384 



John R. Platt 



for an artificial system witli some quasi-neuronal properties, will be seen if we 

 consider the problem of scanning along a curved line, with Z-rotation of the 

 retina to follow the curve, as in Fig. 1. 



If the differential muscle stress or strain or rate of change of either (whichever 

 is the principal sensed variable) about the Y-axis has a fixed ratio r to that about 

 the Z-axis, the eye will sweep up along a line at an angle arctan r to the horizon. 

 If the differential neural spike frequencies/^ and/^ from the two muscle pairs 

 give a quasi-logarithmic representation of the muscle action, a fixed ratio r 

 corresponds to a fixed frequency difference,/^ — /»> which we can call F. A 

 subtractive-frequency mixer tube, and perhaps a similar subtractive mixer neuron, 

 could be devised which would combine two synaptic inputs so that an output 

 pulse is produced only when the input pulses are simultaneous, as suggested in 

 Fig. 3. With suitable cell sensitivity and time constant, this output is the beat 



f,-AF-R 



Fig. 3. Possible proprioceptive analog connections for scanning 

 along a uniform curve. 



frequency, F, the difference of the two input frequencies (1). A neuron used in 

 this way might be called a difference cell. (Determination of the sign of the 

 difference might require another cell.) If the output frequency F is fed back 

 with proper sign to the Jf and 7 muscles, a constant direction of motion can be 

 stabilized. 



The rate of change of direction could be sensed by introducing a time delay 

 and comparing r{t) with r(/ — A) or F{t) with F{t — A) by a second subtractive 

 neuron which generates the frequency AF — a time-differential cell. With a 

 lower sensitivity and a shorter time constant, the same type of cell could be 

 made to fire only for a certain constant pulse interval in the inputs, equal to 

 the time delay. This would be a constant-frequency detector, and could be 

 called a nidi cell. 



A constant Z-rotation of the retina to follow the change of X, F direction in 

 scanning a curve could be detected by a third subtractive neuron which generates 

 the frequency difference/ — F. Call this frequency R. It can again be held at 

 a constant value by suitable feed back into the Z motion, as shown at the right 

 side of Fig. 3. Such a tracking motion permits eeneralization of theorem (3) 

 and (3'): ^ 



