## Forgetfulness Of Purpose • 8

Re: Peirce List Discussion • (1)(2)

Just to review, we were looking at Ashby’s example of a regulation game as given below.

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

I observed that this gives us a triadic relation $G_1 \subseteq D \times R \times O$ whose triples are listed next.

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

Sungchul Ji raised a question about the irreducibility of $G_1$ as a triadic relation, suggesting that it would imply a degree of “communication” or “transfer of information” between $D$ and $R$ as constrained by the relation $G_1.$

For the moment I remain puzzled how we ought to measure various orders and quantities of information that affect the play of regulation games.  That question evidently depends on the kinds of structures that are key to the regulation task.  The quickest way to gain information on those scores is probably to read a little further in Ashby’s text, so I will set a goal of doing that.

On the other hand, the irreducibility of $G_1$ as a triadic relation can be investigated more directly, without considering the information question, so I will try that tack first.

### Reference

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