234 



A. Rapoport 



I will now describe a task which has been adapted to an analysis of the 

 problem-solving process in such a situation.* 



The subject is faced with a board on which nine numbered light bulbs are 

 arranged in a circle, at the center of which is a tenth bulb. Each of the peri- 

 pheral bulbs may be lit by an adjacent button. Moreover, relays are so arranged 

 inside the apparatus that lighting of certain lights may result in the lighting 

 of other lights following a constant 'synaptic delay' of three seconds. A 'prob- 

 lem' is a programming in the apparatus so that certain causal relations are 

 established among the lights. These causal relations are only partially represented 

 by arrows on a chart attached to the mounting board. Examples are given in 

 Figs. 1 and 2. 



Fig. 1. Problem 2 on PSI 



Fig. 2. Problem 3 on PSI 



The point of the problem is that the meanings of the arrows on the chart 

 are ambiguous. An arrow from A to B may mean that A is necessary to light 

 B or sufficient, or both, or that A inhibits B. The subject's task is to obtain 

 sufficient information about these relations, by pushing any button he chooses, 

 to be able to cause the center bulb to be lit by manipulating buttons 4, 5, and 6 

 only. We will refer to these as the circled buttons. 



There is a unique solution to each problem, consisting of a certain sequence 

 of pushes of the circled buttons or of their combinations. For example, the 

 solution to problem 2 (Fig. 1) is the pushing of buttons 4, 6, 5, 6 in the successive 

 time periods. The solution to Problem 3 (Fig. 2) is 5, 0, 45, 6, 45. 



There are a number of 'rational' approaches to the problem. Let us begin 

 by making a chart of the connections indicated by the arrows. Figs. 1 and 2 

 are formally equivalent (as linear graphs) to Figs. 3 and 4. However, many 

 characteristics of the problems are visually displayed in Figs. 3 and 4, which 

 immediately suggest various lines of attack. These charts display what the 



* The apparatus to be described, 'PSI', based on the isomorphism ofcertain networks of relays 

 and the calculus of propositions (previously discovered by Shannon (4) and by McCulloch 

 and Pitts (5)) was developed in Chicago by R. John, J. G. Miller, S. Molnar and H. J. A. 

 RiMOLDi. The adaptation of the instrument to experiments of the type described is largely due 

 to John (3), who has listed a great number of performance parameters to be observed in the 

 problem solving process. Of these the so-called 'inferential lag' (defined below) seems to me of 

 particular importance. John's terminology and definitions diff"er somewhat from those in this 

 paper, but the basic ideas (as yet unpublished) have been the point of departure for the present 

 analysis. 



