Why is it so hard to get machines to reason like our ancestors who produced Euclidean Geometry?

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• Aaron Sloman, University of Birmingham
• Thursday 20 June 2013, 16:00-17:00
• G29, Mech Eng .

If you have a question about this talk, please contact .

Please note that coffee will be served at 3:15 at room 123 (School of Computer Science), followed by the one-hour seminar at 4pm.

The universe seems to include infinitely many domains, of many different sorts, and many different degrees of complexity. Each domain comprises a set of possible structures and processes. Some domains are very simple, (e.g. the domain of possible ways up a coin tossed once can land: heads up or tails up), others more complex, including discrete domains (e.g. sequences of coin-tosses, truth-tables, the domain of initial segments of the natural number series: 1, 1-2, 1-2-3, 1-2-3-4, etc, or the domain of counting processes, setting up correspondences between such segments and collections of other entities), continuous domains (e.g. motions of lines in a plane, motions of a flexible string), mixed continuous/discrete domains (e.g. various biological domains including chemical structures and processes, or the domain of Lego construction processes), meta-domains (e.g. the domain of types of algebraic domains, the domain of types of domains of grammatical sentences, the domain of types of domains of programs expressible in a particular programming language). The elements of some domains can be physically instantiated, whereas others cannot, e.g. the domain of impossible 3-D figures depictable in 2-D line drawings, such as Escher’s pictures, or the domain of possible re-orderings of the set of natural numbers.)

It seems that without a certain type of richness in the domain of possible chemical structures and processes there would not have been life as we know it (Ref T. Ganti). Each form of life has a domain of possible sensory-motor interactions with each of the types of environment in which that life is possible. More complex forms of interaction became possible when evolution produced organisms that could explore and learn about domains and deploy that knowledge, e.g. in planning action sequences, or building maps of extended spatial structures on the basis of sequences of sensory motor interactions. Using such domain knowledge enabled more intelligent animals to detect and reason about positive and negative affordances for action. (Ref: J.J. Gibson). In humans some of that led to meta-knowledge about such competences and eventually to the production of Euclid’s Elements, one of the greatest achievements of biological evolution. Many other forms of mathematical knowledge grew out of later explorations of domains, and then meta-domains of many kinds. One of the key features of such knowledge is that it concerns grasping some set of possibilities and then discovering constraints on those possibilities, e.g. learning that some extensions of a set of possibilities can be described or depicted but are not included in the set, e.g. the penrose triangle or a set of 3 objects combined with a non-overlapping set of 2 objects forming a set of 4 objects. This is totally different from and more fundamental than discovery of probabilities through empirical observations, the current focus of huge amounts of research in AI/Robotics and neuroscience (much of it misguided in my opinion).

In the last few decades there have been tremendous advances in AI theorem proving techniques, and we now have programs that can find and prove theorems that would defeat most humans, including a package that will sell you a new, unique, non-trivial theorem named after you (REF). But it has proved extremely difficult to get computers to engage in the kinds of reasoning even a human toddler can do and some other animals seem able to do that made the development of Euclidean geometry possible. This talk will present some examples and discuss possible ways of making progress, with potential implications for developmental psychology, neuroscience, theories of animal cognition, and philosophy of mathematics, as well as AI and Robotics.

This abstract is available along with additional references and links at

http://tinyurl.com/CogMisc/euclidean-ancestors.html

Examples of simple forms of geometrical reasoning that seem hard to model on computers are in: http://tinyurl.com/CogMisc/triangle-theorem.html Hidden Depths of Triangle Qualia

This is part of the Meta-Morphogenesis project: http://tinyurl.com/CogMisc/meta-morphogenesis.html

This talk is part of the Computer Science Departmental Series series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• G29, Mech Eng
• computer sience

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