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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This entry was posted in Anamnesis, Ashby, 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.

  2. Pingback: Homunculomorphisms • 1 | Inquiry Into Inquiry

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