Streamlining Python Development: A Guide to a Modern Project Setup
100705 pres kr agi count montag_ahmds
1. Psychologically Informed Aspects
of a
A General Mechanism of Intelligence
Presentation for
Aspects of Knowledge Representation in Artificial General Intelligence
2010
Benjamin Angerer, Stefan Schneider
2. A predecessor to AGI... A. Newell und H. A. Simon (1961)
GPS, a program that simulates human thought
idea:
a general problem solver
user defined rules & objects
program generated heuristics …
applicable to formalised problems
General Mechanism of Intelligence
problems:
generating representations/concepts doesn't work
only applicable to manually pre-formalised problems
consequences:
expert systems
SOAR – architecture is a follower
3. How we try to find this/these mechanism(s)?
- Developmental psychology:
- Looking at how abilities develop may give insight into how they work
4. How we try to find this/these mechanism(s)?
- Developmental psychology:
- Looking at how abilities develop may give insight in how they work
- Theoretical psychological and philosophical analysis:
- What has to be possible; how can't it be under any circumstances ...
- e.g. infinitely many representations of individual numbers
5. How we try to find this/these mechanism(s)?
- Developmental psychology:
- Looking at how abilities develop may give insight in how they work
- Theoretical psychological and philosophical analysis:
- What has to be possible, how can't it be under any circumstances...
- e.g. infinitely many representations of individual numbers
- Problem-solving tasks / Interviews with students:
- observing people solving problems and coming up with solutions
- esp. the structure of their argumentation & justifications
7. COUNT
STUDY PROJECT
Sven Spöde Stefan Schneider Benjamin Angerer Alexander Blum
sspoede@uos.de stefschn@uos.de bangerer@uos.de ablum@uos.de
8. COUNT
STUDY PROJECT
If we do not want to believe that ideas are innate
or God-given, but the result of subjective
thinkers' conceptual activity, we have to devise a
model of how elementary mathematical ideas
could be constructed – and such a model will be
plausible only if the raw material it uses is itself
not mathematical.
(Glasersfeld, 64)
10. COUNT
STUDY PROJECT
Why numbers?
- development starts early, lasts long, results in complex & abstract concept
11. COUNT
STUDY PROJECT
Why numbers?
- development starts early, lasts long, results in complex & abstract concept
- numbers are used in diverse contexts (without “real meaning” in themselves)
12. COUNT
STUDY PROJECT
Why numbers?
- development starts early, lasts long, results in complex & abstract concept
- numbers are used in diverse contexts (without “real meaning” in themselves)
- numbers are clearly definable and less fuzzy than most abstract philosophical
concepts
14. COUNT Piaget
STUDY PROJECT
sensorimotor “schemas”
SENSOR
SCHEMA
MOTOR
ORGANISM ENVIRONMENT
15. COUNT Piaget
STUDY PROJECT
“schemas” in general
1 2 3
situation, action, expectation
context operation of result
S
SCH
M
16. COUNT Piaget
STUDY PROJECT
“schemas” in general
1 2 3
situation, action, expectation
context operation of result
Assimilation: grasping of “new” observations as
repetition of sth. already known,
“Integration” through existing schemas
S
Accommodation: Adaptation of schemas
after unsuccessful SCH
assimilation,
“Differentiation” M
21. COUNT
STUDY PROJECT
Clearly, in the head we do not have every number (infinite instances) re
ave procedures to operate with them. So whenever I face a number symbol
number concept
23. Abstraction
psychological ideas
What is being abstracted?
regularities of own actions (not of individual
objects), such as
repetition
rhythmic order
successor relations
25. Encapsulatio Generalisatio
Extraction Coordination
n n
extension of the
extraction of applicability of a
aspects schema
→ assimilation
compositionality principle a well-known schema might
→ new structures become encapsulated into
composed of older ones an object (of another
schema)
26. Encapsulatio Generalisatio
Extraction Coordination
n n
the properties of some task or situation that one extracts
→ what can be done in a certain situation
(think of functional fixedness)
one understands only according to the schemas one already
possesses
thus, extraction is the assimilation of a context through
activation of applicable schemas
extraction / assimilation can take place both on external
circumstances and on internal reflection
an external situation is perceived as “such and such”
in thinking, one realises (extracts), that for some
circumstances a certain schema is applicable
extraction can thus also be thought of as the discovery of an
analogy
27. Encapsulatio Generalisatio
Extraction Coordination
n n
bring schemas in a certain order
possibly resulting in a coordination that solves a problem
temporal order
hierarchical order?
compositionality principle → new schemas out of older
schemas
what guides coordination?
task
every structure might be able to guide the assembly of
others
28. Encapsulatio Generalisatio
Extraction Coordination
n n
encapsulation allows schemas to be grounded
through generating more and more abstract schemas
which only if necessary have to be executed (or filled with) in
detail (if they still can)
through encapsulation coordinated and generalised schemas
can be treated as a single, new schema
this new schema can then be used by other schemas (e.g. in a
coordination process)
29. Encapsulatio Generalisatio
Extraction Coordination
n n
“das geht ja immer” - “that works in all cases”
realising that an operation is applicable to a whole class of
objects or circumstances or
realising that a number of operations is essentially the same
assimilation context → generalising the applicability of a
schema
expectation context → generalising output to a class – e.g.
a number, not a specific number instance
operations → does the operation change through a
generalisation?
(in analogy to functions:) a mapping from an (intensionally
defined!) class to another (intensionally defined) class
→ necessary for encapsulation
30. experimental investigation
Can these principles actually be observed?
How do they work / intertwine in detail?
Are there other mechanisms that play a role in abstraction?
34. experimental investigation
What can be observed in these interviews?
- genesis of schemas
- many people only use the base system without being able to explain it,
therefore some insight in learning something “new” is possible
35. experimental investigation
What can be observed in these interviews?
- genesis of schemas
- many people only use the base system without being able to explain it,
therefore some insight in learning something “new” is possible
- through obfuscation of the numerical representation subjects have to
discover that the constructed sequence is a numerical one at all (takes
surprisingly long)
37. experimental investigation
Points of interest:
- the problem with “0”:
Subject 1:
[3:35] “ 'A' may be zero...”
.
.
. [What is D°D?]
[6:28] “We have to count on D times from D”
counts with fingers: “A,B,C,D”
“So D and then 4 more”
(…)
[6:53] “So, it has to be BD.”
38. experimental investigation
Points of interest:
- generating successors with a general production rule
Subject 1:
[26:00] [given sequence: A,C,BA,...?]
“Seems to be every other number, so
BC”
“Then CA,CC,DA,DC,BAA,BAC,BBA,BBC...”
[27:20] [given sequence: B,D,BB,...?]
“BD,CB,CD,DB,DD,...”
[Why?]
“It's °C, that's leaving one out, that is easy.”
39. experimental investigation
Points of interest:
- generating successors with a general production rule
Subject 2:
[0:20] [given sequence: A,B,C,D,BA,BB...?]
“BC,BD”
[Then?]
[1:10] “We left out A in the 2nd place, so we should
skip C, so DA?”
[And what do we do after DD?]
“We could use E,F,G,H and do the same:
E,F,G,H,FE,FF,FG,FH,HE,...”
40. experimental investigation
Points of interest:
- justification through analogy to base 10:
Subject 1:
[3:35] [What after DD?]
“BAA.”
[Why?]
“DD is like '99', so we have to go on with
'100', which is BAA.”
41. experimental investigation
Points of interest:
- transferring into base 10 before operating and then back again:
Subject 1:
[09:50] [CA°CC?]
“EC.”
[10:20] proposes to “decode” the numbers
“CA is 3 times the 4 digits,so 9.
“CC then is 9+2, so 11.
9+11 is 20,
18 is the nearest factor of 3 to 20, so we
need the 6th letter of the alphabet... No, can't be.”
(…)
[12:40] “BAC!”
“E would have been 4, but here BA is 4,
just written as 'ten' in the decimal system '10'.”
42. experimental investigation
Points of interest:
- operating with numbers:
Subject 1:
[17:30] [What is C°C°C?]
“C°C is … (counts with fingers) BB, no, …
C is 2,and 2 more is BA,
and BA°C is BC.”
43. Wrap Up
Encapsulatio Generalisatio
Extraction Coordination
n n
prioritised schemas in extraction
parametrisation: coordinating schemas - one using the other/s as a
regularity according to which it is applied
coordination requires encapsulation (such that schemas can get
used by another schema)
encapsulation requires generalisation
input / output is generalised to classes
44. Wrap Up
Encapsulatio Generalisatio
Extraction Coordination
n n
it does not suffice that an analogy is noticed
transfer requires attention
distinction btw. domains might eventually fall
competence in a domain, besides understanding the basic
principle (e.g. generating successor) also means possessing a
bag of tricks: shortcuts, strategies, …
it is reasonble to think that the “pure” principle is an abstraction
of the formerly learned everyday tricks
- x: a ~ 0, - x: d steps - makes one for A too → error (A is starting point) conclusion: → discovering an analogy doesn't automatically transfer all functionality of the source domain → one has to conceive of how to transfer it explicitly (in respect to pt. 2 of the schema; building a prosthesis for the target domain)
- “leaving one out” is prominent (and inherent to the sequence) (X) - the successor schema works very well already for this sequence; and is being parametrised to leaving one out and different starting points - such a parametrisation is a form of coord . (and as such the underlying schema has to be already encaps)
- A->D lex. order; bA, bB → bC, bD (still lex.) - skipping A becomes important → most regular system for skipping is turntaking (for him) → generalisation to 4-letter-clusters conclusion: - there are such things as prioritised schemas (skipping), regularities are searched in respect to this (as opposed to others)
→ D is like 9 insofar as both are the highest number of one digit in their respective base systems → regularity as commonality → justification through reference to analogy
→ building succ.; alphabetic vs. numerical → in a base system digits can be calculated seperately (uses algorithmic strategy) → c ~ 2 is prominent → “ 3x4 iterations of abcd and then the first is 9 → div. by 3 because d~3 and last nmb. → in the end: analogy (BA ~ 10)
→ bag of tricks! → div&conq → A->C (A is “empty”) → good application of tricks that subj knows from “normal” numbers → these tricks do essentially contribute to number understanding / competence (e.g. times BA → xxxA) → domains are smorgasbords of tricks → analogy transfer from one domain to the other might bring along tricks (question?)
