236 A. Rapoport 



State of mind of the subject. According to another scheme (labeHng arrows), 

 one can assign the values to the arrows in eighteen different ways at the triple 

 juncture! and in four different ways at each of the three double junctures. 

 Hence there are 18 x 64 different ways. This gives a little over ten bits of 

 uncertainty. According to the last scheme, one has to decide whether to push or 

 not to push each of the circled buttons in the time period when they appear on 

 the chart. Here Problem 2 seems to have four bits of uncertainty and Problem 3 

 seems to have six bits. Clearly, the amounts of uncertainty associated with 

 each scheme are different, but so are the yields of each trial, because one counts 

 the yield in different kinds of statements, which have different a priori probabili- 

 ties of being true. 



One can push the analysis still further and thus reduce the information 

 content of each problem by utiHzing the rule that each problem has a unique 

 solution. In this analysis the 'sample space' v/ould be all possible problems 

 having unique solutions involving the circled buttons at the proper time periods. 

 Several of such problems would 'map' on each solution, and since the number 

 of problems mapping on each solution are not equal, neither are the probabihties 

 of the respective solutions. The value 4 bits for Problem 2 is a consequence 

 of the equi-probability of all sixteen solutions (strictly speaking fifteen, barring 

 the null solution where no button is pushed). If the solutions are not equi- 

 probable the infonnation content is correspondingly reduced. 



This calcu'ation is extremely tedious and has not been carried out. It is 

 mentioned only to stress the general idea that the information content of the 

 PSI problems depends significantly on the 'sample space' according to wliich 

 probabilities are assigned. This sample space is presumably chosen (perhaps 

 unconsciously) by the subject; hence the amount of uncertainty in the problem 

 is a 'subjective' quantity, difficult to ascertain but in principle inferrable from a 

 thoroughgoing analysis of the problem solving process. 



One sees thus that even pursuing a far-reaching analysis and assuming 

 perfect memory, it is not easy to derive the best strategy in the sense of minimiz- 

 ing exploratory trials. When one takes into consideration the ambiguities 

 present in the subject's mind, who may not even have the convenient visual 

 representation of the time sequence in his mind's eye, one realizes that far more 

 psychology than can be formally treated by information theory at this time is 

 involved in the problem. 



Nevertheless, it is possible to cast the problem into information theoretical 

 terms. One hopes, at any rate, that the concepts of information theory can be 

 extended to cover situations where the subject's perception of the problem is 

 an important unknown, That is, information theory may help formulate such 

 situations in quantitative and analytic language. We have attempted to do so 

 in the following way. We record the successive trials. Each trial must yield at 

 least one of the sixteen 'crude facts', i.e. combinations of lights at each juncture 



t In view of the rule that each arrow must have a meaning, the number of ways values can 

 be assigned to the arrows equals the number of distinct irreducible disjunctions among the 

 subsets of the arrows. Thus for three converging arrows there are seven non-null subsets 

 (i.e. 'disjunctions' involving only one subset), tliree disjunctions among the singles involving 

 two singles, three among the doubles involving two doubles, three involving a single and a 

 double, one involving all three doubles, and one involving all three singles, eighteen in all. 



