Here you will learn How to develop, train and use your memory
Page 16 of
22.
CHAPTER XIV.
HOW TO REMEMBER NUMBERS.
The faculty of Numberthat 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 daythis 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
hairbreadths, 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,-998J55. 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 25the 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 itthen 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 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 timesthen 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., it 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 90,910,771 __________ 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.
Our
featured links related to How to develop, train and use your memory
