You Could Look It Up (21 page)

Logarithms have real-world applications, but they are generated according to the principles of pure mathematics. They tell us things about numbers, not about the world, and should therefore be true everywhere and always. A mathematician in another universe, charged with calculating base-10 logarithms, should come up with the same answers as ours. There is nothing empirical about them. Other tables of numbers, though, are dependent on real-world facts, and though expressed in the language of mathematics, they are not really mathematical tables. Astronomy, for instance, is an eminently empirical science, since the only way to tell the location of the stars is to look at them.

Monuments such as Stonehenge and the Goseck Circle tell us people have been keeping track of astronomical phenomena for at least seven thousand years. They got pretty good at it in ancient Babylon, Egypt, Greece, and India—much better than we might expect, since they had to rely on the naked eye to keep track of stars, comets, and planets. Claudius Ptolemy collected the best astronomical observations of his day in his
Prokheiroi kanones
(
Handy Tables
), which a modern historian calls “the first mass produced mathematical table.”
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Not until the early modern era did people fully appreciate that the natural world behaves according to laws that can be understood as mathematical relations. As Galileo famously put it, “Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics.”
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It was one of the most important discoveries our species ever made.

The sixteenth and seventeenth centuries were a time of rapidly progressing knowledge. Astronomers now had telescopes; more and more observations and formulas were accumulating, and reference books were there to provide relief. Stars are relatively easy to track, because they are so far away that they seem immobile. For practical purposes, the stars are fixed. The astronomical bodies that are closer to
us, though, really do seem to move; we can witness this over the course of hours rather than over centuries. Only complicated calculations can tell where the moon will be visible at any given time—likewise for all the planets.

The ancients in many cultures worked on simple tables, and in 1080 a group of astronomers from Toledo, Spain, compiled tables that allowed astronomers to predict the location of the sun, moon, and planets with unprecedented precision. In the thirteenth century a group assembled by Alfonso X of Castile worked to update the Toledan tables, and the result was named for the patron. The Alphonsine tables gave mathematical descriptions of the relations between the sun, the moon, and the planets relative to the fixed stars. After circulating in manuscript for decades, the tables were printed in 1483, and new versions appeared over the next three centuries.

But, while they were adequate for many purposes, the Toledan and Alphonsine tables had serious flaws, and others sought to improve on them. The Danish nobleman Tycho Brahe was the best observational astronomer of the sixteenth century, and his ability to collect data over decades was unmatched. While he was still a student, he realized that the older tables were inaccurate, and he published a series of works based on careful observation of the heavens. In 1592 he produced a catalog of 777 stars—not only the largest such catalog, but the first wholly original one to appear in the West since Ptolemy’s a millennium and a half earlier. Tycho, however, never published most of his observations. He died in 1601, just fifty-four years old, and his
Astronomiæ instauratæ progymnasmata
appeared after his death.

Legend says Tycho’s dying request to his assistant, Johannes Kepler, was to publish his observations, but twenty-three years passed between Tycho’s death and the completion of the tables, and then another three years before the book appeared. Kepler disagreed with his predecessor on the geocentric or heliocentric model of the solar system, and he reworked many of Tycho’s equations and observations to make them consistent with the brilliant system devised by Polish canon Nicolaus Copernicus almost a century earlier. At length Kepler produced in 1627 the
Tabulæ Rudolphinæ
(
Rudolphine Tables
), named for Holy Roman Emperor Rudolf II, Kepler’s onetime patron, who had died in 1612.

The
Tables
were more accurate than any of their predecessors, both because of the careful observations made by both Brahe and Kepler and because they were built on a firmer foundation of Copernican astronomy. Simple to use, at least compared to other astronomical tables, they made it possible to determine the longitude of planets at any time, past, present, or future, and they provided answers that were an order of magnitude more precise than their predecessors. Readers could consult Kepler’s formula by using the logarithms that had been discovered only a few years earlier. Napier’s work had been published in 1614; Kepler was reading him by 1617, and he saw at once their potential.

The early numerical tables, like so many early examples of reference genres, were the works of individual scholars working without substantial assistance. But just as dictionaries and encyclopedias eventually grew too large for lone talents, so did numerical tables eventually require substantial teams.

At the end of the eighteenth century, the French engineer Gaspard Clair François Marie Riche de Prony oversaw one such workshop. Inspired by Adam Smith’s recently published
Treatise on the Wealth of Nations
(1776), he assembled a team of some sixty unemployed hairdressers to do carry out his instructions. (In the wake of the French Revolution there was less call for high-end hairdressers, not least because, thanks to Citizen Joseph-Ignace Guillotin’s eponymous invention, fewer aristocratic heads needed dressing.) The work was carried out on an industrial scale: in just two years, de Prony and his hairdressing computers calculated 10,000 sines to twenty-five decimal places, 2,000 logarithms of sines and tangents to fourteen decimal places, 10,000 logarithms of the proportions of sines and tangents, and the logarithms of numbers from 1 to 10,000 to nineteen decimal places and of numbers from 10,000 to 20,000 to fourteen places. The work filled seventeen folio volumes of manuscript, though they sat unpublished for ninety years.
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The production of tables achieved assembly-line efficiency in the late 1930s. The American Works Progress (later Projects) Administration, founded in 1935 to provide jobs for “employable workers” during the
Great Depression, established the Mathematical Tables Project in 1938 as one of its “small useful projects.” Useful it was, but hardly small: it was one of the largest-scale computing operations in the pre-ENIAC age, headed by a Polish-born mathematician, Gertrude Blanch, who supervised 450 clerks.
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Just as de Prony had learned a lesson from Adam Smith, Blanch took her cue from Henry Ford—she gave each group of workers a single task: some did only addition, some only subtraction. The best were trusted with long division. The resulting tables of logarithms and other functions were published in twenty-eight volumes; in some of them, no one to this day has discovered a single error.

But the work of Briggs, of Kepler, of de Prony, of Blanch was all rendered obsolete in the last third of the twentieth century, because of something no one could have foreseen in the 1940s, let alone in the 1620s—fast, plentiful, and cheap computers. When the newly invented electronic digital computers were first brought to bear on elaborate
calculations, nearly everyone took it for granted that the computers’ job would be to prepare accurate tables. The machines would tirelessly print long tables of logarithms, sines, and cosines, but the comparatively simple operations of adding and subtracting those numbers would continue to be done by hand. Computing time was far too expensive to waste on trivial calculations like adding 3.377306 to 3.213517. According to an often-repeated story, IBM president Thomas J. Watson declared in 1943, “I think there is a world market for maybe five computers.” The remark is almost certainly apocryphal, but it reflects the assumptions of the early digital days: computers were large and expensive, and the mechanical task of manipulating those numbers should be entrusted to minimally skilled laborers. We are left with the strange paradox that mathematical tables were rendered entirely obsolete by the computer, although tables were the main reason computers were invented. The computer itself—the transformative technology of the last sixty years—is an unintentional byproduct of the reference book.

CHAPTER
8 ½

TO BRING PEOPLE TOGETHER

Societies

Reading and writing reference books is generally solitary work. Merriam-Webster's headquarters in Springfield, Massachusetts, has a famously quiet working environment, dating back to Philip Gove's editorship of the
Third New International
, where even whispers can earn dirty looks. It's one of the few remaining places where two honest-to-goodness phone booths can be found, to ensure that conversations don't disturb the lexicographers hard at work. What Peter Sokolowski of Merriam calls “a powerful culture of silence” keeps the place as hushed as a library.

Fortunately for those who thrive only in society, though, there are more companionable outlets for indulging in lexicography and even lexicophilia. The national academies that sponsored many of the great national dictionaries are, for the most part, still busy, centuries after their founding, and they can sometimes be positively rowdy compared to the Merriam offices. One of the oldest private organizations, unsupported by any state, is the Philological Society of London; the group, founded in 1842, called for a “new English dictionary” and set in motion the project that became the
Oxford English Dictionary
. Organizations like the Royal Geographical Society, the American Geographical Society, and the Société de Géographie have promoted cartographical projects. One of the largest scholarly groups for the study of dictionaries is EURALEX, the European Association for Lexicography, founded in 1983; it spawned a series of sibling organizations: AUSTRALEX, the Australasian Association (1990), AFRILEX, the African Association (1995), and ASIALEX, the Asian Association (1997).

The friendliest society of the lot, though, is the Dictionary Society of North America, a group founded “to bring together people interested in
dictionary making, study, collection, and use.” The DSNA was born in 1975 at a colloquium on the history of English dictionaries held at Indiana State University in Terre Haute, Indiana—still the home of one of the best collections of dictionaries in the world. After toying with a number of names—the Society for the Study of English Dictionaries, the Society for the Study of Dictionaries and Lexicography, the Lexic Society, and the Lexicographical Society of America—they settled on the Dictionary Society of North America. The society now boasts more than four hundred members from around the world, and while professional lexicographers and academics are well represented in the membership directory, so, too, are librarians, journalists, book collectors, and plain old enthusiasts.
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The group meets every other year for a gathering that is part scholarly conference and part egghead bacchanal. Meetings have been held sometimes in big cities (Philadelphia, Montreal, Las Vegas), sometimes in smaller university towns (Ann Arbor, Urbana, Durham). The 2011 meeting in Montreal attracted a diverse group of working lexicographers, educators, historians, literary scholars, even computer scientists from all over the world. There were representatives from the
Oxford English Dictionary
and from Merriam-Webster; others included graduate students and professors emeriti, some in shorts and sandals, others in natty tailored suits and bow ties. The presentations ranged from explorations of the typography of Robert Cawdrey's
Table Alphabeticall
to dictionaries of Caribbean creole, from debates over the layout of learner's dictionaries to the practical difficulties of transcribing hip-hop lyrics—sometimes the only evidence of the first occurrence of a new word or sense is a bad bootleg recording of a rap concert from the 1970s.