The authors describe this paper as an attempt to understand more about the process of human design and to discover what lessons can be carried over to building systems that automatically derive algorithms or assist human designers. To this end, they present their analysis and interpretation of one subject’s recorded comments as a first attempt is made to design an algorithm to construct a convex hull. The algorithm is designed, given a set of points, to find a subset of the points which, when suitably joined together, will form a polygon enclosing all the other points.
The interpretation of the subject’s comments is claimed to be based on theories of Newell and Simon [1], which model problem solving as a progress through a problem space from some initial state (the problem) to a final (solution) state under the control of a collection of search rules; these search rules include refinement, means-end analysis, and symbolic execution. The concept of a dataflow problem space is introduced, and an attempt is made to describe the gradual refinement of the algorithm in terms of dataflow concepts.
Conclusions from a final discussion are as follows:
(1) Algorithm representations must necessarily be ambiguous initially.
(2) A variety of search rules must allow for naive and expert problem solving styles.
(3) Means-end analysis must be involved in searching, as well as trying a succession of predetermined operators.
I believe that work of the type described must be persevered, however vague and unsatisfactory it may appear in the reporting, particularly by those accustomed to achieving results by applying formal methods to comparatively trivial problems. Using a subject’s recorded comments as a guide to his or her thought processes of course begs the question of a relationship. The need to actually provide comments would, I think, be certain to modify how the work progresses. However, I have no better method to suggest.
I have two overall comments. First, it seems so often to me that the attempt to formalize a human process mathematically is prone to lose exactly those parts of the process that are significant in some human sense. Second, it seems that there is widespread confusion over what is meant by analysis. I see analysis not as getting to “what is really there,” but as a creative process of constructing a necessarily limited model of an event; the model would inevitably reflect both the skill and the personal biases of the analyst. Building models of human performance clearly depends on the depth and the width of experience of the builder in the particular area concerned. I am not confident that computer science provides the ideal background for this daunting task, but I suppose that we must continue humbly to do our best from wherever we are.
Finally, I am delighted to support the authors’ insistence on the essential need of copying human methods of problem solving because they can be continually augmented and adapted, and because they are flexible and robust; current formally designed “computing systems” are sadly lacking, as they say, in these areas.
