Zero - Charles Seife [21]
The myriad was the biggest grouping in the Greek number system, and by counting myriads the Greeks could denote numbers up to a myriad myriads (100,000,000) and a little further. But Archimedes got beyond this limitation by hitting the reset button. He simply started over at a myriad myriads, setting 100,000,000 equal to one, and counting again, calling these new numbers, numbers of the second order. (Archimedes did not set 100,000,001 equal to one and 100,000,000 equal to zero, which is what a modern mathematician would do. It had never occurred to Archimedes that starting over with zero would make more sense.) The numbers of the second order went from one myriad myriads to a myriad myriad myriad myriads. The numbers of the third order went to one myriad myriad myriad myriad myriad myriads (1,000,000,000,000,000,000,000,000), and so forth, until he reached the numbers of the myriad myriadth order, which he called the numbers of the first period. It was a cumbersome way of doing business, but it got the job done and went far beyond what Archimedes needed to solve his thought experiment. Yet as big as those numbers were, they were finite—and were more than enough to fill the universe to overflowing with sand. The infinite was not needed in the Greek universe.
Perhaps, given more time, Archimedes might have begun to see the lure of the infinite and of zero. But the sand reckoner was destined to meet his fate while reckoning in the sand. The Romans were too powerful for the Syracusans. Taking advantage of a poorly manned watchtower and an easy-to-climb wall, the Romans managed to get some soldiers inside the city. As soon as they realized that Romans were inside the walls of the city, the Syracusans, wild with fear, could not mount a defense. The Romans poured through the city, but Archimedes was deaf to the panic around him. He sat on the ground, drawing circles in the sand, trying to prove a theorem. A Roman soldier saw the bedraggled 75-year-old and demanded that Archimedes follow him. Archimedes refused, since his mathematical proof was not yet finished. The enraged soldier cut him down. Thus died the greatest mind in the ancient world, slaughtered needlessly by the Romans.
Killing Archimedes was one of the biggest Roman contributions to mathematics. The Roman era lasted for about seven centuries. In all that time there were no significant mathematical developments. History marched on: Christianity swept through Europe, the Roman Empire fell, the Library at Alexandria burned, and the Dark Ages began. It would be another seven centuries before zero reappeared in the West. In the meantime two monks created a calendar without zero, damning us to eternal confusion.
Blind Dates
It is a silly, childish discussion and only exposes the want of brains of those who maintain a contrary opinion to that we have stated.
—THE TIMES (LONDON), DECEMBER 26, 1799
This “silly, childish discussion”—whether the new century begins on the year 00 or the year 01—appears and reappears like clockwork every hundred years. If medieval monks had only known of zero, our calendar would not be in such a muddle.
The monks can’t be faulted for their ignorance. Indeed, during the Middle Ages the only Westerners who studied math were the Christian monks. They were the only learned ones left. Monks needed math for two things: prayer and money. To count money, they needed to know how to…well…count. To do this, they used an abacus or a counting board, a device similar to an abacus, where stones or other counters get moved around on a table. It was not a very demanding task, but by ancient standards it was the state of the art. To pray, monks needed to know the time and the date. As a result, timekeeping was vital to the monks’ rituals.