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.