by Arika Okrent
The book in question begins:
Every circle is divided into three hundred and sixty parts, called degrees, whereof each one is sexagesimated, subsexagesimated, resubsexagesimated, and biresubsexagesimated.
Ah, the voices of angels. Though Urquhart did have a sense of humor (in fact, he died from laughing too hard at the news that Charles II had been restored to the throne), he was no satirist. If you take the time to beat your way through his suffocating prose, you will find quite earnest (and humorless) proposals.
It is easy to mistake his universal language proposal for satire because it appeared at a time when such proposals were the latest thing. Seventeenth-century philosophers and scientists were complaining that language obscured thinking, that words got in the way of understanding things. They believed that concepts were clear and universal, but language was ambiguous and unsystematic. A new kind of rational language was needed, one where words perfectly expressed concepts. These ideas were later satirized by Swift in Gulliver’s Travels, when Gulliver visits the “grand academy of Lagado” and learns of its “scheme for entirely abolishing all words whatsoever.” Since “words are only names for things,” people simply carry around all the things they might need to refer to and produce them from their pockets as necessary.
Gulliver observes especially learned men “almost sinking under the weight of their packs, like pedlars among us; who, when they met in the streets, would lay down their loads, open their sacks, and hold conversation for an hour together: then put up their implements, help each other to resume their burthens, and take their leave.”
This scenario illustrates a major problem with the rational language idea. How many “things” do you need in order to communicate? The number of concepts is huge, if not infinite. If you want each word in your language to perfectly express one concept, you need so many words that it will be impossible for anyone to learn them all.
But maybe there was a way around this problem. After all, by learning a few basic numbers and a system for putting them together, we can count to infinity. Couldn’t the same be done for language? Couldn’t we derive everything through a sort of mathematics of concepts?
This was a tremendously exciting idea at the time. In the seventeenth century, mathematical notation was changing everything. Before then, through thousands of years of mathematical developments, there was no plus sign, no minus sign, no symbol for multiplication or square root, no variables, no equations. The concepts behind these notational devices were understood and used, but they were explained in text form. Here, for example, is an expression of the Pythagorean theorem from a Babylonian clay tablet (about fifteen hundred years before Pythagoras):
4 is the length and 5 the diagonal. What is the breadth? Its size is not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? 3 times 3 is 9. 3 is the breadth.
And expressed a little more abstractly by Euclid a couple millennia later:
In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
And Copernicus, over fifteen hundred years after that, taking advantage of the theorem to solve the position of Venus:
It has already been shown that in units whereof DG is 303, hypotenuse AD is 6947 and DF is 4997, and also that if you take DG, made square, out of both AD and FD, made square, there will remain the squares of both AG and GF.
This is how math was done. The clarity of your explanations depended on the vocabulary you chose, the order of your clauses, and your personal style, all of which could cause problems. Here, for example, is Urquhart, in his “voices of angels” trigonometry book, doing something somehow related to the Pythagorean theorem—it’s hard to tell:
The multiplying of the middle termes (which is nothing else but the squaring of the comprehending sides of the prime rectangular) affords two products, equall to the oblongs made of the great subtendent, and his respective segments, the aggregate whereof, by equation, is the same with the square of the chief subtendent, or hypotenusa.
It is possible to do mathematics like this, but the text really gets in the way. Wait, which sides are squared? What is taken out of what? What was that thing three clauses ago that I’m now supposed to add to this thing? Late-sixteenth-century scientists who were engaged in calculating the facts of the universe had a sense that the important ideas, the truths behind the calculations, were struggling against the language in which they were trapped. The astronomer Johannes Kepler had turned to musical notation (already well developed at that time) in an effort to better express his discoveries about the motions of the planets, yielding “the harmony of the spheres.” But musical notation could only go so far. The development of mathematical notation in this context was nothing short of revolutionary.
The notational innovations of the seventeenth century—symbols and variables instead of words, equations instead of sentences—not only made it easier to keep track of which thing was which in a particular calculation; they also made it easier to see fundamental similarities and differences, and to draw generalizations that hadn’t been noticed before. In addition, the notation was universal; it could be understood no matter what your national language was. The pace of innovation in science accelerated rapidly. Modern physics and calculus were born. It seemed that the truth was finally being revealed through this new type of language. A tantalizing idea took hold: just imagine what might be revealed if we could express all of our thoughts this way.
But how do you turn the world of discourse into math? Three primary strategies emerged from the competitive flurry of schemes whipped up by this challenge, two so superficial they allowed the illusion of success (leaving the egos of the authors undisturbed), and one so ambitious that those who attempted to implement it could only be humbled by the enormity of the task it revealed.
The first strategy was to simply use letters in a number-like way. When you combine the letters or do some sort of computation with them (the nature of that computation being very vaguely described), you get a word and—voilà!—a language. This was Urquhart’s approach. He had tried a version of this strategy in his trigonometry book when he assigned letters to concepts, such as E for “side” and L for “secant,” and then formed words out of the letters to express statements like Eradetul, meaning “when any of the sides is Radius, the other of them is a Tangent, and the Subtendent a Secant.” He thought a similar approach could be used to make precise, definition-containing words for everything in the universe. All you needed was the right alphabet, and he claims to have devised one so perfect that not only can it generate distinct words for all possible meanings, but the words for stars will show you their exact position in the sky in degrees and minutes, the words for colors will show their exact mixture of light, shadow, and darkness, the names of individual soldiers will show their exact duty and rank. What’s more, in comparison with all other languages, it produces the best prayers, the most elegant compliments, the pithiest proverbs, and the most “emphatical” interjections. And besides all that, it is the easiest to learn. He stops short of claiming that it whitens your teeth and cures impotence, but he might as well have. His claims can’t be disproved, because he doesn’t provide any examples.
The second strategy was to turn words into numbers. This was the approach of Cave Beck, an Ipswich schoolmaster who published his invention (The Universal Character: By Which All the Nations in the World May Understand One Anothers Conceptions) in 1657. He assigned numbers to concepts: 1 was “to abandon,” 2 “to abash,” 3 “to abate,” 742 “to embroider,” q2126 “gogle-eyed,” r2654 “a loosenesse in the belly,” p2846 “hired mourners at funerals.” (Letters appearing before the numbers were used to indicate part of speech and grammatical concerns such as tense and gender.) He provided a pronunciation key for the numbers so that the language could be spoken out as words (for example, 7 is pronounced “sen”). Though the book opens wi
th a series of poems (by his friends) praising Beck and his invention, his confidence is far less blustery than Urquhart’s; he presents his system as merely a practical tool for translating between languages. However, with an ambitious gleam in his eye, he adds that if it should happen to become a universal language that could unlock “Glorious Truths,” he will “judge this pains of mine happily bestowed.” He provides only one example of the language in action, the fifth commandment. Honor thy father and thy mother, “leb 2314 p2477 & pf2477,” to be pronounced, “Leb toreónfo, pee to-fosénsen et pif tofosénsen.”
There is an assumption in these approaches that all you have to do to build a perfect language is find the right set of symbols—whether letters, numbers, or line drawings. The focus on symbols was influenced by other, related popular pursuits of the time such as cryptography, shorthand, and kabbalism (seeking divine messages in patterns of letters in ancient texts). Another influence was the widespread interest in hieroglyphics and Chinese writing, which were believed to represent concepts more directly than alphabetic writing systems. But if your goal is to craft a language capable of mathematically exposing the truths of the universe, the form of the symbols you use is relatively unimportant. What is more important is that systematic relations obtain between the symbols. The number 1 stands for the concept of oneness, and 100 stands for the concept of onehundredness, but, more important, there is a relationship between oneness and onehundredness that is captured by the relationship between the symbols 1 and 100. And it is the same relationship that obtains between 2 and 200. In Beck’s system there is no such relationship between 1 (abandon) and 100 (agarick—a type of mushroom), and if you do find a way to read a relationship into them, it won’t be the same as the one between 2 (abate) and 200 (an anthem). The numbers are just labels for words. They might as well be words. Both Beck and Urquhart had a vague sense that symbols were capable of systematically capturing relationships between concepts, but they never did the hard work of applying this idea to language.
They could have learned a thing or two from the humble Francis Lodwick, a Dutchman living far from home in London whose 1647 book, A Common Writing, was signed simply “a Well-wilier to Learning.” In his preface he apologizes for the “harshnesse of [his] stile” and entreats “a more abler wit and Pen, to a compleate attyring and perfecting of the Subject.” His modesty was partly due to a feeling of inferiority, life-station-wise. He was a merchant with no formal education, which, in the opinion of the author of a later scheme, made him “unequal to the undertaking.” But his modesty was also of the hard-earned type—the modesty that all thoughtful and honest scholars must come to (whatever their life station) when their work reveals a vast, churning ocean of difficulty just beyond the charming rivulet they had glimpsed from afar.
The important insight of Lodwick’s system wasn’t in the symbols he chose (characters that look like capital letters, with various hooks, dots, and squiggles attached) but in the way his symbols expressed relationships between concepts. For example, as shown in figure 4.1, the symbol for “word,” , is the symbol for “to speak,” , combined with a mark denoting “act of …”: . A word is essentially defined as an act of speaking. The symbol for God, , is the symbol for “to be,” , combined with “act of …,” , and “proper name,” . God is the proper name of the act of being (something like “The Embodiment of Existence”). The symbol for man, , is the symbol for “to understand,” , combined with “one who …,” , and “proper name,” . Man is “The Understander.” Lodwick’s major insight was to derive more complex concepts by adding together more basic ones.
Lodwick had hit upon the third method for creating a mathematics of discourse. It was concerned not with mere letters or numbers or symbols but with the relationships between the concepts they represented. From a limited set of basic concepts, you could derive everything else through combination. Leibniz would later describe this as a “calculus of thought.” The first rule of this calculus was that numbers for concepts “should be produced by multiplying together the symbolic numbers of the terms which compose the concept.” So, “since man is a rational animal, if the number of animal, a, is 2, and of rational, r, is 3, then the number of man, h, will be the same as ar: in this example, 2 × 3, or 6.” The calculations work in reverse as well. If you saw that ape was 10, you could deduce that it was an animal (because it could be divided by 2) but not a rational one (as it can’t be divided by 3).
Figure 4.1: Lodwick’s symbols
Descartes had also considered this idea a decade or two before Lodwick. He mused that if you could “explain correctly what are the simple ideas in the human imagination out of which all human thoughts are compounded … I would dare to hope for a universal language very easy to learn, to speak and to write.” But he never tried his hand at creating such a language, because he thought it would first require a complete understanding of the true nature of everything. While he did think it was “possible to invent such a language and to discover the science on which it depends,” he also thought this was unlikely to occur “outside of a fantasyland.”
Lodwick had hit upon a solution to the problem of how to make a mathematics of language, but the solution introduced a much bigger problem: How do we know what the basic units of meaning are? How do we define everything in terms of those units?
Well, you can start by figuring out the order of the universe. This was not a ridiculous proposition for the seventeenth-century man of science. It was a difficult proposition, and one that anyone could see would most likely never be adequately fulfilled. But that was no reason not to try. This was the age of reason, and so the rational animal got to work.
A Hierarchy of the Universe
The bulk of John Wilkins’s six-hundred-page description of his language is taken up with a hierarchical categorization of everything in the universe. Everything? When I first sat down to confront An Essay Towards a Real Character and a Philosophical Language, I did what any sensible, mature language scholar would do. I tried to look up the word for “shit.”
But where to look? I was holding a dictionary of concepts, not words. They were arranged not alphabetically but by meaning. To get the word for “shit,” I would have to find the concept of shit, which meant I had to figure out which of Wilkins’s forty categories of meaning it fell under.
Wilkins’s categories are organized into an overall structure of the type known as the Aristotelian hierarchy, or Porphyrian tree. This is the genus-species-difference organization we are most familiar with from taxonomies of plant and animal life. The higher positions in the tree are the most general categories, which are split into subcategories on the basis of some distinguishing feature. Daisies, spiders, woodpeckers, tigers, and porcupines all fall under the category of animate substances; they are all living things. But only some of them share the property of being sensate (bye, daisies) or of having blood (bye, spiders) or of being beasts (see ya, woodpeckers) or of being non-rapacious (so long, tigers). As we move down the tree, categories are narrowed and members more precisely defined by their membership.
Figure 5.1 shows Wilkins’s tree of the universe, with his forty numbered categories as the bottom nodes. The first division, general versus special, separates the big abstract metaphysical ideas (notions like existence, truth, and good) from the stuff of the world (the notions those ideas can apply to). This division was consistent with the philosophy of categories, descended from Plato and Aristotle, as practiced at the time. The division between substances and accident (at the second node under “special”) also comes from this tradition. Substances are answers to the question, What is this? and accidents are answers to the question, How/in what way/of what quality is this? A glance at the table will show that these distinctions do not always hold up very well, but, as Wilkins was quite aware, the philosophy was incomplete and this was as good a place to start as any.
The bottom nodes of this tree, the forty main categories, are themselves top-level categories in their own sprawlin
g trees. For example, if we zoom in on category XVIII, “Beasts,” we find it further divided into six subcategories, as shown in figure 5.2.
It doesn’t stop there. Lift a subcategory and you find a tree of sub-subcategories that get even more specific. So under category XVIII (Beasts), subcategory V (oblong-headed), you will find six sub-subcategories under which specific animals are finally named (as shown in figure 5.3).
Figure 5.1: Wilkins’s tree of the universe
Figure 5.2: Subcategories of beasts
Figure 5.3: Subcategories of oblong-headed beasts
Each one of his forty top-level categories expands in this manner into multiple sub- and sub-sub trees. A place is provided for everything from “porcupine” (substances > animate > sensate > sanguineous > beast > clawed > non-rapacious) to “dignity” (accident > quality > habit > instruments of virtue > concerning our conditions in relation to others) to “potentialness” (transcendentals > general > quality > degree of being). We are dealing with an enormous magnum opus here.
But why was all this necessary? What does the idea of a mathematics of language have to do with a gigantic conceptual map of the universe?
We have seen that a mathematics of language required two things: a list of the basic units of meaning, and a knowledge of how everything else was to be derived from those units. In Lodwick’s system “to understand,” “one who …,” and “proper name” were primitives, and “man” was derived from the combination of those three primitives. Man was defined as the one who understands. For Leibniz the primitives were rational and animal, and man was derived by the combination of those primitives—the rational animal. Well, which is it? Is man the rational animal or the understander? It depends on the primitives you’re working with. And finding the right set of primitives depends on finding the right definition. Now, the rational animal and the understander are pretty similar definitions for man—they both focus on man’s capacity to think—but man could be defined in other ways. Why not the upright-walking animal? Or (after Plato) the featherless biped?