Models of Reference

From Aristotle to Leibniz, from Boole to Turing, many people have dreamt of a powerful "mathematics of thought", a precise language allowing us to grasp the essence of concepts and build a new generation of intelligent machines. All the known attempts to build such a language have failed, in one way or another: if computers now can outperform humans in many tasks (such as playing chess), they are still "dumb" compared to toddlers in analogy-making, creativity, learning and many other activities. The Mathematics of Models of Reference is a completely formalized framework - entirely computable - built with the working hypothesis that the basic bricks of physical and mental reality have similar behavior and isomorphic composition rules (as the universe was built using more or less 100 elements and a few laws from physics and chemistry, so with a set of basic concepts and rules from the MMoR we hope to build an intelligent mind).

Technically speaking, the MMoR is based on a strict isomorphism between mind and matter: a perfect way to make more precise this intuition is to develop new tools in the field of non-standard computability and cellular automata theory. We have developed a new "computational universe" in 2 and 3 dimensions: from this basic rappresentation of the physical world, we are able to regain, through the MMoR, the full strength of standard recursion theory.

In our latest works - the book, of course, but also scientific papers, pop-science articles, open source simulations ecc. - we are trying to show that the MMoR is in fact able to replace other, more "orthodox" forms of mathematics now used in a variety of modelling challenges. Moreover, we expect that further studies on the physics of computation will help us see how to link the currently accepted physical theories with our discrete space-time and local rules.

Learn more:
Berto F., Rossi G., Tagliabue J., The Mathematics of Models of Reference, Texts in Computing, 2010