If we assume m(n) of the form m = 2(1/3 +5)n <0 there is an such that for all n> We can further show that for any we can show from (17) that for any the inequality is not satisfied. 0 the inequality is satisfied for all n>0. We therefore take as an estimate of the minimum such that (17) holds for all n the function m = 27/3 2/4 does not While it is certainly true that for small n, m(n) < 2n/3 satisfies (17), we may show for example that m = satisfy (17) for any n> 11. CONCLUSIONS From the results of the above argument it is easy to conclude that it is completely impractical to consider the construction of an actual network of more than a very few inputs which is universal in the sense implied herein. What is perhaps not as obvious but of at least equal interest is the fact that at least one of the 22 abstractions of the input set demands the full complexity of the universal net for its realization. That is to say, if one of the operators were eliminated from the network it would not be capable of some particular abstraction. To see that this is the case assume the contrary to be true, that is with respect to each of the 22 functions, it is possible to eliminate some operator and still compute the desired function. We then note that by our method of construction the threshold operators are indistinguishable (with the exception of the one whose output becomes the network output and can therefore never be eliminated) and therefore one particular operator may be eliminated for each of the functions. This however implies that the network minus one operator is universal, which contradicts the original hypothesis. Thus, we see that this vast complexity is due not so much to the demand for universality, but simply due to the fact that some abstractions of a field of say 103 arguments are intrinsically non-realizable by means of such a network because the number of threshold operators required exceeds the estimated number of atoms in the observable universe. WADD TR 60-600 TECHNICAL SESSION || ANALYSIS OF BIOLOGICAL Moderator: Professor Heinz von Foerster University of Illinois PROBLEMS IN BIO-COMPUTER DESIGN Peter M. Kelly Aeronutronic Division of Ford Motor Company INTRODUCTION This writing reflects the attempt of the writer to outline the important trends and significant problems in the area of activity concerned with the creation of electronic systems that will recognize, learn, and generalize. The inclusion of the phrase "by electronic means" implies that philosophies of the cognitive processes and developments in biology or physiology are of interest only to the extent that they suggest design approaches. No attempt has been made to reference or review all the important work in the field. The writing is not a review; it is rather an attempt at clarification. If there is more searching than finding involved, this may be looked upon as representative of the state of the field or of the mind of the writer or, possibly, of both. RECOGNITION Webster's dictionary defines recognize as meaning to know again, implying that the cognitive mechanism has seen the object before and learned to know it. The related process of classifying objects which have never been previously observed is covered by the topic of generalization which is discussed more completely later along with the concept of abstraction. The basic recognition process is, from the definition given above, closely related to the learning process. The information from the sensory field must be organized to facilitate the recognition or classification process and it is the development of this organization which is the purpose of the learning or self-organizing process. Pre-organization of an appropriate section of a bio-computer defined as a device with the capabilities described in the title is always possible and may significantly reduce the complexity of the self-organizing task. It is implied in the writings of Greene2,3,4 that a complex pre-organization of the sensory field is typical of the cognitive system in man. Such a system is a logical one since |