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C00002 00002	Professor Feigenbaum has  given you  a good feeling  for what  rule-guided
C00012 00003	2  PROPERTIES  OF  "DISCOVERY  TASKS"
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Professor Feigenbaum has  given you  a good feeling  for what  rule-guided
expert reasoning systems are  about: their design and  the scope of  their
applicability.  He  has  really  presented  to  you  a  whole  "theory  of
intelligence" in a nutshell <<SL: 3 parts>>; that theory says:

1. Human cognitive tasks can be cast as searches, as explorations wandering
through some problem space, usually toward some goal.

2.  We are guided in these searches by a large collection of informal
rules of thumb, which we call heuristic rules, or just heuristics.

3. We access relevant heuristics in each situation, and follow their advice.

Intelligence is the ability to zero in on a solution effectively, despite
the apparent size of the search space.

That's it.  It  sounds plausible; in  fact, it sounds  trivial.  And  yet,
when we  went off  and  built prgrams  embodying  this theory,  they  were
capable of expert performance at many tasks.

One of the big surprises was  that this very same methodology is  adequate
not only  for  scientific  problem  solving,  but  for  scientific  theory
formation -- for DISCOVERY tasks  -- as well.  And  that's what I want  to
talk about now.

There are two  main properties  of discovery  that I  want to  communicate
today: <<SL: 2  aspects>> First,  it is MECHANIZABLE.   We've coded  rules
which can guide a program as it explores some scientific domain,  defining
new concepts, gathering empirical data, conjecturing relationships in that
data.  Building and running such programs takes this investigation out the
realm of philosophy and psychology, and makes "the art of discovery"  into
an empirical science.

Second, discovery is UBIQUITOUS.  The same knowledge that guides you <<SL:
6 boxes>>  to find  a stairway  in an  unfamiliar building  can guide  you
effectively in defining a promising new mathematical function.

Let's look at  this "ubiquity"  in more detail,  then we'll  come back  to
mechanizability at the end.

<<SL: Hier.  of heurs>>  Bear in  mind  the heuristics  are not  rules  of
inference, but rules of thumb.  They don't guarantee to preserve anything,
the way Modus Ponens preserves  validity.  They suggest plausible  avenues
to consider, and prune away implausible  ones.  As we see here, the  rules
appear at many levels of generality.  Some  of them are relevant in all  6
cases we considered before, some are quite specific to a particular field:
they  are  the  repository  of  domain-dependent  expertise  as  well   as
domain-independent "common sense".

At first glance, each heuristic seems to have its own sphere of influence,
its own  little domain  of relevance,  outside of  which it's  useless  or
meaningless.  A rule that  talks about E. Coli  can't have any bearing  on
math research, can it?

If we look a little  closer, we see that  the heuristics can be  organized
nicely  into  a  generaliztion/specialization  hierarchy.   For  instance,
"Study gene control signals across species of bacteria" is a special  case
of "Study biol. mechnisms across  species boundaries", which is a  special
case of "Study the scope of a  natural phenomenon".  In that way, it  does
make sense to talk about the first cousin of that E. Coli rule being  some
math   heuristic.    Mathematicians   have   their   stock   of   favorite
counterexamples, just as  geneticists have their  Drosophila and E.  Coli,
and for the same reason: this general rule here: "In a new task, it  helps
if your tools and subtasks are VERY familiar".

What I'm claiming is  that the relevant heuristics,  as a function of  the
task they're being applied to, is a CONTINUOUS function.  If you jump from
one task  to another  far away,  it appears  that the  knowledge you  need
changes completely.  But if  you deform the  first task continuously  into
the second, the heuristics will deform continuously also.

The molecular geneticist  sits down to  plan an experiment,  say where  he
wants to transfer a gene from one bacteria to another. The first thing  he
does is to ignore  the minor experimental steps,  and build up a  skeletal
plan.  That wisdom is not  unlike the knowledge you  and I would bring  to
bear when  faced  with planning  not  a  genetics experiment  but  a  long
automobile route: we would pull out a  map and first ignore all the  minor
roads.

<<<Everyday invention section of Ubiquity of Discovery>>>

<<<Scientific invention section of Ubiquity of Discovery>>>

<<<Judging sci. interest section of Ubiquity of Discovery>>>

This heuristic appears in texts on evaluating art and literature as  well:
If 2  aspects of  a work  were  perceived as  distinct, but  are  suddenly
revealed to be related, then that's interesting.  Charles Disckens  relies
on this heavily, when characters turn out to coincide late in each  novel;
Escher's art is dominated by this as well.


Enough about UBIQUITY; let's discuss the MECHANIZABILITY of discovery.

We built a program, AM, which had the definitions of a hundred finite  set
theory concepts <<SL: concepts>> and a couple hundred heuristics, lik  the
ones displayed up here.  Among  other discoveries, AM came across  natural
numbers.  Using the same line of resoning we did, AM defined prime numbers
and found out a few interesting things about them.



<<<Subset of the AM & Eurisko sections of Ubiquity of Discovery>>>

What we've learned from AM is guiding our current effort to write a program
which discovers new task-dependent heuristics as well as new concepts.  It's
method is to represent each heuristic as a full-fledged concept, with slots
for its definition, origin, generalizations, and so forth.  Other heuristics
can then operate on it, just as they would on any math concept.


We'll probably be working on this problem of "meta-heuristics" for a while
longer, but I'm  still very excited  about it: as  this presentation  must
have made obvious to you, I never met-a-heuristic I didn't like.

2  PROPERTIES  OF  "DISCOVERY  TASKS"



		MECHANIZABILITY
		

		UBIQUITY