Zero - Charles Seife [37]
To Descartes, zero was also implicit in God’s domain, as was the infinite. Since the old Aristotelian doctrine was crumbling, Descartes, true to his Jesuit training, tried to use nought and infinity to replace the old proof of God’s existence.
Like the ancients, Descartes assumed that nothing, not even knowledge, can be created out of nothing, which means that all ideas—all philosophies, all notions, all future discoveries—already exist in people’s 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 being—God—must 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.
However, though zero appeared and reappeared throughout Descartes’s philosophy, Descartes insisted unto his death that the void—the ultimate zero—does not exist. 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.
Figure 21: A parabola, a circle, and an elliptic curve
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.” Yet, like the medieval scholars before him, Descartes believed that nothing truly moved in a straight line, for that would leave a vacuum behind it. Instead, everything in the universe moved in a circular path. It was a truly Aristotelian way of thinking—yet the void would soon unseat Aristotle once and for all.
Even today, children are taught “Nature abhors a vacuum,” while the teachers don’t really understand where that phrase came from. It was an extension of the Aristotelian philosophy: vacuums don’t exist. If someone would attempt to create a vacuum, nature would do anything in its power to prevent it from happening. It was Galileo’s secretary, Evangelista Torricelli, who proved that this wasn’t true—by creating the first vacuum.
In Italy workmen used a kind of pump, which worked more or less like a giant syringe, to raise water out of wells and canals. This pump had a piston that fitted snugly in a tube. The bottom of the tube was placed in the water, so when the piston was raised, the water level followed the plunger upward.
Galileo heard from a worker that these pumps had a problem: they could only lift water about 33 feet. After that, the plunger kept on going upward, yet the water level stayed the same. It was a curious phenomenon, and Galileo passed the problem on to his assistant, Torricelli, who started doing experiments, trying to figure out the reason for the pumps’ curious limitation. In 1643, Torricelli took a long tube that was closed at one end and filled it with mercury. He upended it, placing the open end in a dish also filled with mercury. Now, if Torricelli had upended the tube in air, everyone would expect the mercury to run out, because it would quickly be replaced by air; no vacuum would be created. But when it was upended in a dish of mercury, there was no air to replace the mercury in the tube. If nature truly abhorred a vacuum so much, the mercury in the tube would have to stay put so as not to create