Wolfram Computation Meets Knowledge

Wolfram Summer School


Anton Hufnagl

Summer School

Class of 2006


I was born in 1983 in a country that ceased to exist seven years later. Taking full advantage of the new right to mobility, I have received an honorary high school diploma from East Detroit High School, Michigan, and an American high school diploma and German Abitur from John F. Kennedy School, Berlin, Germany. Addicted to academic degrees ever since, I am currently pursuing a master’s in economics at the University of Mannheim, Germany; a master’s in mathematical statistics at the École Nationale de la Statistique et de l’Administration Économique (ENSAE) in Paris, France; and a bachelor’s in pure mathematics at the Université Denis Diderot, also in Paris.

Spending most of my time working in a very OKS environment of measure theory, bilinear algebra and econometrics, I hope to build a theory of discrete economics using the NKS methodology.

Project: Modeling Information in a Production Economy

Standard microeconomic theory following the works of Arrow, Debreu and Hahn assumes perfectly informed economic agents. My model is designed to test this hypothesis on the production side of the economy. The economy is defined in the form of a Semi-Thue or multiway system, where products are represented as strings, firms are represented by rules, and demand is derived from a utility function over the space of strings. Cost is modeled as attached to the purchase of a resource and each transformation. A transformation of a resource or intermediate product into another product can thus be described as the application of a rule to a given string. Collaboration between firms takes then the form of subsequent applications of different rules. By definition, the complete multiway system describes all possible cooperation between firms. Lack of information about such opportunities is then represented as an abbreviation of the system, which is shown to affect a variety of economic indicators. The model thus underlines the importance of a clearer representation of flows in the production economy in the tradition of the largely abandoned work of Leontieff and others.

Favorite Four-Color, Radius-1/2 Rule

Rule chosen: 198345

After an initial search, I started testing a number of C4 CAs for variations in the initial condition (IC). To my surprise, their complexity and even their precise patterns showed no response to the omission of up to two colors in the first row. Any two colors were sufficient to produce the complex, four-color patterns they exhibited. This behavior seems to be a multi-color equivalent of the decreased sensitivity of complex behavior to ICs studied for ECAs on page 250 of A New Kind of Science. Interested in the generality of this finding, I then wrote a search algorithm isolating cases of complex behavior that are dependent on the existence of all four colors in the IC. Notwithstanding the computational power that would have been required to search the entire rule space, perhaps running each CA on different ICs, I was able to isolate some cases where four-color complex behavior seems to depend on the existence of all four colors in the IC. Based on random ICs, these results are subject to probability. Rule 198345 is one example, where complex structures and their survival depend on the constitution of the ICs.