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, et cetera 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 Bra
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 be accomplished in a half day. This required the memorizing of over
seventy five thousand 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. Wallace 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
days is said to have mentally multiplied two numbers of one hundred figures each.
A youth named Moniemel 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 three million,
seven hundred and ninety six thousand, four hundred and sixteen in thirty seconds and
the tenth route of two hundred and eighty two million, four hundred and seventy
five thousand, two hundred and eighty nine 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 zero. The answer five was
given immediately without putting down 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 eight hundred and sixty eight pounds forty two
shillings one hundred and twenty one pence. Buxton mentally calculated the number of cubical
eighths of an inch there were in a quadrangular mass twenty three million, one
hundred and forty five thousand, seven hundred eighty nine yards long, two million,
six hundred and forty two thousand, seven hundred and thirty two yards wide,
and four thousand, nine hundred and sixty five yards in thickness. He
also figured out mentally the dimensions of an irregular state 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 two thousand, three
hundred and four to the square inch forty eight 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 twenty five million, two hundred and twenty eight thousand, eight hundred
minutes and one billion, five hundred and thirteen million, seven hundred twenty eight
thousand 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 eight progressively to its sixteenth power, the result being two hundred and
eighty one trillion, four hundred and seventy four billion, nine hundred and seventy
six million, seven hundred ten thousand, six hundred and fifty six, and
gave the square route of one hundred and six thousand, nine hundred twenty nine,
which was five. He mentally extracted the cube root of two hundred and
sixty eight million, three hundred thirty six thousand, one hundred and twenty five
and the squares of two hundred forty four million, nine hundred ninety nine thousand,
seven hundred and fifty five and one billion, two hundred and twenty four
million, nine hundred ninety eight thousand, seven hundred and fifty five. In
five seconds, he calculated the cube root of four hundred and thirteen billion,
nine hundred ninety three million, three hundred forty eight thousand, six hundred and
seventy seven. He found the factors of four billion, two hundred ninety four
million, nine hundred and sixty seven thousand, two hundred ninety seven, which
had previously been considered to be a prime number. He mentally calculated the square
of nine hundred ninety nine thousand, nine hundred ninety nine, which is nine
hundred ninety nine billion, nine hundred ninety eight million and one, and then
multiplied that number by forty nine, and the product by the same number,
and the whole by twenty five, 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, the numbers are thought of only in
their abstract phase and nature, and are consequently far more difficult to remember than
are the 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 site 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 eighteen forty eight as an abstract thing,
but comparatively easy for you to remember the sound of eighteen forty eight or
the shape and appearance of eighteen forty eight. 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 thirty nine forty eight. But you may easily remember the sound of
the spoken words thirty nine forty eight eight, or the form of thirty nine
forty eight 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 K. 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 right 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 wool 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 says, 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 forgot it. Others forget the sounds or fail 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 moment's 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, whichever 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 remember the number one hundred
and eighty six thousand, the number of miles per second traveled by light waves
in the ether, by associating it with a number of his father's former place
of business, one eighty six. Another remembered his telephone number one eight seven
six, 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 lou or in eighteen hundred and sixty one our
country 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 textbooks 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 one,
and place behind it a number of knots. Thus one zero zero zero
zero zero zero zero zero zero zero zero zero, as many knots or ciphers
as you wish, Then divide the number by the figure seven. You will
find that the result is always this one forty two, eight fifty seven,
then another one forty two, eight fifty seven, 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 one, four, two,
eight, five, seven by the figure seven, 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 one
one, seven, seven, six, one nine, o nine minus nine
zero nine one six, seven seven one equals two six, eight, four,
five, one three eight, and you will find that the result will
always reduce to nine, and is always a multiple of nine. 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 nine. Thus
one eight, four, one plus eight plus four equals thirteen equals one seventy
one divided by nine equals nineteen. 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.