In remembering, items are used in the form in which they are alleged to have been perceived at some time in the past. In thinking, however, evidence is given and the essential character of the process is to move beyond this evidence, but in line with it, to something for which so far, no exact or complete perceptual basis is claimed. From an experimental point of view the best approach is to consider thinking as a high level skill, and to design experiments in the light of what has been discovered during recent years about the learning, practice and achievements of skill on a psycho-motor level. When this is done, it turns out that the thinking process can usefully be considered as one in which gaps are filled up in accord with specific evidence provided. The fundamental gap-filling processes are either of interpolation or of extrapolation. In the present paper the methodology proposed is developed and illustrated in a preliminary manner.