ALBERT

Notes: Zusammenfassung Anhand der Übertragungseigenschaften der einzelnen Glieder des sog. „inneren” Regelkreises der Willkürbewegung, Rezeptor-Rückenmark-Muskulatur, wurde der Übertragungsfaktor des gesamten Regelkreises aufgestellt. Ganz allgemein gilt danach für die Gliedmaßenbewegung, daß sie den Gesetzen eines Proportional-Integral-Regelsystems gehorcht. Ferner werden die Bedingungen für den Angriff der Führungs-und Störgrößen aus dem abgeleiteten Übertragungsfaktor diskutiert, insbesondere im Hinblick auf die Einspeisung der Führungsgröße an den Muskelspindeln oder in dem Rückenmark.

Notes: Summary Feedback mechanisms exist in all the periferal sense organs including the eye, which acts as a highly efficient position control servo system. Histological studies so far have not revealed the precise circuitry of the eye movement control system but some information about it can be obtained by a study of the sources of feedback. Existing theories have considered three types of feedback originating in the oculomotor tract, in the proprioceptive fibres of the extrinsic eye muscles and from retinal image displacement. In the present experiments an optical arrangement has been used to vary or eliminate the amount of information available from retinal image motion, and the response of the eye to simple harmonic displacement of a target has been recorded. The response curves of gain (eyeball movement divided by target motion) against frequency indicate that the system is lion linear when the image falls in the retinal region which is insensitive to position. Outside this area, retinal image position is used as negative feedback but the information from the oculomotor tract must be regenerative. There is also evidence for feedback proportional to the first derivative of eyeball position and this function is ascribed to the proprioceptive signals; this form of feedback appears to saturate for large amplitude movements, thus avoiding heavy damping of the flick movements. A schematic eye movement control system having the same characteristics as the eye is proposed. The transfer function of this system indicates that it should be unstable if the sign of the retinal image feedback loop is reversed. Experiments with this form of feedback show that steady fixation is impossible and the eye performs a pendular nystagmus.

Notes: Summary It is shown that the traditional antithesis of mind and matter stems from a grave misunderstanding or rather misarrangement of empirical facts. This oblique antithesis and numerous well-known contradictions connected with it are eliminated by careful analysis of the intricate situation from which they arose. The solution of the problem leads to a clear understanding of fundamental concepts upon which Cybernetics is founded, and of the achievements potentially within its reach.

Notes: Summary The level (=arithmetic average of all instantaneous values)of a self-sustained oscillation in general influences all properties of the oscillation, including period, amplitude and shape of the oscillation, and the rate of exchange of energy between the oscillator and its environment. Only when the non-linear damping factor does not depend on the instantaneous value of the oscillating function, but only on the amplitude of the oscillation, are the other properties independent of the average level. The differential equations describing self-sustained oscillations cannot be solved exactly, but methods of approximation are applicable. Numerical solutions to several different forms of the equations will be discussed. In the simplest case (van der Pol equation) all properties of the self-sustained oscillation (e.g. period, amplitude) are extreme when the level is zero. The oscillation continues only within a given range of levels (oscillating range); outside this range, the oscillation damps out. In other modifications of the equation, the oscillating function cannot assume a zero value. In all cases, the extent to which the average level influences the different properties depends on the factor ɛ, which describes the position of the oscillation within the range between harmonic and relaxation types of oscillation. In the elementary van der Pol equation, the correlation between level and frequency changes sign within the oscillating range; that is, the circadian rule, demanding an always positive correlation between level and frequency, cannot be fulfilled. Only with an additional non-linearity in the energy of recoil does the correlation remain unchanged in sign throughout the oscillating range. A stability condition demands a positive sign for this non-linearity, and hence, for the correlation (fulfilling the circadian rule); if the sign is negative (violating the circadian rule), the oscillation becomes unstable. With an additional term of the third order, the oscillation acquires a two-peaked shape typical of many circadian oscillations. A simple differential equation describing all general properties of the circadian periodicity must fulfil these conditions: the oscillation must be self-sustained and limited to positive values; and the energy of recoil must be non-linear with a positive coefficient to obtain the appropriate correlation between level and frequency. In the equations here developed the environment directly influences only one parameter of the oscillation, i.e. the level. In addition to the circadian periodicity, the differential equations here examined describe the behavior of several other biological oscillations.