt to stretch the
high-level analogy beyond its spirit.
The moral is a simple one -- don't press an analogy too far, for it
will always break down. So what good are analogies, anyway? Why bother
with them? What is the purpose of trying to establish a mapping between
two things that DON'T map onto each other, in reality? The answer is very
simple: we humans spend most of our thinking lives doing precisely this,
over and over, in one guise or another. Analogy and similarity, whether
accurate or not, guide all our thought patterns. Being attuned to vague
resemblances is the hallmark of intelligence, for better or for worse.
The fact that we use words and ready-made phrases shows that we funnel
the world down into a fairly constant set of categories. That is, we filter
out "irrelevant" aspects of things to see "what they are". Often we end up
with one word, such as "dog". No two dogs map onto each other exactly, but
we still are happy with the abstraction "dog" that allows us to map any two
dogs onto each other in a more or less reasonable way. Head to head, tail
to tail, fur to fur, eyes to eyes, and so on. The mapping's accuracy comes
to an end if you peer far enough, but we have the good sense to know where
to stop. Our language provides us with units of different fineness. Some
people see no further than "dog" and accordingly use that word; others
perceive the breed as easily as the "dogness", and talk about "that
Airedale". But no matter at what level of detail you cut off your scrutiny,
your perception amounts to filtering out some aspects and funneling the
remainder down into a single conceptual target, a mental symbol labeled
(usually) by just one word (such as "word") or stock phrase (such as "stock
phrase"). Each such mental symbol implicitly stands for the analogical
connection that loosely binds all its examples together.
Beyond the implicit analogies that are hidden in individual words,
explicit analogies occur all the time at a larger scale in our sentences.
We are quite uninhibited in drawing comparisons of unfamiliar things to
things we assume are more familiar. We see grids of all sorts as similar
to checkerboards. We see carefully charted-out actions in life as similar
!
- 10 -
to chess moves. We see the eye as a camera, the atom as a tiny solar
system. Science is constantly being likened to a vast jigsaw puzzle (an
analogy I have never cared for). In their eagerness to stretch and bend
concepts, people turn proper nouns into ordinary nouns, as in the statement
"Brigitte Bardot is the French Marilyn Monroe." The Marilyn Monroe in such
transformations always loses a lot of its uniqueness, and both the Marilyn
Monroe and the Brigitte Bardot are done something of a disservice in the
interests of rapidly telegraphing an idea to an audience.
Then, going one step beyond the explicit linguistic level, there are
the analogies and mappings that we use constantly to guide our thoughts on
a larger scale. The perception of romantic dilemmas is one of the most
striking places where mapping or analogical thinking dominates in an obvious
way. When someone tells us of some romantic woe, we can usually map it
immediately onto some personal experience of our own. In fact, we can
probably draw some parallel between ANY romantic situation and ANY other
one, and it will perhaps yield some insight if looked at properly. Yet
romances are incredibly detailed and idiosyncratic -- no two are alike.
The point is, we skim off some abstractions and are careful not to try to
carry the resemblance too far. And certainly we ignore the trivial aspects.
A romance between John and Mary can certainly map onto one between Sidney
and Candace, despite the fact that the names don't match!
The reason, then, for worrying about human analogical thought is
simply that it is there. It is there, and moreover it permeates our
nature. It is the central fact of our intelligence and to ignore it is
like ignoring Manhattan in trying to understand New York City.
Now let us get back to some concrete problems in our formal domain.
Notice that there is an inherent sort of contradiction in setting up analogy
problems, which are by definition INFORMAL, in a rather formal domain. But
the nice thing is that it shows that the domain is actually just as slippery
as any "informal" domain. Here are four further examples:
I: 1 2 3 3 4 5 6 7 6 5 4 3 3 2 1
J: 1 7 7 6 5 4 3 2 1
K: 6 9 7 3 9 4 1 6
L: 1 2 3 4 5 6 7 8 9 7 8 9 6 5 4 3 2 1
Example I involves what I enjoy referring to as a "Governor" -- namely,
the pair 33. Here again, one role in A has been split into two pieces, for
55 in A was not only the sole PAIR but also the PEAK, while in I, 33 is the
sole pair while 7 plays the role of peak. We are forced to choose between
2 (wife of the Governor) and 6 (wife of the President). Actually, the
Governor has two "wives" -- 2 and 4, so we have to choose between them --
unless we go with 6 as being the wife of President 7.
!
- 11 -
Example J, although it begins with "1776", is not meant to be especially
patriotic. Its interest is primarily in that it draws attention, for the
first time, to the fact of A's symmetry, which we had taken for granted.
When we chose 4 as the President's wife, did we do so because it PRECEDED
or because it FOLLOWED the President? The former would suggest 1 as the
counterpart of 4, the latter would suggest 6. And the latter, although
probably weaker were all other things equal, is here strengthened by the
regular descent from 7 to 1, which corresponds much better to the latter
half of A than the abrupt upward jump in J (1 to 7 in one step!) corresponds
to the former half of A.
Example K is rather obscure. But it has been led up to somewhat by
example J. In particular, example J drew attention to the fact that in A
there are TWO 4's, not just one. Example K plays on the relationship of
those two 4's to each other. In A, there were two numbers in between the
two 4's. We can take that property as defining the role of 4 in A. This
is, to be sure, not the ONLY relationship between the two 4's, but it is
perhaps the most obvious one. So, what number in K occurs twice, with two
intervening numbers? Answer: only 9 -- and so that is it.
Finally, example L. Here, the "central pair" notion gets extended
one further degree of abstraction. We go up happily step by step until
we hit the second 7. It takes us a moment to get our bearings, and when
we recover, we realize that the central pair is not made out of single
integers, but out of "clumps" or "chunks": it consists of two copies of
the unit "789". We can restructure L for the eye this way:
L: 1 2 3 4 5 6 (789) (789) 6 5 4 3 2 1
Now the answer seems glaringly obvious: 6. On the other hand, maybe we
were supposed to get the hint proffered us so generously by the central pair.
And what was that hint? Obviously, that we are supposed to perceive the
WHOLE SEQUENCE in triples, not just the center! In which case, L reparses
into:
L: (123) (456) (789) (789) (654) (321)
Now the answer should be obvious -- except we are still left with a minor
dilemma. Do we take the President's righthand wife (654), or his lefthand
wife (456)? First-come-first-serve chauvinism (or is it left-to-right
chauvinism?) would seem to say that it's just too bad for 654 -- she got
there too late.
Here is an innocent-seeming puzzle that points to still more complex
issues:
M: 1 2 3 4 5 7 7 5 4 3 2 1
!
- 12 -
The way I see it, a very defensible answer might be 6. Someone might object,
"6? But it's not even there!" True, yet it is conspicuous by its absence.
The 4 in A precedes the 5 not only typographically, but also in the abstract:
4 is the numerical predecessor of 5. And what is 5, in A? It could be seen
either as the maximum in A, or as the number forming the central pair of A.
Both carry over to M, yielding 7. Now if you choose to see 4's role in A
abstractly and arithmetically, rather than concretely and typographically,
you can carry your vision directly over to M. Then candidate 6 must be
considered a strong competitor to 5, whose candidacy is based principally
on its position in M and not so much on its magnitude.
This example opens up a whole world of LEVELS OF ABSTRACTION in the
perception of structures. To illustrate it just very briefly, let me propose
the following structures:
N: 1 2 3 4 4 4 5 6 7 8 9 9 8 7 6 5 4 4 4 3 2 1
O: 4 5 5 3 5 5 5 5 5
and the associated puzzle: "What in O plays the role that 6 plays in N?"
Now the numeral "6" occurs twice in N but seems to play no salient role.
As a numeral in N, "6" has no outstanding characteristic, so on first sight
it seems hard to export. However, 6 enters into N's structure in another
way, and a salient one, at that. One of N's most salient features is its
large number of 4's -- in fact, 6 of them. So 6, in its capacity as a
COUNTING NUMBER rather than as a NUMERAL, plays a distinguished role in
structure N. Can we export this role to O?
We have to decide how to characterize (in an exportable way) what it
is that 6 is counting. Saying "the number of 4's" seems a little parochial,
to say the least. Perhaps a better way to see it is as "the number of
occurrences of the most frequent term". After all, 4 is salient in N only
through being so common. This leads us to see 5 in O as playing the role
of 4 in N. Therefore the counterpart of N's 6 would be the number of 5's
in O, namely 7 -- another "invisible" answer, in that it doesn't appear
as a numeral in N.
But it is rather narrow-minded to insist on a big distinction between
being present as a numeral and being present in the more abstract sense --
as a counting number. To put it another way, 7 is invisible in O only if
you think of vision as having no COGNITIVE component -- all we can perceive
is numerals. But this would be very short-sighted. In fact, with our eyes
we are constantly "seeing" abstract qualities. When we look at a television
program, we see more than the dots -- we see people. When you come down to
it, we don't see the dots at all -- we see ONLY people. Somewhere, deep
down in the processing, of course there are components of our visual system
where the dots themselves are "seen" as dots -- but strangely enough, we
would hesitate to call what retinal and other cells do "vision". Vision
implies going BEYOND the obvious visual level. We can "see" that a certain
chess position is ominous, that a certain painting is by Picasso, that
someone is in a bad temper, and so on. In this sense, in which vision
is imbued with a cognitive component, 7 is directly visible in O!
!
- 13 -
By the way, I carefully drew up N so that 6 would appear as a numeral
in it as well as counting the number of 4's. This threw in a kind of
complicating factor, something that one just had to ignore. I could have
made N contain 12 4's, in which case 12 would have "appeared" in N only at
the abstract level of COUNTING NUMBER and not as a NUMERAL. But real life
is seldom so clean. For instance, in thinking about the question "Who is
the Nancy Reagan of England?" you might have felt that this is much harder
than the question "Who is the First Lady of England?", because you may attach
certain uniquely personal qualities to Nancy Reagan, over and above seeing
her as the First Lady of the United States. Think if I had asked for "the
Eleanor Roosevelt of England". Or, turning the tables, who is the Moshe
Dayan of the U.S.? I am almost tempted to say "Douglas MacArther" -- like
Dayan, a famous and successful general and a controversial political figure
-- but damn it all, MacArthur had two eyes! Dayan's patch is perhaps his
most memorable feature.
What happens if you go back and ask, for each structure presented
so far, "What here plays the role of 6 in N?" You will find yourself
discovering new ways of perceiving those earlier structures, simply under
pressure of this new role. Note that superficially, A and N look fairly
similar, so it is surprising how different it feels to map them both onto,
say, J or K. You will go back and "see" those old structures through new
eyes (or perhaps new glasses).
I leave a few challenging examples for you to map onto A and N:
P: 5 4 3 2 1 5 4 3 2 1
Q: 1 2 3 4 9 8 7 6 5 4 3
R: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 1 2 1 7 6 5 4 3 2 1
S: 1 2 3 4 1 2 3 1 2 1 2 1 3 2 1 4 3 2 1
T: 2 1 1 2 2 1 2 2 2 2 9 1 2 3 2
You might enjoy making up some examples of your own that lead a solver to
further unexpected modifications of the perceived role of 4 in A. Can you,
for instance, manufacture an example in which it becomes reasonable and not
narrow-minded to perceive 4 as A's fourth element?
One of the purposes of these puzzles has been to dispel the notion
that the full, rich, intuitive sense of a role, such as that of 4 in A
or that of "First Lady", can be easily captured in words. In fact, it
might be more accurate to assert quite the contrary: that precisely in
its nonverbalizability resides its fluidity, its flexibility. This is
an important idea. Consider how you would try to capture in some phrase
the precise way that you see what 4 is "doing" inside A. No matter what
you say, someone will be able to concoct another example in which your
description does not allow a person to predict what you will perceive
as analogous to 4. An English phrase is like a snapshot that gives
!
- 14 -
a perfect likeness at one moment in time, but fails to show how things
can slip and move. There is something much more fluid in the way that
a mind represents the role internally. Various features are potentially
important in defining the role, but not until an example comes up and makes
one explicit does that feature's relevance emerge.
Puzzle J, for example, showed how the REGULARITY of the descending
part of A could be highlighted and made significant. It made the righthand
"wife" of the "President" in J seem to please us more than did the lefthand
"wife". It is hardly likely that anyone would anticipate such a maneuver
in trying to say what 4 seems to be doing in A. Puzzle K depended on the
separation of the two 4's by two other elements, and nothing more -- another
unexpected twist. The same kind of thing arises when the "First Lady"
concept is stretched. Just how far can it stretch? When does it begin
to go beyond the bounds of credibility?
We are carrying out comparisons all the time. It doesn't seem
particularly noteworthy when someone walks into your kitchen for the
first time and says, "I like the way your kitchen is laid out better than
the way mine is. My kitchen has windows over THERE and the stove is right
HERE, so it's less convenient and the light isn't so good in the morning."
Clearly, the words "here" and "there" conceal implicit mappings of the two
kitchens. Words like "this" and "that" and phrases like "that sort of thing"
are even better at picking up intangible, flexible, implicit meanings that
can be transported across situations differing widely from each other.
Right now, it seems that what artificial intelligence needs is a way
to go beyond "delta function" programs -- programs that are virtuosos in
a very narrow domain, but which have no flexibility or adaptability or
tolerance of errors. It seems that a careful study of judgmental processes
in even such a simple domain as these curious number analogies would afford
fascinating insights into how programs might be made to approach the
flexibility and generality of our own minds.
To show what I mean, I would like to close with the verbatim transcript
of a conversation that I had recently with a friend. It ran this way:
Friend: Last Friday afternoon, I was over at the Poobah Club listening
to a piece on the radio that I was just SURE was Shostakovich. When
it ended and they announced it, sure enough, it was! I was so pleased,
because that sort of thing has only happened to me a couple of times in
my life!
Me: You mean, being at the Poobah Club and hearing a piece on the radio
that you think is Shostakovich on a Friday afternoon?
Friend: You're so DENSE -- when those Scientific American people hear about
that, they probably won't want you to write any more articles for them.
Me: Yeah, I should have known that it didn't have to be on a Friday
afternoon.
Friend: You should have known that it didn't have to be Shostakovich!
!
- 15 -
Quite coincidentally, a recently perfected natural-language program
called "CORTEX" happened to be eavesdropping on us, and just couldn't resist
chiming in at this point, saying, "Oh, say, that reminds me -- something
REALLY similar happened to me the other day. I was at a club whose name
begins with a "P", and the water cooler broke. Ain't that something!" I've
forgotten just how CORTEX went on from there, but you can see how keenly it
had sifted all irrelevancies out and gotten straight to the gist of my
friend's remark. Now THAT's the kind of AI program we should have more of!
-------
---------------
-------
∂16 Jun 1981 1537-PDT CSD.HOFSTADTER analogies, etc.
To: csd.greiner
Russ --
I never met Lindsey Darden. I'd be interested in browsing through
the ANALOG file at Sail, but I'm a little overburdened with mail of one
sort or another, so I think I'd rather not get put on the mailing list.
Now you asked about sending my analogy paper around to the analogy people.
It will appear in the September issue of Scientific American, which comes
out in mid-August, so if it's not too long to wait, I'd probably prefer
that, simply because it would make me feel a little uneasy to have something
making the rounds on the Arpanet without my knowing quite where it's going,
or to whom. On the other hand, if you want to show it to just a couple of
people (making it clear that it is not to be distributed further), I see
no reason not to do that.
Gray tells me that you wanted to get together and talk sometime. I'd
enjoy that. Probably some afternoon next week would be good (maybe Tuesday
June 23?). Why don't you send Gray or me a message? By that time, my other
student Marsha Meredith ought to be here, and I think she'd very much enjoy
such a get-together. Maybe we could include Steve Tappel as well, with whom
Gray and I have been talking occasionally.
-- Doug H.
-------
---------------
∂17 Jun 1981 1357-PDT CSD.GREINER Re: analogies, etc.
To: CSD.HOFSTADTER
cc: CSD.GREINER
In-Reply-To: Your message of 16-Jun-81 1537-PDT
Doug --
Yes, let's meet this Tuesday. For lunch; or afterwards?
Steve and I have talked a little -- he's of course welcome to join in.
I forwarded a copy of your Analogy paper to only one person --
Mike Genesereth, the fellow who told me about its existence in the first
place. I guess I'll send a short comment to other members of the
BB, advising them to see S.A. this September; and leave it at that.
The titles of your various files on SCORE and SAIL are intriguing --
do you mind if others examine their (respective) contents?
(SAIL's general policy is that any unprotected file is in the public domain
-- as anything considered personal can be readily read-protected.
I didn't know whether you'd been following this policy or not...)
Anyway, I look forward to seeing you and your clan this Tuesday.
Russ
-------
∂18 Jun 1981 1557-PDT CSD.HOFSTADTER tuesday
To: CSD.GREINER
How about meeting, say, at 2:00? We could meet wherever Gray's and my
office is (Gray and me's office?) -- I can't remember the number, but
I think you know where it is... I'm glad you forwarded it to Genesereth.
Would he like to talk these things over sometime too?
As for my files on Score and Sail -- it seems to me that everything
at Score is highly protected as a default option. Sail I knew was rather
open, just like IMSSS, where I wrote GEB. However, the convention at
IMSSS was that, although everything was unprotected, it was pretty unkosher
to read other people's things without having some sort of explicit agreement
with them. At least that's how I thought of my directory there, since I
often had some extremely personal files that I would never have wanted
anyone to read. I don't think I have anything very personal on Sail or
Score these days. Anyway, you're welcome to read whatever you find there.
(Most likely at Score you won't be able to access it, of course.)
See you Tuesday at 2:00?
-- Doug
∂22 Jun 1981 1557-PDT CSD.HOFSTADTER meeting
To: csd.greiner
Russ -- Gray's parents arrived in town and Gray is going to be
occupied all day Tuesday. Why don't we postpone our meeting
'til, say, Friday afternoon at 2? Is that OK? Sorry for the
delay.
-- Doug H.
-------
∂22-Jun-81 1703 CSD.GREINER at SU-SCORE Re: meeting
To: CSD.HOFSTADTER at SU-SCORE
cc: rdg at SU-AI
Ok - see you Friday @ 2.
Russ
-------
∂To DARDEN@SUMEX 16:00 22-Jun
How is an Analogy like a Printing Device?
Lindley -
[I spent a while trying to find some connection between
Printers and Analogies -- to be used as a cute heading for this message --
and came up blank. Is it possible there really are no other such
inter-relations, besides their co-occurance in this message? Anyway...]
I just heard you were shopping for a cheapie printer. While I
know very little about such devices, I do know that Horace Judson is
also searching for a full, stand-alone text-editing system, capable of
producing hard-copy output. If I find out what he decides on, I'll
forward it to you.
The time has come to begin serious thinking on thesis topics;
and analogy looms prominently in my unfortunately-still-preliminary
set of ideas.
I'll send you a long message outlining a proposed
research programme, (if and) when I finish concocting it.
Hope all is well there. Any word on your next trip to this part of the world?
Take case,
Russ