Cybernetics • Requisite Variety

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Jon Awbrey

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Dec 30, 2019, 4:24:53 PM12/30/19
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Cybernetics : Requisite Variety : Selection 11
At: https://inquiryintoinquiry.com/2019/12/30/cybernetics-%e2%80%a2-requisite-variety-%e2%80%a2-selection-11/

Ashby now takes a few steps back from the picture of regulation in biological systems,
setting out the framework he needs for a broader perspective on regulation in general.

<QUOTE>

Requisite Variety
=================

11/1. In the previous chapter we considered regulation from the biological point of view, taking it as something
sufficiently well understood. In this chapter we shall examine the process of regulation itself, with the aim of
finding out exactly what is involved and implied. In particular we shall develop ways of measuring the amount or degree
of regulation achieved, and we shall show that this amount has an upper limit.

11/2. The subject of regulation is very wide in its applications, covering as it does most of the activities in
physiology, sociology, ecology, economics, and much of the activities in almost every branch of science and life.
Further, the types of regulator that exist are almost bewildering in their variety. One way of treating the subject
would be to deal seriatim with the various types; and chapter 12 will, in fact, indicate them. In this chapter,
however, we shall be attempting to get at the core of the subject — to find what is common to all.

What is common to all regulators, however, is not, at first sight, much like any particular form. We will therefore
start anew in the next section, making no explicit reference to what has gone before. Only after the new subject has
been sufficiently developed will we begin to consider any relation it may have to regulation.

</QUOTE>

Reference
=========

* Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK. Republished by Methuen and Company,
London, UK, 1964. Online ( http://pespmc1.vub.ac.be/books/IntroCyb.pdf ) .

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Jon Awbrey

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Jan 8, 2020, 2:56:17 PM1/8/20
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Cybernetics : Requisite Variety : Selection 12
At: http://inquiryintoinquiry.com/2020/01/08/cybernetics-%e2%80%a2-requisite-variety-%e2%80%a2-selection-12/

Ashby now invites us to consider a series of games, beginning as follows.

<QUOTE>

Requisite Variety
=================

11/3. Play and outcome. Let us therefore forget all about regulation and simply suppose that we are watching two
players, R and D, who are engaged in a game. We shall follow the fortunes of R, who is attempting to score an "a". The
rules are as follows. They have before them Table 11/3/1, which can be seen by both:

Table 11/3/1 (linked here & attached below)
https://inquiryintoinquiry.files.wordpress.com/2020/01/ashby-cybernetics-table-11.3.1.png

D must play first, by selecting a number, and thus a particular row. R, knowing this number, then selects a Greek
letter, and thus a particular column. The italic letter specified by the intersection of the row and column is the
outcome. If it is an "a", R wins; if not, R loses.

</QUOTE>

I'll pause the play here and give readers a chance to contemplate strategies.
Ashby Cybernetics Table 11.3.1.png

Jon Awbrey

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Jan 9, 2020, 4:56:19 PM1/9/20
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Cybernetics : Requisite Variety : Selection 13
At: http://inquiryintoinquiry.com/2020/01/09/cybernetics-%e2%80%a2-requisite-variety-%e2%80%a2-selection-13/

All,

Our venture into cybernetics, the study of systems whose time evolution signifies an object, brings us to the point of
seeing how pragmatic, semiotic, and systems thinking all have triadic relations at their core.

Recall the game between R and D determined by the following data:
We continue with Ashby's analysis of how the game plays out.

<QUOTE>

Requisite Variety
=================

11/3.[cont.] Examination of the table soon shows that with this particular table R can win always. Whatever value D
selects first, R can always select a Greek letter that will give the desired outcome. Thus if D selects 1, R selects β
(beta); if D selects 2, R selects α (alpha); and so on. In fact, if R acts according to the transformation

Figure 11/3/2 (linked here & attached below)
https://inquiryintoinquiry.files.wordpress.com/2020/01/ashby-cybernetics-figure-11.3.2.png

then he can always force the outcome to be "a".

R's position, with this particular table, is peculiarly favourable, for not only can R always force "a" as the outcome,
but he can as readily force, if desired, "b" or "c" as the outcome. R has, in fact, complete control of the outcome.
Ashby Cybernetics Table 11.3.1.png
Ashby Cybernetics Figure 11.3.2.png
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