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
woul
d 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
◇◇◇ a
n =
n
2 + 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.