Functional Geometry and the Determination of Pattern in Mosaic Receptors 395 



waking brain appears to be processing input information at a constant rate, 

 it would appear that a human brain may be making changed neural connections 

 at rates up to 10^' per day. The necessary sequential spatial order in these con- 

 nections might be the origin of our sense of temporal order in our memories. 



It may be no accident that this rate adds up to the order of 10^'' to 10" 

 neurons per lifetime, comparable to the total number of neurons estimated 

 to be contained in the adult brain; although of course a major fraction of 

 these may be pre-addressed, unchanging after birth. (This number has also 

 been computed as the minimum number of neurons required in a fully- 

 developed decision-net serving 10^ to 10^ input elements (1). But there is 

 no necessary conflict between these two points of view, since it is a familiar 

 property of biological systems that they represent simultaneous optimization 

 of different considerations— as in the two-point resolution of the eye, which 

 is simultaneously limited by diff"raction, by aberrations, and by the mosaic 

 cell size.) By this reckoning, less than one neural junction in a thousand would 

 be changed per week, which might account for the difficulty of detection of 

 histological changes. 



With such a specific moment-by-moment locahzation of new connections, 

 the increasing loss of memory in older persons might be the result of cumulative 

 damage to the neurons, such as radiation damage or microhemorrhages ; 

 or it might be due to a kind of saturation of the address-determining connections, 

 so that either no new relationships are perceived in the continuing flux of 

 inputs, or else those that are perceived are no longer able to modify the network. 



These numerical estimates are not unreasonable; and even if the one-moment 

 one-neuron assumption were dropped, it would not be surprising from the 

 general dimensional considerations in the physics of the problem to find that 

 that assumption would give correct order-of-magnitude relations between 

 the time-constant, the lifetime and the number of neurons and its rate of change. 

 Such a situation is common in order-of-magnitude calculations. 



But this estimate of the rates is defended only so that it can be attacked 

 on other grounds: for it leads to another important biological dilemma, and 

 one that might have an interesting resolution. For it must be remembered 

 that the brain is not merely an electrical network; it is also a biological network 

 — living, breathing, and growing. And a neural connection time of 50 milli- 

 seconds is orders of magnitude too short for the usual cell growth time or 

 atrophy time. While electrochemical channels or barriers might be formed 

 or sudden changes of shape might take place in milliseconds, these can only 

 occur for cells that are already present. 



A few years ago it was supposed that a way out of this dilemma would be 

 to let the new perception or thought be initially established as a closed self- 

 maintaining loop of neural electrical excitation, which could persist long enough 

 afterward for the cell growth and structural change to take place. But a 

 succession of apparently negative experiments seems to have caused this notion 

 to be largely abandoned. 



There is an alternative. It is to let the neural growth take place, not after, 

 but before the chemical and electrical connection to the network, as the elec- 

 trician carries his coils of wire to the site before he hooks them up. The order- 

 of-magnitude gap between the time constants can be got over by supposing 



