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Speaker 1: How to remember numbers. The faculty of number, that is,

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the faculty of knowing, recognizing, and remembering figures in the

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abstract and in their relation to each other, differs very

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materially among different individuals. To some figures and numbers are

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apprehended and remembered with ease, while to others they possess

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no interest, attraction, or affinity, and consequently are not apt

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to be remembered. It is generally admitted by the best

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authorities that the memorizing of dates, figures, numbers, et cetera

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is the most difficult of any of the phases of memory,

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but all agree that the faculty may be developed by

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practice and interest. There have been instances of persons having

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this faculty of the mind developed to a degree almost incredible,

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and other instances of persons having started with an other

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aversion to figures, and then developing an interest which resulted

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in their acquiring a remarkable degree of proficiency. Along these lines,

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many of the celebrated mathematicians and astronomers developed wonderful memories

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for figures. Herschel is said to have been able to

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remember all the details of intricate calculations in his astronomical computations,

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even to the figures of the fractions. It is said

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that he was able to perform the most intricate calculations

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mentally without the use of pen or pencil, and then

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dictated to his assistant the entire details of the process,

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including the final results. Tycho Bra the astronomer, also possessed

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a similar memory. It is said that he rebelled at

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being compelled to refer to the printed tables of square

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roots and cube roots, and set to work to memorize

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the entire set of tables, which almost incredible task be

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accomplished in a half day. This required the memorizing of

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over seventy five thousand figures and their relations to each other.

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Euler the mathematician became blind in his old age, and

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being unable to refer to his tables, memorized them. It

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is said that he was able to repeat from recollection

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the first six powers of all the numbers from one

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to one hundred. Wallace the mathematician was a prodigy in

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this respect. He is reported to have been able to

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mentally extract the square root of a number to forty

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decimal places, and on one occasion mentally extracted the cube

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root of a number consisting of thirty figures days is

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said to have mentally multiplied two numbers of one hundred

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figures each. A youth named Mongiemel was able to perform

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or the most remarkable feats in mental arithmetic. The reports

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show that, upon a celebrated test before members of the

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French Academy of Sciences, he was able to extract the

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cube rute of three million, seven hundred ninety six thousand,

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four hundred and sixteen in thirty seconds and the tenth

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route of two hundred eighty two million, four hundred and

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seventy five thousand, two hundred and eighty nine in three minutes.

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He also immediately solved the following question put to him

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by Arago, What number has the following proportion that if

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five times the number be subtracted from the cube plus

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five times the square of the number, and nine times

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the square of the number be subtracted from that result,

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the remainder will be zero. The answer five was given

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immediately without putting down a figure on paper or board.

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It is related that a cashier of a Chicago bank

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was able to mentally restore the accounts of the bank

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which had been destroyed in the great fire in that city,

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and his account, which was accepted by the bank and

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the depositors, was found to agree perfectly with the other

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memoranda in the case the work performed by him being

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solely the work of his memory. Bidder was able to

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tell instantly the number of farthings in the sum of

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eight hundred and sixty eight pounds forty two shillings one

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hundred and twenty one pence. Buxton mentally calculated the number

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of cubicle eighths of an inch there were in a

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quadrangular mass twenty three million, one hundred forty five thousand,

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seven hundred eighty nine yards long, two million, six hundred

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forty two thousand, seven hundred and thirty two yards wide,

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and fifty twenty four thousand, nine hundred and sixty five

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yards in thickness. He also figured out mentally the dimensions

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of an irregular estate of about one thousand acres, giving

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the contents in acres and perches, then reducing them to

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square inches, and then reducing them to square hair breadths,

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estimating two thousand, three hundred and four to the square

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inch forty eight to each side. The mathematical prodigy zero

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Coalburn was perhaps the most remarkable of any of these

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remarkable people. When a mere child, he began to develop

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the most amazing qualities of mind regarding figures. He was

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able to instantly make the mental calculation of the exact

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number of seconds or minutes there was in a given time.

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On one occasion, he calculated the number of minutes and

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seconds contained in forty eight years, the answer twenty five million,

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two hundred and twenty eight thousand, eight hundred minutes and

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one billion, five hundred thirteen million, seven hundred twenty eight

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thousand seconds being given almost instantaneously. He could instantly multiply

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any number of one to three figures by another number

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consisting of the same number of figures, the factors of

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any number consisting of six or seven figures, the square

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and q brutes, and the prime numbers of any numbers

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given him. He mentally raised the number eight progressively to

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its sixteenth power, the result being two hundred eighty one trillion,

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four hundred and seventy four billion, nine hundred seventy six million,

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seven hundred ten thousand, six hundred and fifty six, and

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gave the square root of one hundred and six thousand,

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nine hundred and twenty nine, which was five. He mentally

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extracted the cube root of two hundred and sixty eight million,

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three hundred and thirty six thousand, one hundred and twenty

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five and the squares of two hundred and forty four million,

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nine hundred and ninety nine thousand, seven hundred and fifty

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five and one billion, two hundred and twenty four million,

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nine hundred ninety eight thousand, seven hundred and fifty five.

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In five seconds, he calculated the cube root of four

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hundred and thirteen billion, nine hundred ninety three million, three

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hundred and forty eight thousand, six hundred and seventy seven.

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He found the factors of four billion, two hundred ninety

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four million, nine hundred and sixty seven thousand, two hundred

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and ninety seven, which had previously been considered to be

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a prime number. He mentally calculated the square of nine

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hundred ninety nine thousand, nine hundred ninety nine, which is

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nine hundred ninety nine billion, nine hundred ninety eight million

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and one, and then multiplied that number by forty nine,

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and the product by the same number, and the whole

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by twenty five, the latter as extra measure. The great

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difficulty in remembering numbers to the majority of persons is

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the fact that numbers do not mean anything to them.

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That is, the numbers are thought of only in their

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abstract phase and nature, and are consequently far more difficult

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to remember than are the impressions received from the senses

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of sight or sound. The remedy, however, becomes apparent when

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we recognize the source of the difficulty. The remedy is

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make the number the subject of sound and site impressions.

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Attach the abstract idea of the numbers to the sense

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of impressions of sight or sound, or both, according to

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which are the best developed. In your particular case, it

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may be difficult for you to remember eighteen forty eight

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as an abstract thing, but comparatively easy for you to

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remember the sound of eighteen forty eight or the shape

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and appearance of eighteen forty eight. If you will repeat

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a number to yourself so that you grasp the sound

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impression of it, or else visualize it so that you

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can remember having seen it, then you will be far

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more apt to remember it than if you merely think

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of it without reference to sound or form. You may

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forget that the number of a certain store or house

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is thirty nine forty eight, but you may easily remember

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the sound of the spoken words thirty nine forty eight eight,

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or the form of thirty nine forty eight as it

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appeared to your sight on the door of the place.

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In the latter case, you associate the number with the door,

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and when you visualize the door, you visualize the number. K.

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Speaking of visualization or the reproduction of mental images of

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things to be remembered, says those who have been distinguished

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for their power to carry out long and intricate processes

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of mental calculation owe it to the same cause. Taine says,

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children accustomed to calculate in their heads right mentally with

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chalk on an imaginary board, the figures in question, then

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all their partial operations, then the final sum, so that

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they see internally the different lines of white figures with

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which they are concerned. Young Colburn, who had never been

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at skins Ghoul and did not know how to read

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or write, said that when making his calculations, he saw

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them clearly before him. Another said that he saw the

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numbers he was working with as if they had been

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written on a slate. Bidder says, if I perform a

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sum mentally. It always proceeds in a visible form in

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my mind. Indeed, I can conceive of no other way

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possible of doing mental arithmetic. We have known office boys

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who could never remember the number of an address until

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it were distinctly repeated to them several times. Then they

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memorized the sound and never forgot it. Others forget the

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sounds or failed to register them in the mind, but

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after once seeing the number on the door of an

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office or store, could repeat it at a moment's notice,

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saying that they mentally could see the figures on the door.

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You will find by a little questioning that the majority

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of people remember figures or numbers in this way, and

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that very few can remember them as abstract things. For

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that matter, it is difficult for the majority of persons

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to even think of a number Abstractly try it yourself

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and ascertain whether you do not remember the number as

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either a sound of words, or else as the mental

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image or visualization of the form of the figures, And,

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by the way, whichever it happens to be sight or sound,

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that particular kind of remembrance is your best way of

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remembering numbers, and consequently gives you the lines upon which

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you should proceed to develop this phase of memory. The

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law of association may be used advantageously in memorizing numbers.

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For instance, we know of a person who remember the

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number one hundred and eighty six two thousand, the number

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of miles per second traveled by light waves in the ether,

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by associating it with the number of his father's former

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place of business one eighty six. Another remembered his telephone

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number one eight seven six by recalling the date of

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the declaration of independence. Another the number of states in

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the Union by associating it with the last two figures

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of the number of his place of business. But by

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far the better way to memorize dates, special numbers connected

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with events, et cetera is to visualize the picture of

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the event with the picture of the date or number,

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thus combining the two things into a mental picture, the

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association of which will be preserved when the picture is recalled.

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Verse of doggerel, such as in fourteen hundred ninety two

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Columbus sailed the ocean blu or in eighteen hundred and

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sixty one our country civil war begun, et cetera, have

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their places and uses, but it is far better to

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cultivate the sight or sound of a number, than to

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depend upon cumbersome associative methods based on artificial links and pegs. Finally,

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as we have said in the preceding chapters, before one

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can develop a good memory of a subject, he must

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first cultivate an interest in that subject. Therefore, if you

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will keep your interest in figures alive by working out

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a few problems in mathematics once in a while, you

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will find that figures will begin to have a new

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interest for you. A little elementary arithmetic, used with interest

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will do more to start you on the road to

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how to remember numbers than a dozen textbooks on the subject.

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In memory, the three the rules are interest, attention, and exercise,

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and the last is the most important, for without it

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the others fail. You will be surprised to see how

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many interesting things there are in figures. As you proceed

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the task of going over the elementary arithmetic will not

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be nearly so dry as when you were a child.

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You will uncover all sorts of queer things in relation

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to numbers. Just as a sample, let us call your

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attention to a few Take the figure one and place

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behind it a number of knots. Thus, one zero zero

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zero zero zero zero zero zero zero zero zero zero

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as many knots or ciphers as you wish, then divide

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the number by the figure seven. You will find that

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the result is always this one forty two, eight fifty seven,

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then another one forty two, eight fifty seven, and so

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on to infinity. If you wish to carry the calculation

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that far these six figures will be repeated over and

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over again, then multiply this one, four, two, eight, five,

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seven by the figure seven, and your product will be

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all ninees. Then take any number and set it down,

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placing beneath it a reversal of itself, and subtract the

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latter from the former. Thus one one, seven, seven, six,

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one nine oh nine minus nine zero nine one six,

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seven seven one equals two six, eight, four, five, one

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three eight, and you will find that the result will

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always reduce to nine and is always a multiple of nine.

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Take any number composed of two or more figures and

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subtract from it the added sum of its separate figures,

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and the result is always a multiple of nine. Thus

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one eight four minus one plus eight plus four equals

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thirteen equals one seventy one divided by nine. Equals nineteen.

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We mention these familiar examples merely to remind you that

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there is much more of interest in mere figures than

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many would suppose. If you can arouse your interest in them,

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then you will be well started on the road to

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the memorizing of numbers. Let figures and numbers mean something

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to you, and the rest will be merely a matter

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of detail.