Alice's Adventures in Wonderland Decoded

by David Day

  The man behind the White Rabbit: Dr. Henry W. Acland.

  Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her and to wonder what was going to happen next. First, she tried to look down and make out what she was coming to, but it was too dark to see anything; then she looked at the sides of the well, and noticed that they were filled with cupboards and book-shelves; here and there she saw maps and pictures hung upon pegs. She took down a jar from one of the shelves as she passed; it was labeled “ORANGE MARMALADE,” but to her great disappointment it was empty: she did not like to drop the jar for fear of killing somebody, so managed to put it into one of the cupboards as she fell past it.

  “Well!” thought Alice to herself, “after such a fall as this, I shall think nothing of tumbling down stairs! How brave they’ll all think me at home! Why, I wouldn’t say anything about it, even if I fell off the top of the house!” (Which was very likely true.)

  “There are some wonderful points in it,” said Carroll: Scene from A Midsummer Night’s Dream. Titania and Bottom, by Edwin Henry Landseer, circa 1850.

  THE ROSICRUCIAN RABBIT Alice’s descent down a rabbit-hole into Wonderland has an historic precedent in the publication of Cabala, Mirror of Art and Nature: in Alchemy. Published in 1615 by Steffan Michelspacher, it was dedicated “to the Brotherhood of the Rosy Cross; than which in this matter let no fuller statement be desired.”

  The Rosicrucian Brotherhood was a secret society whose stated mission was to advance and inspire the arts and sciences through the study of symbolic and spiritual alchemy. Initiates were instructed to undergo certain rites of passage that resulted in the attainment of ancient esoteric knowledge. Rosicrucianism arose in Bohemia in the early seventeenth century, and rapidly spread throughout Europe. In Britain, it was particularly influential in Oxford.

  In the Cabala we discover for the first time in literature and art the pursuit of a rabbit down a rabbit-hole as a major theme in a quest. One of this book’s elaborate engravings reveals that 250 years before Alice ducked down a rabbit-hole, Rosicrucian initiates were being instructed to pursue a fleeing rabbit into a similar mysterious underground world—a theme repeated in later Rosicrucian documents.

  Throughout the Cabala we find the acronym “V.I.T.R.I.O.L.” This stands for the Latin “Visita interiora terrae rectificandoque invenies occultum lapidem verum medicinalem,” an instruction to the Rosicrucian initiate to “visit the interior of the earth and by rectifying discover the true medicinal stone”—the philosopher’s stone. And through text and storyboard illustration, the initiate is encouraged—like Alice—to “visit the interior of the earth” and to “ferret out” the rabbit. In this context it is significant that the White Rabbit of Wonderland is fearfully certain that he will be hunted down: “as sure as ferrets are ferrets!”

  The Rosicrucian notion of a secret repository for universal knowledge was an inspiration not only for the Freemasons Brotherhood and the Royal Society of London for Improving Natural Knowledge but also for Oxford’s Ashmolean Institute and Museum, opened in 1683. Carroll was an active member of the institute, and the Ashmolean possessed one of the world’s great Rosicrucian alchemical libraries. Among the many hermetic books, the Cabala was one that would have been of supreme interest to the young Christ Church sub-librarian Charles Dodgson.

  As the hermetic scholar Joscelyn Godwin has observed, there probably was no such thing as “a card-carrying member of the Brotherhood,” but there were a multitude over the next three centuries “who shared the ideals set forth in its manifestos.” Charles Dodgson—and his alter-ego Lewis Carroll—were certainly numbered among this company.

  Other symbolic images in the Cabala reappear in Wonderland. In the foreground of the engraving, we see an alchemist’s initiate, blindfolded to symbolize a trance, or dream state. The figure to his left is the initiate’s double, which is his dream-self. Like Alice’s dream-self pursuing the White Rabbit, the initiate’s dream-self double pursues a mercurial rabbit down a hole that leads into a vast and mysterious underground world beneath a mountain.

  As in Alice in Wonderland, the Rosicrucian initiate discovers a secret underground great hall for the testing of initiates. The step-pyramid that forms the foundation of the underground hall is labelled with the seven steps of the alchemical process. However, these are in the wrong sequence.

  It is up to the initiate by trial and error to “rectify” and eventually understand the alchemical process, then to put them in the proper order. Similarly, in Wonderland’s underground hall, Alice must learn the proper order of actions so that she may use her golden key and enter the garden.

  The Cabala alchemist’s hall is under a mountain, surmounted by seven gods/planets/metals, and is reminiscent of another of the Rosicrucian legends: the quest to discover the subterranean tomb of Christian Rosencrantz (“Christian Rose-Cross”). This seven-sided tomb was placed in an underground chamber that, like Wonderland’s hall, was fitted with many doors and contained many symbolic objects: magic looking glasses, telescopes, sacred books and keys.

  If we look carefully at the Cabala engraving, we can see on the pinnacle of the Mountain of Alchemy the true goal of the initiate: a miniature rose garden with a hedge around the fountain of Mercury. This garden of the Rosy Cross is the same garden of “bright flowers and those cool fountains” that is Alice’s goal in Wonderland: the rose garden of the King and Queen of Hearts.

  From the Cabala: Mountain of Alchemy, topped by a rose garden.

  FIBONACCI’S RABBIT-HOLE At the beginning of Wonderland, we are told that Alice is “considering in her own mind … whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies, when suddenly a White Rabbit with pink eyes ran close by her … and fortunately [she] was just in time to see it pop down a large rabbit-hole.”

  Note how Carroll has Alice “in her own mind” gathering “a daisy-chain.” As any naturalist or mathematician will tell you, daisies are unique among common flowers in having 13, 21 or 34 petals—that is, three Fibonacci numbers in sequence.

  In Fibonacci’s Liber Abaci, or “Book of the Abacus” (published in 1202), we learn that the discovery of this sequence arose from a mathematical competition in which this problem was set: “Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are one month old, how many pairs of rabbits will there be after a year?”

  Fibonacci’s rabbit puzzle.

  The result is a sequence of numbers, each of which is the sum of the previous two numbers, starting with 0 and 1. Thus, we have an infinite series that continues with:

  1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

  This pattern takes on significance if we write the numbers as decimal fractions:

  1/1 = 1.000, 2/1 = 2.000, 3/2 = 1.500, 5/3 = 1.666…, 8/5 = 1.600, 13/8 = 1.625…, 21/13 = 1.615…, 34/21 = 1.619…, 55/34 = 1.617…, 89/55 = 1.618… and so on.

  Now, with the ratio 89/55 = 1.618 we come to one of the most important and fascinating dimensions of the Fibonacci numbers. The further down we travel with this sequence, the closer two consecutive Fibonacci numbers divided by each other will approach what was known in antiquity as the golden ratio: approximately 1:1.618 (or, slightly more fully, 1:1.6180339887… onward to infinity).

  Since the time of the ancient Greeks, this ratio was believed to be the most aesthetically perfect proportion for the human body, and it has been used in the creation of art, architecture and music. In geometry it was manifest in the golden section, golden rectangle, golden triangle and star pentagram. Fibonacci numbers combined with the golden spiral dictate the shape and growth of patterns in pine cones, pineapples, sunflowers, seashells, trees and honeycombs. Known by the symbol for the Greek letter Φ (phi), it has been called “Nature’s number.”

  All these aspects of mathematics related to golden ratios, sections, series and so on were diligently taug
ht to mathematics students throughout the nineteenth century and were seen as the aesthetical and logical foundation to all the arts and sciences. However, it was only during Lewis Carroll’s Victorian childhood that the anecdotal aspect of Fibonacci’s discovery through the breeding of rabbits became a well-known (and historically accurate) account that was taught to students of mathematics.

  It is said that mathematics makes the invisible visible. So, let us look at Carroll’s rabbit-hole through a mathematician’s eyes. Let us examine a comparable infinite sequence in that popular classic text Excursions in Number Theory (1966) by C.S. Ogilvy and J.T. Anderson. There, the authors chose to create a graph or lattice using irrational √2 ratios as alternating consecutive fractions:

  1/1 = 1.000, 3/2 = 1.500, 7/5 = 1.400, 17/12 = 1.416…, 41/29 = 1.413…, 99/70 = 1.414…

  This creates the walls of a corridor that visually demonstrate how this convergent sequence progresses infinitely toward the exact value of the √2:

  1:1.41421568… and onward to infinity.

  If we can imagine peering down that corridor, Ogilvy and Anderson explain, “then if you were to look in that direction from the origin you would, theoretically, have a clear view … all the way to infinity.”

  If we create a similar graph or lattice using Fibonacci ratios as alternating consecutive fractions in an infinite convergent sequence, we end up with a graph that replicates Carroll’s description of Alice’s descent to Wonderland through this gap in time and space: an infinite sequence of convergents oscillate to form the walls of this rabbit-hole. “Would the fall never come to an end?” The answer is both no and yes.

  We too have constructed a tunnel with a clear view all the way to infinity. So we could answer that Alice’s fall is infinite and will never end; or we may answer that it will end in what is known as an “ideal point” at infinity—which in this case is the infinite golden number, or the golden ratio known as Φ. And as this is, after all, a fairy tale, we must conclude that this “ideal point” is Wonderland: a land existing in that infinite dimension that is the human imagination—where Alice discovers the golden key: Φ.

  Martin Gardner, in his Annotated Alice, compares Alice’s long fall to “the famous ‘thought experiment’ in which Einstein used an imaginary falling elevator to explain certain aspects of relativity theory.” Certainly, Alice’s descent down the rabbit-hole does appear to be some sort of surreal “thought experiment” wherein Carroll’s “dream child” is conscripted into a mathematician’s demonstration.

  In this context, and given Carroll’s love of anagrams, one might wonder why—as Alice falls through this pre-Einstein wormhole in space and time—he has his heroine clutch at an empty jar labelled “ORANGE MARMALADE.” However, if one accepts the proposition (made in the introduction) that Wonderland was constructed by Carroll as an analog of the world and all its secrets, then one might reply that perhaps it is not entirely coincidental that unscrambled, the label reads: “AM ANALOG DREAMER.”

  Then, too, there is the White Rabbit’s belief that he is always a little late. This may be a joke about Oxford’s insistence on keeping “Oxford Time” as opposed to Greenwich Mean Time. The Tom Tower clock at Christ Church was set according to Oxford’s longitudinal position, which is technically five minutes later than Greenwich Time. This made little difference until 1844, when the first railway was put through to Oxford, and suddenly Oxford time came into conflict with the accepted national standard time. Consequently, if Dr. Acland was setting his watch by Oxford time, he might find himself constantly late for his appointments with the Queen in London.

  Besides having real-life above-ground counterparts for each of its fairy-tale characters, Wonderland also has real-life above-ground counterparts for each of its locations. As we have seen, the fairy tale begins in a real-life location: on the banks of the Isis. However, what can Alice expect to discover in the underground world at the bottom of the rabbit-hole?

  Down, down, down. Would the fall never come to an end? “I wonder how many miles I’ve fallen by this time?” she said aloud. “I must be getting somewhere near the centre of the earth. Let me see: that would be four thousand miles down, I think—” (for, you see, Alice had learnt several things of this sort in her lessons in the schoolroom, and though this was not a very good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over) “—yes, that’s about the right distance—but then I wonder what Latitude or Longitude I’ve got to?” (Alice had no idea what Latitude was, or Longitude either, but thought they were nice grand words to say.)

  Presently she began again. “I wonder if I shall fall right through the earth! How funny it’ll seem to come out among the people that walk with their heads downward! The Antipathies, I think—” (she was rather glad there was no one listening, this time, as it didn’t sound at all the right word) “—but I shall have to ask them what the name of the country is, you know. Please, Ma’am, is this New Zealand or Australia?” (and she tried to curtsey as she spoke—fancy curtseying as you’re falling through the air! Do you think you could manage it?) “And what an ignorant little girl she’ll think me for asking! No, it’ll never do to ask: perhaps I shall see it written up somewhere.”

  After her long fall, we are told that Alice lands with a “thump! thump!” but is otherwise unhurt. Immediately she leaps up and chases the White Rabbit down a passage and around a corner into a great hall lit by a row of lamps hanging from the roof. Upon entering Wonderland’s hall in pursuit of the White Rabbit, Alice finds she is alone, and although there are many doors around the hall, they are all locked.

  On a second inspection, Alice discovers a glass table on which she finds a tiny golden key that unlocks a little curtained door leading into “the loveliest garden you ever saw.” But the door is too small for Alice to even get her head through. How will she get to the garden? Why does she wish to gain entry to the garden? And what is this great hall?

  The Great Hall of Christ Church is the above-ground model for the great hall of Wonderland. Christ Church boasted one of the largest and grandest ancient halls in Britain. Built by Cardinal Wolsey in 1524, for nearly five centuries it has been the dining hall for students and faculty. Its walls are lined with portraits of its deans and famous graduates. It has been the scene of many grand dinners with notable heads of state and royalty. It has also been used as a location in numerous films, including as the Great Hall of Hogwarts in the Harry Potter series.

  Down, down, down. There was nothing else to do, so Alice soon began talking again. “Dinah’ll miss me very much to-night, I should think!” (Dinah was the cat.) “I hope they’ll remember her saucer of milk at tea-time. Dinah, my dear! I wish you were down here with me! There are no mice in the air, I’m afraid, but you might catch a bat, and that’s very like a mouse, you know. But do cats eat bats, I wonder?” And here Alice began to get rather sleepy, and went on saying to herself, in a dreamy sort of way, “Do cats eat bats? Do cats eat bats?” and sometimes, “Do bats eat cats?” for, you see, as she couldn’t answer either question, it didn’t much matter which way she put it. She felt that she was dozing off, and had just begun to dream that she was walking hand in hand with Dinah, and saying to her very earnestly, “Now, Dinah, tell me the truth: did you ever eat a bat?” when suddenly, thump! thump! down she came upon a heap of sticks and dry leaves, and the fall was over.

  The Great Hall (where portraits of Dodgson and Dean Liddell now hang).

  BEHIND THE CURTAIN As a classicist and a mathematician, Carroll has created an initiation hall in Wonderland comparable to that of the most ancient cult of mathematicians, the Pythagoreans. This explains the symbolic meaning of the hall’s curtained door. Pythagoreans had two categories of followers: the exoterikoi (exoteric) and the esoterikoi (esoteric); that is, “before the curtain” and “behind the curtain.” The exoterikoi were known as the akousmatikoi (listeners), and they were permitted to hear the master’s lectures only in the oute
r sanctum of the temple. The fully initiated esoterikoi were known as the mathematikoi (learners), and they were allowed to pass through the curtained door into the inner sanctum where the mysteries were fully revealed.

  Alice very much wishes to pass through the curtained door as one of the initiated mathematikoi, but first she is put through a series of tests. To gain entry, she must consider “in her own mind” whether it “would be worth the trouble” of putting together a chain of reasoning: Alice’s metaphoric “daisy-chain.” The neophyte begins with this riddle of the golden key and the curtained door: it is a riddle about ratios and proportions and the proper sequential order.

  Throughout the Wonderland adventures, Alice and the narrator use the phrase “at any rate.” In the Wonderland hall, we are told, the golden key “at any rate” will open only the tiny door, and that the passage behind door is the size of a “rat-hole” (a typical Carrollian riddle: rat-o = ratio), which explains why the golden key—as the golden ratio [1/Φ = 1 + Φ = Φ]—fits the lock of the curtained door.

  Although Alice can open the curtained door with the golden key, the door and the passage beyond are so small that “she could not even get her head through the doorway.” Disappointed, Alice makes a rather peculiar wish and observation: “Oh, how I wish I could shut up like a telescope! I think I could, if I only knew how to begin.” She returns to the glass table, where she hopes to find “at any rate a book of rules for shutting people up like telescopes.”

  One explanation for this wording is that Alice is, in fact, looking for a book of logarithms: a book of mathematical tables that are used for calculating exponential rates of expansion or contraction—a process that might theoretically be used for “shutting people up like telescopes.”