Simulation of Human Problem-Solving Method

One of the most intriguing and potentially important applications of the digital computer is in the simula tion of human thought processes. The objects of thought when suitably coded can be transformed, classified and stored within the computer at will.

The predominant charactertistic of human thought processes is their generality. To make any progress in the simulation of such processes, it is first necessary to isolate a small region and examine it in isolation. As progress is made in one region, it can be ex panded and generalized to include a wider field, and it is likely that many of the methods used in a re stricted field will be susceptible to modification for use in a larger area. It is desirable to work initially in a region in which the relationships between the ob jects of thought are clearly defined.

This report deals with the problem of finding se quences of transformations which constitute proofs of trigonometric identities. The method described need not be confined to this particular problem, but could easily be used in other fields if the allowable transformations are known. The behaviour of a ma chine which has been programmed to carry out this process is described in detail and its responses, when several identities were presented to it for proof, are given.

No attempt is made to use the method of finding proofs by exhaustive search, even though in this case such a search is quite feasible, since the number of "basic" trigonometric transformations which can be applied to a given function is relatively small. It is considered here that such repetitive "trial and error" methods are less interesting than the methods which we shall discuss. It is desirable to decide on the best transformation for a particular problem by compar ing the characteristics of the problem with the prop erties of each transformation in such a way that the machine's performance will improve with experi ence. Exhaustive search methods become useless when the number of possible decisions at each step becomes large.