Wolfram Computation Meets Knowledge

Wolfram Summer School


Charles Reiss

Summer School

Class of 2007


Charles Reiss is an Associate Professor at Concordia University in Montréal, where he teaches linguistics and cognitive science. He received a BA in mathematics from Swarthmore College in 1985, and a PhD in linguistics from Harvard University in 1995. He is co-author of The Phonological Enterprise (with Mark Hale) and I-Language: An Introduction to Linguistics as Cognitive Science (with Daniela Isac), both due out in February 2008 from Oxford University Press. In future research, Charles plans to apply the skills he gained at the NKS Summer School 2007 to modeling phonological rule systems and their acquisition.

Project: Modeling Phonological Computation with Simple Programs

The Computational-Representational Theory of Mind (CRTM) is particularly amenable to study from the NKS perspective, given CRTM assumptions that cognition is best modeled as computation over discrete symbols. In practice, however, CRTM models are rarely implemented, leaving computational tractability an open question. Another problem is that much modeling is done using constraint-based systems. In this project, I implemented a type of widespread phonological process called Vowel Harmony (VH), in which vowels of some morphemes in a word determine the quality of vowels in other morphemes. I implemented equivalent programs for the same Vowel Harmony rule using a cellular automaton, a sequential substitution system and a rewrite rule system based on Mathematica’s StringReplace function.

Comparing these implementations allows us to address the implications of the Principle of Computational Equivalence for doing cognitive science, specifically the Strong/Weak Equivalence distinction. Despite the fact that many of these systems are universal, and thus can emulate each other, a realist view of cognitive science demands that we ask what computations the mind is actually doing. The implementations provide a basis for comparison.

Project-Related Demonstrations

Waveforms and Spectrograms

View demonstration of Wolfram Demonstrations Project

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 4337099

Here is the code for my chosen 3-color, outer totalistic CA. I like this one because it shows how a CA can create a relatively small, yet interesting structure and then terminate. Most of the other patterns I saw were either too simple (just stripes from the second or third step), or nested, or aparently random. This one stood out by not falling into any of those three categories.

ArrayPlot[ CellularAutomaton?[{4337099, {3, {3, 1, 3}}}, {{2}, 1}, 50, {All, All}], PixelConstrained? -> 9, ColorRules? -> {1 -> Red, 0 -> Yellow, 2 -> Black}]