The first thing to happen is the arousal of a feeling of perplexity, the appearance of a problem. The man has been shambling along, doubtless “thinking” in that loose sense referred to. He has perhaps kicked several stones loose that would have set a geologist worrying, and has picked branches from bushes which would have puzzled a botanist. But this man has not had his curiosity aroused until he has come to these footprints. His thinking starts with his perplexity. After this doubt has been aroused the most obvious solution suggests itself—“my own footprints.” But if true, this suggestion involves the co-existence of other facts, some of which are known and some of which may be determined. Thus, _if_ they were his own footprints, it must, among other things, necessarily follow (1) that he had been at that spot before, (2) that nothing had happened since that time to remove the prints, (3) that the footprints corresponded to his own. The first consequence involved—that he had been there before—was a fact, but the others were not, and so the suggestion was dropped. Then a second hypothesis occurred—“the man came in a ship”—and this was tried out in a similar way. Notice that in each case the consequences dependent on the truth of the suggestion are tried out (1) by memory, (2) by observation or experiment. Memory came when he thought of the last time he had walked near the beach and of yesterday’s storm. Observation came when he compared his footprint with the one seen, when he followed the footprints along the sand and noticed where they led, when he climbed a tree and looked for a ship. There were a number of other things which he could have observed. He might have noticed the texture of the sand, what kind of a tree he was climbing, what sort of clouds were in the sky. But he did not observe these interesting things simply because they would throw no light on the truth or falsity of his supposition. In another problem one of these facts might have been of value. It is almost possible to sum up the whole process of thinking as the occurrence of suggestions for the solution of difficulties and the testing out of those suggestions. The suggestions or suppositions are tested by observation, memory, experiment. Supposition and observation alternate. The first facts observed—in the case foregoing, the footprints—make the problem, they suggest the supposition. A supposition is that the man came in a boat. _If_ the man came in a boat such and such would be the case—the boat would still be visible, etc. If the boat is not visible the supposition is given up and another one made; if the boat is visible the supposition is confirmed. This is a case of simple and rudimentary thinking, but it illustrates roughly the process of thought on even the most complicated problems of science. The methods we have been discussing may all be considered simply as means for helping good suggestions occur to us.