The Monas Hieroglyphica, Feynman diagrams, and the Voynich manuscript

by Charlie Huenemann

One of the strangest books to come out of Europe in the sixteenth century – and that is saying a lot – is John Dee’s Monas Hieroglyphica (1564). Dee was an English mathematician, court astrologer, diplomat, and spy. He was also a wizard, or at least an aspirant to wizardry. Like many European intellectuals of the 16th century, Dee devoted himself to what we identify today as esoteric studies, which means an interdisciplinary effort to discern a primordial truth through the study of ancient texts, alchemy, astrology, philosophy, theology, and magical practices. Ancient texts such as the Corpus Hermeticum and the Emerald Tablet promised a brand of wisdom that had made the ancient ages more powerful and knowledgeable than any age since, and their introduction into western Europe during the Renaissance gave scholars a hope of recovering ancient wisdom and restoring human nature to the perfection it had once enjoyed in the Garden of Eden, before – well, that part of the story you probably know already.

Dee wrote the Monas Hieroglyphica in just twelve days, under divine inspiration. The central idea is that the creation of symbols is at the same time a revelation of the primal forces of creation. Begin with a point. Extend the point so as to form a line. Fix one end and rotate the other to create a circle. You have just, in a sense, duplicated the creation of the Sun. Follow Dee’s instructions further – well, try to, for it soon gets pretty confusing – and before long you will have created a very potent symbol. 

(Credit: Wellcome Library, London)

This glyph represents (from top to bottom) the Moon, the Sun, and then something that somehow represents the four elements (earth, air, fire, and water), but also a threefold union of Body, Soul and Spirit. The wavy thing at the bottom is the fire of Mercury (and that’s how alchemy comes in). But the construction of the glyph is not only a recounting of creation, but also a display that establishes metaphysical connections among the elements of creation and the divine purposes of human existence. And there is magic in making the drawing: as you retrace the lines, you are engaging in an act of creation that mirrors the creative processes that make the mystery of creation what it is. It is a holy act, a unification of form and content that should be enough to send any aspirant into heady flights of wonder.

In Dee’s words, explaining the cross in the middle of the glyph, “The Quaternary is produced by the four straight lines enclosing four right angles. Either of these elements, the lines or the right angles, repeated twice, therefore, afford us in the most secret manner the Octad, which I do not believe was known to our predecessors, the Magi, and which you should study with great attention. The threefold magic of the first Fathers and the wise men consisted in Body, Soul and Spirit. Therefore, we have here the first manifested Septenary, that is to say, two straight lines with a common point which make three, and the four lines which converge to form the central point in separating the first two.” It may sound like gibberish to us, but that is only because we are not trained in the arcane arts.

(from Oliver Byrne’s 1847 edition of Euclid’s Elements)

It is not difficult to see the connection between the magic in Dee’s glyph and the magic of Euclidean geometry. For, once again, as we start from a point and create lines and circles and everything else that can be constructed by compass and straightedge, we are recreating what the space of the world can allow. The geometrical objects we construct on paper are essentially the same as the objects in the world we try to understand through geometry. This was especially important for Dee as a mathematician and a teacher of navigation techniques: each navigator presumes that geometrical calculations on paper will duplicate nature’s own calculations, and help the ship to arrive safely at its destination. Anyone untutored in geometry – and maybe those of us tutored in it as well – will regard the connection between lines and arcs on paper and facts about what must be where on the surface of the planet as something nearly magical. Nature knows math, and as we know math, we know nature. Put more ecstatically: God is a geometer, and to the extent we do our math correctly, our thoughts become divine.

Indeed, this (or something like it) is what motivated Kepler and Galileo as they employed mathematics in interpreting the book of nature. And it is a strategy that has been followed by natural scientists ever since. To get to the heart of phenomena, you try to quantify it and cook up the equations that nature seems to be following. Only then have you begun to gain a scientific understanding. Dee was following a similar strategy, though his heavens and earth were stuffed with a lot more than scientists dream of today.

(Two electrons, one photon, Feynman-style)

Nevertheless, Dee’s glyphs have a modern echo in Feynman diagrams. Richard Feynman (1918-1988) was a physicist famous for quantum electrodynamics and his skills as a raconteur. He also developed a method for doing quantum physics through diagrams. In a Feynman diagram, we see lines of particles moving through space and time, splitting and reuniting and exchanging particles and doing all the things particles do in nature. The diagrams are immediately intuitive and seemingly easy to understand, and one might forget that they are also ways of expressing and solving equations. They are not just charming doodles, but as packed with content as a forbidding equation. 

One comes across such passages as the following on the Wikipedia page: “The k-labellings of a graph that conserve momentum (i.e. which has zero boundary) up to redefinitions of k (i.e. up to boundaries of 2-cells) define the first homology of a graph. The number of independent momenta that are not determined is then equal to the number of independent homology loops. For many graphs, this is equal to the number of loops as counted in the most intuitive way.” It may sound like gibberish to us, but that is only because we are not trained in the arcane arts. We may at least observe that counting up loops in an intuitive way will tell us something we otherwise might not have guessed.

Both Dee diagrams and Feynman diagrams are pictures whose structural properties, the way they are put together, reveals the structure of nature. The diagrams capture the information that nature has to work with. And this might cast us into a state of wonder: just how is it that marks on paper can capture the workings of nature? How can a doodle or scribble, by its own formal features, reflect the generative power of physical reality? In general, how can one part of the world (scribbles on paper) be about other parts of the world?

(Beinecke Rare Book and Manuscript Library, Yale University)

Sometimes, of course, symbols fail. Not just any set of symbols will succeed in being about anything. And this brings us to the Voynich manuscript. This is a topic about which mountains of text have been written, but an absurdly brief summary is this. Around the time that Dee was visiting Holy Roman Emperor Rudolf II in Prague, a curious book surfaced, a book with fantastic drawings and written in a set of symbols that has yet to be understood. The language is not known to anyone, nor has it ever been, so far as we can tell. Top codebreakers from the CIA have not been able to make sense of it. Every few years someone claims to have cracked it, but so far their claims are exaggerated or false. This is the Voynich manuscript, named for Wilfrid Voynich, the book dealer responsible for bringing it to the world’s attention in the 20th century. It is the most frequently requested book from Yale’s Beinecke Rare Book and Manuscript Library.

The book’s origins are shrouded in stubborn mystery. My favorite theory is that the book was the work of Edward Kelley, a flimflam man who had accompanied Dee to Prague and whose dubious character would not preclude artfully casting a book in meaningless coded glyphs and selling it to Rudolf II for a princely sum. For there can be little doubt today that the Voynich manuscript is gibberish. Either that, or someone prior to the early 1600s was able to produce a code that has resisted all modern attempts at deciphering, which is about as likely as someone producing a genuine philosopher’s stone. (I look forward to spirited dialogue in the comments below as to the origins of the Voynich manuscript. The mystery is sure to outlive us all.)

(It may not look like gibberish to us, but it is.)

The language of the Voynich manuscript – if language it is – is loaded with structure: it seems to draw from an alphabet and is broken into words, and the statistical frequency of the letters and words accords with what is found in other natural languages. (So at least the text was artfully constructed, perhaps by taking sections from ordinary books and encoding them into appropriately patterned nonsense through the use of a Cardan grille.) The drawings that accompany the script are strange, charming, and sometimes beautiful; and to the extent that that is all they are meant to be, they successfully convey their meanings just by being what they are. 

But the script itself evidently lacks the sort of structure that is required for the marks on the page to actually link up with structures that are in the world. That is to say, the manuscript seems to say something, but doesn’t; it carries no information. What Feynman diagrams have, and what John Dee believed his glyphs to have had, is not shared by the characters in the Voynich manuscript. And this is because those characters were not assembled with any intent to capture structures that are in reality. They were meant only to seem to mean. A set of constructed symbols that is made in an attempt to capture real structures, but fails to do so, is false; one that succeeds in doing so is true; and one that is made to seem as if it is such an attempt, but really isn’t, is bullshit, in the technical sense of the term. And the transformation of bullshit into gold is indeed one kind of alchemy, the kind of alchemy a guy like Edward Kelley could manage.

We often take for granted the magic of symbolic and linguistic representation. If you have read this far, you might have gained some new information – stuff you didn’t know before you started reading. And you gained this information by passing your eyeballs over pixels arranged in such a way as to send signals down your optic nerve and interact with your neurons and … [just try to fill in this blank!] …, resulting in your understanding a text, and new knowledge you may call your own. There is magic in this, all the magic that an aspirant to wizardry could wish for.

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