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 a.s.sistant 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 ma.s.s 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 a.s.sociate 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 a.s.sociation 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 a.s.sociating 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 a.s.sociating 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 a.s.sociation 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 c.u.mbersome a.s.sociative 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.
CHAPTER XV.
HOW TO REMEMBER MUSIC.
Like all of the other faculties of the mind, that of music or tune is manifested in varying degrees by different individuals. To some music seems to be almost instinctively grasped, while to others it is acquired only by great effort and much labor. To some harmony is natural, and inharmony a matter of repulsion, while others fail to recognize the difference between the two except in extreme cases. Some seem to be the very soul of music, while others have no conception of what the soul of music may be. Then there is manifested the different phases of the knowledge of music. Some play correctly by ear, but are clumsy and inefficient when it comes to playing by note. Others play very correctly in a mechanical manner, but fail to retain the memory of music which they have heard. It is indeed a good musician who combines within himself, or herself, both of the two last mentioned faculties--the ear perception of music and the ability to execute correctly from notes.
There are many cases of record in which extraordinary powers of memory of music have been manifested. Fuller relates the following instances of this particular phase of memory: Carolan, the greatest of Irish bards, once met a noted musician and challenged him to a test of their respective musical abilities. The _defi_ was accepted and Carolan"s rival played on his violin one of Vivaldi"s most difficult concertos. On the conclusion of the performance, Carolan, who had never heard the piece before, took his harp and played the concerto through from beginning to end without making a single error. His rival thereupon yielded the palm, thoroughly satisfied of Carolan"s superiority, as well he might be. Beethoven could retain in his memory any musical composition, however complex, that he had listened to, and could reproduce most of it. He could play from memory every one of the compositions in Bach"s "Well Tempered Clavichord," there being forty-eight preludes and the same number of fugues which in intricacy of movement and difficulty of execution are almost unexampled, as each of these compositions is written in the most abstruse style of counterpoint.
"Mozart, at four years of age, could remember note for note, elaborate solos in concertos which he had heard; he could learn a minuet in half an hour, and even composed short pieces at that early age. At six he was able to compose without the aid of an instrument, and continued to advance rapidly in musical memory and knowledge. When fourteen years old he went to Rome in Holy Week. At the Sistine Chapel was performed each day, Allegri"s "Miserere," the score of which Mozart wished to obtain, but he learned that no copies were allowed to be made. He listened attentively to the performance, at the conclusion of which he wrote the whole score from memory without an error. Another time, Mozart was engaged to contribute an original composition to be performed by a noted violinist and himself at Vienna before the Emperor Joseph. On arriving at the appointed place Mozart discovered that he had forgotten to bring his part. Nothing dismayed, he placed a blank sheet of paper before him, and played his part through from memory without a mistake. When the opera of "Don Giovanni" was first performed there was no time to copy the score for the harpsichord, but Mozart was equal to the occasion; he conducted the entire opera and played the harpsichord accompaniment to the songs and choruses without a note before him. There are many well-attested instances of Mendelssohn"s remarkable musical memory. He once gave a grand concert in London, at which his Overture to "Midsummer Night"s Dream" was produced. There was only one copy of the full score, which was taken charge of by the organist of St. Paul"s Cathedral, who unfortunately left it in a hackney coach--whereupon Mendelssohn wrote out another score from memory, without an error. At another time, when about to direct a public performance of Bach"s "Pa.s.sion Music," he found on mounting the conductor"s platform that instead of the score of the work to be performed, that of another composition had been brought by mistake. Without hesitation Mendelssohn successfully conducted this complicated work from memory, automatically turning over leaf after leaf of the score before him as the performance progressed, so that no feeling of uneasiness might enter the minds of the orchestra and singers. Gottschalk, it is said, could play from memory several thousand compositions, including many of the works of Bach. The noted conductor, Vianesi, rarely has the score before him in conducting an opera, knowing every note of many operas from memory."
It will be seen that two phases of memory must enter into the "memory of music"--the memory of tune and the memory of the notes. The memory of tune of course falls into the cla.s.s of ear-impressions, and what has been said regarding them is also applicable to this case. The memory of notes falls into the cla.s.sification of eye-impressions, and the rules of this cla.s.s of memory applies in this case. As to the cultivation of the memory of tune, the principle advice to be given is that the student take an active interest in all that pertains to the sound of music, and also takes every opportunity for listening to good music, and endeavoring to reproduce it in the imagination or memory. Endeavor to enter into the spirit of the music until it becomes a part of yourself.
Rest not content with merely hearing it, but lend yourself to a _feeling_ of its meaning. The more the music "means to you," the more easily will you remember it. The plan followed by many students, particularly those of vocal music, is to have a few bars of a piece played over to them several times, until they are able to hum it correctly; then a few more are added; and then a few more and so on.
Each addition must be reviewed in connection with that which was learned before, so that the chain of a.s.sociation may be kept unbroken. The principle is the same as the child learning his A-B-C--he remembers "B"
because it follows "A." By this constant addition of "just a little bit more," accompanied by frequent reviews, long and difficult pieces may be memorized.
The memory of notes may be developed by the method above named--the method of learning a few bars well, and then adding a few more, and frequently reviewing as far as you have learned, forging the links of a.s.sociation as you go along, by frequent practice. The method being entirely that of eye-impression and subject to its rules, you must observe the idea of visualization--that is learning each bar until you can _see_ it "in your mind"s eye" as you proceed. But in this, as in many other eye-impressions, you will find that you will be greatly aided by your memory of the _sound_ of the notes, in addition to their appearance. Try to a.s.sociate the two as much as possible, so that when you _see_ a note, you will _hear_ the sound of it, and when you _hear_ a note sounded, you will _see_ it as it appears on the score. This combining of the impressions of both sight and sound will give you the benefit of the double sense impression, which results in doubling your memory efficiency. In addition to visualizing the notes themselves, the student should add the appearance of the various symbols denoting the key, the time, the movement, expression, etc., so that he may hum the air from the visualized notes, with expression and with correct interpretation. Changes of key, time or movement should be carefully noted in the memorization of the notes. And above everything else, memorize the _feeling_ of that particular portion of the score, that you may not only see and hear, but also _feel_ that which you are recalling.
We would advise the student to practice memorizing simple songs at first, for various reasons. One of these reasons is that these songs lend themselves readily to memorizing, and the chain of easy a.s.sociation is usually maintained throughout.
In this phase of memory, as in all others, we add the advice to: Take interest; bestow Attention; and Practice and Exercise as often as possible. You may have tired of these words--but they const.i.tute the main principles of the development of a retentive memory. Things must be impressed upon the memory, before they may be recalled. This should be remembered in every consideration of the subject.
CHAPTER XVI.
HOW TO REMEMBER OCCURRENCES.
The phase of memory which manifests in the recording of and recollection of the occurrences and details of one"s every-day life is far more important than would appear at first thought. The average person is under the impression that he remembers very well the occurrences of his every-day business, professional or social life, and is apt to be surprised to have it suggested to him that he really remembers but very little of what happens to him during his waking hours. In order to prove how very little of this kind is really remembered, let each student lay down this book, at this place, and then quieting his mind let him endeavor to recall the incidents of the same day of the preceding week.
He will be surprised to see how very little of what happened on that day he is really capable of recollecting. Then let him try the same experiment with the occurrences of yesterday--this result will also excite surprise. It is true that if he is reminded of some particular occurrence, he will recall it, more or less distinctly, but beyond that he will remember nothing. Let him imagine himself called upon to testify in court, regarding the happenings of the previous day, or the day of the week before, and he will realize his position.
The reason for his failure to easily remember the events referred to is to be found in the fact that he made no effort at the time to impress these happenings upon his subconscious mentality. He allowed them to pa.s.s from his attention like the proverbial "water from the duck"s back." He did not wish to be bothered with the recollection of trifles, and in endeavoring to escape from them, he made the mistake of failing to store them away. There is a vast difference between dwelling on the past, and storing away past records for possible future reference. To allow the records of each day to be destroyed is like tearing up the important business papers in an office in order to avoid giving them a little s.p.a.ce in the files.
It is not advisable to expend much mental effort in fastening each important detail of the day upon the mind, as it occurs; but there is an easier way that will accomplish the purpose, if one will but take a little trouble in that direction. We refer to the practice of _reviewing_ the occurrences of each day, after the active work of the day is over. If you will give to the occurrences of each day a mental review in the evening, you will find that the act of reviewing will employ the attention to such an extent as to register the happenings in such a manner that they will be available if ever needed thereafter. It is akin to the filing of the business papers of the day, for possible future reference. Besides this advantage, these reviews will serve you well as a reminder of many little things of immediate importance which have escaped your recollection by reason of something that followed them in the field of attention.
You will find that a little practice will enable you to review the events of the day, in a very short s.p.a.ce of time, with a surprising degree of accuracy of detail. It seems that the mind will readily respond to this demand upon it. The process appears to be akin to a mental digestion, or rather a mental rumination, similar to that of the cow when it "chews the cud" that it has previously gathered. The thing is largely a "knack" easily acquired by a little practice. It will pay you for the little trouble and time that you expend upon it. As we have said, not only do you gain the advantage of storing away these records of the day for future use, but you also have your attention called to many important details that have escaped you, and you will find that many ideas of importance will come to you in your moments of leisure "rumination." Let this work be done in the evening, when you feel at ease--but do not do it after you retire. The bed is made for sleep, not for thinking. You will find that the subconsciousness will awaken to the fact that it will be called upon later for the records of the day, and will, accordingly, "take notice" of what happens, in a far more diligent and faithful manner. The subconsciousness responds to a call made upon it in an astonishing manner, when it once understands just what is required of it. You will see that much of the virtue of the plan recommended consists in the fact that in the review there is an employment of the attention in a manner impossible during the haste and rush of the day"s work. The faint impressions are brought out for examination, and the attention of the examination and review greatly deepen the impression in each case, so that it may be reproduced thereafter. In a sentence: it is _the deepening of the faint impressions of the day_.
Thurlow Weed, a well-known politician of the last century, testifies to the efficacy of the above mentioned method, in his "Memoirs." His plan was slightly different from that mentioned by us, but you will at once see that it involves the same principles--the same psychology. Mr. Weed says: "Some of my friends used to think that I was "cut out" for a politician, but I saw at once a fatal weakness. My memory was a sieve. I could remember nothing. Dates, names, appointments, faces--everything escaped me. I said to my wife, "Catherine, I shall never make a successful politician, for I cannot remember, and that is a prime necessity of politicians. A politician who sees a man once should remember him forever." My wife told me that I must train my memory. So when I came home that night I sat down alone and spent fifteen minutes trying silently to recall with accuracy the princ.i.p.al events of the day.
I could remember but little at first--now I remember that I could not then recall what I had for breakfast. After a few days" practice I found I could recall more. Events came back to me more minutely, more accurately, and more vividly than at first. After a fortnight or so of this, Catherine said "why don"t you relate to me the events of the day instead of recalling them to yourself? It would be interesting and my interest in it would be a stimulus to you." Having great respect for my wife"s opinion, I began a habit of oral confession, as it were, which was continued for almost fifty years. Every night, the last thing before retiring, I told her everything I could remember that had happened to me, or about me, during the day. I generally recalled the very dishes I had for breakfast, dinner and tea; the people I had seen, and what they had said; the editorials I had written for my paper, giving her a brief abstract of them; I mentioned all the letters I had seen and received, and the very language used, as nearly as possible; when I had walked or ridden--I told her everything that had come within my observation. I found that I could say my lessons better and better every year, and instead of the practice growing irksome, it became a pleasure to go over again the events of the day. I am indebted to this discipline for a memory of unusual tenacity, and I recommend the practice to all who wish to store up facts, or expect to have much to do with influencing men."
The careful student, after reading these words of Thurlow Weed, will see that in them he has not only given a method of recalling the particular cla.s.s of occurrences mentioned in this lesson, but has also pointed out a way whereby the entire field of memory may be trained and developed.
The habit of reviewing and "telling" the things that one perceives, does and thinks during the day, naturally sharpens the powers of future observation, attention and perception. If you are witnessing a thing which you know that you will be called upon to describe to another person, you will instinctively apply your attention to it. The knowledge that you will be called upon for a description of a thing will give the zest of interest or necessity to it, which may be lacking otherwise. If you will "sense" things with the knowledge that you will be called upon to tell of them later on, you will give the interest and attention that go to make sharp, clear and deep impressions on the memory. In this case the seeing and hearing has "a meaning" to you, and a purpose. In addition to this, the work of review establishes a desirable habit of mind. If you don"t care to relate the occurrences to another person--learn to tell them to yourself in the evening. Play the part yourself. There is a valuable secret of memory imbedded in this chapter--if you are wise enough to apply it.
CHAPTER XVII.
HOW TO REMEMBER FACTS.
In speaking of this phase of memory we use the word "fact" in the sense of "an ascertained item of knowledge," rather than in the sense of "a happening," etc. In this sense the Memory of Facts is the ability to store away and recollect items of knowledge bearing upon some particular thing under consideration. If we are considering the subject of "Horse,"
the "facts" that we wish to remember are the various items of information and knowledge regarding the horse, that we have acquired during our experience--facts that we have seen, heard or read, regarding the animal in question and to that which concerns it. We are continually acquiring items of information regarding all kinds of subjects, and yet when we wish to collect them we often find the task rather difficult, even though the original impressions were quite clear. The difficulty is largely due to the fact that the various facts are a.s.sociated in our minds only by contiguity in time or place, or both, the a.s.sociations of relation being lacking. In other words we have not properly cla.s.sified and indexed our bits of information, and do not know where to begin to search for them. It is like the confusion of the business man who kept all of his papers in a barrel, without index, or order. He knew that "they are all _there_" but he had hard work to find any one of them when it was required. Or, we are like the compositor whose type has become "pied," and then thrown into a big box--when he attempts to set up a book page, he will find it very difficult, if not impossible--whereas, if each letter were in its proper "box," he would set up the page in a short time.
This matter of a.s.sociation by relation is one of the most important things in the whole subject of thought, and the degree of correct and efficient thinking depends materially upon it. It does not suffice us to merely "know" a thing--we must know where to find it when we want it. As old Judge Sharswood, of Pennsylvania, once said: "It is not so much to know the law, as to know _where to find it_." Kay says: "Over the a.s.sociations formed by contiguity in time or s.p.a.ce we have but little control. They are in a manner accidental, depending upon the order in which the objects present themselves to the mind. On the other hand, a.s.sociation by similarity is largely put in our own power; for we, in a measure, select those objects that are to be a.s.sociated, and bring them together in the mind. We must be careful, however, only to a.s.sociate together such things as we wish to be a.s.sociated together and to recall each other; and the a.s.sociations we form should be based on fundamental and essential, and not upon mere superficial or casual resemblances.
When things are a.s.sociated by their accidental, and not by their essential qualities,--by their superficial, and not by their fundamental relations, they will not be available when wanted, and will be of little real use. When we a.s.sociate what is new with what most nearly resembles it in the mind already, we give it its proper place in our fabric of thought. By means of a.s.sociation by similarity, we tie up our ideas, as it were, in separate bundles, and it is of the utmost importance that all the ideas that most nearly resemble each other be in one bundle."
The best way to acquire correct a.s.sociations, and many of them, for a separate fact that you wish to store away so that it may be recollected when needed--some useful bit of information or interesting bit of knowledge, that "may come in handy" later on--is to _a.n.a.lyze_ it and its relations. This may be done by asking yourself questions about it--each thing that you a.s.sociate it with in your answers being just one additional "cross-index" whereby you may find it readily when you want it. As Kay says: "The principle of asking questions and obtaining answers to them, may be said to characterize all intellectual effort."
This is the method by which Socrates and Plato drew out the knowledge of their pupils, filling in the gaps and attaching new facts to those already known. When you wish to so consider a fact, ask yourself the following questions about it:
I. Where did it come from or originate?
II. What caused it?