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It is no coincidence that zero and infinity are linked in the vanishing point. Just as multiplying by zero causes the number line to collapse into a point, the vanishing point has caused most of the universe to sit in a tiny dot. This is a singularity, a concept that became very important
but at this early stage, mathematicians knew little more than the artists about the properties of zero. In fact, in the fifteenth century, artists were amateur mathematicians.
Nicholas of Cusa and Nicolaus Copernicus cracked open the nutshell universe of Aristotle and Ptolemy.
No longer was the earth comfortably ensconced in the center of the universe; there was no shell containing the cosmos.
The universe went on into infinity, dotted with innumerable worlds, each inhabited by mysterious creatures. But how could Rome claim to be the seat of the one true Church if its a...
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The attack on the church began in earnest in 1517,
Copernicus’s De Revolutionibus was placed on the Index of forbidden books. An attack on Aristotle was considered an attack upon the church.
The Aristotelian system could not be trusted, and at the same time it could not be rejected. What, then, could be taken for granted? Literally nothing.
I am in a sense something intermediate between God and nought.
—RENÉ DESCARTES, DISCOURSE ON METHOD
the Catholic Church tried to reject zero and the void more strongly than ever, yet zero had already taken root.
Even the most devout intellectuals—the Jesuits—were torn between the old, Aristotelian ways and the new philosophies that included zero and the void, infinity and the infinite.
René Descartes was trained as a Jesuit, and he, too, was torn between the old and the new. He rejected the void but p...
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Descartes would bring zero to the center of the number line, and he would seek a proof of God i...
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Yet Descartes could not reject Aristotle entirely; he was so afraid of the void that...
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Descartes was a mathematician-philosopher; perhaps his most lasting legacy was a mathematical invention—what we...
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symbol (4, 2) represents a point four units to the right and two units upward.
The Origin. Zero
The origin, the point (0, 0), is the foundation of the Cartesian system of coordinates. (Descartes’s notation was slightly different from what we use today.
Descartes quickly realized how powerful his coordinate system was. He used it to turn figures and shapes into equations and numbers;
geometric object—squares, triangles, wavy lines—could be represented by an equation,
a mathematical rela...
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a circle at the origin can be represented by the set of all points where x2 + y2 – 1=0. A parabola might be y – x2=0. Des...
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Zero was at the center of the coordinate system, and zero was implicit in each geometric shape.
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.
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.
“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.”
Descartes believed that nothing truly moved in a straight line, for that would leave a vacuum behind it. Instead, everything in t...
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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.
It’s still the same: infinite, and the value of being an atheist is still negative infinity. It’s still much better to be a Christian. If the probability is 1/10,000 or 1/1,000,000 or one in a gazillion, it comes out the same. The only exception is zero.
The expected value of being a Christian would then be 0 × ∞, and that was gibberish.
Nobody was willing to say that there was zero chance that God exists.
No matter what your outlook, it is always better to believe in God, thanks to the ma...
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Zero and infinity had destroyed the Arisotelian philosophy; the void and the infinite cosmos had eliminated the nutshell universe and the idea of nature’s abhorrence of the vacuum.
Deep within the scientific world’s powerful new tool—calculus—was a paradox.
Zeno’s curse hung over mathematics for two millennia.
Infinity lurked in Zeno’s simple riddle.
Adding infinite things to each other can yield bizarre and contradictory results.
Luckily the physical world made a little more sense than the mathematical one. Adding infinite things to each other seems to work out most of the time,
