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Let us assume that some probability can be determined that measures the likelihood that the decision maker (rat or man) will go to a particular side of the "T," say the side leading to the payoff on the tth stage. We will call this probability the Q probability for the tth stage. The initial value of this probability is not very important since during the learning process the Q probability is successively refined and approaches unity after a great many stages (trials). One can say, however, that the greater the deviation of the initial probability from unity, the greater the number of stages required to obtain some given level near unity.

2 shows, as one example, the time mapping function between several weeks of physical time and a number of periods of entropy time on the N ew York Stock Exchange. process is the daily marketing process, and the value is the number of transactions for that stage. Although this Entropy time. Y. Stock EKChange FIG. 2 t A great deal of attention to the time mapping function is essential to the correct interpretation of economic statistics. Statisticians are considering this problem when they deal with the seasonality of economic time series.

6) has a very important property. When glt+l = qIl' then gIl' and hence qlt+1' must be identical to unity. This can occur, for a value of (Xl and 0:2 subject to the above restrictions, only after an infinite number of stages. This can be seen by assuming an initial Q probability for the first stage, and solving the recursive Eqs. 6) for the probability at any stage, t, in terms of the initial Q probability. 9) If 0 < (Xl < 1, and 0 < (X2 < 1, since lim (X~ t~oo = 0, and then lim qlt = 1. t-sec If (Xl' (X2 = 1, then qlt = qlt for all t.

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