Memorization and Mnemonic Strategies
Timothy P. Grove
Dr. Judith Lingenfelter, Ph.D.
5 May 2006
The voice of Funes, out of the darkness, continued. He told me that
toward 1886 he had devised a new system of enumeration and that in a
very few days he had gone beyond twenty-four thousand. He had not
written it down, for what he once meditated would not be erased. The
first stimulus to his work, I believe, had been his discontent with the fact
that "thirty-three Uruguayans" required two symbols and three words,
rather than a single word and a single symbol. Later he applied his
extravagant principle to the other numbers. In place of seven thousand
thirteen, he would say (for example) Máximo Perez; in place of seven
thousand fourteen, The Train; other numbers were Luis Melián Lafinur,
Olimar, Brimstone, Clubs, The Whale, Gas, The Cauldron, Napoleon,
Agustín de Vedia. In lieu of five hundred, he would say nine. Each word
had a particular sign, a species of mark; the last were very complicated. . . .
I attempted to explain that this rhapsody of unconnected terms was precisely
the contrary of a system of enumeration. I said that to say three hundred and
sixty-five was to say three hundreds, six tens, five units: an analysis which
does not exist in such numbers as The Negro Timoteo or Meat Blanket.
Funes did not understand me, or did not wish to understand me.
--Jorge Luis Borges, Funes el Memorioso (1944)
My own interest in mnemonics arose at the time I learned to read. I started reading during the summer before first grade by learning to “sound out” the signs we passed. When I couldn’t figure one out, sometimes my father or mother would tell me what it said. Through this means, along with reading lessons at school, I became an avid reader over the course of the next year or two.
At the same time, I noticed a parallel phenomenon which puzzled me: my acquisition of the ability to read coincided with the loss of my ability to remember things verbatim. It had once been easy for me to memorize the script of any T.V. commercial after seeing it a few times. After I learned to read, I could no longer do this. I had also been able to recognize the voices used in commercials; when I heard an announcer’s voice, it was almost like seeing a face—I could always recall the different contexts where I had heard it before. When I learned to read, I lost this ability also. It is very interesting for me to remember how during the years before I learned to read, I had seen vivid pictorial representations in my mind whenever something was said. I can best describe these as being somewhat like Egyptian hieroglyphics: colored symbols figured in parallel registers or rows. I believe these were based partly on the meaning of the words, and partly on their sound (since words of unknown meaning were readily represented). To the best of my recollection, the symbols were mainly geometrical shapes arranged in patterns, and of various colors. Some of the words and phrases had a more elaborate representation as a kind of stylized scene (analogous to the introduction to a T.V. show, which is invariable though the program itself is different each week, e.g. the opening sequence of the “Andy Griffith Show,” with Andy and Opie returning from fishing, or the final credits with the pine trees). I can still remember some of the imagery that came to mind every time our family recited the Lord’s Prayer, as well as the symbols for a few other expressions. For example, “General Mills” (a phrase which I often heard on television without knowing what it meant) was conveyed by a dark outline of a square object resembling a telephone, with two blue dots in the center resembling eyes, and two large red dots to the right of it. The symbolism was quite arbitrary, somewhat in the manner of Chinese characters. In other words, the symbol for “General Motors” would probably have had little or no relation to the one for “General Mills."
I remember wondering about these symbols sometimes—about where they came from and whether other people saw them as well; I believe I even asked my mother about it once, but I was not able to make her understand exactly what I meant. I concluded eventually that even if other people saw pictures as I did, they were probably not exactly the same pictures. But I remember thinking, if I could find one other person who saw the same pictures I did, it would be easy, using crayons, to write a message to him or her, and so in a sense I already knew how to read and write! Unfortunately I never did attempt to record any of my “hieroglyphics,” and after learning to read, instead of the pictures I used to see, I started seeing printed words. The details of my little hieroglyphs were soon forgotten.
My ability to readily memorize things gradually diminished. I remember that during first and second grades I could memorize a Bible passage (7-10 verses) quite easily during the 8:30 church service, despite the distraction of the singing and the sermon, so that I could recite it perfectly during Sunday School and get my gold star. This would be very hard for me to do nowadays in such a short time, even without distractions.
Unusual capacity to remember is frequently associated with synaesthesia, which occurs when input through one of the senses triggers perceptions involving one or more other senses. For example, musical tones may be associated with various colors, or shapes and colors may trigger parallel perceptions involving taste, smell, or texture.
A. R. Luria documents a remarkable case of photographic memory in The Mind of a Mnemonist (1968). His subject, S., reported having experienced synaesthetic reactions at a very early age: “When I was about two or three years old I was taught the words of a Hebrew prayer. I didn’t understand them, and what happened was that the words settled in my mind as puffs of steam or splashes…Even now I see these puffs or splashes when I hear certain sounds” (Luria, 1968: 24). S. experienced musical tones not only as sounds, but also as shades of color, which varied according to their pitch and volume. He experienced human voices in much the same way: “‘What a crumbly, yellow voice you have,’ he once told L. S. Vygotsky while conversing with him” (Luria, 1968: 25). For S., every speech sound was associated with a “striking visual image, for it had its own distinct form, colour and taste. Vowels appeared to him as simple figures, consonants as splashes, some of them solid configurations, others more scattered—but all of them retaining some distinct form. As he described it: ‘A is something white and long; I moves off somewhere ahead so that you just can’t sketch it, whereas Y is pointed in form’” (Luria, 1968: 26). S. experienced numbers in much the same way:
1 is a pointed number—which has nothing to do with the way it’s written.
It’s because it’s somehow firm and complete. 2 is flatter, rectangular, whitish
in colour, sometimes almost a grey. 3 is a pointed segment which rotates. 4
is also square and dull; it looks like 2 but has more substance to it, it’s thicker.
5 is absolutely complete and takes the form of a cone or a tower—something
substantial. 6, the first number after 5, has a whitish hue; 8 somehow has a
naïve quality, it’s milky blue like lime . . . (Luria, 1968: 27).
Luria seems to have believed that pure synaesthesia was characteristic of early childhood, and tended to weaken during later stages of development. Perhaps all children experience synaesthesia before they become capable of understanding and using speech—a stage of development of which, since it is pre-verbal, adults retain little or no memory. In other words, we were all once capable of “seeing” sound and “hearing” colors. This is known as the Neonatal Synaesthesia Hypothesis (Baron-Cohen, 1996). It is also interesting to note that one of the most commonly reported effects of L.S.D. is the experience of synaesthesia—“Sometimes you can smell the green, when your mind is feeling fine” (Aliotta-Haynes-Jeremiah, “Lake Shore Drive,” 1971; this was a hit single in Chicago when I was growing up).
For S., synaesthesia persisted throughout his adult life. According to Luria, S. had two ways of remembering things. One was to use what is commonly known as “photographic memory.” S. had merely to concentrate for a short time on a page of writing, whether text or a list of numbers, and he would later (even years later) be able to close his eyes and “see” it in detail. His visual recollection was so exact that he would sometimes “misread” similar symbols, such as 3 and 8, if they had been written carelessly on the page (Luria, 1968).
“Photographic memory” of the sort which Luria describes is simply a highly developed version of the memory which we all possess to a greater or lesser degree, and which the Romans designated by the term “natural memory” (memoria naturalis), in contradistinction to another kind of memory which they called “artificial memory” (memoria artificiosa) (Rhetorica ad Herennium, III.xvi.28). Artificial Memory (later known as ars memorativa) is potentially of great interest to educators, linguists, and practically everyone else. It entails the conscious cultivation of strategies for remembering, sometimes involving mnemonic systems of remarkable complexity and ingenuity. This is illustrated by S’s other method of remembering, which was to convert data into visual images:
Formerly, in order to remember a thing, I would have to summon up an image of the whole scene. Now all I have to do is take some detail I’ve decided on in advance that will signify the whole image. Say I’m given the word horseman. All it takes now is an image of a foot in a spur. Earlier, if I’d been given the word restaurant, I’d have seen the entrance to the restaurant, people sitting inside, a Roumanian orchestra tuning up, and a lot else . . . Now if I’m given the word, I’d see something rather like a store and an entranceway with a bit of something white showing from inside—that’s all, and I’d remember the word. So my images have changed quite a bit. Earlier they were more clear-cut, more realistic. The ones I have now are not as well-defined or as vivid as the earlier ones. . . I try just to single out one detail I’ll need in order to remember a word (Luria, 1968: 37).
In contrast to the purely synaesthetic reactions to numbers noted above, S. also converted them into images: “Take the number 1. This is a proud, well-built man; 2 is a high-spirited woman; 3 a gloomy person (why, I don’t know); 6 a man with a swollen foot; 7 a man with a moustache; 8 a very stout woman—a sack within a sack” (Luria, 1968: 30). S. was able to process all words and numbers in this way, and even unfamiliar or foreign words were registered by means of some visual impression he associated with them, which was “related to the phonetic qualities of the word rather than to its meaning” (Luria, 1968: 30).
When he wanted to remember a long series of data, S. had devised a way of distributing his visual images along a road or street which he visualized in his mind, either a street in his home town or a street in Moscow where he lived as an adult. By mentally traveling along the street, he could quickly retrieve a series of data either forwards or backwards. “Sometimes,” he confessed, “I put a word in a dark place and have trouble seeing it as I go by” (Luria, 1968: 33).
S. created this system independently, and was apparently unaware of any writings on the subject. In fact, Artificial Memory very much like the system S. developed was cultivated in antiquity, and is discussed by several important classical authors. The most extensive discussion is found in the anonymous Rhetorica ad Herennium (III.xv-xxiv). Parallel passages are found in Cicero De Oratore (II.lvxxxvi-lvxxxviii) and in Quintilian’s Institutio Oratoria (XI.ii), both of which present similar material but add some important details. In all these works, reference is made to earlier Greek authorities on the subject, including Simonides, Charmadas, and Metrodorus of Scepsis. However, apart from a brief passage in the Dissoi Logoi (ca. 400 B.C.), no Greek writings on the subject have survived. Ancient practitioners of memoria artificiosa were capable of some astounding feats: “Seneca the Elder tells us (Controversiae 1.19) that Cicero’s famous rival Hortensius once in answer to a challenge sat through an auction all day long and at the end of the day was able to give from memory the full list of articles, buyers, and prices in order without a mistake” (Post, 1932: 107).
Three Kinds of Artificial Memory
Traditionally, Artificial Memory (or Mnemotechnic) was of two kinds: Memoria rerum (“memory for things,”) and Memoria verborum (“memory for words”) (Rhetorica ad Herennium, III.xxiv). To these may be added a third, Memoria numerorum (“memory for numbers”), which appears to have been invented in the 17th century. In mediaeval times, memoria verborum was also known as memoria verbatim, memoria verbaliter, or memoria ad verbum, while memoria rerum was also called memoria summatim, memoria sentialiter, or memoria ad res (Carruthers & Ziolkowski, 2002).
Memoria Rerum: The System of Loci
Memoria rerum encompassed various strategies for remembering facts and details, usually in a specific order. The strategy which S. devised independently was strikingly similar to an ancient technique known as the system of loci, which is most fully described in the Rhetorica ad Herennium. If one wants to use this system, the first step is to memorize a series of loci (“places” or “backgrounds”). These “memory places” may be rooms, buildings, the walls of a city, or outdoor locations of any kind, either real or imaginary. Quintilian suggests “a spacious house divided into a number of rooms" (Institutio Oratoria, XI.ii.18). However, they must always be recalled in the same order. For this reason, a sequence of familiar rooms in a house or a well-known public building is useful. A university or a museum, a church or school—any public building would be an excellent choice, as long as one is thoroughly familiar with its rooms and buildings so that one can mentally traverse them in order. Another useful way to accomplish this is to visualize points along a familiar route or street, as S. did (Quintilian, Institutio Oratoria, XI.ii.21). Once the series of loci has been set up, it is important to review it constantly in order to become thoroughly familiar with the loci in their correct sequence and to develop facility in their use. The second component of the system is the creation of imagines (“images”). Any image may be used to symbolize an idea or a specific word, as long as the image readily brings its subject to mind. The more strange, vivid, or ridiculous the images are, the more effective they will be; and individual practitioners of the system should develop whatever images they find most memorable—one’s own images are always more memorable than someone else’s. The Auctor ad Herennium (III.xxii.37) suggests that images be “as striking as possible . .. if we assign to them exceptional beauty or singular ugliness; if we dress some of them with crowns or purple cloaks, . . . if we somehow disfigure them, as by introducing one stained with blood or soiled with mud or smeared with red paint, so that its form is more striking, or by assigning certain comic effects to our images, for that, too, will ensure our remembering them more readily.” For example, Thomas Bradwardine (c1290-1349) suggested that to remember the word “bitterness,” one should create an image of someone gagging on a bitter substance (Carruthers & Ziolkowski, 2002). Indeed, many of the examples presented in Renaissance treatises on mnemonics were scandalous, even pornographic (Rossi, 2002: 30). Clearly, concrete images, especially those which involve violence or strong emotion, are more effective as memory tools than abstract ideas. Another important principle to be considered is that “memory delights in brevity”—information to be remembered is best stored in knowledge-rich but brief units, as S. demonstrated when he reduced a “horseman” to “a foot in a spur” (Carruthers & Ziolkowski, 2002). The devising of both loci and imagines requires much careful thought.
In order to use the system, one places the images of the things one needs to remember in the appropriate places. For example, I might use the house I lived in from 1973 to 1987 to create a series of loci. Supposing I want to remember the signs of the zodiac in order. I will begin by imagining a ram on the front porch. When I open the door, there is a bull in the hallway. I open the closet to hang up my coat and there are two boys in there. Going into my Mom’s office, I notice there is a large crab on the desk. From there I go out into the garage, where I narrowly escape a lion. Running in through the laundry room, I find a young woman washing clothes, and so on.
Although the Auctor ad Herennium (III.xxii.37) cautions against placing too many images in the same locus, he and several other writers on the ars memorativa recommend the creation of tableaux uniting several images in the same background. Thomas Bradwardine suggests a way of combining three images in each locus, placing the first in the center, the second to the right, and the third to the left (Carruthers, 1990).
It is not enough to simply “place” the images in their loci. Before leaving, one must take a moment to establish some “similitude” (connection or similarity) between the image and its locus in order to create an association (Carruthers & Ziolkowski, 2002). In the example above, the woman must actually be using the washing machine to wash clothes, not just standing there. The crab on the desk must be pictured ransacking the things in the drawer with its claws. In this way a vivid connection can be created between the image and its locus.
It is remarkable that S. came up independently with a system of locations and images which is almost precisely similar to the system of loci described by the classical authors—right down to the directive that “the loci ought to be neither too bright nor too dim, so that the shadows may not obscure the images nor the luster make them glitter” (Rhetorica ad Herennium, III.xix.32).
Different versions of the system of loci
The system of loci as described by the classical authors was essentially an architectural system. It consisted of a building of some kind, perhaps a series of buildings, in which all the memory places could be found. Some of these were in the form of architectural niches (“spaces between columns”, according to the Auctor ad Herennium) in which statues could be placed. Even when some of the loci were outdoor scenes or imaginary places, these were arranged in sequence with all the rest, like glass cases in a museum or a series of views from windows. One modern mnemonist has carefully analyzed the Oz books by Frank Baum, in order to create a detailed plan of the palace in the Emerald City (M. Grandy, n.d.). Some Renaissance memory experts, like Matteo Ricci, the Jesuit missionary to China, created elaborate “memory palaces” consisting of several hundred buildings. Francesco Panigarola, who may have been one of Ricci’s teachers, had developed a mental system comprising 100,000 loci! (Spence, 1984).
It was also possible to create fantastical connections between various architectural structures. In the example given above, if I discover that I need to create a very large number of subcategories for “Gemini,” which I have placed in the hall closet, I can install an imaginary door which opens from the back of the closet. Passing through this door, I find myself in the street outside my church. Using the church as a sub-system of loci, I can create as many loci there as necessary, all of them subordinate to the closet, which is the third locus in my house.
Closely related to this is the mnemonic “room system.” Instead of an entire house, one uses a single room, such as one’s office, with which one is extremely familiar. Assuming the furniture and most of the objects in the room tend to remain in the same places, it becomes possible to “pigeonhole” mnemonic images in a series of places around the room. It is still necessary, of course, to create an invariable “itinerary” from one place to the next, reviewing it frequently so that the proper sequence is assured. For example, upon entering the door, one could visit each corner of the room in a clockwise direction, ending up in the center of the room. This would create an invariable sequence of five “places” within each room. Like the “magic door” in my hall closet, the room system could also be used to create innumerable subdivisions in a basic architectural layout.
In cases where it is necessary to organize data into categories, but in no particular sequence, a map can be used. For example, a student of French might use his hometown to organize nouns according to their gender, placing masculine nouns on one side of the tracks and feminine nouns on the other. A student of German would have to divide the town into three sectors (to accommodate masculine, feminine, and neuter nouns). A person who is thoroughly familiar with geography could use the continents, oceans, nations and their provinces as a matrix to organize information.
It is possible to create an imaginary theatre whose various sections and individual seats can be used as a system of loci. The imagines are conceived as spectators occupying the seats, as seen from the stage. Systems of this kind were described by Giulio Camillo (Idea del Teatro, 1548) and by Robert Fludd (Utriusque Cosmi, Maioris scilicet et Minoris, metaphysica, physica, atque technica Historia, 1621). Camillo actually constructed and demonstrated for the king of France a miniature theatre according to his plan, large enough for several people to enter; presumably this included a large set of dolls to be used as spectators (Yates, 1966). This system bears some relation to one devised by a teacher I read about somewhere. His mnemonic system was based on his first group of 20 students. He continued to use this classroom as a mnemonic device for years afterward!
The method of placing images along a familiar itinerary, as S. described, is an example of a “journey system.” This approach is mentioned in Quintilian’s Institutio Oratoria, XI.ii.21. A repeated journey, such as one’s daily drive to work, is an excellent basis for this system, since the points and landmarks along the way become extremely familiar. When I lived in rural Wisconsin, my parents and I had to drive 30 miles (from Sister Bay to Sturgeon Bay) at least once a week to do essential shopping. I still have a good memory of most of the points we passed along the way, so for me, this would be a good choice. Another option is a very memorable journey one has made, such as the Grand Tour of the Continent which so many aristocratic Englishmen made in the late 18th century; my own trip through Upper Burma in the summer of 2004 could provide a wealth of “memory places,” which could be refreshed using a map and the series of pictures I took along the way. A further variation on this would be to use a railway as the basis for a journey system, such as the (for me) familiar sequence of 13 stops on the Northwestern between Wheaton and Chicago. In order to create subsystems, one would imagine getting off the train at one of the stations and traveling down one of the streets leading away from the railroad. It might even prove useful to actually drive around in that locality, in order to become acquainted with those streets and where they lead.
Quintilian (Institutio Oratoria XI.ii.21) mentions “pictures” (picturis) as one way of creating a series of loci. This gave rise to a very active use of pictures as mnemonic aids during the Middle Ages and the Renaissance. Indeed, in view of the widespread cultivation of Artificial Memory during that period (during which it was considered an indispensable part of education), it has been suggested that many of the artworks of that time were planned as mnemonic aids. A gallery of pictures could easily be used as a system of loci. In my childhood, my parents purchased a book called The Bible in Pictures for Little Eyes by Ken Taylor, a series of 184 color pictures beginning with Genesis 1 and ending with Paul’s shipwreck (Acts 27-28). We read from that book every night, and its pictures became thoroughly familiar to me long before I had learned to read, or even understood what the pictures meant. Such a book could be used extremely effectively as a gallery system.
Literary text systems
In the same way that pictures may be used as mnemonic devices, such a use can be made of literary texts. Dante’s Divina Comedia, for example, provides a comprehensive series of loci in its three divisions (Inferno, Purgatorio, Paradiso). There is reason to believe that Dante had this in mind when he composed the work, and it appears to have gained some currency as a mnemonic device (Eco, 1992).
Texts which have been memorized verbatim can themselves be used as mnemonic peg systems. Since the text has been mastered by rote, its invariable sequence of words, images, and sentences can provide a structure to which imagines can be attached (Carruthers, 1998). A short memorized text like the Lord’s Prayer or the 23rd Psalm can be used to provide a short sequence of pegs (The Lord—my shepherd—I shall not want—He maketh me—to lie down—in green pastures . . .). To use this text to memorize, for example, the stops Northwestern stops on the West Line out of Chicago, I would create the following associations: The Lord + Chicago, My shepherd + Kedzie, I shall not want + Oak Park, He maketh me + River Forest, To lie down + Maywood, In green pastures + Bellwood, He leadeth me + Berkeley, Beside the still waters + Elmhurst, and so on. If this does not work well, it is possible to condense the series down to its visual symbols (Shepherd, Green Pastures, Still Waters, Paths of Righteousness, Valley of the Shadow of Death, Rod, Staff, Table, Mine Enemies, My Head, Oil, Cup, House of the Lord), and this sequence can be used in the same way.
When long texts have been committed to memory, such as the entire book of Psalms (as was commonly done in the Middle Ages), or the entire Torah (as rabbinic students continue to do even today), the result is a “memory palace” of truly imposing proportions!
The letters of the alphabet have commonly been used as a system of loci, using a series of words beginning with each letter (e.g. Ape, Bee, Camel, Dog, Egg). This is sometimes called a “peg system.” The great advantage of such a system is that the order of the series is easily maintained. Some Renaissance writers on mnemonics presented multiple alphabets which could be used for various purposes, such as an alphabet of birds (Anser [goose], Bubo [owl], Ciconia [stork], etc.). Boncompagno da Signa, in his treatise
De memoria, speaks of using an alphabet of images “which can scarcely be written down on these perishable pages”, by which he learned the full names of 500 students, along with their places of origin (Carruthers & Ziolkowski, 2002: 114).
The use of the Zodiac and its subdivisions as a mnemonic device was well known in ancient times, and was associated with Metrodorus of Scepsis (1st century B. C.) Quintilian (Institutio Oratoria, XI.ii.22) reports that “Metrodorus . . . found three hundred and sixty different localities in the twelve signs of the Zodiac through which the sun passes.” According to Cicero, “Metrodorus of Scepsis in Asia, who is said to be still living, . . . used to say that he wrote down things he wanted to remember in certain ‘localities’ in his possession by means of images, just as if he were inscribing letters on wax” (De oratore, II.lxxxviii.360). W. Den Boer (1986) notes the “great importance [in classical antiquity] of astrology as a mnemonic and organizing system. . . . Metrodorus’ ‘topical system of mnemonics’ remains worthy of attention. By means of this system one acquires 12 x 30 sections to arrange the memory’s stock in one large circle of the Zodiac” (p. 14). Observing that Greek historical works abound in astrological data, Den Boer suggests that these astrological references may embody a mnemonic system, a “treasure-chamber of memory . . . , i.e. the Zodiac and its sections or loci, in which the imagines of history are stored” (p. 30). Den Boer believes that modern scholars have ignored “what the [Greek] authors took for granted, namely, a principle of division derived from astrology” (p. 35). He maintains that although no specific examples of Metrodorus’ method are known, that is merely because “a quest for them has never been made” (p. 35).
It may be that Den Boer is assuming a wider currency for the system of Metrodorus than it actually had, but there is no doubt that subdivisions of the Zodiac were extremely familiar to the ancients and that they were represented by a series of well-known symbols. For example, Aries, the first sign, is symbolized as a ram. The 30 degrees of Aries are divided into three decanates, each comprising 10 degrees. The first decanate of Aries is called Senator, and it is “the image of a black man, standing and cloathed in a white garment, girdled about, of a great body, with reddish eyes, and great strength, and like one that is angry.” The second decanate of Aries (called Senacher) is “a form of a woman, outwardly cloathed with a red garment, and under it a white, spreading abroad over her feet.” The third decanate of Aries (called Sentacher) is “the figure of a white man, pale, with reddish hair, and cloathed with a red garment, who carrying on the one hand a golden Bracelet, and holding forth a wooden staff, is restless, and like one in wrath, because he cannot perform that good he would” (Agrippa von Nettesheim, 1533). The 36 decanates have their origin in Egyptian astrology, and are represented in several important Egyptian monuments. Their images are recorded (with some variation) in numerous sources, some of them datable to late classical antiquity, along with their names, which are Latinized corruptions of their original Egyptian designations.
L. A. Post (1932) assumes that the practice of Metrodorus was to group “ten artificial backgrounds under each decan figure. He would thus have a series of loci numbered from one to 360, which he could use in his operations. With a little calculation he could find any background by its number, and he was insured against missing a background, since all were arranged in numerical order” (p. 109). However, in addition to the 36 decanates, each of the individual degrees also had a traditional image associated with it. The earliest written source for these is from the 14th century (Petrus de Abano, first printed in Johannes Angelus, Astrolabium planum in tabulis ascendens, 1488). However, it is possible that they derive from some lost classical source. In any case, it seems likely that Metrodorus made use of some similar scheme. The symbols for the first ten degrees of Aries, corresponding to the decanate of Senator, are as follows:
1 A man holding a sickle in his right hand and a crossbow in his left.
2 A man with the head of a dog, stretching forth his right hand and holding a staff in his left.
3 A man showing off various valuables with his right hand while reaching for his belt with his left hand.
4 A man with curled hair, holding a falcon in his right hand, and a whip in his left.
5 Two men: one cutting wood with an axe, the other holding a scepter in his right hand.
6 A crowned king, holding an orb in his right hand and a scepter in his left.
7 A heavily armored man, holding arrows in his right hand.
8 A man with a helmet on his head but otherwise unarmed, holding a crossbow in his right hand.
9 A man, bareheaded but otherwise well dressed, holding a dagger in his left hand.
10 A bareheaded man, running a bear through with a spear.
In later times, many other sets of symbols for the 360 degrees were published, including those of P. Christian (Calendrier des Thèbes, 1863), Charubel [John Thomas] (1893), Antonio Borelli (1907), I. Kozminski (1917), M. E. Jones (Sabian Symbols, 1925), and Janduz (1930). The modern sets of degree-symbols tend to be more striking than the rather wooden characters listed by Petrus de Abano. For example, the Sabian Symbol for the 10th degree of Taurus is “A Red Cross nurse,” while that for the 29th degree of Sagittarius is “A fat boy mowing the lawn.” Charubel’s symbol for the 20th degree of Gemini is “A red tree covered with golden fruit.”
The traditional symbols for the decanates also formed an important part of the mnemonic techniques elaborated by Giordano Bruno (1548-1600). Bruno, who ended his career by being burned at the stake, believed that the combinatory use of astrological and other symbols could give its practitioner supernatural powers of memory and even some degree of control over fate and natural circumstances.
Hugh of St. Victor (c1078-1141) recommended the use of a number line as a mnemonic device: “Learn to construct in your mind a line numbered from one on, in however long a sequence you want, extended as it were before the eyes of your mind. When you hear any number at all called out, become accustomed to quickly turning your mind there where its sum is enclosed, as though to that specific point at which in full this number is completed. For example, when you hear ten, think of the tenth place, or when twelve, think of the twelfth, so that you conceive of the whole according to its outer extent, and likewise for the other (numbers). Make this conception and this way of imagining it practiced and habitual, so that you conceive of the limit and extent of all numbers visually, just as though placed in particular places” (Carruthers & Ziolkowski, 2002: 36).
Those for whom mere numbers are not as memorable as they apparently were for Hugh of St. Victor can use the “major system” (described below) for remembering the numbers in sequence. This functions like the Alphabet systems, but instead of 26 pegs, it furnishes 100 or 1000 pegs. The things one wants to remember are simply associated with the number-symbols in order. This was my own practice at one time, but I discovered that unless significant effort was put into establishing a “similitude” between the two images, the “remembered” information became irretrievable.
A good example of this is found in Graham Best’s Memory made easy (1980). Best provides mnemonic symbols to help remember the contents of each chapter in the New Testament, rather like the series I put together for the book of Numbers; moreover, Best uses key words from the “major system,” just as I did, to recall which chapter the symbols go with (this is a remarkable coincidence, since I was completely unaware of Best’s book when I did that project!). Best organizes Acts 5 around the key word “hill,” which stands for the number five (see below under memoria numerorum).
(1) Ananias and Sapphira sin and die.
(2) The apostles spend the night in jail but are released by an angel and told to speak the message of life.
On a hill (key word) a hanon with eyes (Ananias) falls dead beside a burning sofa (“sofa fire” is the alternate for Sapphira). A hill inside a jail surrounded by pistols (apostles). An angel on the hill points and holds Life cereal, again a sufficient reminder that the apostles were freed by an angel and told to preach the message of life (Best, 1980: 73-75) [appendix G].
Other systems of loci
The six colors of the spectrum can provide a convenient 6-peg system, and perhaps many more for a person who is sensitive to many shades of color.
For those well-versed in pop music, familiar record albums can be used to create a system of mnemonic loci. The Beatles released 14 albums between 1963 and 1970, comprising 28 album sides and 196 songs. The Jefferson Airplane released 10 albums from 1966 to 1974. A person who is deeply familiar with these tends to think of each album side as a separate unit, and each song on the side as a distinct landscape, color, or feeling. One useful application of this is that the details of an acid trip (which might otherwise be lost forever) can be recalled and organized by their association with the various album tracks that were playing at the time. For others, the weekly TV schedule functions in the same way. It is not hard to use either of these as matrices for organizing thoughts, ideas, and information.
The human body is a useful mnemonic system (the 206 bones in the human skeletal system, for example, or the 248 parts of the human body according to rabbinic tradition). Filippo Gesualdo (Plutosofia, 1592) created a system of 42 loci based on the human body (21 loci on the right side, and 21 on the left) (Eco, 1992) [appendix E].
Elaborate systems arose based on the joints of the hands, including the “Guidonian hand” system which was used to represent musical intervals (Carruthers & Ziolkowski, 2002), and many others published as late as the 17th century. A modern survival of these is the well-known way of remembering the number of days in each month according to the knuckles of one hand.
Other approaches to memoria rerum
Although it was an indispensable part of the teaching of classical rhetoric until early modern times, few people today would find the system of loci easy to use. However, although Artificial Memory is no longer part of most people’s education, mnemonics are still widely used for various purposes. Mnemonics in general use today include the following: simple mnemonics, acrostics, mnemonic rhymes, mnemonic stories, linked symbols, flat representations, and mnemonic apparatus.
Simple mnemonics are used for spelling; for example, one might remember the spelling of “friend” as “fri-END.”
Acrostics are used to remember small sets of information, and may take the form of words or entire sentences. Examples include TULIP (Total depravity, Unconditional Election, Limited Atonement, Irresistible Grace, Perseverance of the Saints), “Every good boy does fine” (lines of the treble staff), and “Fat cats go down alleys eating bugs” (order of sharps). The sentence “Can Queen Victoria eat cold apple pie?” is useful for remembering the seven hills of Rome (Capitoline, Quirinal, Viminal, Esquiline, Coelian, Aretine, Palatine) (A dictionary of mnemonics, 1972: 73).
Mnemonic rhymes are widely used throughout the world. An interesting example is the jingle used to distinguish the deadly coral snake from the harmless scarlet kingsnake: “Red touch yellow, kill a fellow. Red touch black, friend of Jack” (A variation is “Red touch yellow, kill a fellow. Red touch black, venom lack”).
Mnemonic stories combine items of information to create a narrative. For example, to remember the New England states (Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island): “The water MAIN broke. When the guy came to fix it, we were so grateful that we invited him in for a HAM dinner. Unfortunately, there were WORMs in it—he got sick and died; since he was a Catholic, we attended his funeral MASS. When we got to the church, it was dark because the electricity was disCONNECTed. So instead, they held the funeral out in the ROAD.” Ridiculous, but quite effective, at least in the short term.
The technique of linked symbols is similar to a mnemonic story, except that it connects the symbols together in some way other than a story. One way to do this is called “stacking.” Here, the symbols are piled up vertically as high as possible, with results suggestive of an illustration by Dr. Seuss.
This practice of linking symbols together is described in Thomas Bradwardine’s De memoria artificiali:
Suppose that someone must memorize the twelve zodiacal signs,
that is the ram, the bull, etc. So he should make for himself in the front of
the first location a very white ram standing up and rearing on his hind
feet, with (if you like) golden horns. Likewise one places a very red
bull to the right of the ram, kicking the ram with his rear feet; standing
erect, the ram then with his right foot kicks the bull above his large and
super-swollen testicles, causing a copious infusion of blood. And by
means of the testicles one will recall that it is a bull, not a castrated ox or
In a similar manner, a woman is placed before the bull as though laboring
in birth, and from her uterus are figured coming forth two most beautiful
twins, playing with a horrible, intensely red crab, which holds captive the
hand of one of the little sons and thus compels him to weeping and to such
signs, the remaining child wondering yet nonetheless caressing the crab
in a childish way. Or the two twins are placed there born not of a woman
but from the bull in a marvelous manner, so that the principle of economy
of material may be observed. To the left of the ram a dreadful lion is
placed, who with open mouth and rearing on its legs attacks a virgin,
beautifully adorned, by tearing her ornate garments. With its left foot
the ram inflicts a wound to the lion’s head. The virgin truly holds in her
right hand scales for which might be fashioned a balance-beam of silver
with a plumb-line of red silk, and then weighing-pans of gold; on her left is
placed a scorpion wondrously fighting her so that her whole arm is swollen, and
which she strives to weigh in the aforesaid scales (Carruthers, 1990: 283-84).
A flat representation (also called a “group portrait”) is a picture which attempts to connect a number of symbols in some meaningful way, in which all the parts are related harmonically to a single composition, Carruthers & Ziolkowski, 2002). Examples of this include a 17th century engraving representing the content of II Kings (Rieger, 2000: 392) [appendix A], Johannes Buno’s representation of the historical events of the 17th century [appendix B], and an earlier set of woodcuts representing each chapter of the four gospels (A method for recollecting the Gospels, ca. 1470) [appendix C].
A mnemonic apparatus organizes a complete set of information to be remembered as a logical system of interrelationships. These were sometimes rendered graphically like a flat representation, but could also be presented through words alone. Examples of mnemonic apparatus are Alanus de Insulis, On the six-winged seraph, in which the seraph’s wings and their feathers are used to organize the subdivisions of theology; the Viridarium Aristotelis ethicum [appendix D], which categorizes the philosopher’s ethical thought using the branches of a tree; and Hugh of St. Victor’s De arca Noë mystica, which is an extremely ambitious geometrical conception of Noah’s Ark as a sort of “memory palace,” a memoria summatim containing an outline of theology and biblical history, complete with the Old Testament genealogies, a list of all the popes, and a summary of all creation in the form of the Mediaeval “chain of being” (Carruthers & Ziolkowski, 2002)].
During the Renaissance, the system of loci and related techniques were refined far beyond anything known to the Greeks and Romans. Extremely ingenious and elaborate schemes were published by Host von Romberch, Guglielmo Grataroli, and many others.
Grataroli developed a tripartite system of place, object, and figure.
After designing a memory location on conventional lines, he then
positioned in each an object—a chamber pot, a box of salve, a bowl of
plaster were his first three examples—and then had separate figures,
each based on an individual he knew well and each carefully named, jolt
the scenes into mnemonic action. Thus in rapid sequence Grataroli
presented his friend Peter as picking up the chamber pot full of urine
and pouring it over James, Martin putting his finger in the ointment box
and wiping it over Henry’s anus, and Andrew taking some plaster from
the bowl and smearing it over Francis’s face. If one could link these
vignettes by pun, analogy, or association of ideas to given concepts, one
could be guaranteed never to forget them (Spence, 1984: 136).
The obscenity typical of so many of these treatises (most of which were written by Dominicans) eventually led to the rejection of the ars memorativa by Protestants, and as a result it did not survive as an organized system into modern times.
Memoria verborum: Rote memorization
Memoria verborum is usually accomplished by means of rote repetition (from the Latin rota, meaning “wheel”). This is what I was doing during the adult church service, as I scrambled to commit 10 verses from the King James Bible to memory. Unless frequently reviewed, the results of this kind of memorization are quickly lost. Even with frequent review, it is possible for small errors to creep in, especially where prepositions and conjunctions are concerned. I have found that rote memorization is easier to do in a foreign language than in English (perhaps because there is less cognitive “interference”). This has been my experience, at least—I haven’t had time to research this question.
The most effective approach to rote memorization is to use the mediaeval principle of “dividing and collecting” (divisio & compositio); a long text is divided into manageable units, with an organized structure (conspectus) which can be taken in at a glance (Carruthers & Ziolkowski, 2002). Thus, Hugh of St. Victor suggests that each psalm be reduced to its incipit (e.g. Beatus vir [Psalm 1], Confitebor tibi Domine [Psalm 9], which is then associated with its number. Each psalm is then built up from this foundation or “stub,” and individual psalms are in turn laid out into their component verses. The structure thus becomes a powerful mnemonic aid, of equal importance to the content. This approach to memorization is the practical motivation behind the division of the Bible into chapters and verses.
Two effective aids to rote memorization, group recitation and corporal punishment, are seldom used today. Group recitation roots out individual errors very effectively, and is still used by rabbinic students. Teachers used to mete out corporal punishment to students, not only for misbehavior, but also for incorrect answers and for errors in memorization. This surely provided some degree of motivation for the students. My own difficulties in trying to learn Chinese have tempted me to experiment with this method myself, perhaps by holding my hand over a candle for a moment every time a new character is introduced!
Artificial memoria verborum
The verbatim memorization of texts is discussed in all the ancient sources on mnemonics. The devising of some means to facilitate this has been sought ever since— really this is the “Holy Grail” of mnemonics!
Mnemonics for the purpose of memoria verborum are usually rebus-like associations of various kinds. For example, in the Dissoi logoi, a Greek text on rhetoric from around 400 B.C., it is suggested that one recall the word pyrilampes by thinking of pyr (fire) and lampein (to shine) (Carruthers & Ziolkowski, 2002).
The Latin authors have little to add to this basic principle. The Auctor ad Herennium gives some examples; to remember the line Iam domum itionem reges Atridae parant (“And now their home-coming the kings, the sons of Atreus, are making ready”), he suggests, “in our first locus we should put Domitius, raising hands to heaven while he is lashed by the Marcii Reges.” Thus, domum itionem (“home-coming”)is encoded as Domitium (a member of a well-known plebeian family), and reges is called to mind by Marcii Reges (the members of a rival family of patricians); since itionem is accusative, while reges (“kings”) is in the nominative case, it is necessary to picture them doing something to Domitius, hence the idea of lashing; “in the second background,” the text continues, “Aesopus and Cimber, being dressed as for the roles of Agamemnon and Menelaus in Iphigenia—that will represent ‘Atridae parant’” (Rhetorica ad Herennium, III.xxi.34). So Atridae is encoded as Agamemnon and Menelaus, in the guise of well-known actors in those roles, and parant by the actors getting ready to go on stage.
This approach to memorization has been current ever since. Modern handbooks on memory propose such rebuses as “Chick car go” (for Chicago), “I owe her” (for Iowa), “mini soda” (for Minnesota), “new brass car” (for Nebraska), and “whiz con sin” (for Wisconsin) (Lorayne, 1975: 155). These seem quite ludicrous—is it so hard just to remember “Wisconsin”? Still, maybe some people find this easier than getting hold of a proper name. Other writers suggest applying this method to names (for Andy, think of “Raggedy Andy”; for Peter, think of “Peter Pan”). This method is especially useful for surnames: for Klingenhut, it is suggested, think of someone clinging to a hut; for Eyberg, think of an eye on an iceberg (Browning, 1983). Some publications include long indices of common given names and surnames, with suggested mnemonic equivalents (Lorayne, 1975). Quintilian also discusses an approach to remembering proper names based on their meaning. Thus Fabius is associated with the famous Fabius Maximus (Hannibal’s opponent when he crossed the Alps to invade Italy), much as we would do with “Lincoln” today. Aper, Ursus, Naso, and Crispus are associated with their meanings (“boar,” “bear,” “long-nose,” and “curly,” respectively). Cicero and Aurelius are remembered by means of their derivations (“sower of chickpea [cicer]” and “child of the sun [a sole],” respectively) (Institutio Oratoria, XI.ii.30-31). Harry Lorayne (1975) provides an interesting mnemonic series for the twelve months, employing the methods of both rebus and association: janitor [rebus], brrr [rebus and association], march [pun], ape [rebus], maypole [association], bride [association], firecracker [assocation], gust of wind [rebus], scepter [rebus], octopus [rebus], turkey [assocation], Santa Claus [assocation] (pp. 181-82)
The classical sources question the value of an extensive use of this method, suggesting that its use be limited to difficult words or unusual names, and as an exercise to strengthen one’s ability to memorize (Rhetorica ad Herennium, III.xxiv.39).
The extensive use of mnemonics for memoria verborum is described by the third-century rhetorician Longinus: “Simonides and many since his time have published methods of memory, introducing the juxtaposition of images and places in order to be able to remember nouns and verbs. It is nothing but seeing together things similar to any desired new thing and connecting them one with another. For the familiar thing is a symbol and a track and a hold and a starting-point for the thing that is to be recognized. In this way it is possible to grasp even the speech of foreigners, putting in juxtaposition with the familiar that which corresponds to it, and keeping in view the symbols of the things” (Post, 1932: 107-108).
Graham Best, in his book Memory made easy (1980), gives some astonishing examples of how this method might be applied to memorizing Bible verses:
“7th commandment: You shall not commit adultery. A tree shines a flashlight on itself; it is a dull tree (adultery). The cow caught in its branches tells us that this is the seventh commandment [this last is derived from the “major system,” described below].
9th commandment: You shall not bear false witness against your neighbor. A bear holds a wet nest (bear false witness) as it is being stung by a bee [which stands for the number 9]” (Best, 1980: 66) [appendix F].
“James 5:8 You too be patient; strengthen your hearts, for the coming of the Lord is at hand. In a heart is a letter U and the number 2 to remind us of “You too be patient.” The heart is lifting weights to strengthen itself and to remind us, strengthen your heart.” The heart is standing on a hand; “the coming of the Lord is at hand.” (Best, 1980: 150).
Extended examples like these are perhaps more trouble than learning by simple rote repetition. Still, everyone who attempts to learn a text verbatim must face the difficulty of how to memorize such things as articles, conjunctions, and prepositions, which are not “content words.” This difficulty was recognized in antiquity. In the example given above, it will be noted that the Auctor ad Herennium makes no attempt to represent the adverb iam (“now”). Quintilian writes: “I do not mention the fact that some things, certainly conjunctions, for example, cannot be represented by images.” He goes on to say, however, that “we may, it is true, like shorthand writers (qui notis scribunt), have definite symbols for everything, and may select an infinite number of places to recall all the words contained in the five books of the second pleading against Verres [for example], and we may even remember them all as if they were deposits placed in safe-keeping (Intitutio Oratoria, XI.ii.25). “Shorthand writers” is clearly a reference to the Notae Tironianae (“Tiro’s notes”), a system of shorthand invented by Cicero’s secretary and widely used until around 1000 A.D. [for extensive examples of the Notae Tironianae, see Henke (n. d.), and Boge (1974)]. There is some evidence to suggest that the Tironian symbols for conjunctions, prepositions, and other short words were sometimes used in conjunction with the system of loci. In the example already quoted from the Rhetorica ad Herennium, the missing word iam could have been rendered by its Tironian shorthand equivalent, which was an angular symbol pointing to the right, like the “greater than” symbol (>), but with the angle less acute. This could have been added to the image in the first locus (the Marcii Reges lashing Domitius with a crooked stick, for example), or it could have been made to occupy a locus of its own (as an angle from Euclid’s geometry, perhaps).
For this same purpose, I have made some use of symbols of my own, based in part upon dim recollections of the mental hieroglyphs I once had. For example, I associate the words “that” and “which” with little black acute triangles, pointing up for “that” and pointing down for “which”. The idea behind this is that “that” sounds like “hat” and “which” sounds like “wedge”. An ambiguity arises, however, since the “hat” symbol looks like a witch-hat! I also sometimes use the symbol of a hand pointing (the way it is printed in old books) for “and,” and an image of the full moon (as it appears in calendars and almanacs) to represent the word “so.” For “the,” I sometimes use the Thomas shorthand symbol (a tiny circle).
Quintilian recommends mentally “underlining” difficult passages in memorized material: “If certain portions prove especially difficult to remember, it will be found advantageous to indicate them by certain marks, the remembrance of which will refresh and stimulate the memory. For there can be but few whose memory is so barren that they will fail to recognize the symbols with which they have marked different passages” (Institutio Oratoria, XI.ii.28-29). Possibly he means that one should mark the passages in the book from which one is memorizing, so that the marks will accompany the passages when they are brought to mind.
Thomas Bradwardine (c1290-1349) made an important contribution to memoria verborum. He recommended learning a keyword to represent every possible syllable. For example, for AB, he suggests using the word abbas (abbot). For BA, one could use another word such as ballisterius (crossbowman), or, alternately, one could turn the abbot upside down! Bradwardine was also innovative in suggesting that one could use mnemonic keywords not only from Latin, but from any language one was familiar with (Carruthers & Ziolkowski, 2002).
Giordano Bruno (1548-1600) devised an extremely bizarre mechanism for memoria verborum. This is presented in his Ars Memoriae (1582), in which he associated each of the letters with a character from classical mythology. For each character he composed a simple description consisting of the character itself + its activity + some passive condition. Thus, for the letter D he had “Argus in bovis custodiam caputiatus” (“Argus [a monster with 100 eyes] guarding the cow [the assignment Zeus gave him] beheaded [his manner of death]”). The entire series of characters, activities, and conditions were inscribed on three imaginary concentric wheels, with the characters on the inner wheel, their activities on the middle wheel, and their conditions on the outer wheel. The wheels were then turned to spell words. For example, the word AMO (“I love”) would result in a juxtaposition of the character Lycas (who represented A) performing the activity of Medea (who represented M), in the condition of Pluto (who represented O). The image which would emerge, therefore, is of a Centaur (Lycas) killing its children (as Medea did) in Hades (the abode of Pluto). It is hard to understand how such a cumbersome system could be useful, at least as applied to memoria verborum. However, Bruno’s idea of subjects with predication was quite original and has been taken up in our own day by Dominic O’Brien, who has used it to develop a very useful system (see “Dominic System,” below).
Memoria verborum and foreign languages
A special use of memoria verborum is its application to foreign languages. Quintilian reports that “Mithridates is recorded to have known twenty-two languages, that being the number of the different nations included in his empire; Crassus, surnamed the Rich, when commanding in Asia had such a complete mastery of five different Greek dialects, that he would give judgement in the dialect employed by the plaintiff in putting forward his suit” (Institutio Oratoria, XI.ii.50). Quintilian attributes these feats to a combination of natural ability and some form of memoria artificiosa. As we know from Longinus, quoted above, one recognized application of mnemonics was “to grasp even the speech of foreigners, putting in juxtaposition with the familiar that which corresponds to it, and keeping in view the symbols of the things” (Post, 1932: 108).
It is often useful to create some mnemonic connection between one’s own language and the target language. For example, if I want to learn the Korean word for “book” (chaek), it is easy to remember it by thinking of a “checkbook.”
“An English learner of German, trying to remember the meaning of Raupe (“Caterpillar”) could associate Raupe with the English word rope (sound similarity), and construct a mental image representing a caterpillar stretched out in more than its fullest length (exaggeration helps!) on a rope. An English learner of French, trying to remember paon (“peacock), might use the word pawn as mediator, imagining a chess board on which all pawns look like peacocks” (Hulstijn, 1997: 205).
Often it is useful to construct sentences containing both the foreign word and its translation. For example, to remember the French word fâché (“angry”), one could use the sentence, “A fascist makes me ‘fâché’” (Hulstijn, 1997: 206).
Numbers are especially difficult to remember. However, there is no evidence that the Greeks or Romans ever devised a system for remembering numbers (Post, 1932). The writer of Rhetorica ad Herennium suggests that the loci be numbered, indicating every fifth locus with a hand, and every tenth locus with an acquaintance named Decimus. Later, Thomas Bradwardine refined this by suggesting that every 10th locus be marked with a cross (the Roman numeral X). Hugh of St. Victor writes as if numbers were striking and memorable symbols in themselves (Carruthers & Ziolkowski, 2002). However, for most people, the memorization of numbers presents a great challenge. Since the 17th century, a number of number memorization systems have been invented. These systems have two uses: to remember numerical data, and to create a template for remembering a list of non-numerical data in sequence.
A simple way to remember numbers is to group them in some way that is meaningful. For example, my office phone number is 944-0351 x5105. One way to group the numbers is 9-440-351, 5-10-5. Nine is easy to remember; next comes 440 (the frequency of a tuning fork for A), then 3, 5, 1 (the first three odd numbers, beginning with 3 and cycling back to 1), then five, ten, five (this makes me think of Franklin’s Five-and-Ten Store). Some people accomplish this by remembering the position of the numbers on the telephone key-pad, and the motions necessary to dial them (horizontal, vertical, diagonal).
There are several ways to encode numbers for memorization. One is to use the letters which appear on the telephone dial. My number could be encoded as WIG Zero-DJ-One K-Ten-K. This might be a little easier to remember than the numbers themselves, but is not terribly useful.
Those who have a good memory for historical dates might use them as a means for remembering other numbers. In the example above, 944 could be encoded as 1944 (attaching a “one” at the beginning), and associated with the Battle of the Bulge. 0351 could be encoded as 1035 (by wrapping around the “one” to the beginning) and associated with the death of king Canute. Finally, 5105 could be encoded as 1055 (wrapping around the “five” to the end), and then associated with the capture of Baghdad by the Seljuq Turks.
Numbers can also be symbolized by the number of letters in a word. For example, a well-known mnemonic for the first 15 digits of Pi (3.14159265358979) is the following: “How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics.”
Related to this (or perhaps unclassifiable) are the mnemonics used to memorize Morse Code. Words and phrases are employed which have the same rhythm as the dots and dashes which represent their initial letter, e. g. Alone (dot-dash), Bountifully (dash-dot-dot-dot), Correspondent (dash-dot-dash-dot), Doubtfully (dash-dot-dot), Egg (dot), For as much as (dash-dot-dash-dot), Good gracious! (dash-dash-dot), Ha ha ha ha (dot-dot-dot-dot), Japan’s Jam Jars (dot-dash-dash-dash), Kingdom come (dash-dot-dash) (A dictionary of mnemonics, 1972: 54-55).
Another way to encode numbers is to use any of the several “minor systems” which have been devised for the purpose. A “minor system” is one which is used to encode the ten digits only; there is no specially provision for encoding longer numbers, except to repeat the short ones.
The best known of the minor systems associates numbers with rhyming words:
Bun, Shoe, Tree, Door, Hive, Sticks, Heaven, Bait, Vine, Hen (there are numerous variations on this).
Another widely-known minor system associates numbers with objects of similar shape:
1 = a rocket
2 = a swan
3 = a heart
4 = a sailboat
5 = a fishhook
6 = a quail [or a snail]
7 = a tomahawk
8 = an hourglass
9 = a shepherd’s crook
0 = a donut
Another minor system is actually derived from the “major system’ (see next section), since it associates the same ten sounds with the ten digits. Listed below are two of many possible ways of doing this (Best, 1980: 59-60, 70). The first of these comprises words with the encoded consonant only; the second combines those consonants with H (which has no numerical value):
1 = Tie 1 = Hat
2 = Noah 2 = Honey
3 = Ma 3 = Home
4 = Ear 4 = Hair
5 = Law 5 = Hill
6 = Shoe 6 = Hatch
7 = Cow 7 = Hawk
8 = Ivy 8 = Hive
9 = Bee 9 = Hoop
0 = Donut 0 = Hose
Still another system of this kind are the codes used by retail stores to indicate the wholesale cost they paid for an item. For example, at Long Drugs and many other stores, prices are converted into the corresponding letters from the word “Charleston”:
1 = C
2 = H
3 = A
4 = R
5 = L
6 = E
7 = S
8 = T
9 = O
0 = N
Thus, if the tag of an item priced at $3.99 includes the letters ANT, that indicates that the actual cost to the retailer was $3.08, with a markup of 91 cents. Other codes of this kind include BRUSHCLEAN (formerly used by Walgreen’s) and BRUNCHSALE (widely used) (Drugstore El President, 2006).
A “major system” is one which associates digits with phonemes (usually consonants, sometimes both consonants and vowels), which are then used to encode strings of digits as words or even sentences.
The inventor of this appears to have been one Stanislaus Mink von Wenusheim (or Weinsheim or Winkelmann), who published the particulars of his system in a paper entitled Parnassus (1648). In it, he shared the details of his “most fertile secret,” a way of expressing numbers by words. Winckelmann’s key was as follows:
1 = B, P, W
2 = C, K, Z
3 = F, V
4 = G
5 = L
6 = M
7 = N
8 = R
9 = S
0 = T
Thus, 2006 could be encoded as CTTM (or KTTM or ZTTM). To remember this, you could use words (Cat-tame, cat-at-home, kitty-ma), or sentences as an acrostic (Come to the museum, Katie talked to me, Zebras try to mate). Winckelmann himself, a user of Latin, gave as an example the nonsense phrase apio imo agor (“I am led by the deepest celery”), to represent 1648. The vowels and H have no numerical value, and so can be inserted as needed; the same is true of the letters D, J, Q, X, and Y (Middleton, 1885). Winckelmann’s system is rather crude, and its partial adherence to alphabetical order, along with its seemingly arbitrary omission of D, J, Q, and X, seems to have no rational basis. Nevertheless, it was a remarkable innovation, and nearly all subsequent systems for remembering numerical data are variations on it. One of these was devised by Leibniz as part of his attempt to create a universal language.
A very interesting and influential system was published in 1730 by Richard Grey, D. D., entitled Memoria Technica. This was reprinted many times until as late as 1880, and in English-speaking countries it was the premier method used for memorizing historical dates for more than a century. Dr. Grey used both vowels and consonants to encode numbers. His key was as follows:
Thus, a and b both stand for 1, e and d for 2, and so on, with either of the two letters being used. In addition, Grey used g to represent hundreds, th to represent thousands, and m to represent millions. In order to avoid confusion between I (3) and Y (0), Grey requires “that y is to be pronounced as w, for the more easily distinguishing it from i, as syd = 602, pronounce swid, typ = 307, pronounce twip” (Grey, 1872: 3). After thoroughly learning the key, the reader is then "to exercise himself in the formation and resolution of words in this manner:– 10, az; 325, tel; 381 teib; 1921 aneb; 1491 afna; 1012 bybe; 536 uts; 7967, pousoi; 431 fib; 553 lut; 680 seiz &c.” (Grey, 1872: 2).
Since both consonants and vowels are used, there are multiple ways of representing the same numbers: “325 tel, or idu, 154 buf, or blo, or alf, or alo, 93,451 ni-ola, or out-fub, or ni-fla, or out-olb, &c.” (Grey, 1872: 3).
The bulk of Grey’s Memoria Technica is a presentation of tables of historical dates, along with mnemonic hexameter verses for use in remembering them:
The ages of the world before our Saviour’s time are, by
chronologers, generally divided into six: the first, from the creation to
the deluge; the second, form the deluge to the call of Abraham, &c.
according to the following periods:
4004 1. The Creation of the world
2348 2. The universal DELuge
1921 3. The call of Abraham
1491 4. Exodus, or the departure of the Israelites from Egypt
1012 5. The foundation of Solomon’s TEMple
536 6. CYRus, or the end of the captivity
The birth of Christ.
All this is expressed in one line belonging to Table I., as follows:
Crothf Deletok Abaneb Exafna Tembybe Cyruts.
Cr denotes the Creation, othf 4004, Del the Deluge, Ab the calling of
Abraham, Ex Exodus, Tem the Temple, and Cyr Cyrus. The technical
endings of each represent the respective year, according to the rules
already laid down (Grey, 1872: 5).
Since the composition and recitation of Latin hexameter verses was a fundamental part of a classical education, Grey’s assembly of his material into “verses” was intended to work as an aid to memory. When properly scanned, the above hexameter would have been pronounced as follows (stressed syllables in bold type):
Crothf Dele-tok Aba-neb Ex-af-na Tem-bybe Cy-ruts.
There were some, even in Grey’s time, who rebelled at the prospect of memorizing these barbarisms. As Middleton (1885) puts it, “Dr. Grey fell into the error of replacing arbitrary characters [i. e. numbers] by others almost as arbitrary.” However, Grey’s Memoria Technica went through multiple editions, and a great many people both in England and America applied themselves seriously to learning his mnemonic verses. For example, Lucius J. Polk (1808-1869), a Tennessee planter, transcribed much of Grey’s system into a notebook dated 1821 (Polk, 1821).
Gregor von Feinagle gave a series of lectures in Paris (1807) entitled “New system of mnemonics and methodics.” The details of Feinagle’s lectures were compiled and published by his students. They included a rearrangement of Winckelmann’s key:
1 = T
2 = N
3 = M
4 = R
5 = L
6 = D
7 = K, G, Q, hard C
8 = B, W, V, H
9 = P, F
0 = S, X, Z, soft C
Feinagle explained the basis for some of his choices: N was used to represent 2 because it had two humps, M was used for 3 because it had three humps; R represented 4 because the word for “four” has an R in most European languages (four, vier, quatre, quattro), and L represented 5 by analogy with the Roman numeral fifty (L). Feinagle used these to form words just as Winckelmann had done: “The number 12 can be readily expressed by the words tin, ton, tiny, eaten, oaten; 20 nose, onyx, noose; 47 by rook, ark, rake; 547 by lark, lyric; and 1605 by tidy-seal” (Middleton, 1885).
In his lectures, Feinagle went even further, describing a system of bewildering complexity:
With this system he combined the plan of dividing a room into
fifty consecutive spaces, and indelibly associating a mental image or
hieroglyphic to each compartment. In forming this chain, he appears
to have lost sight of the possibility of forming words which would
immediately suggest the number it represented. His chain of symbols
is formed chiefly of striking objects, their consecutiveness being
ensured by the position they were supposed to occupy in each room.
Thus, the first compartment was supposed to contain an image of the
Tower of Babel. To fix the date of the Norman Conquest, he formed
a mental picture of a willow tree with a piece of dead laurel on it, and
associated it with the first space. The willow suggested William;
laurel, the Conqueror; being in the first space made it William I.; and
the consonants in the words "dead" gave him the numbers 66, which,
with the thousand understood to be dropped, gave 1066, the date of the
Conquest (Middleton, 1885).
Feinagle’s system became well-known in England through translations of his work, and the English word “finagle” is derived from his name! Feinagle’s major system is certainly an improvement on Winckelmann’s, but is still defective in that the consonant pairs T/D, P/F, and F/V represent different numerals, which are thus liable to become confused.
Numerous systems of this kind were published in the course of the 19th century (Middleton counts 24 which appeared between 1830 and 1885!). The version most commonly used today, generally known as the “Mnemonic Major System,” was published by Pliny Miles in his Elements of Mnemotechny (1845). Miles lectured on mnemonics in the U.S., Canada, and London between 1844 and 1850 (Middleton, 1885).
Miles’ system was as follows:
1 = T, D, TH
2 = N
3 = M
4 = R
5 = L
6 = CH, J, SH; ZH (as in measure)
7 = K, G
8 = F, V
9 = B, P
0 = S, Z
As with the systems of Winckelmann and Feinagle, vowels have no numerical value, and can be inserted wherever needed to form words. H, W, and Y can be used in the same way.
I first became acquainted with this system when I was trying to get a job with the U.S. Post Office. The exam to qualify is notoriously difficult, and part of it involves memorizing a list of 25 addresses (ironically, no one who actually works for the U.S. Post Office is ever asked to perform such a task). Because of this difficulty, there are professional test-preparation seminars available to prepare for this exam, and that is how I learned this system.
Pliny Miles’ “Mnemonic Major System” has become fairly well-known. L. A. Post used it to remember his U. S. Army serial number (3,181,853): “Once I had translated this into My two feet fail me, I was not likely to forget it” (Post, 1932: 106). Most people who learn this system create their own set of words to represent the numbers 11 through 99. That way, it is not necessary to waste time thinking of a word to use. For example, I always use “tin” for 12, “Nero” for 24, and “Chevy” for 68. It is also possible to memorize a complete set of 3-consonant words to represent the numbers from 100 through 999. Thus, “nomad” = 231, “sheriff” = 648, “Kickapoo” = 779, “Yellowknife” = 528, and so on. William D. Hersey’s Blueprints for Memory (1990) presents a complete set of these (pp. 117-132). There are also computer programs written for this purpose (e. g. soundnumbers.com), which will provide a list of possible equivalents for any series of digits.
A very creative way of memorizing numbers was devised by Dominic O’Brien. One begins with a key:
1 = A
2 = B
3 = C
4 = D
5 = E
6 = S
7 = G
8 = H
9 = N
0 = O
Next, it is necessary to think of a person to represent every number from 00 to 99, whose initials correspond to that number. For example, 63 could be Santa Claus, 15 could be Albert Einstein, and 78 could be George Harrison. For each person, a characteristic action is associated (Santa Claus putting gifts under the Christmas tree, Albert Einstein writing equations on a chalkboard, George Harrison playing the guitar). The subject (the person himself) will be used to indicate the first two digits, while the predicate (the person’s characteristic action) will be used to indicate the third and fourth digits. Thus, “Einstein writing on the board” represents 1515, while “Einstein playing the guitar” represents 1578. “George Harrison delivering presents” is 7863. “Santa Claus playing the guitar” is 6378 (Hale-Evans, 2006).
Expanding memory systems
Instead of memorizing words of three or more consonants (“Kickapoo”) to represent large numbers, it is possible to expand the two-digit series by another means. Assuming that one has memorized a series of symbols for the numbers from 00 to 99, the set can be expanded by using a “key” like the following:
1 = frozen in ice
2 = covered with oil
3 = in flames
4 = pulsating violently
5 = made of velvet
6 = completely transparent
7 = giving off a fragrance
8 = made of rubber
9 = covered with hair
0 = chrome-plated
This way, to remember the number 871, we take a cat (the symbol for 71), and imagine that it is made of rubber (8). A cat frozen in ice would represent the number 171. A Chevy (68) in flames (3) = 368. A baby (99) covered with hair (9) = 999. To expand further, we need another key:
1 = red
2 = orange
3 = yellow
4 = green
5 = blue
6 = indigo
7 = violet
8 = white
9 = grey
0 = black
These will represent thousands, so a red Chevy in flames = 1368, a cat made of green rubber = 4871, and so on (Expanding memory systems, 1998).
Hebrew, along with Greek and a number of other languages, does not use numerals, but instead uses letters to represent numbers. Thus, any word can also be read as a number. For example, the word Bavel (“Babylon”) has the consonants B-B-L. Since B represents 2 and L represents 300, the word has a numerical value of 304. The word tov (“good”) is written T-W-B (9 + 6 + 2), so its numerical value is 17. Words can quickly be found to represent most numbers, and there are also published lists available. Phrases can also be used in place of single words. The system is extremely versatile since, unlike a decimal system, the letters can be used in any order without altering their numerical value.
Non-Western Mnemonic Systems
Memorization continues to play a very important part in education in most parts of the world, just as it did in the West until historically recent times, when “the memory has been effectively unloaded into books” (Gerhardsson 1998: 123), or into computers. Memorization is especially associated with the educational systems of the world’s major religions (Judaism, Islam, Hinduism, Confucianism). In all of these traditions, students are expected to memorize vast quantities of material verbatim, such as the entire Qur’an, the entire Torah and Mishnah, or the entire corpus of the Confucian classics. In general, students at the elementary levels memorize the material without understanding it; indeed, often without even understanding the language in which the texts are recited. “The material is first committed to memory, and then an attempt at understanding is undertaken” (Gerhardsson 1998: 126).
In light of all that I have been able to find out about the Western mnemotechnical systems, it seems likely that parallel systems should have arisen in each of these non-Western traditions. Material on this is not easy to find, and probably I have only scratched the surface. Nevertheless, “it is only to be expected prima facie that certain mnemonic observations are made in every milieu in which large quantities of oral material are transmitted” (Gerhardsson, 1998: 150). In this section, I will present what I have been able to discover about these non-Western mnemonic techniques, based on interviews and published sources.
Memorization in Judaism
The Hebrew Torah and other scriptures, as well as the Mishnah and the Talmud, are regarded primarily as works of oral literature. When questions arise as to the “reading” of a text, the issue is resolved not by consulting a printed edition but through a group comparison of its oral transmission. A student learning a text for the first time was taught to repeat it several hundred times, until it was “in his purse”; subsequent review (as, for example, a weekly portion of the Torah) involved fewer repetitions (24 times and 40 times are mentioned). The Talmud (Taanim 7b-8a) states, “If you have a pupil for whom the study of the Talmud appears to be heavy as iron, that is because his knowledge of the Mishnah is not fluent” (Gerhardsson, 1998: 105-106).
Initial emphasis was placed on the correct repetition of the entire text, without regard to comprehension. Only after this task was accomplished was attention given to the meaning of the text. “The object of the elementary training was to transmit the whole Bible without any attempt to understand it. Therefore, mnemonics were used, and usually the memorization was based on ‘. . . mechanical associations, arbitrary, ingenious aids [and] endless repetitions. . . According to Morris, ‘. . . the history of education knows no parallel to this collective feat of memory’” (Phillips, 1956).
Like the European monks, rabbinic students used the principles of divisio and compositio (dividing and collecting). This was accomplished through the division of the
Torah into 54 sections called parashot. This made it possible for students to study one parashah each week. Each parashah was in turn divided into seven aliyot, short sections of approximately 10 verses each, appropriate for a single day’s study. The 10 parashot of the book of Numbers (Bamidbar) are as follows:
Bamidbar (1:1-4:20) [“in the wilderness]
Naso (4:21-7:32) [“take”]
Beha’aloscha (8:1-12:16) [“when you set up”]
Shlach (Lekha) (13:1-15:41) [“send (for you)”]
Korach (16:1-18:32) [“Korah”]
Chukas (19:1-22:1) [“decree”]
Balak (22:2-25:9) [“Balak”]
Pinchas (25:10-30:1) [“Phineas”]
Matos (30:2-32:42) [“tribes”]
Masei (33:1-36:13) [“journeys”]
Usually the parashah derives its name from the first distinctive word in the passage. For example, “bamidbar” is the fifth word, but the first distinctive word, in Numbers 1; “beha’aloscha” is the eleventh word, but the first distinctive word, in Numbers 8.
Throughout the Talmud, there appear numerous simanim (“mnemonic signs”, from the Greek semeion). These take the form of memory-words or memory-sentences which help the student to remember longer passages. Oftentimes these simanim are “meaningless words or nonsense verses” (Gerhardsson, 1998: 155). For example, to remember that “the loaves for the wave offering were seven hand-breadths long and four wide and their horns were four finger-breadths. The loaves of shewbread were ten hand-breadths long and five wide and their horns were seven finger-breadths” (M Men. XI.4), the siman is “ZaDaD YaHaZ”, a meaningless phrase which may be read (since Hebrew letters also function as numerals) as “7, 4, 4, 10, 5, 7.” (Gerhardsson, 1998: 155).
Another example is the mnemonic given by R. Yehudah to remember the Ten Plagues of Egypt: De’eTSaQ ‘ADaSH Be’ACHaV. This phrase also is meaningless, or nearly so, but its ten consonants form an acrostic:
D-Ts-Q = dam, tsefardya, qinim (blood, frogs, lice)
‘-D-Sh = ‘arov, dever, shechin (wild animals, pestilence, boils)
B-’-Ch-B = barad, ’arbeh, choshech, makat bechorot (hail, locusts, darkness,
death of the firstborn)
Another Talmudic siman:
It may be learned . . . in respect of MiKDaSH [holiness]. When a
sacrifice is made out of bounds or after time, it is invalidated by intention
[Mahshabeth]. In both cases, the illegitimate intention, even in respect
of a part or portion [Karath] . . . disqualifies it. Both disqualify only if
expressed during the service in connection with the sprinkling of blood
[Dam]. The third [Shelish] day is mentioned in connection with both in
order to provide an analogy between the two cases (Phillips, 1956).
Another kind of simanim found in the Masoretic notes to the Old Testament is used to recall the occurrences of rare Hebrew words. For example, next to the word yashar (“pleasing”) in I Chron. 13:4, there appears an Aramaic gloss, ‘ytyhybt pxrwt’ lqhl’ (“the pot was given to the assembly”). The purpose of this is to indicate the three
verses in the Old Testament where the form yashar is found: Jer. 27:5, Jer. 18:4, and I Chron. 13:4. The three words of the gloss are Aramaic translations of distinctive words which occur in each of these three verses (Marcus, 1999). Using this siman, it is possible for one who has already memorized the Old Testament to quickly compare occurrences of a rare word.
Various mnemonic devices were used at a more elementary level. For example, children learning the alphabet “were taught to use the shapes of the Hebrew letters as mnemonic aids” (Phillips, 1956). Thus, the third and fourth letters of the alphabet, gimmel and daleth, are described as follows in the Talmud (Shabbat 104c):
Gimmel Daleth [means] “show kindness to the poor” (gemol dallia).
Why is the foot of the Gimmel stretched toward the Daleth? Because
it is fitting for the benevolent to run after the poor. And why is the top
of the Daleth stretched out toward the Gimmel? Because he [the poor]
must make himself available to him. And why is the face of the Daleth
turned away from the Gimmel? Because he must give him help in secret,
lest he be ashamed of him.
In similar fashion, the first two letters, aleph and beth, were remembered as “learn wisdom” (aleph binah). Waw, heth, teth, yod, kaph, lamed (the seventh through eleventh letters) were remembered as follows: “If thou doest thus, the Holy One, blessed be He will sustain [zan] thee, be gracious [hen] unto thee, show goodness [meTib] to thee, give thee a heritage [yerushah], and bind a crown [kether] on thee in the world to come [‘oLam habah].” Likewise, qoph stands for “holy” [qadosh], and resh for “wicked” [rasha]. Shin stands for “falsehood” [sheker], and tau for “truth” [emeTh] (Shabbat 104c).
Memorization in Islam
The memorization and oral recitation of the Qur’an is required of all devout Muslims. The process begins in early childhood. This was described for me by an acquaintance of mine in graduate school, Mustafiz Rahman, back in 1984. Mr. Rahman was from Bangladesh, so for him Arabic was a completely alien language. Nevertheless, he and his classmates were required to recite the Qur’an in Arabic, the emphasis being on correct pronunciation without regard to meaning or understanding. His father also hired an old man to come to the house and tutor him in Qur’an recitation. From time to time his father would listen to him recite, and he would be beaten if his pronunciation contained any inaccuracies. His father’s fear was that he would not grow up to be a “good Muslim” if he did not memorize the Qur’an accurately. This seems not to have worked, however, since at the time I knew him, Mr. Rahman described himself as having no religion.
The memorization of texts is ideally undertaken as a group. The leader of the group recites the verses or phrases one by one, and the group repeats after him. I have not been able to find a published source which describes the details of doing this, but I did find numerous websites (in English) which are devoted to Qur’an recitation. “Virtual” Qur’an recitation groups can be formed on-line, and the sura under study can be downloaded in MP3 format and listened to repeatedly. Participants describing their experience of committing the Qur’an to memory frequently make reference to repeating the passage several hundred times in a week.
Undoubtedly many mnemonic devices and tricks have been devised in the context of Qur’anic memorization, but so far I have not been able to find much specific information. I did find one very interesting scheme for memorizing the Arabic alphabet called “Abjad’s Rainbow Pyramid” [appendix H]. The 28 letters are arranged in a pyramid, with the letter ha (“the queen of the letters,” ”the only letter with two ‘hands’” at the apex. Next come ta and za (“the two ladies in waiting”), then kaf, mim, and ya (“the three princesses”), then ba, ta, tha, and fa (“the four letters of the north”) and so on, with seven letters at the base of the pyramid. Each of the seven levels is color-coded, ha being red, and the descending rows being orange, yellow, green, blue, indigo, and violet.
An educational product is marketed in association with this scheme, consisting of a set of plastic letters in the appropriate colors. Since the Arabic letters have various forms depending on their position in a word, these plastic letters have joints so that their “hands” and “tails” can be retracted or extended as necessary—a wonderful tool for kinesthetic learning! (Abjad Ltd., 2003).
Memorization in Hinduism
Like Judaism and Islam, Hinduism has always placed a high value on large-scale memorization of texts, often using sophisticated mnemonic techniques. The composition and transmission of the Vedic texts, some of which may date as far back as 2000 B.C., as well as the later epics, was entirely oral. Although these works were not recorded in writing until much later (around 500 A.D.), there is reason to believe that their transmission remained faithful to the originals in every detail. This is because of the “unique and ingenious techniques employed by the Brahmin priests in preserving the texts intact over three and half millennia” (A tribute to Hinduism, n. d.).
This has been accomplished through the tradition of reciting the texts in various elaborate ways which ensure that nothing is altered or lost. “The chief purpose of such methods . . . is to ensure that not even a syllable of a mantra is altered to the slightest extent. The words are braided together, so to speak, and recited back and forth . . . The words tally in all these methods of chanting and there is the assurance that the original form will not be altered” (Bhattathiry, 2004).
The first way of reciting a text, called samhitapatha, is simply to recite the lines in their usual order, connecting words across word-boundaries according to the rules of Sanskrit sandhi (phonological processes).
The second way, called padapatha, involves reciting each word individually in its pausal form, breaking the sandhi. Compound words are also broken into their component parts, inserting the word iti (“thus”) between them. Written recensions of the Vedic texts survive written in both samhitapatha and padapatha form.
Vakyapatha is intermediate between samhitapatha and padapatha. It involves some limited use of sandhi. These three methods (samhitapatha, padapatha, and vakyapatha) are called prakrtipatha (natural way of chanting) since the words are recited only once and in their natural order. (Bhattathiry, 2004). The other methods are belong to the vikrtipatha (artificial way of chanting) category.
Another way of reciting texts is called kramapatha (or krama parayanam). This involves reciting the text as a “chain,” the first word with the second word, then the second word with the third (1,2; 2,3; 3,4; 4,5; 5,6; 6,7 and so on).
Another way, called jatapatha (jataparayanam), is similar to kramapatha, but involves reversing each set of two words before continuing to the next. Thus, one recites the first word with the second word, then the second word with the first,; the second with the third, then the third with the second (1,2,2,1; 2,3,3,2; 3,4,4,3 and so on) (Sri Jagadguru trust, n.d.).
Still another way to recite the text is called sikhapatha. Here, the pattern consists of three words instead of two (1,2,3,3,2,1; 2,3,4,4,3,2; 3,4,5,5,4,3 and so on) (Bhattathiry, 2004).
The recitation method known as ghanapatha is exceedingly complex. “There are four types of this method. Here also the words of a mantra are chanted back and forth and there is a system of permutation and combination in the chanting. To explain all of it would be like conducting a class of arithmetic” (Bhattathiry, 2004). In one type of ghanapatha, the word order is 1221123321123, 2332234432234, etc. “Here, the swara will modify according to the rules of swara, depending on how the phrase is split. There are probably only around 200 "ghanapathi's", who can recite the ghanapatha of their whole samhita portion in the whole of India” (Saxena, 1998).
There are several other methods as well, including varnakrama, malapatha, rekhapatha, dhvajapatha, dandapatha, and rathapatha.
Concerning these various methods of recitation, it is said, “Padapatha is twice as beneficial as samhitapatha; kramapatha is four times more beneficial; the method called varnakrama is a hundred times more beneficial; while jatapatha is a thousand times more beneficial” (Saraswathi, n. d.)
Memorization in China
The verbatim memorization of the Confucian classics was the cornerstone of Chinese education, and was the basis of the government examinations which qualified scholars for bureaucratic positions. Many Chinese scholars were famous for their feats of memory, including Ni Heng, “who remembered all the stone tomb inscriptions after he returned from a long journey” and Lu Jiangdao, “who after one reading could recite books both forward and backward” (Spence, 1984: 156).
Presumably some sophisticated memorization techniques were developed over the many centuries that the examination system was in place, but so far I have not been able to find much information about them. J. D. Spence (1984) makes reference to “diligent study along traditional Chinese lines of repetition and recitation, aided perhaps by the mnemonic poems and rhyming jingles that were part of current [i. e. 16th century] Chinese memory practice” (p. 4).
Matteo Ricci (1552-1610), one of the earliest Jesuit missionaries to China, astonished the Chinese by his ability to master their language. He accomplished this by means of a system of loci, which worked especially well for the Chinese language since it lacks inflectional forms: “Unlike Greek sentences, which had to be remembered in all their detailed complexity, a Chinese sentence could be presented in sharp detail as a series of images” (Spence, 1984: 137). These techniques enabled Ricci, after living in China for many years, to rapidly memorize lists of four or five hundred Chinese characters (Spence, 1984). In a letter to an acquaintance, Ricci described his success:
One day, when I was invited to a party by some holders of the
first-level literary degree, something happened that gave me quite
a reputation among them and among all the other literati in the city.
The thing was that I had constructed a Memory Place System for
many of the Chinese ideographs, . . . I told them that they should write
down a large number of Chinese letters in any manner they chose on a
sheet of paper, without there being any order among them, because
after reading them only once, I would be able to say them all by heart
in the same way and order in which they had been written. They did so,
writing many letters without any order, all of which I, after reading them
once, was able to repeat by memory in the manner in which they were
written: such that they were all astonished, it seeming to them a great
matter. And I, in order to increase their wonder, began to recite them all
by memory backward in the same manner, beginning with the very last
until reaching the first. By which they all became utterly astounded and
as if beside themselves. And at once they began to beg me to consent to
teach them this divine rule by which such a memory was made. . . .For
in truth this Memory Place System seems as if it had been invented for
Chinese letters, for which it has particular effectiveness and use, in that
each letter is a figure that means a thing (Spence, 1984: 138-139).
Ricci eventually published a treatise in Chinese on ars memorativa, entitled Jifa (“Treatise on Mnemonic Arts”), which is one of the better expositions of the Art of Memory as it was practiced in the Renaissance. However, while “all [the Chinese] admired the subtlety of the system, not all of them were willing to take the trouble to learn how to use it” (Spence, 1984: 4). One of Ricci’s students complained that mastering the system was harder than simply learning through rote repetition: “Though the precepts are the true rules of memory, one has to have a remarkably fine memory to make any use of them” (Spence, 1984: 4).
My wife, Gloria, is from Taiwan, and in the course of a discussion of the current paper, I learned from her that the Chinese have a simple and effective way of remembering numbers by converting them into phrases which have the same sound, but different meaning. For example, to remember the number 79 [ch’ih1 chiu3], one thinks of the phrase “drink wine” [ch’ih1 chiu3], which has the same pronunciation but is written with different characters. In cases where this cannot be done, is sometimes possible to fashion an approximately similar phrase which alters some of the phonemes but retains the same sequence of tones. This is analogous to rhyming in English, but is somewhat difficult for our ears to recognize.
Recently, I saw a very interesting example of a “flat representation” in an exhibit at the Crystal Cathedral on “The Bible in China.” A large carving, made from a single piece of wood, depicts 75 stories from the life of Christ in six horizontal rows. The sequence begins with the birth of Christ (lower left), and ends with His crucifixion, resurrection, and ascension (top right).
Japan: the goroawase system
The Japanese have developed an ingenious system called goroawase for remembering numbers, more flexible than the “major system” described above, and much easier to use because the numbers are not only encoded as words, but the words themselves can be arranged to form phrases which are reminders of what the encoded number represents. This bears some resemblance to Grey’s mnemonic hexameters.
The goroawase system is as follows:
0 = rei, re, o
1 = ichi, i, hitotsu, hito, hi, wan
2 = ni, futatsu, fu, futa, tsuu
3 = san, sa, mitsu, mi
4 = yon, yo, shi, yotsu, foa
5 = go, itsutsu, itsu
6 = roku, ro, mutsu, mu
7 = shichi, nana, nanatsu, na
8 = hachi, ha, yatsu, ya
9 = kyu, ku, kokonotsu, ko
The numerous alternate forms arise from archaic stages in the development of the language, as well as borrowings from Chinese. This provides great flexibility. Ichi (“one”) can be used to form more than a hundred other words (Takahashi, n. d.). For example, if one wishes to remember that America was discovered in 1492, one could use the phrase Iyo! Kuni ga mieta! (“Wow! I found a country!”). Only the first part of the phrase (iyokuni) is needed to encode “1492”; the rest of the sentence is added to complete the associated meaning (Mnemonic goroawase system, n.d.).
Goroawase is familiar to everyone in Japan, and is used in education. One of my students, Hosana Anjiki (personal communication, April 11, 2006), reports as follows:
The first time I learned about GOROAWASE was in the history class.
When I was in the elementary school, we needed to memorize a lot of dates.
And teacher taught us that by using GOROAWASE we could memorize
them easily. For example, 1192 ( IIKUNI TSUKUROU KAMAKURA BAKUFU)
means "lets make a good country." This is the year that YORITOMO
MINAMOTO made Japan's feudal government in EDO. So, we memorized all of
the dates with GOROAWASE. And this was actually very helpful. And there are
many books that taught us many GOROAWASE of dates in history. So, almost
all students get that kind of books and learned GOROAWASE.
Also, we use GOROAWASE to memorize phone numbers. In the
TV commercial there are a lot of phone numbers using GOROAWASE
and making people memorize and call. For example, in the commercial
about hair restoration, at the end of the commercial they sing a song,
"call 0120-KUROGURO FUSAFUSA (0120 is Japanese toll free #,
and 9696-2323, meaning angry and luxuriant.)
So, I think everyone in Japan know how to do this. You know we can
create GOROAWASE by ourselves. I always do GOROAWASE to
remember the number, it is easier for me. My birthday is April, 3rd so,
I usually told people that my birthday is "SHIMI NO HI" This means
One Japanese website (http://www.asahi-net.or.jp/~iu8y-tti/goro01.html) lists goroawase for several thousand numbers. In cases where it is difficult or impossible to represent a number precisely with an appropriate phrase, it is permissible to approximate it. Here are some goroawase from the Yokohama District Yellow Pages:
647418 = mushi-nashi-ii-ha (“no decayed teeth, good teeth”) [dentist]
0120449852 = omoi-ni-wa-shikkari-yoku-hakobu (“heavy articles carefully safely carried”) [moving company]
307645 = mina-mujiko (“everyone with no accident”) [driving school]
375476 = mina-koshi-yoku-naru (“everyone gets better back”) [chiropractor]
812074 = hai-tsumari-nashi (“no more clogging”) [plumber] (Takahashi, n. d.)
Memorization in Korea
Korean students do a great deal of rote memorization. This is often accomplished by writing out the same material, such as English sentences, over and over again until it fills up several pages. These are known as “black papers” because they are covered with ink. Often, Korean students show their parents how hard they have been studying by displaying how many pages of “black paper” they have created in the course of an evening.
In order to learn English vocabulary, Korean students often devise Korean sentences which associate the English word with its meaning in Korean. For example, to remember the meaning of “church”, one student told me he thinks of Churchill, and how he won World War Two with God’s help. Another student remembered “church” by somehow associating it with the Korean phrase cha-cha-da (“knock him out” [as in boxing]). Students share these sentences with each other, and especially clever ones are extensively borrowed, since they’re quite hard to devise. One student told me she memorizes 100 new English words each day (this strategy seems not to be the best use of her time, however, since she’s failing most of her classes!).
Koreans also make some limited use of a system like the Japanese goroawase. For example, many realtors use the number 4989, which sounds like sagu-palgu (“buy and sell”). Churches often use 9191, which sounds like guwun-guwun (“salvation”). Moving companies use 2424, which sounds like a phrase meaning “move-move”).
Another Korean student told me about a well-known seminary, Gwang-naru Jang-shin-dae, which publishes a famous picture book of mnemonics for memorizing the contents of every chapter in the Bible. These take the form of “flat representations,” all the pictures for each book being combined into a single composition.
Criticisms of Artificial Memory
At least one study found that persons using the method of loci as a mnemonic device performed no better than a control group at the task of memorizing 25 “high imagery words” (Carter, n. d.). On the other hand, L. A. Post (1932) found it to be highly effective as a tool for memorizing lines of poetry in order. It seems to me that the Carter study was flawed in that the material for memorization consisted of “high imagery words.” Probably most people would be able to perform this task successfully with or without a mnemonic strategy. A task involving “low imagery” data (such as abstract nouns or numbers) would have been a better test of the system.
D. A. and E. C. Laird (1960) are derisive of traditional mnemonic systems: “On no other topic of psychology have there been as many useful and well-confirmed discoveries which make the old “systems” seem like one-horse shays in a jet age” (p. 7). However, their book, entitled Techniques for Efficient Remembering, firmly rooted in the behaviorism of the 1950s, in fact presents no techniques at all. Examples of the “discoveries” this book presents: Writing things down, breaking down long numbers into groups, use grouping and rhythm, visualize, “memorize by meanings rather than by sounds,” “try to remember the whole thing, not a bit at a time,” “associate it with things you already remember”. Set goals. Get enough sleep. Repeat what you want to remember. Preview what you need to learn.
For Matteo Ricci, at least, mnemonics worked astonishingly well. Although the material is sometimes difficult to locate, there is a long tradition and a vast literature on the subject of mnemonics. Although some of the techniques seem difficult, cumbersome, and absurd, many of them are truly ingenious. These methods have been developed over a long period of time by extremely clever people living in many different cultures. Many of them have been used and refined over many centuries. Probably everyone could benefit from some acquaintance with this subject; there is surely some method which will appeal to each learner and to each learning style. There is also much room for creativity and personal preference. Stefan Rieger (2000) describes mnemonics as an arsenal of “pedagogical weapons against forgetting” (pädagogische Waffe gegen das Vergessen) (p. 392). Browning (1983) gives some excellent advice: “As you become familiar with mnemonic systems you will see you can make sense out of almost every piece of information you want to remember. You simply select the correct memory tool to fit each case” (p. 4).
Above all, it must be understood that mnemonics are a technology; the German word for “mnemonic systems” is Seelenmaschinen (“soul-machines”). This phrase describes them well—they enable us to accomplish tasks that we could not accomplish without their assistance.
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Appendix (photocopies attached)
A. II Kings (17th century engraving) (Rieger, 2000: 392).
B. Johannes Buno: 17. Jahrhundert (Rieger, 2000: 647).
C. The second image of Luke, from A method for recollecting the Gospels (ca. 1470) (Carruthers & Ziolkowski, 2002: 283).
D. Viridarium Aristotelis ethicum (Rieger, 2000: 499).
E. Filippo Gesualdo: Il corpo umano come sistema di luoghi (Plutosofia, 1592)
(Eco, 1992: 41).
F. Mnemonic images for the ten commandments (Best, 1980: 67-68).
G. Mnemonic images for the book of Acts (Best, 1980: 72-73).
H. Abjad’s rainbow pyramid. Abjad Ltd. (2003).