. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 14/15 DESIGN FOR A BRAIN of the two active variables ; and so on. If all the variables are inactive, the line becomes a point. Thus a three-variable system might give the line of behaviour shown in Figure 14/15/1. An absolute system composed of part-functions has also the property that if a variable changes from inactive to active, then amongst the variables which affect that variable directly there must, at that moment, have been at least one which was active. One might say, more vividly
. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 14/15 DESIGN FOR A BRAIN of the two active variables ; and so on. If all the variables are inactive, the line becomes a point. Thus a three-variable system might give the line of behaviour shown in Figure 14/15/1. An absolute system composed of part-functions has also the property that if a variable changes from inactive to active, then amongst the variables which affect that variable directly there must, at that moment, have been at least one which was active. One might say, more vividly but less accurately, that activity in one variable can be obtained only from activity in others. A proof is given in S. 24/16, but the reason is not difficult to see. Suppose for simplicity that a variable A is directly affected only by B and C, so that the diagram of immediate effects is B C. Figure 14/15/1. In the dif- ferent stages the active variables are: A, y; B, y and z; C, z; D, x\ E, y; F, x and 2. Suppose that over a finite interval of time all three have been constant, and that the whole is absolute. If B and C remain at these constant values, and if A is started at the same value as before, then by the absoluteness A's behaviour must be the same as before, A must stay constant. The property has nothing to do with energy or its conservation ; nor does it attempt to dogmatise about what real 4 machines ' can or cannot do ; it simply says that if B and C remain constant and A changes from inactive to active, then the system cannot be absolute—in other words, it is not completely isolated. The sparks which wander in charred paper give a vivid picture of this property : they can spread, one can become multiple, or several can converge ; but no spark can arise in an unburning region. 14/16. Part-functions were introduced primarily in the hope that they would provide a system more readily stabilised than one of full-functions. It can now be shown that this is so. 1
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