Anastomotic Nets Combating Noise 289 



compute fifteen out of the sixteen possible functions. Had I drawn it 

 for neurons with three inputs each, it could have been switched so as 

 to compute each of 253 out of the 256 logical functions of three 

 arguments. I strongly suspect that this is why we have in the eye 

 some 100 million receptors and only approximately one million 

 ganglion cells, but note that it depends upon interaction of afferents. 



Finally, Manuel Blum has recently proved that this interaction 

 enables him to design nets that will compute any one specified 

 function of any finite number of inputs with a fixed threshold of 

 the neuron at a small, absolute value, say, 1 or 0. This prevents 

 the neuron from having to detect the small difference of two large 

 numbers, thus allowing the brain a far greater precision of response 

 to many inputs per neuron, despite a fluctuation of a given per 

 cent of the threshold 6. This fluctuation of 6 is the first source of 

 noise which I wish to consider. 



The effective threshold of a neuron cannot be more constant 

 than that of the spot at which its propagated impulse is initiated. 

 This trigger point is a small area of membrane, with a high 

 resistance, and it operates at body temperature. It is, therefore, 

 a source of thermal noise. The best model for such a trigger is 

 the Node of Ranvier, and the most precise measurements of its 

 value are those of Verveen. For axons '■^A^ in diameter, he finds 

 it to be ^^ ±1 per cent of 0; it is larger for small axons. Moreover, 

 his analysis of his data proves that the fluctuations have the random 

 distribution expected of thermal noise. There are, of course, no 

 equally good chances to measure it in the central nervous system, 

 for one cannot tell how much of a fluctuation is due to signals or 

 to stray currents from other cells. Our own crude attempt on the 

 dorsal column of the spinal cord indicates far greater noise, but 

 not its source. 



What goes for thresholds goes, of course, for signal strength; 

 and for fine fibers, say, 0.1^, the root mean-square value of the 

 fluctuation calculated by the equation of Fatt and Katz is —0.5 mv. 

 If we accept a threshold value of 15 mv., this is several per cent. 

 It may be much larger. 



Moreover, it is impossible that the details of synapsis are per- 

 fectly specified by our genes, preserved in our growth, or perfected 

 by adaptation. They are certainly disordered by disease and injury. 



