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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 with 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