Cybernetics, Artificial Intelligence and the Avoidance
of Mathematical Blind Spots

Prof. Roger W. Brockett
An Wang Professor of Computer
Science and Electrical Engineering
Harvard University
Cambridge, MA., U.S.A. 
Abstract
When first discussed by Wiener, cybernetics captured the imagination of the scientific public and
served as the rallying cry for groups of scientists and engineers seeking a broadly encompassing view
of what engineering and life scientists might hope to achieve by working together. Aided by the work
of luminaries such as John von Neumann and Claude Shannon, a rosy picture emerged, warmed by
the aura of mathematical truth. Looking back, it seems fair to say that the results achieved by this
movement in the 50's and 60's are more apparent in terms of the organizations and journals that
flourished, rather than the new modes of thought that emerged. When the proponents of artificial
intelligence came along a bit later, cybernetics was not able to hold its ground. The same fate awaited
artificial intelligence as its first summer soon fell prey to the famous AI winter during which it lost
considerable credibility. However, today we have, for example, robots that do our work and search
engines that supplement our memory, fulfilling at least part of the vision that fueled the early hopes for
cybernetics.
In this talk we will trace this history and peer into the future, interpreting the various stages of these
developments in terms of the mathematical paradigms each stage relied on. In a nutshell, Wiener set
the world down a path dominated by continuous mathematics, Fourier transforms, and stationary
stochastic processes. AI took a different path based on the expectation that loosely structured
computer programs could replicate in machine form, most of what was needed. In this talk I will argue
that a great deal of the conceptual progress in these areas has come from work lying close to the
boundary between continuous and discrete mathematics and that progress has been slowed by our
lack of courageous exploration of this area. I will illustrate with examples showing how amorphous this
boundary is and how fruitful its exploration has been.
About the speaker
Roger Brockett is the An Wang professor of electrical engineering and Computer Science at Harvard
University. He has been exploring questions in engineering and applied sciences since starting
graduate school in 1960, and has been teaching since his appointment as an Assistant Professor at
MIT in 1963. He is one of the most influencial pioneers and leaders in the field of systems and control
theory with seminal contributions to differential geometric methods in nonlinear control, the geometric
approach to the sufficient statistics problem in nonlinear estimation, formal languages for motion
control, hybrid systems, flows for computation related to integrable systems, stabilization theory,
quantum control, and, most recently, optimal control of Markov processes. He has received major
awards from IEEE (Institute of Electrical and Electronic Engineers), ASME (American Society of
Mechanical Engineers), SIAM (Society of Industrial and Applied Mathematics), and AACC (American
Automatic Control Council), is a member of the US National Academy of Engineering and is this year
recipient of the IEEE Leon Kirchmayer Award for Graduate Education. He has directed approximately
60 Ph.D. theses and authored about 200 research papers.
For further information see http://people.seas.harvard.edu/~brockett/brockett.html.
Date: 
Friday, April 24, 2009 
Time: 
2 p.m. 
Location: 
Lecture Room V 7.03, Pfaffenwaldring 7, Campus StuttgartVaihingen 
