4/18 AN INTRODUCTION TO CYBERNETICS 



shall use the words "very large" to imply that some definite observer 

 is given, with definite resources and techniques, and that the system 

 is, in some practical way, too large for him ; so that he cannot observe 

 it completely, or control it completely, or carry out the calculations 

 for prediction completely. In other words, he says the system is 

 "very large" if in some way it beats him by its richness and complexity. 



Such systems are common enough. A classic case occurred when 

 the theoretical physicist of the nineteenth century tried to use 

 Newtonian mechanics to calculate how a gas would behave. The 

 number of particles in an ordinary volume of gas is so vast that no 

 practical observation could record the system's state, and no practical 

 calculation could predict its future. Such a system was "very 

 large" in relation to the nineteenth century physicist. 



The stock-breeder faces a "very large" system in the genes he is 

 trying to mould to a new pattern. Their number and the com- 

 plexities of their interactions makes a detailed control of them by 

 him impossible in practice. 



Such systems, in relation to our present resources for observation 

 and control, are very common in the biological world, and in its 

 social and econoiTiic relatives. They are certainly common in the 

 brain, though for many years the essential complexity was given only 

 grudging recognition. It is now coming to be recognised, however, 

 that this complexity is something that can be ignored no longer. 

 "Even the simplest bit of behavior", says Lashley, "requires the 

 integrated action of millions of neurons. ... I have come to believe 

 that almost every nerve cell in the cerebral cortex may be excited 

 in every activity. . . . The same neurons which maintain the 

 memory traces and participate in the revival of a memory are also 

 involved, in different combinations, in thousands of other memories 

 and acts." And von Neumann: "The number of neurons in the 

 central nervous system is somewhere of the order of lO^o. We have 

 absolutely no past experience with systems of this degree of com- 

 plexity. All artificial automata made by man have numbers of parts 

 which by any comparably schematic count are of the order 10^ to 

 10^." {Cerebral Mechanisms in Behavior.) 



4/18. It should be noticed that largeness /J^r se in no way invalidates 

 the principles, arguments, and theorems of the previous chapters. 

 Though the examples have been confined to systems with only a 

 few states or a few variables, this restriction was solely for the 

 author's and reader's convenience: the arguments remain valid 

 without any restriction on the number of states or variables in the 

 system. It is a peculiar advantage of the method of arguing about 



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