by Jack Lynch
CHAPTER 3 ½
EASY AS ABC
The Rise (and Fall?) of Alphabetical Order
Samuel Johnson’s first definition of dictionary is “A book containing the words of any language in alphabetical order, with explanations of their meaning.” But many early dictionaries were not alphabetical because there was not yet an alphabet.
Writing is more than five thousand years old. Mesopotamians were using their cuneiform script around 3300 B.C.E., and Egyptian hieroglyphs followed about a century later. But these systems were not alphabets. A symbol in either system could stand for an entire word, or sometimes a syllable, but not for a single sound. The Sumerians used around a thousand different cuneiform symbols, the Egyptians around five thousand hieroglyphs. Because there were so many, there was no order to them. The modern Chinese language works the same way: with nearly fifty thousand characters, no one could be expected to memorize them in any arbitrary order.
Reference books from the ancient world therefore cannot count on any obvious order. Urra=hubullu is, by some accounts, the oldest dictionary in the world. But it has no handy thumb tabs bearing the letters of the alphabet; instead it is organized thematically, and the divisions strike moderns as distinctly eccentric. Trees appear on tablet 3, but other plants on tablet 17; most animals are on tablets 13–14, but birds and fish show up on tablet 18.1 It must have made sense to its original users, and it serves as a reminder that our familiar ways of looking at the universe are not the only ways.
Although both cuneiform and hieroglyphics eventually assumed some of the features of alphabets, most historians say the first true alphabet arose among the Semitic peoples of central Egypt around 2000 B.C.E. It was adapted from Egyptian hieroglyphs, and we can still make out increasingly stylized versions of the original forms in some of the letters. But the system took on a new logic: a symbol represented not a word, not a syllable, but an individual phoneme. By the time the system reached Phoenicia (modern Lebanon) around 1050 B.C.E., there was no longer any obvious resemblance between the letter forms and the pictures from which they evolved, and all pretense to being pictographic was abandoned. Symbols now represented not things but sounds. They had become an alphabet, achieving both economy and flexibility.
Phoenicians were the great traders of the ancient Mediterranean. Their ships could be found everywhere, and their alphabet came along for the ride. From the Phoenician alphabet came the Aramaic alphabet, which in turn spawned modern Hebrew and Arabic. Phoenician also produced the Greek alphabet, which gave birth to the Latin alphabet, which in turn is the basis of the Western European languages (as well as many languages outside Europe). The Cyrillic alphabet, too, came (much later) out of the Greek.
Some of the alphabet’s advantages must have been immediately obvious—it is much easier to learn to read with an alphabet than with a logographic system. But one benefit came only much later—alphabetical order. The alphabet need not be in any particular order: there is no reason alpha should come before beta. We could arrange the letters as QWERTY or FUTHORC or PYFGCRL or MARESIDOT, but for a still-unknown reason we settled on ABCDEFG.
It was a long time before anyone used this order for practical purposes. Ancient Greeks and Romans had ordered alphabets, but they hardly ever used that order in reference books. Alphabetical order started to appear in reference books in Europe in the thirteenth or fourteenth centuries,2 but readers still needed to have it explained to them. In 1286, Johannes Balbus wrote in his Catholicon, “I will discuss amo before bibo because a is the first letter of amo and b is the first letter of bibo and a is before b in the alphabet.”3 More than three hundred years later, in 1604, alphabetical order was still so alien to English readers that Robert Cawdrey had to explain its use. “If thou be desirous (gentle Reader) rightly and readily to vnderstand, and to profit by this Table,” he patiently advised, “then thou must learn the Alphabet, to wit, the order of the Letters as they stand.” The reader should learn the alphabet “perfectly without booke”—by heart—“where euery Letter standeth: as (b) neere the beginning, (n) about the middest, and (t) towards the end.”4 Shakespeare’s contemporaries needed to be taught their ABCs.
Even after alphabetical order was familiar, many reference books were arranged topically or thematically, using the alphabet only within sections—so an encyclopedia’s section on trees might put ash before beech, but the trees were kept together. Only in the seventeenth and eighteenth century did people realize how difficult it was to come up with a taxonomy of knowledge more intuitive than the alphabet. Alphabetical order still had enemies, who hated the thought of subjecting all human knowledge—a field that was supposed to be rationally structured—to the tyranny of an arbitrary order. It felt like failure. As the historian Peter Burke says, complete alphabetization “appears to have been adopted, originally at least, out of a sense of defeat by the forces of intellectual entropy at a time when new knowledge was coming into the system too fast to be digested or methodized.”5
Given the hardiness of alphabetical order for so many thousands of years, it will likely remain in use for a long time to come, and parents will continue to beam proudly at their children as they learn to recite the letters in order—something they have been doing to music in the Anglophone world since 1835, when Charles Bradlee published Louis Le Maire’s sheet music to “The A.B.C., a German Air with Variations for the Flute with an Easy Accompaniment for the Piano Forte.” (The “German Air” was actually lifted from an eighteenth-century French folksong, which had been adapted by Mozart and had already shown up in English in 1806 as “Twinkle, Twinkle, Little Star.”)
Still, alphabetical order occupies a less prominent place in our lives, especially in reference works, than it once did. Printed reference works need order because their information is spread through space—through pages and through volumes—and readers need help to navigate that space. In the electronic world, though, information takes up only a few molecules on a silicon chip or a few magnetized particles on a hard drive. There is an internal structure of the terabytes of information stored on Google’s servers—information must be structured if it’s to be found—but it’s not as if all the information related to aardvarks and abacuses is stored on one part of their servers and the information on zydeco and zygotes on another. The user has no reason to care how that information is organized on the hard drives, as long as a query turns up the appropriate information when it is needed. As electronic reference works continue to displace print, and as searches continue to displace browsing, the world may have less reason to care about their ABCs.
CHAPTER 4
ROUND EARTH’S IMAGINED CORNERS
Mapping the World
Claudius Ptolemy
Geographike hyphegesis
c. 150 C.E.
The Domesday Book
1086
Some say the cave walls at Lascaux, France, painted around 16,500 C.E., include star charts. If they are right, cartography has been an obsession of our species since we lived in caves. But even if the dots on Lascaux’s walls amount to nothing, maps go back an almost unimaginably long way—more than eight thousand years, long before the first word was written down.
The earliest maps must have involved a truly dazzling act of imagination. For eons, when human beings saw the landscape, they saw it more or less from ground level. They must have climbed trees, hills, even mountains for a better view from time to time. But they always looked out over a landscape, never down on it. Maps demanded an imaginative leap: the viewer assumes a position no human being had ever actually occupied. Maps show the world as it had been seen only by birds—and the gods. They made it possible to think about physical space in new ways.
We know nothing about these earliest human attempts to capture the contours of their environment on a manageable scale. It is easy to suppose maps were drawn in the sand with a stick or etched in bark, but without evidence, all we have is speculation. Starting in the late seventh millennium B.C.E., though, we have unambi
guous examples of cartography. In Catal Hüyük, Anatolia (modern Turkey), archaeologist James Mellaart discovered a map from around 6200 B.C.E. The nine-foot-long (277-cm) painting on the wall of a shrine, perhaps part of an even larger map, clearly represents the position of roughly eighty buildings, arranged in terraces, each higher than the one before it. A two-coned volcano, corresponding to the mountain Hasan Dag, appears in the distance, in mideruption, with fire running down its slopes. The locals knew the volcano well, because it was the source of the obsidian they used to make jewelry, tools, and weapons.1
Over the succeeding eight millennia there have been countless attempts to draw some part of the world, and these graphical “mediators between an inner mental world and an outer physical world” are milestones in our species’ intellectual evolution.2 Maps described faraway coastlines for adventurers and dreamers; they recorded conquests of foreign territory for rulers who needed to keep track of boundaries, whether to police their borders with troops or to collect taxes from the inhabitants. This last is especially important: cartographic advancement was often a byproduct of imperial conquest. Sometime around 324 B.C.E., for example, scholars in the employ of Alexander the Great compiled the Satrapies, a list of places Alexander had conquered as he expanded his empire. The Satrapies began with a strictly administrative purpose but later became guides to geography throughout what was then the known world.
Long before Columbus, people knew the world was spherical. Eighteen hundred years before the Niña, Pinta, and Santa María left Spain, Greek geographers made impressively accurate estimates of the size of the globe. Eratosthenes, for instance, the chief librarian at the Library of Alexandria in the late third century B.C.E., started with the distance between two cities on the same latitude, Swenet and Alexandria: 5,000 stadia. He then performed an ingenious calculation, observing the elevation of the sun in these two cities by measuring shadows, which showed that Swenet and Alexandria were 7° 12’ apart—one fiftieth of 360°, and therefore one fiftieth of the way around the earth. The rest of the computation was simple. If 5,000 stadia goes one fiftieth of the way around the earth, then the entire circumference should be 5,000 × 50 = 250,000 stadia. He then adjusted his estimate (for various technical reasons) to 252,000 stadia, the first scientific estimate of the distance around the whole earth. We don’t know for certain how accurate it was, because we don’t know exactly how long a stade was. An Attic stade, the Greek standard, was 185 meters, but an Egyptian stade was shorter, about 157.5 meters, and it is unclear which he was using. If he used the Greek measurement, his circumference of the earth came out to 46,620 kilometers—about 16 percent high, not bad for premodern measurement. If he used the Egyptian unit, then his answer was 39,690 km, less than one percent from the actual figure of 40,075 km.
Eratosthenes put all this knowledge to use in his book Geographike, an important bridge to modern maps. He divided the earth into zones based on their latitudes: a tropical zone around the equator, a pair of temperate zones to the north and the south of the equator, and a pair of freezing zones at the north and south poles. He then imagined a system of lines running in a grid across the surface of the earth, parallels and meridians, the functional equivalent of the latitude and longitude system that would be used two millennia later, and he used these lines to locate cities on the earth. It was the beginning of systematic geography.
A major development came at the beginning of the common era. The man Klaudios Ptolemaios (or Claudius Ptolemy) is a mystery, and we know neither where nor when he was born or died. He probably began his work in Alexandria, Upper Egypt, in the mid-120s C.E., and he refers to cities founded around 130 C.E., so the best guess is that he was born around the year 100. But though we know depressingly little about him, his works on astronomy, astrology, trigonometry, optics, harmonics, and chronology reveal a wide-ranging mind. And his modern translators are to the point: “On any list of ancient scientific works, Ptolemy’s Geography will occupy a distinguished place.”3 His Geography (also known as Geographica or the Greek Geographike hyphegesis) was one of the West’s first systematic attempts to collect all of the ancient world’s cartographic knowledge in one place. Ptolemy was interested in both globes and two-dimensional maps, and he recognized the differences between them, because the three dimensions of the earth can never be represented on a flat surface without distortion.
Although he made observations of astronomical phenomena when he was in Alexandria, Ptolemy was no sextant-toting field cartographer. Instead, he drew on the combined experience of generations of Greek and Roman cartographers, synthesized it, and made the results available to the world. His Geographike hyphegesis is not a map, exactly; rather it is an instruction book for a map, a list of coordinates—thousands of them, from the British Isles to India, China, and Sri Lanka—that, when plotted on a grid, describe a map of the inhabited world. Since it is much easier to copy text (digital information) than images (analog information), Ptolemy’s decision to give coordinates gave his book a longevity that no actual map would ever have.4 Even so, the manuscripts that survive are messy, fragmentary, and sometimes contradictory, so it is no easy feat to put together the text.
TITLE: Γεωγραφικ φγησις (A guide to geography)
COMPILER: Claudius Ptolemaios (c. 100–c. 170 C.E.)
ORGANIZATION: Book 1, introduction; book 2, Ireland through Dalmatia; book 3, Italy, Greece, and the lower Danube; book 4, North Africa; book 5, Asia Minor through Babylonia; book 6, former Persian Empire; book 7, India and world map; book 8, overview of the regional maps
PUBLISHED: c. 150 C.E.
ENTRIES: 8,000
VOLUMES: 8
TOTAL WORDS: 83,000
The Geographike hyphegesis is in eight books. The first serves as an introduction, and it features a substantial critique of the maps of one of Ptolemy’s predecessors, Marinos of Tyre. We know nothing about Marinos beyond what we can gather from Ptolemy’s text, which called him “the latest [author] in our time to have undertaken this subject,”5 so he probably lived not long before Ptolemy himself. Ptolemy criticized his shortcomings, such as his inaccurate estimates of the size of the earth and his technical problems with his understanding of the projection of latitude and longitude onto the spherical surface of the earth. But still he borrowed from Marinos at length.
With book 2, Ptolemy introduced the coordinates that occupy most of his work, starting in the far west: Ireland, Britain, Hispania, Gaul, Germany, and the upper Danube. Book 3 covers the Italian and Greek peninsulas and the islands around them, as well as the lower Danube. Book 4 crosses the Mediterranean into northern Africa, and Ptolemy progressed from west to east, from Egypt to Ethiopia. Book 5 starts in Asia Minor—modern Turkey—and covers Armenia, Cyprus, Syria, and most of the Middle East. Book 6 is devoted to the regions that had once formed the Persian Empire. Book 7 is devoted to the Indian subcontinent, and included a description of a complete world map. Book 8—which some critics believe may include material not written by Ptolemy—surveys more than two dozen regional maps.6
A typical section shows Ptolemy’s method:
In Hispania, known by the Greeks as Iberia, there are three provinces, Baetica and Lusitania and Tarraconensis. And the west and north borders of Baetica are determined by Lusitania and part of Tarraconensis respectively, a description of which is made as follows:
To the east the mouth of the river Ana
4
⅓
37
½
Before the river turns east
6
⅓
39
Where the river touches the Lusitanian border
9
39
And the line drawn from there along the border of Tarraconensis to the end of the Balearic sea
12
37
¼
Where the well
springs of the river overflow
14
40
Ptolemy measured his coordinates in degrees, with 360 to a circle, as we do today; he also provided fractions of a degree to approximate minutes: 4⅓ is 4 degrees 20 minutes. Coordinates, of course, have meaning only in relation to some known point. The equator provided him with a natural reference for latitude. The prime meridian is nothing natural, only a social convention, and at that time none was recognized. Greenwich was not used even by British cartographers until the late eighteenth century, and it was not adopted internationally until 1884. Ptolemy picked the “Fortunate Isles,” probably what we call the Canary Islands, for his starting point. There are of course plenty of inaccuracies in his reports; he was least reliable in reporting the east–west dimensions of the Mediterranean and in believing that some sort of land bridge connected Africa to China. But his was the most complete and most accurate picture of the world that could be had at the time.
With the collapse of the Western Roman Empire in the fifth century, the European field of vision narrowed considerably, and cartography suffered. Not so in the Muslim world: at the end of the first millennium, Islam’s maps were more accurate than anything Europe had to offer. And in Muslim hands, Ptolemy’s Geography took on new prominence, thanks to one of the most learned figures in the world. All we have are probablys for most of the basic facts of his life: he was probably born around the year 780 in or near Baghdad, was probably of Persian origin, and was probably based at Baghdad’s Bayt al-Hikma, or House of Wisdom, during the Abbasid Caliphate. We can be certain, though, that Muhammad ibn Musa al-Khwarizmi was a polymath. He gave us two words whose importance has only grown in the centuries since he lived: the title of his book Kitab al-muktasar fi hisab al-jabr wal-muqabala, or The Concise Book on Calculation by Restoration and Compensation, is the source of the word algebra (al-jabr means “compensation”), and his name, al-Khwarizmi, once Latinized and then passed around through the modern languages, gave us the algorithm. Every high-tech computer calculation pays tribute to the ninth-century Islamic genius.
