As far as I know very few researchers on vision have any interest in the role of
vision in mathematical discovery and reasoning (the topic that
first drew me into Artificial Intelligence in 1971 as a possible route to
solving old philosophical problems about the nature of mathematics, and
defending Kant). Nearly four and a half decades later the problems are still
unsolved. Worse, they seem to be ignored by almost all researchers in
AI/Robotics, psychology, neuroscience and philosophy. A few years ago, inspired
by Turing's paper on Morphogenesis published in 1952, I wondered what he might
have done had he not died two years later. My tentative answer is
the Meta-Morphogenesis project
-- a long term multi-disciplinary project aiming to
identify and explain the many transitions in biological information processing
since pre-biotic molecules. Recently this led to an investigation of the
evolution of many kinds of biological construction-kits (concrete, abstract and
hybrid), including meta-construction-kits for producing new construction kits. I
shall try to show how unsolved problems relating the amazing mathematical
discoveries leading to Euclid's Elements, the many toddler theorems apparently
discovered (unwittingly) by pre-verbal children, gaps in Gibson's theories of
affordances, varieties of intelligence in other species, and closely related
weaknesses in philosophy, psychology, neuroscience, linguistics, robotics and AI
(obscured by their narrowly-focused successes) may perhaps be addressed in this
project. It may turn out to require new forms of computation. In part, the talk
will be an invitation to join in. The presentation will be example-based and
partly audience-driven.
