. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 2/16 DESIGN FOR A BRAIN is both necessary and sufficient; so all state-determined systems are absolute. We shall use this fact repeatedly. The field of an absolute system is characteristic : from every point there goes only one line of behaviour whether the point is initial on the line or not. The field of the two-variable system just mentioned is sketched in Figure 2/15/1; through every point passes only one line. These relations may be made clearer if this field is contrasted with one t
. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. 2/16 DESIGN FOR A BRAIN is both necessary and sufficient; so all state-determined systems are absolute. We shall use this fact repeatedly. The field of an absolute system is characteristic : from every point there goes only one line of behaviour whether the point is initial on the line or not. The field of the two-variable system just mentioned is sketched in Figure 2/15/1; through every point passes only one line. These relations may be made clearer if this field is contrasted with one that is regular but not absolute. Figure 2/15/2 shows such a field (the system is described in S. 19/15). The system's regularity would be established if we found that the system, started at A, always went to A\ and, started at B, always went to B\ But such a system is not absolute ; for to say that the repre- sentative point is leaving C is insuf- ficient to define its future line of behaviour, which may go to A' or B'. Figure 2/15/2 : The field Even if the lines from A and B always Figure ™ in ran to A' and B', the regularity in no way restricts what would happen if the system were started at C: it might go to D. If the system were absolute, the lines CA', CB\ and CD would coincide. A system's absoluteness is determined by its field ; the property is therefore wholly objective. An absolute system's field does not change with time. 2/16. We can now return to the question of what we mean when we say that a system's variables have a c natural ' association. What we need is not a verbal explanation but a definition, which must have these properties : (1) it must be in the form of a test, separating all systems into two classes ; (2) its application must be wholly objective ; (3) its result must agree with common sense in typical and undisputed cases. The third property makes clear that we cannot expect a proposed definition to be established by a few lines of verbal a
Size: 1453px × 1719px
Photo credit: © Central Historic Books / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookpublishernewyorkwiley, booksubjectneurophys
