Memory: How to Develop, Train, and Use It/Chapter 14
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., 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 90,916,771 ——————————— 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.