Preface to the lecture, 1

180

 

basic principle of cybernetics

 

 

Fig. 8.6:    Control technical analysis of the dual equations 

of the hydromagnetic field.

 

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unified theory_______________________________________________________________ 181

 

8.6 Basic principle of cybernetics

 

Surely can be attributed also information to the potential vortex. But how should infor-

 

mation be formed? Is information a form of energy? Energy occurs as a consequence of

 

the formation of potential vortices. Without this phenomenon there wouldn't be any

 

energy! 

Can information be described by means of a mathematical equation?

 

To be able to answer these questions, we subject the fundamental field equation to a 

control technical analysis. If it actually concerns a world equation, then an answers should 

be possible.

 

We again take up Ampere's law 5.1* from fig. 5.1 and remodel it according to the time 

derivative (5.1**). If the equation now is integrated over the time (5.1***), a signal flow 

diagram can be drawn (fig. 8.6).

 

The structure of a regulatory circuit is clearly visible. The individual paragraphs are 

described in an analogous way as for a technical control system. The execution of the curl 

operation on the field pointer of the magnetic field strength H and the multiplication with 

  accordingly form an adaptation of driving factors. In the comparator the difference for 

control from driving factor w and controlling factor x is formed and supplied to an 

integral controller. The control path has a purely proportional behaviour and consists of 

the processing of the measurement value of the electric field strength E with 

 in which

 

 

describes the relaxation time of the eddy currents. 

In technical control systems such a structure is found remarkably seldom, although it has 

an invaluable advantage: it possesses a stability in principle. Not a single adjustment of 

the controller exists, in which the closed regulatory circuit could become unstable, 

because it shows a proportionally delaying behaviour of first order. Possible changes of 

the adjustment of the controller or of the control path merely take effect on the speed, with 

which the regulatory circuit is able to follow changes of the driving factor. 

This control technical basic principle convinces by its simplicity and efficiency. It meets 

us again in identical form in the second field equation 5.4*, the extended Faraday's law of 

induction. In dual formulation the electric field strength now appears as input factor and 

the magnetic field strength as output factor. Both regulatory circuits are coupled and 

connected with each other, by deriving their driving factor each time from the controlling 

factor of their dual partner. Is this structure actually efficient and meaningful? 

Every regulatory circuit needs a target value, which is dictated from the outside. Let us 

think of the numerous control systems in nature. At all events a higher intelligence would 

be necessary for all the target values. This problematic is comparable to the question, what 

existed first: the egg from which a hen hatches or the hen without which no eggs can exist. 

Without a given target, evolution would not exist.

 

The connected regulatory circuit structure provides the matching answer: cybernetic 

systems, which usually and as is well-known strive to a state of balance, get their target 

value from their dual "partner". It is crucial that correspondingly dual systems are self- 

sufficient and can form and develop independently out of themselves without target values 

of a third side. This basic principle of cybernetics undoubtedly is brilliant.

 

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182

 

adaptive regulatory circuit structure

 

 

Fig. 8.7:      Signal flow diagram of the fundamental field 

equation 

with adaptive structure. 

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unified theory ________________________________________________________ 183

 

8.7 Adaptive regulatory circuit structure

 

If out of the nowhere something like the cosmos or like life on earth should form, then the 

connected regulatory circuit structure basing on duality probably is the only possible and 

conceivable. Thus it merely concerns the control technical representation of the funda- 

mental field equation.

 

The question for the efficiency not only concerns the stability, but equally the possibility 

of both systems, to oscillate and to communicate with each other by the coupling and the 

associated exchange of information.

 

Fig. 8.7 shows the signal flow diagram of both regulatory circuits. These are switched in 

line and form a coupled circuit, which itself can be interpreted as a third regulatory circuit. 

Also this one shows a change of sign in the circuit like the other two circuits.

 

The information technical interpretation could turn out as follows: information about a 

regulatory process in the lower regulatory circuit F

11

 caused for instance by a disturbance 

is communicated over the coupled circuit to the upper regulatory circuit F

J2

. In this case 

F

11

 acts as transmitter and F

12

 as receiver of the information. Afterwards both exchange 

their places, because F

12

 for its part reacts by a regulatory process and reports to F

11

. The 

regulatory circuits adapt to each other. Obviously it concerns the basic structure of an 

adaptive regulatory circuit.

 

To analyse the coupled circuit the examination of individual special cases is 

recommended. If the regulatory circuits F

11

 and F

12

 are opened up in the way that the time 

constants tau

1

 and tau

2

 go towards infinity, then the double integral effect is left. Analyses of 

technical regulatory circuit teach us that such systems always tend to instability. Because 

in addition the target value is zero, an oscillation around zero will arise, which we call 

electromagnetic wave.

 

If one of both time constants becomes finite, e.g.

  then damping of the waves will occur. 

The "subordinate" cascade regulatory circuit F

12

 will adjust itself and now has a propor- 

tional delaying behaviour of first order. Together with the integral controller of the open 

F

11

- circuit the coupled circuit will show the typical and more or less optimal regulatory 

behaviour of a damped oscillation.

 

These special cases correspond with the mathematical (fig. 5.2) and the physical (fig. 5.3) 

interpretation of the fundamental field equation. In addition a spatial rotation, a swirling 

will occur because of the double execution of the curl operation.

 

If interpreted control technically then vortices are the temporally stable, spatial swing of a 

field pointer around a centre, the vortex centre.

 

Without potential vortices no stability, no matter, no energy nor information would exist!

 

As can be looked up in Goethe's Faust, it always has been a desire of humanity, to find 

out, "what keeps the world together in the heart of hearts".

 

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