What Just Happened: A Chronicle From the Information Frontier

  “We know that formal logic is the invention of Greek culture after it had interiorized the technology of alphabetic writing,” Walter Ong says—it is true of India and China as well—“and so made a permanent part of its noetic resources the kind of thinking that alphabetic writing made possible.”♦ For evidence Ong turns to fieldwork of the Russian psychologist Aleksandr Romanovich Luria among illiterate peoples in remote Uzbekistan and Kyrgyzstan in Central Asia in the 1930s.♦ Luria found striking differences between illiterate and even slightly literate subjects, not in what they knew, but in how they thought. Logic implicates symbolism directly: things are members of classes; they possess qualities, which are abstracted and generalized. Oral people lacked the categories that become second nature even to illiterate individuals in literate cultures: for example, for geometrical shapes. Shown drawings of circles and squares, they named them as “plate, sieve, bucket, watch, or moon” and “mirror, door, house, apricot drying board.” They could not, or would not, accept logical syllogisms. A typical question:

  In the Far North, where there is snow, all bears are white.

  Novaya Zembla is in the Far North and there is always snow there.

  What color are the bears?

  Typical response: “I don’t know. I’ve seen a black bear. I’ve never seen any others.… Each locality has its own animals.”

  By contrast, a man who has just learned to read and write responds, “To go by your words, they should all be white.” To go by your words—in that phrase, a level is crossed. The information has been detached from any person, detached from the speaker’s experience. Now it lives in the words, little life-support modules. Spoken words also transport information, but not with the self-consciousness that writing brings. Literate people take for granted their own awareness of words, along with the array of word-related machinery: classification, reference, definition. Before literacy, there is nothing obvious about such techniques. “Try to explain to me what a tree is,” Luria says, and a peasant replies, “Why should I? Everyone knows what a tree is, they don’t need me telling them.”

  “Basically the peasant was right,”♦ Ong comments. “There is no way to refute the world of primary orality. All you can do is walk away from it into literacy.”

  It is a twisting journey from things to words, from words to categories, from categories to metaphor and logic. Unnatural as it seemed to define tree, it was even trickier to define word, and helpful ancillary words like define were not at first available, the need never having existed. “In the infancy of logic, a form of thought has to be invented before the content can be filled up,”♦ said Benjamin Jowett, Aristotle’s nineteenth-century translator. Spoken languages needed further evolution.

  Language and reasoning fit so well that users could not always see the flaws and gaps. Still, as soon as any culture invented logic, paradoxes appeared. In China, nearly contemporaneously with Aristotle, the philosopher Gongsun Long captured some of these in the form of a dialogue, known as “When a White Horse Is Not a Horse.”♦ It was written on bamboo strips, tied with string, before the invention of paper. It begins:

  Can it be that a white horse is not a horse?

  It can.

  How?

  “Horse” is that by means of which one names the shape. “White” is that by means of which one names the color. What names the color is not what names the shape. Hence, I say that a white horse is not a horse.

  On its face, this is unfathomable. It begins to come into focus as a statement about language and logic. Gongsun Long was a member of the Mingjia, the School of Names, and his delving into these paradoxes formed part of what Chinese historians call the “language crisis,” a running debate over the nature of language. Names are not the things they name. Classes are not coextensive with subclasses. Thus innocent-seeming inferences get derailed: “a man dislikes white horses” does not imply “a man dislikes horses.”

  You think that horses that are colored are not horses. In the world, it is not the case that there are horses with no color. Can it be that there are no horses in the world?

  The philosopher shines his light on the process of abstracting into classes based on properties: whiteness; horsiness. Are these classes part of reality, or do they exist only in language?

  Horses certainly have color. Hence, there are white horses. If it were the case that horses had no color, there would simply be horses, and then how could one select a white horse? A white horse is a horse and white. A horse and a white horse are different. Hence, I say that a white horse is not a horse.

  Two millennia later, philosophers continue to struggle with these texts. The paths of logic into modern thought are roundabout, broken, and complex. Since the paradoxes seem to be in language, or about language, one way to banish them was to purify the medium: eliminate ambiguous words and woolly syntax, employ symbols that were rigorous and pure. To turn, that is, to mathematics. By the beginning of the twentieth century, it seemed that only a system of purpose-built symbols could make logic work properly—free of error and paradoxes. This dream was to prove illusory; the paradoxes would creep back in, but no one could hope to understand until the paths of logic and mathematics converged.

  Mathematics, too, followed from the invention of writing. Greece is often thought of as the springhead for the river that becomes modern mathematics, with all its many tributaries down the centuries. But the Greeks themselves alluded to another tradition—to them, ancient—which they called Chaldean, and which we understand to be Babylonian. That tradition vanished into the sands, not to surface until the end of the nineteenth century, when tablets of clay were dug up from the mounds of lost cities.

  First there were scores, then thousands of tablets, typically the size of a human hand, etched with a distinctive, edgy, angular writing called cuneiform, “wedge shaped.” Mature cuneiform was neither pictographic (the symbols were spare and abstract) nor alphabetic (they were far too numerous). By 3000 BCE a system with about seven hundred symbols flourished in Uruk, the walled city, probably the largest in the world, home of the hero-king Gilgamesh, in the alluvial marshes near the Euphrates River. German archeologists excavated Uruk in a series of digs all through the twentieth century. The materials for this most ancient of information technologies lay readily at hand. With damp clay held in one hand and a stylus of sharpened reed in the other, a scribe would imprint tiny characters in columns and rows.

  The result: cryptic messages from an alien culture. They took generations to decipher. “Writing, like a theater curtain going up on these dazzling civilizations, lets us stare directly but imperfectly at them,”♦ writes the psychologist Julian Jaynes. Some Europeans took umbrage at first. “To the Assyrians, the Chaldeans, and Egyptians,” wrote the seventeenth-century divine Thomas Sprat, “we owe the Invention” but also the “Corruption of knowledge,”♦ when they concealed it with their strange scripts. “It was the custom of their Wise men, to wrap up their Observations on Nature, and the Manners of Men, in the dark Shadows of Hieroglyphicks” (as though friendlier ancients would have used an alphabet more familiar to Sprat). The earliest examples of cuneiform baffled archeologists and paleolinguists the longest, because the first language to be written, Sumerian, left no other traces in culture or speech. Sumerian turned out to be a linguistic rarity, an isolate, with no known descendants. When scholars did learn to read the Uruk tablets, they found them to be, in their way, humdrum: civic memoranda, contracts and laws, and receipts and bills for barley, livestock, oil, reed mats, and pottery. Nothing like poetry or literature appeared in cuneiform for hundreds of years to come. The tablets were the quotidiana of nascent commerce and bureaucracy. The tablets not only recorded the commerce and the bureaucracy but, in the first place, made them possible.

  A CUNEIFORM TABLET

  Even then, cuneiform incorporated signs for counting and measurement. Different characters, used in different ways, could denote numbers and weights. A more systematic approach to the writing of numbers did n
ot take shape until the time of Hammurabi, 1750 BCE, when Mesopotamia was unified around the great city of Babylon. Hammurabi himself was probably the first literate king, writing his own cuneiform rather than depending on scribes, and his empire building manifested the connection between writing and social control. “This process of conquest and influence is made possible by letters and tablets and stelae in an abundance that had never been known before,”♦ Jaynes declares. “Writing was a new method of civil direction, indeed the model that begins our own memo-communicating government.”

  The writing of numbers had evolved into an elaborate system. Numerals were composed of just two basic parts, a vertical wedge for 1 () and an angle wedge for 10 (). These were combined to form the standard characters, so that represented 3 and represented 16, and so on. But the Babylonian system was not decimal, base 10; it was sexagesimal, base 60. Each of the numerals from 1 to 60 had its own character. To form large numbers, the Babylonians used numerals in places: was 70 (one 60 plus ten 1s); was 616 (ten 60s plus sixteen 1s), and so on.♦ None of this was clear when the tablets first began to surface. A basic theme with variations, encountered many times, proved to be multiplication tables. In a sexagesimal system these had to cover the numbers from 1 to 19 as well as 20, 30, 40, and 50. Even more difficult to unravel were tables of reciprocals, making possible division and fractional numbers: in the 60-based system, reciprocals were 2:30, 3:20, 4:15, 5:12 … and then, using extra places, 8:7,30, 9:6,40, and so on.♦

  A MATHEMATICAL TABLE ON A CUNEIFORM TABLET ANALYZED BY ASGER AABOE

  These symbols were hardly words—or they were words of a peculiar, slender, rigid sort. They seemed to arrange themselves into visible patterns in the clay, repetitious, almost artistic, not like any prose or poetry archeologists had encountered. They were like maps of a mysterious city. This was the key to deciphering them, finally: the ordered chaos that seems to guarantee the presence of meaning. It seemed like a task for mathematicians, anyway, and finally it was. They recognized geometric progressions, tables of powers, and even instructions for computing square roots and cube roots. Familiar as they were with the rise of mathematics a millennium later in ancient Greece, these scholars were astounded at the breadth and depth of mathematical knowledge that existed before in Mesopotamia. “It was assumed that the Babylonians had had some sort of number mysticism or numerology,” wrote Asger Aaboe in 1963, “but we now know how far short of the truth this assumption was.”♦ The Babylonians computed linear equations, quadratic equations, and Pythagorean numbers long before Pythagoras. In contrast to the Greek mathematics that followed, Babylonian mathematics did not emphasize geometry, except for practical problems; the Babylonians calculated areas and perimeters but did not prove theorems. Yet they could (in effect) reduce elaborate second-degree polynomials. Their mathematics seemed to value computational power above all.

  That could not be appreciated until computational power began to mean something. By the time modern mathematicians turned their attention to Babylon, many important tablets had already been destroyed or scattered. Fragments retrieved from Uruk before 1914, for example, were dispersed to Berlin, Paris, and Chicago and only fifty years later were discovered to hold the beginning methods of astronomy. To demonstrate this, Otto Neugebauer, the leading twentieth-century historian of ancient mathematics, had to reassemble tablets whose fragments had made their way to opposite sides of the Atlantic Ocean. In 1949, when the number of cuneiform tablets housed in museums reached (at his rough guess) a half million, Neugebauer lamented, “Our task can therefore properly be compared with restoring the history of mathematics from a few torn pages which have accidentally survived the destruction of a great library.”♦

  In 1972, Donald Knuth, an early computer scientist at Stanford, looked at the remains of an Old Babylonian tablet the size of a paperback book, half lying in the British Museum in London, one-fourth in the Staatliche Museen in Berlin, and the rest missing, and saw what he could only describe, anachronistically, as an algorithm:

  A cistern.

  The height is 3,20, and a volume of 27,46,40 has been excavated.

  The length exceeds the width by 50.

  You should take the reciprocal of the height, 3,20, obtaining 18.

  Multiply this by the volume, 27,46,40, obtaining 8,20.

  Take half of 50 and square it, obtaining 10,25.

  Add 8,20, and you get 8,30,25.

  The square root is 2,55.

  Make two copies of this, adding to the one and subtracting from the other.

  You find that 3,20 is the length and 2,30 is the width.

  This is the procedure.♦

  “This is the procedure” was a standard closing, like a benediction, and for Knuth redolent with meaning. In the Louvre he found a “procedure” that reminded him of a stack program on a Burroughs B5500. “We can commend the Babylonians for developing a nice way to explain an algorithm by example as the algorithm itself was being defined,” said Knuth. By then he himself was engrossed in the project of defining and explaining the algorithm; he was amazed by what he found on the ancient tablets. The scribes wrote instructions for placing numbers in certain locations—for making “copies” of a number, and for keeping a number “in your head.” This idea, of abstract quantities occupying abstract places, would not come back to life till much later.

  Where is a symbol? What is a symbol? Even to ask such questions required a self-consciousness that did not come naturally. Once asked, the questions continued to loom. Look at these signs, philosophers implored. What are they?

  “Fundamentally letters are shapes indicating voices,”♦ explained John of Salisbury in medieval England. “Hence they represent things which they bring to mind through the windows of the eyes.” John served as secretary and scribe to the Archbishop of Canterbury in the twelfth century. He served the cause of Aristotle as an advocate and salesman. His Metalogicon not only set forth the principles of Aristotelian logic but urged his contemporaries to convert, as though to a new religion. (He did not mince words: “Let him who is not come to logic be plagued with continuous and everlasting filth.”) Putting pen to parchment in this time of barest literacy, he tried to examine the act of writing and the effect of words: “Frequently they speak voicelessly the utterances of the absent.” The idea of writing was still entangled with the idea of speaking. The mixing of the visual and the auditory continued to create puzzles, and so also did the mixing of past and future: utterances of the absent. Writing leapt across these levels.

  Every user of this technology was a novice. Those composing formal legal documents, such as charters and deeds, often felt the need to express their sensation of speaking to an invisible audience: “Oh! all ye who shall have heard this and have seen!”♦ (They found it awkward to keep tenses straight, like voicemail novices leaving their first messages circa 1980.) Many charters ended with the word “Goodbye.” Before writing could feel natural in itself—could become second nature—these echoes of voices had to fade away. Writing in and of itself had to reshape human consciousness.

  Among the many abilities gained by the written culture, not the least was the power of looking inward upon itself. Writers loved to discuss writing, far more than bards ever bothered to discuss speech. They could see the medium and its messages, hold them up to the mind’s eye for study and analysis. And they could criticize it—for from the very start, the new abilities were accompanied by a nagging sense of loss. It was a form of nostalgia. Plato felt it:

  I cannot help feeling, Phaedrus, [says Socrates] that writing is unfortunately like painting; for the creations of the painter have the attitude of life, and yet if you ask them a question they preserve a solemn silence.… You would imagine that they had intelligence, but if you want to know anything and put a question to one of them, the speaker always gives one unvarying answer.♦

  Unfortunately the written word stands still. It is stable and immobile. Plato’s qualms were mostly set aside in the succeeding millennia, as the culture
of literacy developed its many gifts: history and the law; the sciences and philosophy; the reflective explication of art and literature itself. None of that could have emerged from pure orality. Great poetry could and did, but it was expensive and rare. To make the epics of Homer, to let them be heard, to sustain them across the years and the miles required a considerable share of the available cultural energy.