Free Zero by Charles Seife Page A

zero seconds past midnight; the second hour starts at 1 AM , and the third hour starts at 2 AM . Though we count with the ordinals (first, second, third), we mark time with the cardinals (0, 1, 2). All of us have assimilated this way of thinking, whether we appreciate it or not. After a baby finishes his 12th month, we all say that the child is one year old; he has finished his first 12 months of life. If the baby turns one when she’s already lived a year, isn’t the only consistent choice to say that the baby is zero years old before that time? Of course, we say that the child is six weeks old or nine months old instead—a clever way of getting around the fact that the baby is zero.
    Dionysius didn’t have a zero, so he started the calendar with year 1, just as the ancients before him had started theirs. People of those times thought in terms of the old-style equivalence of cardinality and ordinality. That was just fine…for them. If zero never entered their minds, it could hardly be a problem.
    The Gaping Void
    It was not absolute nothingness. It was a kind of formlessness without any definition…. True reasoning convinced me that I should wholly subtract all remnants of every kind of form if I wished to conceive the absolutely formless. I could not achieve this.
    â€”S AINT A UGUSTINE , C ONFESSIONS
    It’s hard to blame the monks for their ignorance. The world of Dionysius Exiguus, Boethius, and Bede was dark indeed. Rome had collapsed, and Western civilization seemed but a shadow of Rome’s past glory. The future seemed more horrid than the past. It is no wonder that in the search for wisdom medieval scholars didn’t look to their peers for ideas. Instead, they turned to the ancients like Aristotle and the Neoplatonists. As these medieval thinkers imported the philosophy and science of the ancients, they inherited the ancient prejudices: a fear of the infinite and a horror of the void.
    Medieval scholars branded void as evil—and evil as void. Satan was quite literally nothing. Boethius made the argument as follows: God is omnipotent. There is nothing God cannot do. But God, the ultimate goodness, cannot do evil. Therefore evil is nothing. It made perfect sense to the medieval mind.
    Lurking underneath the veil of medieval philosophy, however, was a conflict. The Aristotelian system was Greek, but the Judeo-Christian story of creation was Semitic—and Semites didn’t have such a fear of the void. The very act of creation was out of a chaotic void, and theologians like Saint Augustine, who lived in the fourth century, tried to explain it away by referring to the state before creation as “a nothing something” that is empty of form but yet “falls short of utter nothingness.” The fear of the void was so great that Christian scholars tried to fix the Bible to match Aristotle rather than vice versa.
    Luckily, not all civilizations were so afraid of zero.

Chapter 3
Nothing Ventured
    [ ZERO GOES EAST ]
    Where there is the Infinite there is joy. There is no joy in the finite.
    â€”T HE C HANDOGYA U PANISHAD
    T hough the West was afraid of the void, the East welcomed it. In Europe, zero was an outcast, but in India and later in the Arab lands, it flourished.
    When we last saw zero, it was simply a placeholder. It was a blank spot in the Babylonian system of numeration. Zero was useful but was not truly a number on its own—it had no value. It only took its meaning from the digits to its left; the symbol for zero literally meant nothing if it was by itself. In India, all this changed.
    In the fourth century BC , Alexander the Great marched with his Persian troops from Babylon to India. It was through this invasion that Indian mathematicians first learned about the Babylonian system of numbers—and about zero. When Alexander died in 323 BC , his squabbling generals split his empire into pieces. Rome rose to power in the second century BC and swallowed up