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.