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Wolfram Summer School

June 18–July 7, 2017
Bentley University, Waltham, MA
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Frederico Meinberg

Class of 2003


At present Fred is completing an MA in Romance Linguistics at Freiburg University, Germany. He describes his main activity in linguistics as involving empirical research on grammatical structures across the world's languages (so-called linguistic typology). Another of his projects is the development of a Mathematica-based tool for doing corpus and computational linguistics. Outside linguistics, some of his interests are the implications of Stephen Wolfram's A New Kind of Science to economics, the foundations of mathematics, and philosophy of science. Fred is originally from Brazil and spends a small part of his time running a farm there. Besides looking after his fitness with regular swimming, cycling and visits to the gym, he enjoys trekking and horse riding in the mountains of Minas Gerais state.

Project: Studying Simple Symbolic Systems

My work in the NKS Summer School was concerned with so-called symbolic systems. Wolfram (2002) presents symbolic systems as one class of simple programs, besides cellular automata, Turing machines, register machines, and others. The evolution of a symbolic system consists in the application of a set of one or more rules of the form lhs -> rhs to an initial expression. Following the directions set by Wolfram (2002), the simplest forms of symbolic systems were investigated, in search for the threshold of complex behavior. The parameters investigated were number of rules, number of operators, and the size of lhs and rhs, as well as the size of the initial conditions. It was found out that the threshold of complexity is reached with rather small sizes of rules and initial conditions. Other issues dealt with were how to visualize symbolic systems and how the evaluation scheme used to apply the rules affects the evolution of the system.

Favorite Three-Color Cellular Automaton

Rule Chosen: 2476560193074

Additional Information

Meinberg F. "Studying Simple Symbolic Systems." Presentation at NKS 2004, Boston, MA, 2004. [abstract]