Presenters for 2004:   Stephanie Andrews   Christopher Bailey   Joanna Berzowska   Shushil Bhakar   and Eric Hortop   Cliff Burgess   Paulo Chagas   Dennis Dollens   Dan Falk   Sarah Filley   Ivette Fuentes-Guridi   Lila Kari   Narendra Pachkhede   Chris Salter   Chelsea Smock   Clara Ursitti   Derek van der Kooy   Yon Visell   Fabian Winkler   Panel Discussion Symposium, 2004 Computational thought: a mathematician's theory of mind By Chelsea Smock Boston University, Boston, MA Mathematical modeling, much like art, seeks to provide insight into the nature of a system by condensing the system down to a few essential characteristics, and then representing the relationships between these characteristics in some way. While artists use paint, film and other media to create representations, mathematicians develop systems of equations to relate the characteristics. Ideally, in mathematics, the model itself is as simple as possible, while still capturing the complexity of the system. We would also like our model to predict actual observations in some quantitative or qualitative sense; that is, we would like our model to reflect "reality" in a meaningful way. I am interested in considering the connection between the mind and the brain, and how we might use mathematics to understand that connection. To this end, I will begin by presenting the Hodgkin-Huxley model for the time course of an action potential in a single neuron. This model, published in 1952 and still widely used today, won them a Nobel Prize and is considered by many to be the most important accomplishment of 20th century neuroscience. The system of equations demonstrates the powerful elegance of modeling, and gives us a glimpse into the overwhelming complexity of the nervous system. Using Hodgkin and Huxley's work as a platform, I consider the concept of modeling a thought computationally, and will discuss the concept of modeling the brain as a creative, self-reflective process. By virtue of our construction, there is no such thing as direct experience. Therefore, looking at the filter of perception as our neurological commentary on nature, specifically, our actions within nature, or us as actors, brings to the forefront the actor/observer question. Instead of looking at thought as a logical system, as they might have done in the age of reason, posing thought as a creative process, yet explaining it in specific mathematical terms, yields insight into artistic creation, theory of mind, and the behavior of individuals. A computational model of theory of mind as a creative process might perhaps be the limits of the human mind's ability to abstract. This presentation attempts to explore those limits with the elegance and specificity of mathematics and art. Biography: Chelsea Smock is interested in the intricate philosophical and physiological connections between the mind, the brain and the body. Currently a graduate student in Boston University's Center for Biodynamics, she is researching mathematics with Dr. Nancy Kopell. Past endeavors include work under the guidance of performance artist Sandy Stone and a presentation at the Museum of Contemporary Art in Chicago.   Page Top Copyright © 2004 Subtle Technologies Festival