6.0 E-ELEMENTS #

6.1 #

The considerations of 5.0 have defined the main principles for the treatment of CA. We continue now on this basis, with somewhat more specific and technical detail.

In order to do this it is necessary to use some schematic picture for the functioning of the standard element of the device: Indeed, the decisions regarding the arithmetical and the logical control procedures of the device, as well as its other functions, can only be made on the basis of some assumptions about the functioning of the elements.

The ideal procedure would be to treat the elements as what they are intended to be: as vacuum tubes. However, this would necessitate a detailed analysis of specific radio engineering questions at this early stage of the discussion, when too many alternatives are still open to be treated all exhaustively and in detail. Also, the numerous alternative possibilities for arranging arithmetical procedures, logical control, etc., would superpose on the equally numerous possibilities for the choice of types and sizes of vacuum tubes and other circuit elements from the point of view of practical performance, etc. All this would produce an involved and opaque situation in which the preliminary orientation which we are now attempting would be hardly possible.

In order to avoid this we will base our considerations on a hypothetical element, which functions essentially like a vacuum tube—e.g. like a triode with an appropriate associated RLC-circuit—but which can be discussed as an isolated entity, without going into detailed radio frequency electromagnetic considerations. We re-emphasize: This simplification is only temporary, only a transient standpoint, to make the present preliminary discussion possible. After the conclusions of the preliminary discussion the elements will have to be reconsidered in their true electromagnetic nature. But at that time the decisions of the preliminary discussion will be available, and the corresponding alternatives accordingly eliminated.

6.2 #

The analogs of human neurons, discussed in 4.2–4.3 and again referred to at the end of 5.1, seem to provide elements of just the kind postulated at the end of 6.1. We propose to use them accordingly for the purpose described there: As the constituent elements of the device, for the duration of the preliminary discussion. We must therefore give a precise account of the properties which we postulate for these elements.

The element which we will discuss, to be called an E-element, will be represented to be a circle ◯, which receives the excitatory and inhibitory stimuli, and emits its own stimuli along a line attached to it: ◯−−. This axon may branch: ◯−−<, ◯−−<−−. The emission along it follows the original stimulation by a synaptic delay, which we can assume to be a fixed time, the same for all E-elements, to be denoted by τ . We propose to neglect the other delays (due to conduction of the stimuli along the lines) aside of τ . We will mark the presence of the delay τ by an arrow on the line: ◯→−, ◯→−<. This will also serve to identify the origin and the direction of the line.

6.3 #

At this point the following observation is necessary. In the human nervous system the conduction times along the lines ( axons) can be longer than the synaptic delays, hence our above procedure of neglecting them aside of τ would be unsound. In the actually intended vacuum tube interpretation, however, this procedure is justified: τ is to be about a microsecond, an electromagnetic impulse travels in this time 300 meters, and as the lines are likely to be short compared to this, the conduction times may indeed by neglected. (It would take an ultra high frequency device— \(\tau \approx 10^{-8}\) \(\) seconds or less—to vitiate this argument.)

Another point of essential divergence between the human nervous system and our intended application consists in our use of a well-defined dispersionless synaptic delay τ , common to all E-elements. (The emphasis is on the exclusion of a dispersion. We will actually use E-elements with a synaptic delay 2τ , cf. {6.4, 7.3}.) We propose to use the delays τ as absolute units of time which can be relied upon to synchronize the functions of various parts of the device. The advantages of such an arrangement are immediately plausible, specific technical reasons will appear in {}.

In order to achieve this, it is necessary to conceive the device as synchronous in the sense of 4.1. The central clock is best thought of as an electrical oscillator, which emits in every period τ a short, standard pulse of a length τ‘ of about (1/5)τ – (1/2)τ . The stimuli emitted nominally by an E-element are actually pulses of the clock, for which the pulse acts as a gate. There is clearly a wide tolerance for the period during which the gate must be kept open, to pass the clock-pulse without distortion. Cf. Figure 1. Thus the opening of the gate can be controlled by any electric delay device with a mean delay time τ , but considerable permissible dispersion. Nevertheless the effective synaptic delay will be τ with the full precision of the clock, and the stimulus is completely renewed and synchronized after each step. For a more detailed description in terms of vacuum tubes, cf. {}.

6.4 #

Let us now return to the description of the E-elements.

An E-element receives the stimuli of its antecedents across excitatory synapses: −−◯→−, or inhibitory synapses: −−•◯→−. As pointed out in 4.2, we will consider E-elements with thresholds 1, 2, and 3, that is, which get excited by these minimum numbers of simultaneous excitatory stimuli.

All inhibitory stimuli, on the other hand, will be assumed to be absolute. E-elements with the above thresholds will be denoted by ◯, ➁ , ➂ , respectively.

Since we have a strict synchronism of stimuli arriving only at times which are integer multiples of τ , we may disregard phenomena of tiring, facilitation, etc. We also disregard relative inhibition, temporal summation of stimuli, changes of threshold, changes of synapses, etc. In all this we are following the procedure of W.J. MacCulloch and W. Pitts (cf. loc. cit. 4.2). We will also use E-elements with double synaptic delay 2τ : −−◯→−→−, and mixed types: −−◯→−<→−.

The reason for our using these variants is that they give a greater flexibility in putting together simple structures, and they can all be realized by vacuum tube circuits of the same complexity.

It should be observed that the authors quoted above have shown that most of these elements can be built up from each other. Thus −−◯→−→− is clearly equivalent to −−◯→−◯→−, and in the case of ➁→− at least ==➁→− is equivalent to the network of Figure 2. However, it would seem to be misleading in our application to represent these functions as if they required 2 or 3 E-elements, since their complexity in a vacuum tube realization is not essentially greater than that of the simplest E-element −−◯→−, cf. {}.

We conclude by observing that in planning networks of E-elements, all backtracks of stimuli along the connecting lines must be avoided. Specifically: The excitatory and the inhibitory synapses and the emission points—that is the three connections on ==•◯→− will be treated as one-way valves for stimuli—from left to right in the above picture. But everywhere else the lines and their connections >•< will be assumed to pass stimuli in all directions. For the delays →− either assumption can be made, this last point does not happen to matter in our networks.

6.5 #

Comparison of some typical E-element networks with their vacuum tube realizations indicates that it takes usually 1–2 vacuum tubes for each E-element. In complicated networks, with many stimulating lines for each E-element, this number may become somewhat higher. On the average, however, counting 2 vacuum tubes per E-element would seem to be a reasonable estimate. This should take care of amplification and pulse-shaping requirements too, but of course not of the power supply. For some of the details, cf. {}.