Zero: The Biography of a Dangerous Idea: Chapters 3–4

In Europe, zero was an outcast, but in India and later in the Arab lands, it flourished.

While Hinduism retained its popular rituals and devotion to its pantheon, at its core Hinduism became monotheistic and introspective. All the gods became aspects of an all- encompassing god, Brahma.

At about the same time that the Greeks were rising in the Western world, Hinduism was becoming less like the Western myths; the individual gods became less distinct and the religion became more and more mystical. The mysticism was patently Eastern.

Like many Eastern religions, Hinduism was steeped in the symbolism of duality. (Of course, this idea occasionally came up in the Western world, where it was promptly branded as heretical. One example is the Manichaean heresy, which saw the world as being under the influence of equal and opposite sources of good and evil.)

But once you are able to separate yourself from the whims of the flesh and embrace the silence and nothingness of your soul, you will be liberated. Your Atman will fly from the web of human desire and join the collective consciousness—the infinite soul that suffuses the universe, at once everywhere and nowhere at the same time. It is infinity, and it is nothing.

You can’t remove a three-acre swath from a two-acre field, but nothing prevents you from subtracting three from two.

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."

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."

Zero’s rise to preeminence had to begin in the East.

Al-Khowarizmi wrote several important books, like Al-jabr 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.

Nothingness is being and being nothingness....Our limited mind can not grasp or fathom this, for it joins infinity.

As Islam spread, zero diffused throughout the Muslim-controlled world, everywhere conflicting with Aristotle’s doctrine.

This is what drove Maimonides, the twelfth-century rabbi, to write a tome to reconcile the Semitic, Eastern Bible with the Greek, Western philosophy that permeated Europe.

Reproducing the Greek arguments faithfully, Maimonides contended that the hollow spheres that twirled about the earth had to be moved by something, say, the next sphere out.

Maimonides stated that the act of creation came from nothing. It was creatio ex nihilo, despite the Aristotelian ban on the vacuum. With that stroke the void moved from sacrilege to holiness.

For instance, Genesis 49:10 states, “The scepter shall not depart from Judah...until Shiloh come.” The Hebrew phrase for “until Shiloh come" has a value of 358, exactly the same for the Hebrew word meshiach, messiah. Hence, the passage presages the coming of the Messiah.

Certain numbers were holy or evil, according to the kabbalists—and they looked through the Bible for these numbers and for hidden messages found by scanning through it in various ways. A recent bestseller, The Bible Code, purported to find prophecies by this method.

The Hebrew term ein sof, which meant “infinite,” represented the creator aspect of God, the part of the deity that made the universe and that permeates every corner of the cosmos.

The church would cling to Aristotle for a few more centuries, but the fall of Aristotle and the rise of the void and the infinite were clearly beginning. It was a propitious time for zero to arrive in the West.

Though this sequence is the source of Fibonacci’s fame, Fibonacci’s Liber Abaci had a much more important purpose than animal husbandry.

In 1299, Florence banned Arabic numerals. The ostensible reason was that the numbers were easily changed and falsified. (A 0 could be turned into a 6 with a simple flourish of a pen, for instance.)

The Aristotelian wall was crumbling, thanks to the influence of the Muslims and the Hindus, and by the 1400s even the staunchest European supporters of Aristotelianism had their doubts.

At first the papacy was blind to the danger. High-ranking clergymen experimented with the dangerous ideas of the void and the infinite, even though the ideas struck at the core of the ancient Greek philosophy that the church cherished so much.

Squashed along its length, the line becomes a point, an infinitesimal nothing with no length, no width, and no height.

This is a singularity, a concept that became very important later in the history of science—but at this early stage, mathematicians knew little more than the artists about the properties of zero.

To account for the planets’ bizarre behavior, Ptolemy added epicycles to his planetary clockwork: little circles within circles could explain the backward, or retrograde, motion of the planets.

Copernicus published his magnum opus on his deathbed—in 1543, just before the church started clamping down on new ideas.

Luther’s constipation was legendary. Some scholars believe that his great revelation about faith came to him when he was sitting on the privy. “Luther's release from the constricting bondage of fear corresponded to the release of his bowels,” notes one text, commenting on this theory.

By the 1530s, in a quest to ensure an orderly succession to the throne, Henry VIII had spurned the authority of the pope, declaring himself the head of the English clergy.

The Catholic Church had to strike back. Though it had been experimenting with other philosophies for several centuries, when threatened with schism it turned orthodox once again.

It fell back upon its orthodox teachings—the Aristotelian-based philosophies of scholars like Saint Augustine and Boethius, as well as Aristotle’s proof of God.

No longer could cardinals and clerics question the ancient doctrines.

Zero was at the center of the coordinate system, and zero was implicit in each geometric shape.

A child of the Counter-Reformation, Descartes learned about Aristotle at the very moment when the church was relying upon his principles the most. As a result, Descartes, indoctrinated with the Aristotelian philosophy, denied the existence of the vacuum.

It was a difficult position to take; Descartes was certainly mindful of the metaphysical problems of rejecting the vacuum entirely. Later in his life he wrote about atoms and the vacuum: “About these things that involve a contradiction, it can absolutely be said that they cannot happen. However, one shouldn't deny that they can be done by God, namely, if he were to change the laws of nature."

He was cared for by a group of Jansenists, Catholics who belonged to a sect based largely on a hatred of the Jesuit order.

Bishop Jansen, the founder of the sect, had declared that science was sinful; curiosity about the natural world was akin to lust. Luckily, Pascal’s lust was greater than his religious fervor for a time, because he would use science to unravel the secret of the vacuum.

But Pascal’s simple experiment demolished Aristotle’s assertion that nature abhors a vacuum. Pascal wrote, “But until now one could find no one who took this...view, that nature has no repugnance for the vacuum, that it makes no effort to avoid it, and that it admits vacuum without difficulty and without resistance.’’

It was also in zero and the infinite that Pascal, the devout Jansenist, sought to prove God’s existence. He did it in a very profane way.

Even when it came to arguing about God’s existence, he kept coming back to those crass gambling Frenchmen. Pascal argued that it was best to believe in God, because it was a good bet.