Now it is true that I have deliberately made up the cases 46) to 49) so as to make a conjecture of this kind seem reasonable. But I have also deliberately made them up so as not to contain a conjecture. We can, if we like, make the hypothesis that the tribe would never use such a form of expression as that used in 49), etc. if experience had not shown them that … etc. But this is an assumption which, though possibly correct, is in no way presupposed in the games 46) to 49) as I have actually described them.
62).   Let the game be this: A writes down a row of numbers. B watches him and tries to find a system in the sequence of these numbers. When he has done so he says: “Now I can go on”. This example is particularly instructive because “being able to
56.
go on” here seems to be something setting in suddenly in the form of a clearly outlined event. ‒ ‒ Suppose then that A had written down the row 1,5,11,19,29. At that point B shouts, “Now I can go on”. What was it that happened when suddenly he saw how to go on? A great many different things might have happened. Let us assume then that in the present case while A wrote one number after the other B busied himself with trying out several algebraic formulae to see whether they fitted. When A had written “19” B had been led to try the formula ◇◇◇ an = n2 + n ‒ 1. A's writing 29 confirms his guess.
63).   Or, no formula came into B's mind. After looking at the growing row of numbers A was || is writing, possibly with a feeling of tension and with hazy ideas floating in his mind, he said to himself the words, “He's squaring and always adding one more”; then he made up the next number of the sequence and found it to agree with the numbers A then wrote down. ‒ ‒
64).   Or the row A wrote down was 2, 4, 6, 8. B looks at it, and says, “Of course I can go on”, and continues the series of even numbers. Or he says nothing, and just goes on. Perhaps when looking at the row 2, 4, 6, 8 which A had written down, he had some sensation, or sensations, often accompanying such words as, “That's easy!” A sensation of this kind is for instance, the experience of a slight, quick intake of breath, what one might call a slight start.