100,000,001 100,010,002 100,030,003 100,060,004 100,100,005 100,150,006 100,210,007 100,280,008.
For a hundred or even a thousand terms they continued to follow the new law relating to the triangular numbers, but after watching them for 2761 terms we find that this law fails at the 2762nd term.
If we continue to observe we shall discover another law then coming into action which also is different, dependent, but in a different manner, on triangular numbers because a number of points agreeing with their term may be placed in the form of a triangle, thus:—
(1 dot.) (3 dots in the form of a triangle.) (6 dots in the form of a triangle.) (10 dots in the form of a triangle.) (one, three, six, ten).
This will continue through about 1430 terms, when a new law is again introduced over about 950 terms, and this too, like its predecessors, fails and gives place to other laws which appear at different intervals."), and asking what effect this phenomenon had upon the theory of Induction. Huxley replied as follows:—]
Grand Hotel, Eastbourne, July 21, 1890.
Dear Sir,
I knew Mr. Babbage, and am quite sure that he was not the man to say anything on the topic of calculating machines which he could not justify.
I do not see that what he says affects the philosophy of induction as rightly understood. No induction, however broad its basis, can confer certainty—in the strict sense of the word. The experience of the whole human race through innumerable years has shown that stones unsupported fall to the ground, but that does not make it certain that any day next week unsupported stones will not move the other way. All that it does justify is the very strong expectation, which hitherto has been invariably verified, that they will do just the contrary.
Only one absolute certainty is possible to man—namely, that at any given moment the feeling which he has exists.