COMMENT ⊗   VALID 00011 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.DEVICE XGP
C00003 00003	.COMMENT Primes
C00004 00004	.COMMENT Extreme sets of nos
C00005 00005	.COMMENT chain of discoveries
C00006 00006	.COMMENT 3 tasks
C00007 00007	.COMMENT Given core, and Facets
C00009 00008	.COMMENT 2 kinds of operators
C00011 00009	.COMMENT Control
C00013 00010	.COMMENT Sys Results
C00014 00011	.COMMENT Sys Results
C00015 ENDMK
C⊗;
.DEVICE XGP
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.TURN ON "↑α[]↓_π{"
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.PREFACE 2
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.PREFACE 1
.!XGPLFTMAR←100
.MACRO B ⊂ BEGIN NOFILL SELECT 9 INDENT 0 GROUP PREFACE 0 MILLS TURN OFF "{↑↓}[]α" ⊃
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.SELECT 1
.COMMENT Primes;
.GROUP SKIP 20
.BEGIN CENTER SELECT 2

A natural number p is ↓_prime_↓ 

iff

its only divisors are 1 and p.

.END
.SKIP TO COLUMN 1
.COMMENT Extreme sets of nos;
.BEGIN CENTER SELECT 2 TURN OFF "{}"
.GROUP SKIP 2

Numbers having no divisors
{ }

Numbers having only 1 divisor
{ 1 }

Numbers having only 2 divisors
{ 2, 3, 5, 7, 11, 13, ... }

Numbers having only 3 divisors
{ 4, 9, 25, 49, 121, 169, ... }

Numbers having only 4 divisors
{ 6, 10, 14, 15, 21, 22, ... }
.END
.SKIP TO COLUMN 1
.COMMENT chain of discoveries;
.BEGIN CENTER SELECT 2 TURN OFF "↑↓" PREFACE 0
Discovery of Prime Numbers
|	
|	
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⊗7Look at extrema⊗*
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Discovery of Divisors-of
|	
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⊗7Look at inverses⊗*
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Discovery of Multiplication
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 .........

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⊗4(BASE OF KNOWN   CONCEPTS)⊗*
.END
.COMMENT Overlay onto this a slide of spreading-out lines going upward;
.COMMENT Overlay onto this a slide of diff-colored nodes/ops, to repr heurs.;
.SKIP TO COLUMN 1
.COMMENT 3 tasks;
.GROUP SKIP 4
.ONCE CENTER SELECT 2
↓_To form new theories:_↓

.BEGIN SELECT 2 PREFACE 2 INDENT 20 SKIP 4


1) Starting knowledge
2) Legal operators
3) Heuristic strategies

.END
.SKIP TO COLUMN 1
.COMMENT Given core, and Facets;
.BEGIN SELECT 7 PREFACE 0 TABS 35 TURN ON "\"

.ONCE SELECT 2
↓_Initial Concepts_↓\   ↓_Facets_↓

OBJECTS\Facets which ⊗4characterize⊗*
Structures\Name(s)
Lists\Definitions
Sets\Algorithms
Bags\Domain/Range
Ord-pairs\Abstract representations
Ordered-sets
Constants\Facets indicating ⊗4ties⊗*
Variables\Specializations
Atoms\Up (things this concept IS-A)
Conjectures\Generalizations
Theorems\Examples
Counterexs\Ops one can do to this concept
Examples\Ops resulting in this concept
Analogies\Analogies to this concept
Theories\Conjectures involving it
Relation
Operation\Facets containing ⊗4heuristics⊗*
Predicate\Worth of this concept
\Ways in which it can be Interesting
ACTIVITIES\How to fill-in
Compose\How to check
Insert\Rules for suggesting new jobs
Delete
Union
Intersect
Substitute
Repeat
Reverse-ordered-pair
Disjoin
Conjoin
Negate
Imply
Set-equality
Containment
Assume
Deduce
Cases
Isomorphic
Homomorphic
Canonical
Check
Fill-in
.END
.SKIP TO COLUMN 1
.COMMENT 2 kinds of operators;
.GROUP SKIP 2
.ONCE CENTER SELECT 2
↓_Fill in a blank facet_↓

.BEGIN SELECT 7 PREFACE 0 TABS 50 TURN ON "\↑↓_"

⊗2   ↓_COMPOSE_↓⊗*\⊗2   ↓_COMPOSE_↓⊗*
Definition:\Definition:
Domain/Range:\Domain/Range:
Algorithms:\Algorithms:
Examples:\Examples:
Up isa:\Up isa:
Generalizations:\Generalizations:
 ...\ ...

.GROUP SKIP 4
.ONCE CENTER SELECT 2
↓_Blow up a facet into a whole new concept_↓


⊗2   ↓_COMPOSE_↓⊗*\⊗2↓_Union⊗7↑o⊗*Complement_↓⊗*
Definition:\Definition:
Domain/Range:\Domain/Range:
Algorithms:\Algorithms:
Examples:\Examples:
Up isa:\Up isa:
Generalizations:\Generalizations:
 ...\ ...
.END
.SKIP TO COLUMN 1
.COMMENT Control;

.ONCE CENTER SELECT 2
↓_Control Structure_↓

.BEGIN SELECT 7 TABS 15,25,48  TURN ON "\↑↓←\" PREFACE 0


↓_⊗4AGENDA⊗*_↓ OF THINGS WORTH DOING

⊗4(Fill in Generalizations facet of Equality concept)⊗*
\\Priority=700 
\\Reasons=((Equality is rarely satisfied) 
\\          (No known genls of Equality))

⊗4(Fill in Examples facet of Primes concept)⊗*
\\Priority=400 
\\Reasons=((No known exs of primes yet))

⊗4(Fill in new Algorithms for Compose concept)⊗*
\\Priority=300 
\\Reasons=((Empirical: taking too long))


.GROUP SKIP 7



REPEATEDLY:
	1) Select 1 job from the agenda
	2) Assemble relevant heuristics
	3) Execute them
.END
.SKIP TO COLUMN 1
.COMMENT Sys Results;
.GROUP SKIP 7

.BEGIN SELECT 2 CENTER  TURN ON "\↑↓←\" PREFACE 0

Set-equality ⊗4(given concept)⊗*
↓
Same-length 
↓	
Numbers
↓
Multiply
↓
Divisors
↓
Primes
↓
Unique factorization
.END
.SKIP TO COLUMN 1
.COMMENT Sys Results;
.GROUP SKIP 6

.BEGIN SELECT 2 NOFILL  TURN ON "→↑↓←\" PREFACE 0








 

 
→Maximally-divisible
→numbers 
 
.END
.SKIP TO COLUMN 1