By John Mattingly
Cherishing Ed Quillen’s aversion to sentimentality, I will note that the human tendency to attribute special significance to years with zeros has a long and rich history.
Zero is very special. Yet it had to take a tortuous, and tortured, path on its way to being the real champion of our number system.
The Church fought the notion of zero, because for zero to exist, it meant that nothing, as nothing, could exist; in prior centuries this directly conflicted with dominant notions of the biblically directed universe in which the only entity capable of understanding, having or working with zero was god himself. Only god could create something from nothing. Creation ex nihlo.
“In the beginning was the ratio, and the ratio was with god, and the ratio was god.” John 1:1
This was true of the ideo-hermeneutical positions taken by both the Catholic and Protestant churches. At that time, The Church was the sole patron of such aristocratic hobbies as pure mathematics. the Church stated that god was infinite, therefore nothing, aka zero, could not exist except as a facet of an infinite god. Once again, The Church stood in the way of human progress.
Without zero, every number in the system had to have a unique character. It doesn’t take long – say, around 100 – before the system gets unwieldy, and long before you get to a million, complex operations are impossible. The genius of zero is that, with it, we need only ten numeric characters to create infinite numbers.
It was, therefore, the irresistible economy of calculation that eventually overcame the resistance from the Church, even though several mathematicians were flogged or hung along the way as heretics for using and advocating for zero.
Zero finally emerged with standing in Western Europe as recently as the sixteenth century, and became an integral integer with special powers and special rules of conduct. Anything multiplied by zero must be zero, even though this is slightly counterintuitive. Why isn’t any integer multiplied by zero simply that integer? If I have an apple and multiply it by no apples, I still have an apple. The action of multiplying by nothing does not somehow consume the apple.
As the great Polish mathematician Waclaw Sierpinski famously said to his wife, “I’ve lost a piece of luggage.” “No dear,” said his wife Boubolini, “All five pieces are here.” “That can’t be true!” cried Waclaw, “I counted them several times: zero, one, two, three, four!”
The Church began to embrace zero when it learned that the special rules of zero could be used in settling the estates of donors to get a larger share of that estate. By simply adding a couple of zeros to a sum, which was basically nothing, the Church found its beneficiaries bequeathing significantly greater sums. One gold piece could become a hundred by the addition of a pair of nothings.
For philosophers in Western Europe, zero became a crucial reference point for all of reality.
“What is man in nature? Nothing in relation to the infinite but everything in relation to nothing, a mean between nothing and everything.” Pascal from Pensees.
“We are but amphibians between being and non-being.” Leibniz.
Rene Descartes (“I think therefore I am”) said, “I am, in a sense, something intermediate between god and nought.”
Jean-Paul Sartre came along later and said, “Nothingness is being, and being nothingness.”
Physicists claim that a vacuum is much more lively than one would think. It is the vacuum upon which all good experiments are performed.
“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 are scarcely in your thoughts advanced to the stage of pure science.” William Thompson, Lord Kelvin, who derived the physical concept of Absolute Zero (the lowest temperature possible).
The other route zero followed to prominence was by association with its close relative: infinity.
“When, after a thousand years of stupor, European thought shook off the effect of the sleeping powders so skillfully administered by the Christian Fathers, the problem of infinity was one of the first to be revived.” Thomas Danzig.
Zero and infinity are essentially the same, and nothingness is as incomprehensible as infinity. It’s a giant mathematical circle which starts and ends in the same incomprehensible, but eminently practical, point: ZERO.
There is, perhaps, real significance expressed in our affection for those years that end in zero …
John Mattingly cultivates prose, among other things, and was most recently seen near Creede.
