# Ideatypics; or, an Art of Memory/Chapter 6

NUMBER.
Another most important principle now comes under consideration, useful to all classes of men who employ the Arabic numerals, 1, 2, 3, 4, etc.
These being signs of signs, must be brought under forms that admit of association. Letters which are substituted for figures, are also signs of signs; but they are a very different class of signs, and admit of an arrangement that brings us within the sphere of the most familiar objects.
The ancients used letters for figures. They had no Arithmetical signs. Dr. Grey, among the moderns, first applied letters to Mnemonics. His plan was much thought of at the time, and possesses some value, on account of the principle it involves; yet great difficulties lie in the way of its application: e. g. these technical w7ords are almost as difficult to remember as the numbers for which they are substituted.
| 381 | . . . . . . | 1921 | . . . . . . | 1491 | . . . . . . | 7967 |
| teib. | | aneb. | | afna. | | pousoi. |
| Tcrræ magnitudo | Termagnit. . . . . .eso. . . . . .klaum. |
| Magnitude of the Earth | 264,856,000,000 Cubic miles. |
​The design is good, and this must be apparent to a superficial observer; for who could remember a series of figures like the following without contrivance?
793730383799867379.
If consonants be substituted for the figures, and any vowels be added to complete the sense, it will make a phrase, as in this instance (vide Plate II. Fig. 3, for the numerical scale employed here).
| “Know | then | this | truth | (enough | for | man | to | know).” |
| 7 9 | 3 7 | 3 0 | 3 8 3 | 7 9 | 9 8 | 6 7 | 3 | 7 9. |
Such phrases, Ideatyped, are easily retained in the memory.
Elphinstone’s table of affinity, or analogical association of sounds, and other sources, have enabled me to arrange a table nearly allied to the genius of many languages or dialects.
We must agree that the following letters shall represent certain figures.
| SIBILANTS | | or hissing sounds.s.c.z (sc&c.) . . . . . . . | | put for | 0 |
| LABIAL | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Simple . . . . . . b.p . . . . . . . . . . . . . . . . | | put for ” | 1 |
| LABIAL | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Aspirate. . . . v.w.f.ph, gh as f, and gh as w | | put for ” | 9 |
| GUTTURALS or Hard sounds | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | Simple . . . . . . . . . . . c.k.q.g hard | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Substitutes or Representatives of | 2 |
| GUTTURALS or Hard sounds | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | Aspirate . . . . . . . . . . ch. gh hard” | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Substitutes or Representatives of | 2 |
| GUTTURALS or Hard sounds | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | Compd. sibilating, etc. x.sk.sq.ck | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Substitutes or Representatives of | 2 |
| DENTAL | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Simple . . . . . . . . . . . . . . t.d | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Substitutes” | 3 |
| DENTAL | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Aspirate . . . . . . . . . . . . . th | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,$ | Substitutes” | 3 |
| COMPOUND | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | Aspirates . . . . . . j.g.ch.tch and cognates tu su | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Substitutes” | 4 |
| COMPOUND | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | Sibilating Aspirates.sh and cognates ti.si.zi.sch ​ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,$ | Substitutes” | 4 |
| liquids | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | l . . . . . . . . . . . . . . . . . . . . . . . . . . . | 5 |
| liquids | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | m . . . . . . . . . . . . . . . . . . . . . . . . . . . | 6 |
| liquids | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | n . . . . . . . . . . . . . . . . . . . . . . . . . . . | 7 |
| liquids | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | r (augh & ough as r). . . . . . . . . . . . | 8 |
Or thus:—
| | labial. 1 | guttural. 2 | dental. 3 |
| sibilants. 0 | compound. 4 | lingual liquid. 5 | labial liquid. 6 |
| | dental liquid. 7 | guttural liquid. 8 | labial. 9 |
1 and 9 Labials are opposite each other, as 3 and 7 Dentals, and as 2 and 8 Gutturals are; Diagonals would pass through the odd numbers.
In Pl. II. Fig. 3, the whole is arranged in subsquares, and the consonants have their localities assigned them according to the figures they are intended to represent.
To assign to each division as wide a range as possible, I make ng and dg also represent 4. These with j make the word judging, which is 444. y and h, as a separate consonant, may be used anywhere, but they do not represent a number. Throughout, for purposes of convenience, y may always be regarded as a vowel, and w always as a consonant (vide No. 9, above).
​There is an aim in the whole contrivance to combine something like philosophical order with conventional practices. In doing this, there is always danger of leaning too much on one side. Attempts have been made, by some writers, to determine the number of distinct sounds which the human voice is capable of producing. If we consider a little, we shall perceive they are essentially infinite, and admit of no limitation. It is necessary, however, to employ symbols of sound, and to arrange them; and it is worth while attending to the various opinions that belong to the subject, that we may derive advantage where we can.
The result of my enquiries is given in the scale, Pl. II. Fig. 3. The pupil has only to consider how each subsquare stands, and to know its place from what he has learnt previously, and then what consonants I have assigned to each of these subsquares; so that when figures are to be committed to memory, certain consonants can be substituted for those figures, and any vowels added to complete the words and make sense. The task of the learner is really a very simple one. The order of the consonants, apart from the distribution according to sound, is simple, for it runs with the alphabet. b, c, d, is 1, 2, 3; j is 4, and l, m, n, r, is 5, 6, 7, 8. The last four may be remembered by ​inserting two vowels, and making the word Limner. w is 9, and the last. The rest of the consonants may be traced by the sounds which they have analogous to this or that letter, that may be considered the principal one of each subsquare. By omitting the vowels in our series, we can use them where we please, because they have no numerical value assigned them.
The vowels are like ligaments, and the consonants like parts of a skeleton that require to be held together.
Fenaigle and Goodluck have adopted letters as near as possible like the figures. Fenaigle put t for 1, on account of their similarity; n also for 2, because two strokes were required to make it; m for 3, and so on. Beniowski seems to have followed Feinagle in his scale. Dr. Crook followed the order of the alphabet, by placing
| B C | for | 1 |
| D F | for” | 2 |
| G H | for” | 3 |
Here the letters assigned to each number are not cognates. A difficulty will be found in this and in all similarly constructed tables, when we pass from a letter not suited for a word, and try to bring in another, because the sounds of the letters that are placed together are unlike. This is an important consideration, well known to those who have tried both ways, yet hardly understood, perhaps,
Plate II.
Fig. 1.
Fig. 2.
Fig. 3.
​ by those who have only used one. The letters that belong to the several subsquares may be variously remembered, for the index consonants, or the principal consonants of the subsquares that have even numbers, are contained in the word cashmere. These subsquares may also have a circle drawn in them, or they may be colored. c or g (both being hard sounds, as c in cash; g in got, gash, etc., and not as g in age,) may be distinguished by the color green; sh, or ch soft, by a chocolate color; m, by amber; and r, by red.
I will now make a particular application of the Scale, (Pl. II. Fig. 3.) which I have designated Ideatyphonicon, from its connection with Ideatypics, and its supplying us with ideas in the substitution of consonants, arranged as nearly as possible according to sound. Suppose a series of figures to be learnt immediately—39, 17, 64, 38, 71,—refer, mentally, to the scale (the scale, or the table from which it is derived, must be committed to memory) for the subsquare containing the number you want. Then you may adopt the method used by Mrs. Slater in her Chronology, or Mr. Goodluck in his,—that is, let each letter, substituted for a figure, be the initial letter of a word. This mode, however, must be used in close connection with objects. I have found that by en​creasing the number of objects, under certain regulations, the recollection is assisted, while mere words rarely have the same effect, however well applied they may be; and when those applications originate with the individual who uses them, the result is still very uncertain. Another mode is, to take the two first consonants of a word. In 3 subsquare you find d, t, th. Take one of the three consonants, and for the next figure, 9, take one of the consonants in subsquare 9. Then make a word of these two consonants. Never mind how many letters there are in the word you employ, only let the two consonants that are chosen be first in it, as they only will be considered the representatives of the numbers.
Taking the figures two by two, we have a series of words any of which we may adopt. We have here five rows of words answering, from left to right, to the row of figures above them.
| 3 9 | 1 7 | 6 4 | 3 8 | 7 1 |
| Towel | painted | much | deer | nabob |
| Down | bonnet | meshes | draught | nobody |
| Tough | pint | matches | train | nibble |
| Thief | pincers | manger | terror | nap |
| Dove | punt | motion | threat | nip |
This method is adopted for quickness, as it will be seen hundreds of words are at our disposal that we can instantly associate, reading them off ​in the order of the numbers. If speed be the object, three figures at a time will not do so well; as there is then a smaller choice of words. Five words may be associated in each subsquare, if you wish to locate them in any room, and in every square we may put 50 words with ease; so that if each word be numbered, the word and the number can be given in every instance. This, however, is not the mode to be adopted for committing to memory in study and in a serious way. We must employ a little more labour to arrange phrases, and then the matter in connection will be indelibly fixed in the mind, and space and time economised.
Take the series of figures above and make a phrase thus:—
| | 3 9 | | 1 7 6 | 4 3 | 8 7 | 1 |
| A | thief, | a | paynim | cheat, | ran | by. |
Here every consonant, or the equivalent to a single figure, is to be considered as a numeral representative.
We may fix the events of a whole year, register appointments, enrol the payment of bills, and other mercantile concerns, on ideal almanacs, made by taking four walls, and dividing each into three stripes, each stripe being divided into three parts. We may take the wall as a subsquare divided into nine places, and again into subplaces for the days of the month. Suppose we wish to ​remember an occurrence or circumstance of business or pleasure, connected with the 25th of April, we should take the figures 4, 25, (fourth month, 25th day,) and change them into letters. These would be sh, k, l; of this we might make shekel, or any other word that would associate with the nature of the event. We can make ourselves many ideal repositories to enchain and fix passing incidents, whether of an amusing character or connected with money matters, dates, &c.
Other valuable modes of employing the principle will suggest themselves to the student. How advantageously the system may be employed in the business of life, our every-day concerns, to remember the No. of a cab or other vehicle, the number of a bank note, a number of articles that we have to purchase, many persons that we ought to call upon, etc. etc. Arithmetical Tables, Statistics, Mathematical Formulas, etc., are instanced in the examples.
There are certain “Disciplinæ,” however, connected with these things, (the Mathematics) as well as with Language, in which memory is but a handmaid, and holds an inferior place to the judgment. Through these Disciplines, mind is considered as passing to attain a condition of right ​judgment, or certain and correct habitudes of thought. The first four rules of Arithmetic, which are generally considered as elementary, are resolvable into still simpler forms, through which the mind should be led. This would give an ability to go through a multiplication table of great extent, without either learning it by rote or by Ideatypics.
To those, however, who would learn it by this System, it is an easy affair. A few squares, subsquared and divided into places, in which objects are supposed to be put, made out of the letters that are the representatives of the figures to be remembered, settles the business. There are hundreds of tables and thousands of figures connected with different branches of Education, that require to be learnt by rote, and are used as materials for the exercise of the judgment. These will be the first object of the teacher in employing this System, Let no false exercises or false knowledge be committed to memory. Men have devised systems of Logic to aid us in thinking rightly, because of our erring judgment; let us, then, not strengthen wrong tendencies. It does not follow that you can recollect the real because you can retain the false, as some pretend, any more than it would follow that you can recollect the face of a person because you are able to remember a distorted image of the man, in fact, a caricature ​more striking than the reality. If a system be good, it is wrong not to exclude from it every thing that is of questionable value. I intend to give no false stimulus to the public mind, as an enticement to the practice of that which I have here presented. My duty, as a Teacher, does not allow me to encourage morbid feelings, but to give a plain, unvarnished statement of the principles of my System and of my practice. I shall be content to lead others to rapid progress in real knowledge, and not to presume upon it by what I can shew of advancement in that which is false.
Under the head of examples, we are enabled to introduce subjects that are likely to solve the most important queries of the learner.
EXAMPLES.
| Beauty | 13 | Girl | 285 | Quench | 274 |
| Bought (as R) | 183 | Goose | 20 | Rapture (tu pron.ch) | 8148 |
| Bow | 19 | Age (G soft) | 4 | | |
| Cow | 29 | Hedging | 44 | Sicily | 005 |
| Cough (as F) | 29 | Jew | 49 | Thatch | 34 |
| Caught (as R) | 283 | King | 24 | Thing | 3 |
| Cask | 22 | Language | 544 | Thought (as R) | 383 |
| Casque | 22 | Mantua-maker | 673628 | Taught | 383 |
| Catch | 24 | Numb | 76 | Vinegar | 9728 |
| Daughter | 3838 | Knight | 73 | Weeping | 914 |
| Flash | 954 | Prejudice | 18430 | Xenophon | 2797 |
| Friendship | 987341 | | | Zany | 07 |
EXAMPLES.
1.—The distance of the moon from the earth is 236847 miles, or (Get home, urchin,) associate moon and urchin.
2.—Muskets invented, a. d. 1521 (Plug up). When a musket is not used, they put a cork in the muzzle.
​3.—Numbers necessary in computing areas of circles: 3.1416, or 3.1415926536 (A deep ship. Leave a camel at home).
Note.—A circle brings to mind the earth, with a deep ship sailing round it; and then comes the idea of the disadvantage, or the uselessness, of having a camel on board. The transition of the thought is easy, and the result certain.
4.—A great source of error in the statement of temperature, is the different modes of estimation used by scientific men in different countries; as,
| Boiling Point.— | Fahrenheit. | Centigrade. | Reaumur | De Lisle |
| | 212° (cubic). | 100° (passes). | 80° (rose). | 0°. |
| Freezing Point.— | 32° (thick). | 0°. | 0°. | 150° (bells) |
Associate the words in whatever way you please, or select others.
5.—A few dates of important facts.
6.—Wales, a big rock, (1282) quite subdued by the arms (860) of Edw. I., after an independence of 860 years.
7.—Imagine a piece of moss (60) to be put on some part of Westminster Abbey, and it will bring to mind the number of years that edifice took in building.
8.—For Latitudes and Longitudes. An acquaintance with the Geographicon will enable any one to ​decide upon the Longitude being East or West? or the Latitude North or South. Let the Latitude always precede the Longitude. Then the following is the Lat. and Lon. of Jerusalem.
| LAT. 30° | (dependance) 47′ (shunning) N. |
| LON. 35° | (tells you) .. 20′ (causes) E. of Jerusalem's decline. |
Note.—My idea in connection with this, is the continual departure of the Jews from GOD.
EXERCISES on NUMBER.
1.—Berzelius calcined human bones, 100 parts of which contained
| Phosphate of Lime | 81.9 |
| Fluate of Lime | 3.0 |
| Lime | 10.0 |
| Phosphate of Magnesia | 1.1 |
| Soda | 2.0 |
| Carbonic Acid | 2.0 |
| | 100 |
Ideatype the above Table.
2.—What is the specific gravity of Quicksilver, Chlorine, Sulphur, etc.?
3.—What is the Lat. and Lon. of London, Paris, Madrid, Amsterdam, Berlin, Berne, Rome, etc.?
4.—Take six points about a mill for the different measures of a mile, five points about a cur for the different measures of an acre, four points about the next object, and so on till you have associated and located all that belongs to Square Measure.
5.—What is the height of the mountains Snowden, Cader Idris, Vesuvius, Ætna, Bernard, Blanc, etc.?
6.—What is the length of the Thames, Seine, Tagus, Rhone, Rhine, Don, Volga, Euphrates, Indus, etc.?
​7.—Put into Ideatypics the following numbers frequently used in calculation:—
| Square of 3.14159265359 | = 9.869604399639 |
| Area of a Circle to diameter 1 | = .785398163397448 |
| Surface of a Sphere to radius 1 | = 12.566370614 |
| Solidity of a Sphere to radius 1 | = 4.188790205 |
| Square of a circumference of a circle x .07957747 | = area |
| One hour | = 3600 seconds |
| Twelve hours | = 43200 „ |
| Mean diameter of the Earth | = 7912 miles |
| Mean radius of the Earth | = 20887680 |
| A degree on the Equator | = 365144 feet |
| English mile | = 5280 feet |
| Geographical mile | = 6075.6 feet |
| Time of the diurnal rotation of the Earth | = 861640.908 sec. |
| Length of the Solar or tropical year | = 365.24223 days |
| „ „ Seconds’ Pendulum at London | = 39.1393 inches |
| Force of Gravity at London | = 32.1908 feet. |
* ↑ At some of the Colleges, the papers are headed Disciplinæ.
* ↑ Many of my pupils can give a date for almost every particular circumstance in Modern History, with the births and deaths of all the remarkable men. On this subject alone they have always at hand 10,000 figures; and from themselves I have it, that they find it more difficult to forget than to remember.