http://www.birmingham.ac.uk/schools/mathematics/news-and-events/birmingham-popular-maths-lecture.aspx
Birmingham Popular Maths Lectures
Hosted by
the School of Mathematics
The University of Birmingham
All welcome to attend. The lectures are free of charge.
Contact/Enquiries
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8 to 9 pm, 17 April 2013 (Refreshments 7:30pm, School of Mathematics)
Lecture Room A (LRA) of the Watson Building
(Building R15 on Campus Map).
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Abstract
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.
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.
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.
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Installed: 26 Feb 2013
Last updated: 1 Apr 2013; 29 Aug 2013 (reformatted)
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham