WEBVTT 1 00:00:00.360 --> 00:00:06.719 How to remember numbers. The faculty of number, that is, the faculty 2 00:00:06.719 --> 00:00:12.560 of knowing, recognizing, and remembering figures in the abstract and in their relation 3 00:00:12.640 --> 00:00:19.640 to each other, differs very materially among different individuals. To some figures and 4 00:00:19.760 --> 00:00:26.239 numbers are apprehended and remembered with ease, while to others they possess no interest, 5 00:00:26.320 --> 00:00:31.199 attraction, or affinity, and consequently are not apt to be remembered. 6 00:00:32.399 --> 00:00:38.159 It is generally admitted by the best authorities that the memorizing of dates, figures, 7 00:00:38.240 --> 00:00:42.240 numbers, et cetera is the most difficult of any of the phases of 8 00:00:42.320 --> 00:00:48.799 memory, but all agree that the faculty may be developed by practice and interest. 9 00:00:49.560 --> 00:00:54.479 There have been instances of persons having this faculty of the mind developed to 10 00:00:54.520 --> 00:01:00.479 a degree almost incredible, and other instances of persons having started with an aversion 11 00:01:00.520 --> 00:01:06.840 to figures and then developing an interest which resulted in their acquiring a remarkable degree 12 00:01:06.840 --> 00:01:14.519 of proficiency. Along these lines, many of the celebrated mathematicians and astronomers developed 13 00:01:14.599 --> 00:01:19.760 wonderful memories for figures. Herschel is said to have been able to remember all 14 00:01:19.799 --> 00:01:26.480 the details of intricate calculations in his astronomical computations, even to the figures of 15 00:01:26.519 --> 00:01:30.840 the fractions. It is said that he was able to perform the most intricate 16 00:01:30.840 --> 00:01:37.680 calculations mentally without the use of pen or pencil, and then dictated to his 17 00:01:37.760 --> 00:01:45.040 assistant the entire details of the process, including the final results. Tycho Bra 18 00:01:45.439 --> 00:01:51.239 the astronomer, also possessed a similar memory. It is said that he rebelled 19 00:01:51.239 --> 00:01:56.040 at being compelled to refer to the printed tables of square roots and cube roots, 20 00:01:56.480 --> 00:02:00.040 and set to work to memorize the entire set of tables, which almost 21 00:02:00.159 --> 00:02:07.719 incredible task be accomplished in a half day. This required the memorizing of over 22 00:02:07.920 --> 00:02:15.759 seventy five thousand figures and their relations to each other. Euler the mathematician became 23 00:02:15.879 --> 00:02:20.439 blind in his old age, and being unable to refer to his tables, 24 00:02:20.520 --> 00:02:24.479 memorized them. It is said that he was able to repeat from recollection the 25 00:02:24.560 --> 00:02:30.800 first six powers of all the numbers from one to one hundred. Wallace the 26 00:02:30.840 --> 00:02:37.360 mathematician was a prodigy in this respect. He is reported to have been able 27 00:02:37.360 --> 00:02:42.879 to mentally extract the square root of a number to forty decimal places, and 28 00:02:43.080 --> 00:02:47.960 on one occasion mentally extracted the cube root of a number consisting of thirty figures 29 00:02:50.520 --> 00:02:54.680 days is said to have mentally multiplied two numbers of one hundred figures each. 30 00:02:55.759 --> 00:03:02.000 A youth named Moniemel was able to perform the most remarkable feats in mental arithmetic. 31 00:03:02.879 --> 00:03:07.719 The reports show that upon a celebrated test before members of the French Academy 32 00:03:07.759 --> 00:03:13.840 of Sciences, he was able to extract the cube root of three million, 33 00:03:14.039 --> 00:03:20.000 seven hundred and ninety six thousand, four hundred and sixteen in thirty seconds and 34 00:03:20.159 --> 00:03:23.840 the tenth route of two hundred and eighty two million, four hundred and seventy 35 00:03:23.879 --> 00:03:30.479 five thousand, two hundred and eighty nine in three minutes. He also immediately 36 00:03:30.560 --> 00:03:37.759 solved the following question put to him by Arago, What number has the following 37 00:03:37.800 --> 00:03:45.080 proportion that if five times the number be subtracted from the cube plus five times 38 00:03:45.120 --> 00:03:49.520 the square of the number, and nine times the square of the number be 39 00:03:49.639 --> 00:03:57.280 subtracted from that result, the remainder will be zero. The answer five was 40 00:03:57.360 --> 00:04:02.960 given immediately without putting down figure on paper or board. It is related that 41 00:04:03.039 --> 00:04:09.479 a cashier of a Chicago bank was able to mentally restore the accounts of the 42 00:04:09.560 --> 00:04:13.719 bank, which had been destroyed in the Great fire in that city, and 43 00:04:13.919 --> 00:04:17.680 his account, which was accepted by the bank and the depositors, was found 44 00:04:17.680 --> 00:04:24.319 to agree perfectly with the other memoranda in the case the work performed by him 45 00:04:24.319 --> 00:04:30.279 being solely the work of his memory. Bidder was able to tell instantly the 46 00:04:30.399 --> 00:04:34.279 number of farthings in the sum of eight hundred and sixty eight pounds forty two 47 00:04:34.319 --> 00:04:42.839 shillings one hundred and twenty one pence. Buxton mentally calculated the number of cubical 48 00:04:42.920 --> 00:04:47.040 eighths of an inch there were in a quadrangular mass twenty three million, one 49 00:04:47.120 --> 00:04:53.920 hundred and forty five thousand, seven hundred eighty nine yards long, two million, 50 00:04:54.120 --> 00:04:58.879 six hundred and forty two thousand, seven hundred and thirty two yards wide, 51 00:04:59.360 --> 00:05:04.120 and four thousand, nine hundred and sixty five yards in thickness. He 52 00:05:04.240 --> 00:05:11.519 also figured out mentally the dimensions of an irregular state of about a thousand acres, 53 00:05:12.000 --> 00:05:16.680 giving the contents in acres and perches, then reducing them to square inches, 54 00:05:17.160 --> 00:05:23.759 and then reducing them to square hair breadths, estimating two thousand, three 55 00:05:23.839 --> 00:05:30.120 hundred and four to the square inch forty eight to each side. The mathematical 56 00:05:30.199 --> 00:05:35.720 prodigy Zerah Colburn was perhaps the most remarkable of any of these remarkable people. 57 00:05:36.920 --> 00:05:42.839 When a mere child, he began to develop the most amazing qualities of mind 58 00:05:42.959 --> 00:05:48.000 regarding figures. He was able to instantly make the mental calculation of the exact 59 00:05:48.160 --> 00:05:55.000 number of seconds or minutes there was in a given time. On one occasion, 60 00:05:55.519 --> 00:06:00.360 he calculated the number of minutes and seconds contained in forty eight years, 61 00:06:00.160 --> 00:06:05.160 the answer twenty five million, two hundred and twenty eight thousand, eight hundred 62 00:06:05.199 --> 00:06:12.959 minutes and one billion, five hundred and thirteen million, seven hundred twenty eight 63 00:06:13.000 --> 00:06:20.199 thousand seconds being given almost instantaneously. He could instantly multiply any number of one 64 00:06:20.319 --> 00:06:27.360 to three figures by another number consisting of the same number of figures, the 65 00:06:27.399 --> 00:06:32.279 factors of any number consisting of six or seven figures, the square and cube 66 00:06:32.399 --> 00:06:39.480 roots, and the prime numbers of any numbers given him. He mentally raised 67 00:06:39.480 --> 00:06:46.240 the number eight progressively to its sixteenth power, the result being two hundred and 68 00:06:46.319 --> 00:06:51.079 eighty one trillion, four hundred and seventy four billion, nine hundred and seventy 69 00:06:51.160 --> 00:06:58.560 six million, seven hundred ten thousand, six hundred and fifty six, and 70 00:06:58.759 --> 00:07:02.759 gave the square route of one hundred and six thousand, nine hundred twenty nine, 71 00:07:03.079 --> 00:07:09.720 which was five. He mentally extracted the cube root of two hundred and 72 00:07:09.759 --> 00:07:14.759 sixty eight million, three hundred thirty six thousand, one hundred and twenty five 73 00:07:15.279 --> 00:07:20.319 and the squares of two hundred forty four million, nine hundred ninety nine thousand, 74 00:07:20.600 --> 00:07:26.720 seven hundred and fifty five and one billion, two hundred and twenty four 75 00:07:26.800 --> 00:07:32.360 million, nine hundred ninety eight thousand, seven hundred and fifty five. In 76 00:07:32.519 --> 00:07:38.839 five seconds, he calculated the cube root of four hundred and thirteen billion, 77 00:07:39.160 --> 00:07:44.680 nine hundred ninety three million, three hundred forty eight thousand, six hundred and 78 00:07:44.800 --> 00:07:49.879 seventy seven. He found the factors of four billion, two hundred ninety four 79 00:07:50.040 --> 00:07:56.920 million, nine hundred and sixty seven thousand, two hundred ninety seven, which 80 00:07:56.920 --> 00:08:03.399 had previously been considered to be a prime number. He mentally calculated the square 81 00:08:03.600 --> 00:08:09.079 of nine hundred ninety nine thousand, nine hundred ninety nine, which is nine 82 00:08:09.199 --> 00:08:15.399 hundred ninety nine billion, nine hundred ninety eight million and one, and then 83 00:08:15.519 --> 00:08:20.319 multiplied that number by forty nine, and the product by the same number, 84 00:08:20.639 --> 00:08:28.199 and the whole by twenty five, the latter as extra measure the great difficulty 85 00:08:28.360 --> 00:08:33.480 in remembering numbers to the majority of persons is the fact that numbers do not 86 00:08:33.639 --> 00:08:37.320 mean anything to them. That is, the numbers are thought of only in 87 00:08:37.360 --> 00:08:43.440 their abstract phase and nature, and are consequently far more difficult to remember than 88 00:08:43.480 --> 00:08:50.080 are the impressions received from the senses of sight or sound. The remedy, 89 00:08:50.240 --> 00:08:56.559 however, becomes apparent when we recognize the source of the difficulty. The remedy 90 00:08:56.759 --> 00:09:03.240 is make the number the subject of sound and site impressions. Attach the abstract 91 00:09:03.320 --> 00:09:07.919 idea of the numbers to the sense of impressions of sight or sound, or 92 00:09:09.080 --> 00:09:13.360 both, according to which are the best developed. In your particular case, 93 00:09:13.480 --> 00:09:18.720 it may be difficult for you to remember eighteen forty eight as an abstract thing, 94 00:09:20.559 --> 00:09:26.480 but comparatively easy for you to remember the sound of eighteen forty eight or 95 00:09:26.600 --> 00:09:31.639 the shape and appearance of eighteen forty eight. If you will repeat a number 96 00:09:31.679 --> 00:09:37.240 to yourself so that you grasp the sound impression of it, or else visualize 97 00:09:37.240 --> 00:09:41.000 it so that you can remember having seen it, then you will be far 98 00:09:41.120 --> 00:09:46.080 more apt to remember it than if you merely think of it without reference to 99 00:09:46.200 --> 00:09:50.480 sound or form. You may forget that the number of a certain store or 100 00:09:50.600 --> 00:09:56.000 house is thirty nine forty eight. But you may easily remember the sound of 101 00:09:56.000 --> 00:10:01.759 the spoken words thirty nine forty eight eight, or the form of thirty nine 102 00:10:01.879 --> 00:10:05.639 forty eight as it appeared to your sight on the door of the place. 103 00:10:07.759 --> 00:10:11.399 In the latter case, you associate the number with the door, and when 104 00:10:11.399 --> 00:10:18.200 you visualize the door, you visualize the number K. Speaking of visualization, 105 00:10:18.679 --> 00:10:24.039 or the reproduction of mental images of things to be remembered, says those who 106 00:10:24.080 --> 00:10:30.600 have been distinguished for their power to carry out long and intricate processes of mental 107 00:10:30.679 --> 00:10:37.639 calculation owe it to the same cause. Taine says, children accustomed to calculate 108 00:10:37.679 --> 00:10:43.519 in their heads right mentally with chalk on an imaginary board, the figures in 109 00:10:43.639 --> 00:10:50.840 question, then all their partial operations, then the final sum, so that 110 00:10:50.919 --> 00:10:56.000 they see internally the different lines of white figures with which they are concerned. 111 00:10:56.279 --> 00:11:01.639 Young Colburn, who had never been at wool and did not know how to 112 00:11:01.679 --> 00:11:07.360 read or write, said that when making his calculations, he saw them clearly 113 00:11:07.440 --> 00:11:11.720 before him. Another said that he saw the numbers he was working with as 114 00:11:11.720 --> 00:11:18.600 if they had been written on a slate. Bidder says, if I perform 115 00:11:18.679 --> 00:11:22.480 a sum mentally, it always proceeds in a visible form in my mind. 116 00:11:24.360 --> 00:11:28.240 Indeed, I can conceive of no other way possible of doing mental arithmetic. 117 00:11:30.559 --> 00:11:35.279 We have known office boys who could never remember the number of an address until 118 00:11:35.320 --> 00:11:41.360 it were distinctly repeated to them several times. Then they memorized the sound and 119 00:11:41.559 --> 00:11:46.200 never forgot it. Others forget the sounds or fail to register them in the 120 00:11:46.279 --> 00:11:50.960 mind, but after once seeing the number on the door of an office or 121 00:11:52.120 --> 00:11:56.559 store, could repeat it at a moment's notice, saying that they mentally could 122 00:11:56.559 --> 00:12:01.320 see the figures on the door. You will find, by a little questioning 123 00:12:01.679 --> 00:12:07.480 that the majority of people remember figures or numbers in this way, and that 124 00:12:07.600 --> 00:12:11.679 very few can remember them as abstract things. For that matter, it is 125 00:12:11.720 --> 00:12:18.600 difficult for the majority of persons to even think of a number Abstractly, try 126 00:12:18.639 --> 00:12:22.919 it yourself and ascertain whether you do not remember the number as either a sound 127 00:12:22.960 --> 00:12:28.279 of words, or else as the mental image or visualization of the form of 128 00:12:28.320 --> 00:12:35.159 the figures, And, by the way, whichever it happens to be sight 129 00:12:35.360 --> 00:12:41.919 or sound, that particular kind of remembrance is your best way of remembering numbers, 130 00:12:41.039 --> 00:12:46.720 and consequently gives you the lines upon which you should proceed to develop This 131 00:12:46.799 --> 00:12:54.039 phase of memory. The law of association may be used advantageously in memorizing numbers. 132 00:12:54.159 --> 00:12:58.360 For instance, we know of a person who remember the number one hundred 133 00:12:58.360 --> 00:13:03.480 and eighty six thousand, the number of miles per second traveled by light waves 134 00:13:03.480 --> 00:13:09.279 in the ether, by associating it with a number of his father's former place 135 00:13:09.320 --> 00:13:16.759 of business, one eighty six. Another remembered his telephone number one eight seven 136 00:13:16.919 --> 00:13:22.639 six, by recalling the date of the declaration of independence. Another the number 137 00:13:22.639 --> 00:13:28.360 of states in the Union by associating it with the last two figures of the 138 00:13:28.440 --> 00:13:33.879 number of his place of business. But by far the better way to memorize 139 00:13:33.039 --> 00:13:39.279 dates, special numbers connected with events, etc. Is to visualize the picture 140 00:13:39.320 --> 00:13:43.960 of the event with the picture of the date or number, thus combining the 141 00:13:45.000 --> 00:13:50.519 two things into a mental picture, the association of which will be preserved when 142 00:13:50.519 --> 00:13:56.360 the picture is recalled. Verse of doggerel, such as in fourteen hundred and 143 00:13:56.440 --> 00:14:03.559 ninety two Columbus sailed the ocean lou or in eighteen hundred and sixty one our 144 00:14:03.639 --> 00:14:09.679 country civil war begun, etc. Have their places and uses, but it 145 00:14:09.799 --> 00:14:15.559 is far better to cultivate the sight or sound of a number than to depend 146 00:14:15.639 --> 00:14:22.399 upon cumbersome associative methods based on artificial links and pegs. Finally, as we 147 00:14:22.480 --> 00:14:28.279 have said in the preceding chapters, before one can develop a good memory of 148 00:14:28.279 --> 00:14:33.799 a subject, he must first cultivate an interest in that subject. Therefore, 149 00:14:33.399 --> 00:14:39.120 if you will keep your interest in figures alive by working out a few problems 150 00:14:39.120 --> 00:14:43.039 in mathematics once in a while, you will find that figures will begin to 151 00:14:43.080 --> 00:14:50.080 have a new interest for you. A little elementary arithmetic, used with interest 152 00:14:50.480 --> 00:14:54.080 will do more to start you on the road to how to remember numbers than 153 00:14:54.120 --> 00:15:01.679 a dozen textbooks on the subject. In memory, the three rules are interest, 154 00:15:01.919 --> 00:15:07.519 attention, and exercise, and the last is the most important, for 155 00:15:07.759 --> 00:15:13.639 without it the others fail. You will be surprised to see how many interesting 156 00:15:13.720 --> 00:15:18.919 things there are in figures. As you proceed the task of going over the 157 00:15:18.960 --> 00:15:22.600 elementary arithmetic will not be nearly so dry as when you were a child. 158 00:15:24.000 --> 00:15:30.759 You will uncover all sorts of queer things in relation to numbers. Just as 159 00:15:30.759 --> 00:15:35.240 a sample, let us call your attention to a few Take the figure one, 160 00:15:35.720 --> 00:15:43.279 and place behind it a number of knots. Thus one zero zero zero 161 00:15:43.399 --> 00:15:50.320 zero zero zero zero zero zero zero zero zero, as many knots or ciphers 162 00:15:50.360 --> 00:15:56.440 as you wish, Then divide the number by the figure seven. You will 163 00:15:56.480 --> 00:16:00.840 find that the result is always this one forty two, eight fifty seven, 164 00:16:02.240 --> 00:16:07.600 then another one forty two, eight fifty seven, and so on to infinity. 165 00:16:07.759 --> 00:16:12.240 If you wish to carry the calculation that far these six figures will be 166 00:16:12.320 --> 00:16:18.360 repeated over and over again, then multiply this one, four, two, 167 00:16:18.519 --> 00:16:23.240 eight, five, seven by the figure seven, and your product will be 168 00:16:23.399 --> 00:16:30.000 all nines. Then take any number and set it down, placing beneath it 169 00:16:30.039 --> 00:16:37.440 a reversal of itself, and subtract the latter from the former. Thus one 170 00:16:37.519 --> 00:16:41.600 one, seven, seven, six, one nine, o nine minus nine 171 00:16:41.720 --> 00:16:48.679 zero nine one six, seven seven one equals two six, eight, four, 172 00:16:48.840 --> 00:16:53.759 five, one three eight, and you will find that the result will 173 00:16:53.799 --> 00:17:00.559 always reduce to nine, and is always a multiple of nine. Take any 174 00:17:00.639 --> 00:17:04.960 number composed of two or more figures and subtract from it the added sum of 175 00:17:04.960 --> 00:17:11.920 its separate figures, and the result is always a multiple of nine. Thus 176 00:17:11.200 --> 00:17:21.759 one eight, four, one plus eight plus four equals thirteen equals one seventy 177 00:17:21.759 --> 00:17:29.920 one divided by nine equals nineteen. We mention these familiar examples merely to remind 178 00:17:29.960 --> 00:17:33.279 you that there is much more of interest in mere figures than many would suppose. 179 00:17:34.440 --> 00:17:37.839 If you can arouse your interest in them, then you will be well 180 00:17:37.920 --> 00:17:44.640 started on the road to the memorizing of numbers. Let figures and numbers mean 181 00:17:44.759 --> 00:17:48.759 something to you, and the rest will be merely a matter of detail.