Brooklyn College

Project Title

The Algorithmic Information of Categories

Project Summary

Much of modern mathematics and theoretical physics is written in the language of category theory. These are abstract structures that can uniformly express what is needed for modern research in these areas. We are interested in measuring the amount of information a categorical structure can express. Computer scientists measure the inherent amount of information in a string by looking at the length of the shortest computer algorithm that can describe the string. If a short algorithm can describe the string then it is compressible and has little information. In contrast, if the string can only be reproduced with a long algorithm, it is less compressible and has much information. We would like to generalize what was done for strings to arbitrary categorical structures. We first need a programming language that can describe categorical structures. We will then measure the shortest programs for different structures. The goal is to compare and contrast different structures and their informational content. Philosophically, we are interested in why Occam's razor seems to work so well. Occam demands that physical phenomena be expressed in mathematical structures of less informational content.

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