Life and Habit | Page 7

instruction, which in the case of most people would require a long
education. The account of Zerah Colburn, as quoted from Mr. Baily in
Dr. Carpenter's "Mental Physiology," may perhaps be given here.
"He raised any number consisting of ONE figure progressively to the
tenth power, giving the results (by actual multiplication and not by
memory) FASTER THAN THEY COULD BE SET DOWN IN
FIGURES by the person appointed to record them. He raised the
number 8 progressively to the SIXTEENTH power, and in naming the
last result, which consisted of 15 figures, he was right in every one.
Some numbers consisting of TWO figures he raised as high as the
eighth power, though he found a difficulty in proceeding when the
products became very large.
"On being asked the SQUARE ROOT of 106,929, he answered 327
before the original number could be written down. He was then
required to find the cube root of 268,336,125, and with equal facility
and promptness he replied 645.
"He was asked how many minutes there are in 48 years, and before the
question could be taken down he replied 25,228,800, and immediately
afterwards he gave the correct number of seconds.
"On being requested to give the factors which would produce the

number 247,483, he immediately named 941 and 263, which are the
only two numbers from the multiplication of which it would result. On
171,395 being proposed, he named 5 x 34,279, 7 x 24,485, 59 x 2905,
83 x 2065, 35 x 4897, 295 x 581, and 413 x 415.
"He was then asked to give the factors of 36,083, but he immediately
replied that it had none, which was really the case, this being a prime
number. Other numbers being proposed to him indiscriminately, he
always succeeded in giving the correct factors except in the case of
prime numbers, which he generally discovered almost as soon as they
were proposed to him. The number 4,294,967,297, which is 2^32 + 1,
having been given him, he discovered, as Euler had previously done,
that it was not the prime number which Fermat had supposed it to be,
but that it is the product of the factors 6,700,417 x 641. The solution of
this problem was only given after the lapse of some weeks, but the
method he took to obtain it clearly showed that he had not derived his
information from any extraneous source.
"When he was asked to multiply together numbers both consisting of
more than these figures, he seemed to decompose one or both of them
into its factors, and to work with them separately. Thus, on being asked
to give the square of 4395, he multiplied 293 by itself, and then twice
multiplied the product by 15. And on being asked to tell the square of
999,999 he obtained the correct result, 999,998,000,001, by twice
multiplying the square of 37,037 by 27. He then of his own accord
multiplied that product by 49, and said that the result (viz.,
48,999,902,000,049) was equal to the square of 6,999,993. He
afterwards multiplied this product by 49, and observed that the result
(viz., 2,400,995,198,002,401) was equal to the square of 48,999,951.
He was again asked to multiply the product by 25, and in naming the
result (viz., 60,024,879,950,060,025) he said it was equal to the square
of 244,999,755.
"On being interrogated as to the manner in which he obtained these
results, the boy constantly said he did not know HOW the answers
came into his mind. In the act of multiplying two numbers together, and
in the raising of powers, it was evident (alike from the facts just stated
and from the motion of his lips) that SOME operation was going
forward in his mind; yet that operation could not (from the readiness
with which his answers were furnished) have been at all allied to the

usual modes of procedure, of which, indeed, he was entirely ignorant,
not being able to perform on paper a simple sum in multiplication or
division. But in the extraction of roots, and in the discovery of the
factors of large numbers, it did not appear that any operation COULD
take place, since he gave answers IMMEDIATELY, or in a very few
seconds, which, according to the ordinary methods, would have
required very difficult and laborious calculations, and prime numbers
cannot be recognised as such by any known rule."
I should hope that many of the above figures are wrong. I have verified
them carefully with Dr. Carpenter's quotation, but further than this I
cannot and will not go. Also I am happy to find that in the end the boy
overcame the mathematics, and turned out a useful but by no means
particularly calculating member of society.
The case, however, is typical of others in which persons have been