11/3 THE FULLY-JOINED SYSTEM 



as the case is central.) We ask, how many trials will, on the average, 

 be required for adaptation ? 



Each variable has a probability J of being kept within its limits. 

 At any one trial the probability that all of 100 will be kept in is 

 (J) 100 , and so the average number of trials will be 2 100 , by S. 22/7. 

 How long will this take, at, say, one per second ? The answer is: 

 about 10 22 years, a time unimaginably vaster than all astronomic- 

 ally meaningful time ! For practical purposes this is equivalent 

 to never, and so we arrive at our major problem : the brain, though 

 having many components, does adapt in a fairly short time — the 

 1,000-unit Homeostat, though of vastly fewer components, does 

 not. What is wrong ? 



It can hardly be that the brain does not use the basic process of 

 ultrast ability, for the arguments of S. 7/8 show that any system 

 made of parts that obey the ordinary laws of cause and effect 

 must use this method. Further, there is no reason to suppose 

 that the function 2 N , where N is the number of essential variables, 

 is seriously in error, even though it is somewhat uncertain: other 

 lines of reasoning (given below) also lead to the same order of 

 size, a size far too large to be compatible with the known facts. 

 There seems to be little doubt that a 1,000-unit Homeostat would 

 quite fail, by its slowness in getting adapted, to resemble the 

 mammalian brain. Wherein, then, does this system not resemble 

 (in an essential way) the system of brain and environment ? 



11/3. In the previous section the dynamic nature of the brain and 

 environment was really ignored, for the calculation was based on 

 a direct relation between step-mechanisms and essential variables, 

 while what connected them was ignored. Let us now ask the 

 question again, ignoring the essential variables but observing the 

 dynamic systems of environment and reacting part (Figure 7/2/1). 

 Two type-cases are worth consideration (by S. 2/17). 



The first case occurs when the system is linear, like the Homeo- 

 stat, so that it has only one state of equilibrium, which can be 

 stable or unstable. In this case, unstable fields are of no use to 

 the organism, for they do not persist; only the stable can be of 

 enduring use, for only they persist. Let us ask then: if a Homeo- 

 stat had a thousand units, how many trials would be necessary 

 for a stable field to be found ? Though the answer to this ques- 

 tion is not known, for the mathematical problem has not yet 



149 



