## 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.
This entry was posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory and tagged , , , , , , , , . Bookmark the permalink.

### 2 Responses to Forgetfulness Of Purpose • 5

1. As a game, it becomes a little (but only a little) more interesting when R&D make their selections in ignorance of the other’s choice. From my brief glance, it looks like (under those constraints) a random choice matrix becomes the only one that “works” for both, where “works” means provides any chance of breaking even. But my intuitions on such things are demonstrably crappy, so I look forward to the next entry.

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