COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.S(Questions and Answers)
C00009 ENDMK
C⊗;
.S(Questions and Answers)

.BEGIN NOFILL


(1) Contribution  to  knowledge?   Using the  historical paradigm  of
heuristic  search  to automate  some  of the  activities  involved in
developing  new  math  theories:  directing  attention  to  plausible
concepts to investigate, finding the desired empirical data, inducing
new   concepts   to  study   based   on  the   results   of  previous
investigations.


(2) What exactly are the primitives of AM's behaviors?  AM can define
new concepts by  joining or modifying defns of existing concepts.  AM
can use the heuristic rules it  possesses to fill in new entries  for
concepts.  AM  can itself suggest new  tasks for its own  agenda.  AM
can  modify facets (e.g., Worth ratings),  print messages, prune away
losers, etc.    This  is such  a  universal  set of  behaviors  that,
unconstrained,  it   has  little  to  do  with   math  research.  The
plausibility constraints (heurs) give it its character.


(3) What is another use for the heuristic rule which says...
	Look at f↑-↑1(b):
		groups with very few subgroups;
		maximally-divisibles;
		f=divisors-of, b=tripletons: result is a kind of squares;
	Generalize f if very few examples:
		Congruence→Similarity;
		Reverse-all-levels→Reverse-top-level
		Perfects→Multiply-perfects


(4)  Explain the  intu's,  their failure,  etc.   These  were  opaque
(uninspectable by  AM) functions which were simulations of real-world
scenarios: seesaws, elevators,  archery, etc. AM  was supposed to  be
able to analogize between various  concepts and certain intu's (e.g.,
set(ops)  and Venn diagrams). Unfortunately,  this contained too much
pre-programmed help (e.g., all  the Venn relationships are  true, and
they are too  easy to get that way;  OR: See-saws are anti-symmetric,
and that relation is too easy  to get from Seesaws). It wasn't  fair:
no relations/connepts were  disccvered which the user  hadn't forseen
at the time the  intutions were coded.  So they were all excised, and
not used to make any of the discovereis mentioned herein.


(5) 4 ways to get Multiplications:
	Repeated +
	Analogue to cross-product: Count(AxB)= [Count(A) ? Count(B)]
	Power sets of union: Count(2↑[A∪B]) = [Count(2↑A) ? Count(2↑B)]
	Subst A for each element of B, then apply Union to the result.

(6) What does "A. M." stand for? SAM slide: Jim Guard and Eastman.

(7) Uses for AM: 
	The heuristics themselves:
Everything that AM does can be viewed as testing  the underlying body
of heuristics.   If AM ever succeeds in a big way, then it might be worthwhile
teaching these heuristics explicitly to math students, just as it might
be a good idea for medical students to learn MYCIN-like rules.
	AM itself: get people interested in math, give them a feel for research
	Existence of AM: feasibility of automating this kind of process using Heur search
	Actually constructing  a computer model of this activity has provided
an  experimental  vehicle for  studying  the  dynamics  of  plausible
empirical  inference.



.END

Suggestions from EAF:

Don't try to  defend AM as the  right way to automate  math research;
rather,  defend  it  as  a  continuation  of  a  historical  line  of
application programs,  using  heuristic search  to  automate  various
aspects of research in assorted sciences. There are some new wrinkles
(agenda,  large body of heuristic plausible move generators, allowing
the system  to  define new  concepts  and explore  them, to  give  up
whenever  it wanted to,etc).   Defend  on the  basis of  merely ↓_A_↓
contribution to knowledge, not THE answer to everything.

Emphasize that heuristic search will cause AM to explore a few narrow
ribbons of chanins of discoveries. Vast  amounts of valuable concepts
will  be missed in this  way, but it  is ONE way to  beat the combin.
explosion.   Even  so, we  saw a  minor  explosion of  red  heuristic
arrows! Alternate schemes  (e.g., mutate and select)  might work, but
they are different:neither better nor worse.