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Zero is powerful because it is infinitys twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The atomists embraced the concept of the infinite vacuuminfinity and zero wrapped into one. This is the prime mover: God. When Christianity swept through the West, it became closely tied to the Aristotelian view of the universe and the proof of Gods existence. Atomism became associated with atheism. Questioning the Aristotelian doctrine was tantamount to questioning Gods existence. Aristotles system was extremely successful. His most famous student, Alexander the Great, spread the doctrine as far east as India before Alexanders untimely death in 323 BC. The Aristotelian system would outlast Alexanders empire; it would survive until Elizabethan times, the sixteenth century. With this long-standing acceptance of Aristotle came a rejection of the infiniteand the void, for Aristotles denial of the infinite required a denial of the void, because the void implies the existence of the infinite. In both cases the existence of the void implies the existence of the infinite. Void/zero destroys Aristotles neat argument, his refutation of Zeno, and his proof of God. So as Aristotles arguments were accepted, the Greeks were forced to reject zero, void, the infinite, and infinity. Eventually, one ancient Greek surpassed Zeno in matters of the infinite: Archimedes, the eccentric mathematician of Syracuse. He was the only thinker of his day to glimpse the infinite. Calculating the date of Easter was no mean feat, thanks to a clash of calendars. The seat of the church was Rome, and Christians used the Roman solar calendar that was 365 days (and change) long. But Jesus was a Jew, and he used the Jewish lunar calendar that was only 354 days (and change) long. Calculating the date of Easter was no mean feat, thanks to a clash of calendars. The seat of the church was Rome, and Christians used the Roman solar calendar that was 365 days (and change) long. But Jesus was a Jew, and he used the Jewish lunar calendar that was only 354 days (and change) long. The big events in Jesus life were marked with reference to the moon, while everyday life was ruled by the sun. The two calendars drifted with respect to each other, making it very difficult to predict when a holiday was due. Medieval scholars branded void as eviland 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. The goal of the Hindu is to free the Atman entirely from the cycle of rebirth, to stop wandering from death to death. The way to achieve the ultimate liberation through lifelessness is to cease paying heed to the illusion of reality. The body, the house of the spirit, is under the power of pleasure and pain, explains a god. And if a man is ruled by his body then this man can never be free. 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 consciousnessthe infinite soul that suffuses the universe, at once everywhere and nowhere at the same time. It is infinity, and it is nothing. So India, as a society that actively explored the void and the infinite, accepted zero. By the seventh century, the West had withered with the fall of Rome, but the East was flourishing. Indias 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 Indiaand the West would eventually take it from Islam. Zeros rise to preeminence had to begin in the East. The very word zero smacks of its Hindu and Arabic roots. When the Arabs adopted Hindu-Arabic numerals, they also adopted zero. The Indian name for zero was sunya, meaning empty, which the Arabs turned into sifr. When some Western scholars described the new number to their colleagues, they turned sifr into a Latin-sounding word, yielding zephirus, which is the root of our word zero. Other Western mathematicians didnt change the word so heavily and called zero cifra, which became cipher. Zero was so important to the new set of numbers that people started calling all numbers ciphers, which gave the French their term chiffre, digit. Al-Khowarizmi wrote several important books, like Aljabr wal 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 worldalong with algorithms, the tricks for multiplying and dividing Hindu numerals quickly. In fact, the word algorithm was a corruption of al-Khowarizmis name. Though the Arabs took the notation from India, the rest of the world would dub the new system Arabic numerals. He noted that instead of accepting Aristotles proof of God, the Muslim scholars turned to the atomists, Aristotles old rivals, whose doctrine, though out of favor, managed to survive the ravages of time. The atomists, remember, held that matter was composed of individual particles called atoms, and if these particles were able to move about, there had to be a vacuum between them, otherwise the atoms would be bumping into one another, unable to get out of one anothers way. The Muslims seized upon the atomists ideas; after all, now that zero was around, the void was again a respectable idea. Aristotle hated the void; the atomists required it. The Bible told of the creation from the void, while the Greek doctrine rejected the possibility. The Christians, cowed by the power of Greek philosophy, chose Aristotle over their Bible. The Muslims, on the other hand, made the opposite choice. Zero and the infinite were at the very center of the philosophical war taking place during the sixteenth and seventeenth centuries. The void had weakened Aristotles philosophy, and the idea of an infinitely large cosmos helped shatter the nutshell universe. The earth could not be at the center of Gods creation. As the papacy lost its hold on its flock, the Catholic Church tried to reject zero and the void more strongly than ever, yet zero had already taken root. Even the most devout intellectualsthe Jesuitswere torn between the old, Aristotelian ways and the new philosophies that included zero and the void, infinity and the infinite. Like the ancients, Descartes assumed that nothing, not even knowledge, can be created out of nothing, which means that all ideasall philosophies, all notions, all future discoveriesalready exist in peoples brains when they are born. Learning is just the process of uncovering that previously imprinted code of laws about the workings of the universe. Since we have a concept of an infinite perfect being in our minds, Descartes then argued that this infinite and perfect beingGodmust exist. All other beings are less than divine; they are finite. They all lie somewhere between God and nought. They are a combination of infinity and zero. What is man in nature? Nothing in relation to the infinite, everything in relation to nothing, a mean between nothing and everything. BLAISE PASCAL, PENSÉES The tangent problem and the area problem both ran afoul of the same difficulties with infinities and zeros. Its no wonder, because the tangent problem and the area problem are actually the same thing. They are both aspects of calculus, a scientific tool far more powerful than anything ever seen before. Differential equations are not like the everyday equations that we are all familiar with. An everyday equation is like a machine; you feed numbers into the machine and out pops another number. A differential equation is also like a machine, but this time you feed equations into the machine and out pop new equations. Plug in an equation that describes the conditions of the problem (is the ball moving at a constant rate, or is a force acting on the ball?) and out pops the equation that encodes the answer that you seek (the ball moves in a straight line or in a parabola). All polynomials of degree nthose that have a leading term of xnsplit into n distinct terms. This is the fundamental theorem of algebra. Then Kepler imagined that the second focus was infinitely far away: the second focus was a point at infinity. All of a sudden the ellipse becomes a parabola, and all of the lines that converged to a point become parallel lines. A parabola is simply an ellipse with one focus at infinity Zero and infinity are eternally locked in a struggle to engulf all the numbers. Like a Manichaean nightmare, the two sit on opposite poles of the number sphere, sucking numbers in like tiny black holes. When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science. WILLIAM THOMSON, LORD KELVIN Absolute zero was a discovery that had a very different flavor from Newtons laws. Newtons equations gave physicists power. They could predict the orbits of the planets and the motion of objects with great accuracy. On the other hand, Kelvins discovery of absolute zero told physicists what they couldnt do. They couldnt ever reach absolute zero. This barrier was disappointing news to the physics world, but it was the beginning of a new branch of physics: thermodynamics. During most of its life, a star is in an uneasy equilibrium: the propensity to collapse under its own gravity is balanced by the energy that comes from the fusing hydrogen in its center. For the foreseeable future, banishing zero from the universe with string theory is a philosophical idea rather than a scientific one. String theory might well be correct, but we may never have the means to find out. Zero has not yet been banished; indeed, zero seems to be what created the cosmos.