4.0 ELEMENTS, SYNCHRONISM, NEURON ANALOGY #

4.1 #

We begin the discussion with some general remarks:

Every digital computing device contains certain relay like elements, with discrete equilibria. Such an element has two or more distinct states in which it can exist indefinitely. These may be perfect equilibria, in each of which the element will remain without any outside support, while appropriate outside stimuli will transfer it from one equilibrium into another. Or, alternatively, there may be two states, one of which is an equilibrium which exists when there is no outside support, while the other depends for its existence upon the presence of an outside stimulus. The relay action manifests itself in the omission of stimuli by the element whenever it has itself received a stimulus of the type indicated above. The emitted stimuli must be of the same kind as the received one, that is, they must be able to stimulate other elements. There must, however, be no energy relation between the received and the emitted stimuli, that is, an element which has received one stimulus, must be able to emit several of the same intensity. In other words: Being a relay, the element must receive its energy supply from another source than the incoming stimulus.

In existing digital computing devices various mechanical or electrical devices have been used as elements: Wheels, which can be locked into any one of ten (or more) significant positions, and which on moving from one position to another transmit electric pulses that may cause other similar wheels to move; single or combined telegraph relays, actuated by an electromagnet and opening or closing electric circuits; combinations of these two elements;—and finally there exists the plausible and tempting possibility of using vacuum tubes, the grid acting as a valve for the cathode-plate circuit. In the last mentioned case the grid may also be replaced by deflecting organs, i.e. the vacuum tube by a cathode ray tube—but it is likely that for some time to come the greater availability and various electrical advantages of the vacuum tubes proper will keep the first procedure in the foreground.

Any such device may time itself autonomously, by the successive reaction times of its elements. In this case all stimuli must ultimately originate in the input. Alternatively, they may have their timing impressed by a fixed clock, which provides certain stimuli that are necessary for its functioning at definite periodically recurrent moments. This clock may be a rotating axis in a mechanical or a mixed, mechanico-electrical device; and it may be an electrical oscillator ( possibly crystal controlled) in a purely electrical device. If reliance is to be placed on synchronisms of several distinct sequences of operations performed simultaneously by the device, the clock impressed timing is obviously preferable. We will use the term element in the above defined technical sense, and call the device synchronous or asynchronous, according to whether its timing is impressed by a clock or autonomous, as described above.

4.2 #

It is worth mentioning, that the neurons of the higher animals are definitely elements in the above sense. They have all-or-none character, that is two states: Quiescent and excited. They fulfill the requirements of 4.1 with an interesting variant: An excited neuron emits the standard stimulus along many lines (axons). Such a line can, however, be connected in two different ways to the next neuron: First: In an excitatory synapse, so that the stimulus causes the excitation of the neuron. Second: In an inhibitory synapse, so that the stimulus absolutely prevents the excitation of the neuron by any stimulus on any other (excitatory) synapse. The neuron also has a definite reaction time, between the reception of a stimulus and the emission of the stimuli caused by it, the synaptic delay.

Following W.S. MacCulloch and W. Pitts (“A logical calculus of the ideas immanent in nervous activity,” Bull. Math.Biophysics, Vol. 5 (1943), pp. 115–133) we ignore the more complicated aspects of neuron functioning: Thresholds, temporal summation, relative inhibition, changes of the threshold by after-effects of stimulation beyond the synaptic delay, etc. It is, however, convenient to consider occasionally neurons with fixed thresholds 2 and 3, that is, neurons which can be excited only by (simultaneous) stimuli on 2 or 3 excitatory synapses (and none on an inhibitory synapse). (cf. {6.4})

It is easily seen that these simplified neuron functions can be imitated by telegraph relays or by vacuum tubes. Although the nervous system is presumably asynchronous (for the synaptic delays), precise synaptic delays can be obtained by using synchronous setups. (cf. {6.3})

4.3 #

It is clear that a very high speed computing device should ideally have vacuum tube elements. Vacuum tube aggregates like counters and scalers have been used and found reliable at reaction times (synaptic delays) as short as a microsecond (= 10−6 seconds), this is a performance which no other device can approximate. Indeed: Purely mechanical devices may be entirely disregarded and practical telegraph relay reaction times are of the order of 10 milliseconds (= \(10^{-2}\) seconds) or more. It is interesting to note that the synaptic time of a human neuron is of the order of a millisecond (= \(10^{-3}\) seconds).

In the considerations which follow we will assume accordingly, that the device has vacuum tubes as elements. We will also try to make all estimates of numbers of tubes involved, timing, etc., on the basis that the types of tubes used are the conventional and commercially available ones. That is, that no tubes of unusual complexity or with fundamentally new functions are to be used. The possibilities for the use of new types of tubes will actually become clearer and more definite after a thorough analysis with the conventional types (or some equivalent elements, cf. {}) has been carried out.

Finally, it will appear that a synchronous device has considerable advantages (cf. {6.3}).