Speaker 1: 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 other
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 Mongiemel was able to perform
or 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 rute of three million, seven hundred ninety six thousand,
four hundred and sixteen in thirty seconds and the tenth
route of two hundred 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 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
eight hundred and sixty eight pounds forty two shillings one
hundred and twenty one pence. Buxton mentally calculated the number
of cubicle eighths of an inch there were in a
quadrangular mass twenty three million, one hundred forty five thousand,
seven hundred eighty nine yards long, two million, six hundred
forty two thousand, seven hundred and thirty two yards wide,
and fifty twenty four thousand, nine hundred and sixty five
yards in thickness. He also figured out mentally the dimensions
of an irregular estate of about one 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 zero
Coalburn 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 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 q brutes, 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 eighty one trillion,
four hundred and seventy four billion, nine hundred seventy six million,
seven hundred ten thousand, six hundred and fifty six, and
gave the square root of one hundred and six thousand,
nine hundred and twenty nine, which was five. He mentally
extracted the cube root of two hundred and sixty eight million,
three hundred and thirty six thousand, one hundred and twenty
five and the squares of two hundred and forty four million,
nine hundred and 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 and 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
and 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 skins Ghoul 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 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 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 two thousand, 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 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, et cetera 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 ninety two
Columbus sailed the ocean blu or in eighteen hundred and
sixty one our country civil war begun, et cetera, 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 the 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 ninees. 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 oh 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 minus 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.