On the Role of T ime and Space in

One of the most interesting scientific developments during the next two decades will be the unraveling of the structure of computation in living organisms. Since the information processing capabilities of living organisms are in many aspects superior to those of our current artificial computing machinery, this is likely to have significant consequences for the way in which computers and robots will be designed in the year 2020. Traditionally theoretical computer science has played the role of a scout that explores novel approaches towards computing well in advance of other sciences. Curiously enough, this did not happen so far in the case of computation in living organisms, and it may be worthwhile to ponder for a moment about the possible reasons for that. One obstacle may result from the fact that theoretical computer science has become to a large extent "technique-driven", i.e., one typically looks for new problems that can be solved by variations and extensions of a body of fascinating mathematical tools that one has come to like, and that form the heart of current theoretical computer science. In contrast, to have a serious impact on theoretical research in neural computation, a theoretical researcher has to be to a larger extent "problem-driven", i.e., he/she has to employ and develop those mathematical concepts and tools that are most adequate for the problem at hand. On the positive side, I would like to mention a success story regarding an earlier very fruitful interaction between the areas which are nowadays called compuational neuroscience and theoretical computer science. McCulloch and Pi t ts [McCulloch and Pitts, 1943] developed an abstract mathematical model for computation in living organisms: circuits of "McCulloch-Pitts neurons" or threshold gates, as they are now called in theoretical computer science. Kleene [Kleene, 1956] proved that they were equivalent to his notion of a finite automaton. Thus "historically finite automata were first used to model neuron nets"