The Association for Science Education
Will hold its annual conference at
The University of Birmingham
on Wednesday 8th to Saturday 11th January 2014
http://www.ase.org.uk/conferences/annual-conference/

(Abbreviated link to this page: http://tinyurl.com/CogMisc/ase14.html )

"Could a baby robot grow up to be a mathematician?"

(Time and place to be decided.)

Abstract

-----

Short Abstract

Since Turing discussed the possibility of intelligent machines in 1950 there have been
many outstanding achievements in artificial intelligence, robotics and computational
cognitive science -- including logical and algebraic theorem provers and proof checkers.
Yet we don't know how to give a machine spatial reasoning abilities found in very young
children and many other animals, apparently required for the discovery of the simplest
truths and proofs in Euclidean geometry leading up to Euclid's Elements. Can we understand
what's missing and how it evolved? Perhaps mathematical spatial reasoning requires
new forms of computation?

Longer Abstract
(Provisional)

Euclidean geometry is one of the greatest products of human minds, brought together in
Euclid's Elements over two millenia ago.

However, at some distant earlier time there were no geometry textbooks and no teachers.
So, long before Euclid, our ancestors, perhaps while building huts, temples and pyramids,
measuring fields, making tools or weapons, or reasoning about routes, must have noticed
facts about spatial structures and processes that are both useful (like facts about
physics, geography, biology, and human languages), but are also demonstrable by reasoning
with logic and diagrams. Mathematicians do not have to keep checking that their
discoveries remain true at high altitudes, or in cold weather, or on surfaces with unusual
materials or colours -- because they can prove things.

Without teachers to help, biological evolution must somehow have produced
information-processing mechanisms that allowed ancient humans to develop the concepts,
notice the relationships and discover the proofs that their descendants are taught at
school, but which we have the ability to discover for ourselves, as our ancestors did.

This suggests that normal human children have the potential to make those discoveries
themselves, under appropriate conditions. I suspect there are also deep connections with
competences that have evolved in other intelligent species that understand spatial
structures, relationships and processes -- such as nest-building birds, squirrels that
steal nuts from bird feeders, elephants that manipulate water, mud, sand and foliage with
their trunks, and apes coping with many complex structures as they move through and feed
in tree-tops.


      [How did the squirrel get up to the bird feeder?]

Can we replicate evolution's achievements, and create robots that start off with
competences of young children and later, as they develop, make simple discoveries in
Euclidean geometry? I'll explain why that's hard to do -- but perhaps not impossible.
There have been great advances getting computers to reason logically, algebraically and
arithmetically, but the kinds of reasoning in Euclid, e.g. using diagrams, are very
different.

Many current robots perform physical tasks, like walking, juggling, climbing, swimming and
recovering lost balance very impressively, yet they cannot reason about what they have
done or why it works or what else could have been done -- abilities required for discovery
of geometrical constraints on spatial structures and processes implied by Euclid's axioms.

I'll discuss some of the problems and possible ways forward. Perhaps someone now studying
geometry and computing at school will one day design the first baby robot that grows up to
be a self-taught robot geometer, and, like some of our ancestors, discovers for itself why
the angles of a triangle must add up to exactly half a rotation.

This is part of the Meta-Morphogenesis Project

For more on the current state of Artificial Intelligence see http://aitopics.org/

Adam Ford has a large and growing collection of video interviews and recorded workshop and
conference presentations related to AI and other computing advances, by many scientists,
philosophers, artists, and others, here:
http://www.youtube.com/user/TheRationalFuture/  

Maintained by Aaron Sloman
School of Computer Science
The University of Birmingham