Zero - Charles Seife [28]
Just as 2 – 3 was now a number, so was 2 – 2. It was zero. Not just a mere placeholder zero that represents an empty space on the abacus, but zero the number. It had a specific value, a fixed place on the number line. Since zero was equal to 2 – 2, then it had to be placed between one (2 – 1) and negative one (2 – 3). Nothing else made sense. No longer could zero sit to the right of nine, just as it does on the top of the computer keyboard; zero had a position in the number line that was all its own. A number line without zero could no more exist than a number system without two. Zero had finally arrived.
However, even the Indians thought that zero was a pretty bizarre number, for all the usual reasons. After all, zero multiplied by anything is zero; it sucks everything into itself. And when you divide with it, all hell breaks loose. Brahmagupta tried to figure out what 0 ÷ 0 and 1 ÷ 0 were, and failed. “Cipher divided by cipher is naught,” he wrote. “Positive or negative divided by cipher is a fraction with that for a denominator.” In other words, he thought 0 ÷ 0 was 0 (he was wrong, as we will see), and he thought that 1 ÷ 0 was, well, we don’t really know, because he doesn’t make a whole lot of sense. Basically, he was waving his hands and hoping that the problem would go away.
Brahmagupta’s mistake did not last for very long. In time the Indians realized that 1 ÷ 0 was infinite. “This fraction of which the denominator is a cipher, is termed an infinite quantity,” writes Bhaskara, a twelfth-century Indian mathematician, who tells of what happens when you add a number to 1 ÷ 0. “There is no alteration, though many be inserted or extracted; as no change takes place in the infinite and immutable God.”
God was found in infinity—and in zero.
The Arab Numeral
Does man forget that We created him out of the void?
—THE KORAN
By the seventh century, the West had withered with the fall of Rome, but the East was flourishing. India’s growth was eclipsed by another Eastern civilization. As the star of the West sank below the horizon, another star was rising: Islam. Islam would take zero from India—and the West would eventually take it from Islam. Zero’s rise to preeminence had to begin in the East.
One evening in 610 AD, Mohammed, a thirty-year-old native of Mecca, fell into a trance on Mount Hira. According to legend, the angel Gabriel told him, “Recite!” Mohammed did, and his divine revelations started a wildfire. A decade after Mohammed’s death in 632, his followers had captured Egypt, Syria, Mesopotamia, and Persia. Jerusalem, the holy city of the Jews and the Christians, had fallen. By 700, Islam stretched as far as the Indus River in the East and Algiers in the West. In 711 the Muslims captured Spain, and they advanced as far as France. In the East they defeated the Chinese in 751. Their empire stretched farther than even Alexander could have imagined. Along the way to China, the Muslims conquered India. And there the Arabs learned about Indian numerals.
The Muslims were quick to absorb the wisdom of the peoples that they conquered. Scholars started translating texts into Arabic, and in the ninth century Caliph al-Mamun founded a great library: the House of Wisdom at Baghdad. It was to become the center of learning in the Eastern world—and one of its first scholars was the mathematician Mohammed ibn-Musa al-Khowarizmi.
Al-Khowarizmi wrote several important books, like Aljabr wa’l muqabala, a treatise on how to solve elementary equations; the Al-jabr in the title (which means something like “completion”) gave us the term algebra. He also wrote a book about the Hindu numeral system, which allowed the new style of numbers to spread quickly through the Arab world—along with algorithms, the tricks for multiplying and dividing Hindu numerals quickly. In fact, the word algorithm was a corruption of al-Khowarizmi