Answering The Mathematical Objection to Machine Intelligence: An Application of Machine Self-Reflection
By Professor John Case, Ph.D.
Computer and Information Sciences Department
University of Delaware, Newark, DE
Date : Wednesday, October 17th, 2007
Time : 7:30 PM
Location: Armstrong Auditorium, Caputo Hall 210
In this talk I briefly consider the standard infinite regress paradox in the notion of a machine ``having'' a complete model of itself and show how to circumvent it. Then I pictorially present a simple theoretical/mathematical application of machine self-reflection and use this application as a vehicle to illustrate what Turing in his seminal paper on machine intelligence called the mathematical objection to machine intelligence. Lastly I employ machine self-reflection to completely answer this objection, and, in the process, point out a seeming limitation of human intelligence that suitably ``clever'' machines do not have.
John W. Case was born in Clinton, Iowa, USA, and received the B.S. degree (with honors) in Physics from Iowa State University in Ames in 1964 and the M.S. and Ph.D. degrees in Mathematics in 1966 and 1969, respectively, from the University of Illinois in Champaign-Urbana.
Since 1989 he has been at the University of Delaware, Newark, where he is Professor of Computer and Information Sciences and was Chair of the department 1989-1994. Previously he was in the Computer Science Departments of SUNY at Buffalo 1973-1989 and of the University of Kansas 1969-1973. He was Visiting Professor, School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, Fall 2001, Visiting Professor of Computer Science at the University of Rochester in NY 1987-1988, Associate Dean in the Faculty of Natural Science and Mathematics at SUNY Buffalo, 1985, Visiting Associate Professor of Computer Science at Courant Institute, New York University and Visiting Fellow in Computer Science at Yale University 1980-1981, and a National Science Foundation Graduate Fellow in Mathematics at the University of Illinois 1966-1969.
He is best known for his work in computability-theoretic learning and inductive inference and for his theoretical work involving machine self-reference. He collaborates regularly with international colleagues on three continents besides North America. He is interested in application of his theory work to cognitive science, philosophy of science, and applied machine learning. His research has also included the application of computability-theoretic techniques to the study of the structure, succinctness, and complexity of programs. He has been additionally interested in interconnection scheme, processor, and algorithm design for multi-dimensional lattice computers with application to the discretized, analogical representation of motion in space. He recently completed a project with a biologist colleague involving machine learning applied to bioinformatics. He is just beginning a new, empirical project with another biologist colleague on the learning of communication in the cuttlefish, an intelligent but asocial mollusc.
He has graduated so far twelve Ph.D. students, four of whom are or were full professors at research universities, one of these former head of his school and director of an associated research institute, now a Deputy Vice Chancellor for Research and Commercialization. Two more of his former Ph.D. students are professors at teaching universities. He has also supervised three bioinformatics postdocs.
For background reading, I recommend the following classic paper.
A. Turing, Computing machinery and intelligence, Mind, 59:433--460, 1950.
This paper has been reprinted in a number of collections, including, The Philosophy of Artificial Intelligence, edited by Margaret Boden, Oxford University Press, 1990.