MEMORY, HOW TO DEVELOP, TRAIN AND USE IT/PART 14
CHAPTER XIV.
HOW TO REMEMBER NUMBERS.
The
faculty of Number—that is the faculty of knowing, recognizing and remembering
figures in the abstract and in their relation to each other, differs very materially
among different individuals. To some, figures and numbers are apprehended and
remembered with ease, while to others they possess no interest, attraction or
affinity, and consequently are not apt to be remembered. It is generally
admitted by the best authorities that the memorizing of dates, figures,
numbers, etc., is the most difficult of any of the phases of memory. But all
agree that the faculty may be developed by practice and interest. There have
been instances of persons having this faculty of the mind developed to a degree
almost incredible; and other instances of persons having started with an
aversion to figures and then developing an interest which resulted in
their acquiring a remarkable degree of proficiency along these lines.
Many
of the celebrated mathematicians and astronomers developed wonderful memories
for figures. Herschel is said to have been able to remember all the details of
intricate calculations in his astronomical computations, even to the figures of
the fractions. It is said that he was able to perform the most intricate
calculations mentally, without the use of pen or pencil, and then dictated to
his assistant the entire details of the process, including the final results.
Tycho Brahe, the astronomer, also possessed a similar memory. It is said that
he rebelled at being compelled to refer to the printed tables of square roots
and cube roots, and set to work to memorize the entire set of tables, which
almost incredible task he accomplished in a half day—this required the memorizing
of over 75,000 figures, and their relations to each other. Euler the
mathematician became blind in his old age, and being unable to refer to his
tables, memorized them. It is said that he was able to repeat from recollection
the first six powers of all the numbers from one to one hundred.
Wallis
the mathematician was a prodigy in this respect. He is reported to have been
able to mentally extract the square root of a number to forty decimal places,
and on one occasion mentally extracted the cube root of a number consisting of
thirty figures. Dase is said to have mentally multiplied two numbers of one
hundred figures each. A youth named Mangiamele was able to perform the most
remarkable feats in mental arithmetic. The reports show that upon a celebrated
test before members of the French Academy of Sciences he was able to extract
the cube root of 3,796,416 in thirty seconds; and the tenth root of 282,475,289
in three minutes. He also immediately solved the following question put to him
by Arago: "What number has the following proportion: That if five times
the number be subtracted from the cube plus five times the square of the
number, and nine times the square of the number be subtracted from that result,
the remainder will be 0?" The answer, "5" was given immediately,
without putting down a figure on paper or board. It is related that a cashier
of a Chicago bank was able to mentally restore the accounts of the bank,
which had been destroyed in the great fire in that city, and his account which
was accepted by the bank and the depositors, was found to agree perfectly with
the other memoranda in the case, the work performed by him being solely the
work of his memory.
Bidder
was able to tell instantly the number of farthings in the sum of £868, 42s,
121d. Buxton mentally calculated the number of cubical eighths of an inch there
were in a quadrangular mass 23,145,789 yards long, 2,642,732 yards wide and
54,965 yards in thickness. He also figured out mentally, the dimensions of an
irregular estate of about a thousand acres, giving the contents in acres and
perches, then reducing them to square inches, and then reducing them to square
hair-breadths, estimating 2,304 to the square inch, 48 to each side. The
mathematical prodigy, Zerah Colburn, was perhaps the most remarkable of any of
these remarkable people. When a mere child, he began to develop the most
amazing qualities of mind regarding figures. He was able to instantly make the
mental calculation of the exact number of seconds or minutes there was in
a given time. On one occasion he calculated the number of minutes and seconds
contained in forty-eight years, the answer: "25,228,800 minutes, and
1,513,728,000 seconds," being given almost instantaneously. He could
instantly multiply any number of one to three figures, by another number
consisting of the same number of figures; the factors of any number consisting
of six or seven figures; the square, and cube roots, and the prime numbers of
any numbers given him. He mentally raised the number 8, progressively, to its
sixteenth power, the result being 281,474,976,710,656; and gave the square root
of 106,929, which was 5. He mentally extracted the cube root of 268,336,125; and
the squares of 244,999,755 and 1,224,998,755. In five seconds he calculated the
cube root of 413,993,348,677. He found the factors of 4,294,967,297, which had
previously been considered to be a prime number. He mentally calculated the
square of 999,999, which is 999,998,000,001 and then multiplied that number by
49, and the product by the same number, and the whole by 25—the latter as extra
measure.
The
great difficulty in remembering numbers, to the majority of persons, is the
fact that numbers "do not mean anything to them"—that is, that
numbers are thought of only in their abstract phase and nature, and are
consequently far more difficult to remember than are impressions received from
the senses of sight or sound. The remedy, however, becomes apparent when we
recognize the source of the difficulty. The remedy is: Make the number
the subject of sound and sight impressions. Attach the abstract idea
of the numbers to the sense of impressions of sight or sound, or both,
according to which are the best developed in your particular case. It may be
difficult for you to remember "1848" as an abstract thing, but
comparatively easy for you to remember the sound of
"eighteen forty-eight," or the shape and appearance of
"1848." If you will repeat a number to yourself, so that you grasp
the sound impression of it, or else visualize it so that you can remember
having seen it—then you will be far more apt to remember it
than if you merely think of it without reference to sound or form. You may
forget that the number of a certain store or house is 3948, but you may
easily remember the sound of the spoken words "thirty-nine
forty-eight," or the form of "3948" as it appeared to your sight
on the door of the place. In the latter case, you associate the number with the
door and when you visualize the door you visualize the number.
Kay,
speaking of visualization, or the reproduction of mental images of things to be
remembered, says: "Those who have been distinguished for their power to
carry out long and intricate processes of mental calculation owe it to the same
cause." Taine says: "Children accustomed to calculate in their heads
write mentally with chalk on an imaginary board the figures in question, then
all their partial operations, then the final sum, so that they see internally
the different lines of white figures with which they are concerned. Young
Colburn, who had never been at school and did not know how to read or write,
said that, when making his calculations 'he saw them clearly before him.'
Another said that he 'saw the numbers he was working with as if they had been
written on a slate.'" Bidder said: "If I perform a sum mentally,
it always proceeds in a visible form in my mind; indeed, I can conceive of no
other way possible of doing mental arithmetic."
We
have known office boys who could never remember the number of an address until
it were distinctly repeated to them several times—then they memorized the sound and
never forget it. Others forget the sounds, or failed to register them in the
mind, but after once seeing the number on the door of an office or store, could
repeat it at a moments notice, saying that they mentally "could see the
figures on the door." You will find by a little questioning that the
majority of people remember figures or numbers in this way, and that very few
can remember them as abstract things. For that matter it is difficult for the
majority of persons to even think of a number, abstractly. Try it yourself, and
ascertain whether you do not remember the number as either a sound of
words, or else as the mental image or visualization of the form of
the figures. And, by the way, which ever it happens to be, sight or sound,
that particular kind of remembrance is your best way
of remembering numbers, and consequently gives you the lines upon which
you should proceed to develop this phase of memory.
The
law of Association may be used advantageously in memorizing numbers; for
instance we know of a person who remembered the number 186,000 (the number of
miles per second traveled by light-waves in the ether) by associating it with
the number of his father's former place of business, "186." Another
remembered his telephone number "1876" by recalling the date of the
Declaration of Independence. Another, the number of States in the Union, by
associating it with the last two figures of the number of his place of
business. But by far the better way to memorize dates, special numbers
connected with events, etc., is to visualize the picture of the event with the
picture of the date or number, thus combining the two things into a mental
picture, the association of which will be preserved when the picture is
recalled. Verse of doggerel, such as "In fourteen hundred and ninety-two,
Columbus sailed the ocean blue;" or "In eighteen hundred and sixty-one,
our country's Civil war begun," etc., have their places and uses. But
it is far better to cultivate the "sight or sound" of a number, than
to depend upon cumbersome associative methods based on artificial links and
pegs.
Finally,
as we have said in the preceding chapters, before one can develop a good memory
of a subject, he must first cultivate an interest in that subject. Therefore,
if you will keep your interest in figures alive by working out a few problems
in mathematics, once in a while, you will find that figures will begin to have
a new interest for you. A little elementary arithmetic, used with interest,
will do more to start you on the road to "How to Remember Numbers"
than a dozen text books on the subject. In memory, the three rules are: "Interest,
Attention and Exercise"—and the last is the most important, for without it
the others fail. You will be surprised to see how many interesting things there
are in figures, as you proceed. The task of going over the elementary
arithmetic will not be nearly so "dry" as when you were a child. You
will uncover all sorts of "queer" things in relation to numbers. Just
as a "sample" let us call your attention to a few:
Take
the figure "1" and place behind it a number of "naughts,"
thus: 1,000,000,000,000,—as many "naughts" or ciphers as you wish.
Then divide the number by the figure "7." You will find that the
result is always this "142,857" then another "142,857," and
so on to infinity, if you wish to carry the calculation that far. These six
figures will be repeated over and over again. Then multiply this
"142,857" by the figure "7," and your product will be all
nines. Then take any number, and set it down, placing beneath it a reversal
of itself and subtract the latter from the former, thus:
117,761,909
90,916,771
26,845,138
and
you will find that the result will always reduce to nine, and is always a
multiple of 9. Take any number composed of two or more figures, and subtract
from it the added sum of its separate figures, and the result is always a
multiple of 9, thus:
184
1 + 8 + 4 = 13
171 ÷ 9 = 19
We
mention these familiar examples merely to remind you that there is much more of
interest in mere figures than many would suppose. If you can arouse your
interest in them, then you will be well started on the road to the memorizing
of numbers. Let figures and numbers "mean something" to you, and the
rest will be merely a matter of detail.
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