University of Birmingham > Talks@bham > Artificial Intelligence and Natural Computation seminars > Why current AI and neuroscience fail to replicate or explain ancient forms of spatial reasoning and mathematical consciousness

## Why current AI and neuroscience fail to replicate or explain ancient forms of spatial reasoning and mathematical consciousnessAdd to your list(s) Download to your calendar using vCal - Prof Aaron Sloman (Honorary Professor of Artificial Intelligence and Cognitive Science, School of Computer Science, University of Birmingham, UK)
- Monday 02 September 2019, 11:00-12:00
- Computer Science, The Sloman Lounge (UG).
If you have a question about this talk, please contact Hector Basevi. It is widely, but erroneously, believed that Immanuel Kant’s philosophy of mathematics in his Critique of Pure Reason (1781) was disproved by Einstein’s theory of general relativity (confirmed by Eddington’s observations of the solar eclipse in 1919, establishing that physical space is non-Euclidean). My 1962 DPhil thesis (now online) defended a slightly modified version of Kant’s claim that many important mathematical discoveries are non-empirical, non-contingent, and non-analytic (i.e. not just logical consequences of axioms and definitions), but did not explain how brains or machines could make such discoveries. I later encountered AI, learnt to program, and hoped to show how to build a baby robot that could grow up to be a mathematician making discoveries like those of Archimedes, Euclid, Zeno, etc., and many other deep discoveries made long before the development of modern logic and formal proof procedures. I think those mathematical abilities are closely related to the spatial intelligence of pre-verbal human toddlers, and other intelligent animals, e.g. squirrels, elephants, crows, apes, and perhaps octopuses[†]—whose abilities are not yet replicated in AI/Robotics systems nor explained by current theories in neuroscience or psychology. Insofar as such mathematical discoveries involve This version of Kant’s theory rules out natural and artificial neural nets and related forms of deep learning, E.g. they cannot learn that something is impossible, such as a largest prime number, or a finite volume bounded by three plane surfaces. I have a large, and steadily growing, collection of examples to be explained by any adequate theory of mathematical consciousness. I’ll present a small sample during the talk.[‡] Alan Turing’s comments in his PhD thesis on the difference between mathematical intuition and mathematical ingenuity seem to me to echo Kant’s insights, and I suspect (though the evidence is flimsy) that Turing’s 1952 paper on chemistry-based morphogenesis (nowadays his I’ll present examples of spatial/mathematical reasoning illustrating Kant’s claims. E.g. what sorts of brain mechanisms enable a child to understand that it’s The implications for the current wave of enthusiasm for deep learning are potentially devastating—but invisible to people who have never studied Kant, or philosophy of mathematics. Which is not to deny that deep learning can be very useful, if used properly. [†] https://www.bbc.co.uk/iplayer/episode/m0007snt/natural-world-20192020-5-the-octopus-in-my-house [‡] A disorganised collection of additional examples can be found here, with links to many more: http://www.cs.bham.ac.uk/research/projects/cogaff/misc/impossible.html (also pdf) This talk is part of the Artificial Intelligence and Natural Computation seminars series. ## This talk is included in these lists:- Artificial Intelligence and Natural Computation seminars
- Computer Science Departmental Series
- Computer Science Distinguished Seminars
- Computer Science, The Sloman Lounge (UG)
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