Wolfram Computation Meets Knowledge

Wolfram Summer School


Hector Zenil

Summer School

Class of 2005


Hector Zenil graduated with his B.S. degree in mathematics from the National University of Mexico (UNAM). He is currently accepted with a full scholarship for a Ph.D. at Paris I University (Pantheon-Sorbonne) in the theory of minds and machines. He has been an official international books and papers reviewer for the IEEE Computer Society and the Association for Computing Machinery (ACM) since 2000, mainly in the theoretical computer science field. His research interests in math are logic, foundations of mathematics, complexity, and recursion function theory. He had been working in alternative models of computation and trying to figure out what the hyperarithmetical hierarchy looks like.

One of his research goals is to solve the question of finding the computational power of the brain and what kind of artificial intelligence is possible in terms of the computational universe. He claims that another kind of life is arising from everyday computers, which will become more and more complex in their behavior when their rules (hardware and software) became more and more simple. He enjoys thinking about philosophical and epistemological questions like what reality is and what truth means. He likes to deal with great scientific and philosophical questions even if he cannot figure out the answers… yet.

Project: Enumerating Quantified Axiom Systems

The main purpose of this project is to take a look at the beginning of the universe of all possible mathematical theories. To achieve that purpose it is necessary to enumerate all quantified axiom systems. It was found that the number of axiomatic systems generated for each length grows exponentially. However, most axiomatic systems generated are inconsistent and contain axioms that are not all independent of each other. This method could be of interest because when dealing with mathematical theories as a whole, it is possible to ask some very general questions about the foundations of mathematics and the way we do mathematics based on axioms and trying to prove theorems.

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 452141

After a while symmetry emerges clearly (reflecting with an imaginary horizontal axis). Just 400 steps after, fractal and nested patterns emerge from both sides. This very rich structure of a cellular automaton is full of different patterns. At the border there is a band of fractal patterns. In the middle, there are also nested patterns with other interesting red patterns that flow through the whole structure.