Tutorial at Diagrams 2018 -- Monday June 18th: 14:00-15:30
http://www.diagrams-conference.org/2018/
Were "Super-Turing" diagrammatic reasoning competences
ancient products of biological evolution?
Alternative, shorter title:
Evolved "diagrammatic" spatial intelligence.
PRESENTER Aaron Sloman
http://www.cs.bham.ac.uk/~axs/
School of Computer Science, University of Birmingham
-
Introduction.
-- Audience Composition
-- Audience views
-- The current state of AI
-- What's missing?
-- Links to
-- psychology, neuroscience, philosophy, biology, computer science,
mathematics,...
-
What is mathematics?
How does it differ from other disciplines?
Kant: three features.
-- non-empirical,
--
not analytic (not based solely on logic + definitions),
-- concerned with
--
necessity/impossibility/possibility (but not "possible world semantics")
-- see Cathy Legg's talk, and several others in this conference.
-
Links with work of Immanuel Kant, and (possibly) Alan Turing.
Also Piaget, especially his last two books on children reasoning about
Possibility and Necessity
-
The case of propositional/Boolean logic
Figure Logic: Which inference is valid, and why?
Here exhaustive analysis of a discrete finite collection of possibilities
suffices (though for more atomic propositions the set of possibilities increases
exponentially.
What about continuously varying sets of possibilities?
Finite exhaustive analysis is no longer possible.
WHAT MECHANISMS ALLOWED ANCIENT MATHEMATICIANS TO MAKE THEIR AMAZING
DISCOVERIES?
-
Background: Evolution and mathematics
-
Some examples:
EXAMPLES
-
WHY WAS KANT RIGHT ABOUT ARITHMETIC?
The concept of number essentially involves 1-1 correspondence: a topological
relationship.
Understanding cardinals requires grasping that 1-1 correspondence is transitive
and symmetric, and therefore produces equivalence classes.
Very few psychologistss or neuroscientists understand the implications.
Piaget did, but failed to propose adequate explanatory mechanisms.
How do we come to know that this relationship is necessarily transitive and
symmetric?
... and can therefore generate equivalence classes?
Spatial/diagrammatic reasoning can help us understand this, but
we have to see that individual diagrams represent an infinity of distinct cases!
Compare the logicist explanations (Peano, Frege, Russell, etc.) whose
psychological plausibility is zero.
NB There are pseudo numerical, much simpler competences whose inadeqacies most
psychological and neural research ignores.
-- They merely involve pattern recognition in small clusters.
Challenge for my view: What neural mechanisms, or sub-neural mechanisms can
support these capabilities.
NOBODY KNOWS, AND ALMOST NOBODY IS ASKING.
If there's time we can come back to the problem of finding biological
precursors.
-
WHAT TRANSITIONS IN INFORMATION PROCESSING DID EVOLUTION PRODUCE?
Why?
-
WHAT SORTS OF PROCESS ARE INVOLVED IN GENE EXPRESSION?
THE META-CONFIGURED GENOME
(Work with Jackie Chappell (2007))
WHICH PARTS INCLUDE ROLES FOR MATHEMATICAL COGNITION?
-
REQUIREMENTS FOR AN ALTERNATIVE TO TURING MACHINERY?
-- Replace the Turing Machine tape
With what? 1-D, 2-D, 3-D, 4-D elements?
-- Replace the Turing Machine engine
-- Some quarter-baked thoughts
For more on this see
-- Audience Composition
-- Audience views
-- The current state of AI
-- What's missing?
-- Links to
-- psychology, neuroscience, philosophy, biology, computer science,
mathematics,...
How does it differ from other disciplines?
Kant: three features.
-- non-empirical,
-- not analytic (not based solely on logic + definitions),
-- concerned with
-- necessity/impossibility/possibility (but not "possible world semantics")
-- see Cathy Legg's talk, and several others in this conference.
Also Piaget, especially his last two books on children reasoning about Possibility and Necessity
What about continuously varying sets of possibilities?
Finite exhaustive analysis is no longer possible.
The concept of number essentially involves 1-1 correspondence: a topological relationship.
Understanding cardinals requires grasping that 1-1 correspondence is transitive and symmetric, and therefore produces equivalence classes.
Very few psychologistss or neuroscientists understand the implications.
Piaget did, but failed to propose adequate explanatory mechanisms.
How do we come to know that this relationship is necessarily transitive and
symmetric?
... and can therefore generate equivalence classes?
Spatial/diagrammatic reasoning can help us understand this, but we have to see that individual diagrams represent an infinity of distinct cases!
Compare the logicist explanations (Peano, Frege, Russell, etc.) whose psychological plausibility is zero.
NB There are pseudo numerical, much simpler competences whose inadeqacies most
psychological and neural research ignores.
-- They merely involve pattern recognition in small clusters.
Challenge for my view: What neural mechanisms, or sub-neural mechanisms can support these capabilities.
NOBODY KNOWS, AND ALMOST NOBODY IS ASKING.
If there's time we can come back to the problem of finding biological precursors.
Why?
THE META-CONFIGURED GENOME
(Work with Jackie Chappell (2007))
WHICH PARTS INCLUDE ROLES FOR MATHEMATICAL COGNITION?
-- Replace the Turing Machine tape
With what? 1-D, 2-D, 3-D, 4-D elements?
-- Replace the Turing Machine engine
-- Some quarter-baked thoughts
For more on this see
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/super-turing-geom.html
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/super-turing-phil.html
WE NEED NEW MORE POWERFUL EXPLANATORY MECHANISMS
THEY MUST EXIST BECAUSE THEY ARE NEEDED FOR KNOWN FORMS OF INTELLIGENCE, IN HUMANS AND OTHER INTELLIGENT ANIMALS.
Some initial, half-baked (quarter-baked) thoughts about this can be found in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/super-turing-geom.html
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/super-turing-geom.html
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham