## Forgetfulness Of Purpose • 6

Just enough time for an incidental observation.

Consider the table Ashby uses to describe his first example of a regulation game.

$\begin{array}{cc|ccc} \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt] & & & R & \\ & & \alpha & \beta & \gamma \\ \hline & 1 & b & a & c \\ D & 2 & a & c & b \\ & 3 & c & b & a \end{array}$

A table like that is a compact way of describing a triadic relation, in this case a relation $L \subseteq D \times R \times O$ whose triples are displayed in the following relational data table.

$\begin{matrix} D & R & O \\ \hline 1 & \alpha & b \\ 1 & \beta & a \\ 1 & \gamma & c \\ 2 & \alpha & a \\ 2 & \beta & c \\ 2 & \gamma & b \\ 3 & \alpha & c \\ 3 & \beta & b \\ 3 & \gamma & a \end{matrix}$

May you find food for thought, a late night snack on those tables.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

## Forgetfulness Of Purpose • 5

Recall the game between R and D determined by the following data.

$\begin{array}{cc|ccc} \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt] & & & R & \\ & & \alpha & \beta & \gamma \\ \hline & 1 & b & a & c \\ D & 2 & a & c & b \\ & 3 & c & b & a \end{array}$

Here is Ashby’s analysis of how it plays out.

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;  if D selects 2, R selects α;  and so on.  In fact, if R acts according to the transformation

$\begin{array}{cccc} & 1 & 2 & 3 \\ \downarrow & & & \\ & \beta & \alpha & \gamma \end{array}$

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.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
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## Forgetfulness Of Purpose • 4

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

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:

$\begin{array}{cc|ccc} \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt] & & & R & \\ & & \alpha & \beta & \gamma \\ \hline & 1 & b & a & c \\ D & 2 & a & c & b \\ & 3 & c & b & a \end{array}$

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.

I’ll pause the play here and give readers a chance to contemplate strategies.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

## Forgetfulness Of Purpose • 3

Here is the first part of Ashby’s setup for the schematic example I had in mind.

## 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.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

## Forgetfulness Of Purpose • 2

I had planned to get down to brass tacks as quickly as possible, with an object example from Ashby’s Cybernetics that made an impression on me at an early stage in my thinking about intelligent systems.  But while I was looking for that my eye fell on on another passage that so well articulates one of the deepest roots of scientific reasoning that I could not resist reciting it here.

## Quantity of Variety

7/1.   In Part I we considered the main properties of the machine, usually with the assumption that we had before us the actual thing, about which we would make some definite statement, with reference to what it is doing here and now.  To progress in cybernetics, however, we shall have to extend our range of consideration.  The fundamental questions in regulation and control can be answered only when we are able to consider the broader set of what it might do, when “might” is given some exact specification.

Throughout Part II, therefore, we shall be considering always a set of possibilities.  The study will lead us into the subjects of information and communication, and how they are coded in their passages through mechanism.  This study is essential for the thorough understanding of regulation and control.  We shall start from the most elementary or basic considerations possible.

7/2.   A second reason for considering a set of possibilities is that science is little interested in some fact that is valid only for a single experiment, conducted on a single day;  it seeks always for generalisations, statements that shall be true for all of a set of experiments, conducted in a variety of laboratories and on a variety of occasions.  Galileo’s discovery of the law of the pendulum would have been of little interest had it been valid only for that pendulum on that afternoon.  Its great importance is due precisely to the fact that it is true over a great range of space and time and materials.  Science looks for the repetitive.

7/3.   This fact, that it is the set that science refers to, is often obscured by a manner of speech.  “The chloride ion …”, says the lecturer, when clearly he means his statement to apply to all chloride ions.  So we get references to the petrol engine, the growing child, the chronic drunkard, and to other objects in the singular, when the reference is in fact to the set of all such objects.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.