Reference: Newtonian Mechanics by A. P. French.
“Look at this mathematician,” said the logician. “He observes that the first 99 numbers are less than 100 and infers, hence, by what he calls induction, that all numbers are less than a hundred.” “A physicist believes,” said the mathematician, “that 60 is divisible by 1, 2, 3, 4, 5 and 6. He examines a few more cases, such as 10, 20 and 30, taken at random (as he says). Since 60 is also divisible by these, he considers the experimental evidence sufficient.” “Yes, but look at the engineers,” said the physicist. “An engineer suspected that all odd numbers are prime numbers. At any rate, 1 can be considered as a prime number, he argued. Then, there come 3, 5 and 7, all indubitably primes. Then, there comes 9, an awkward case; it does not seem to be a prime number. Yet, 11 and 13 are certainly primes. “Coming back to 9,” he said, ‘I conclude that 9 must be an experimental error. ‘” But, having done his teasing, George Polya adds these remarks:
It is only too obvious that induction can lead to error. Yet it is remarkable that induction sometimes leads to truth, since the chances of error seem overwhelming. Should we begin with the study of the obvious cases in which induction succeeds? The study of precious stones is understandably more attractive than that of ordinary pebbles and , moreover, it was much more the precious stones than the pebbles that led the mineralogists to the wonderful science of crystallography.
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