The God of Mathematics
The God of Mathematics
In the small hours of morning, when sleep has fled and the strange noises of night crowd young imaginations, numbers can be magical. I do not mean math proper, not yet; I mean the solidity and reality of counting. We counted sheep, we counted our toes and small fingers, our elbows and knees—strange preparation for the infinite, uncountable stars that awaited in the velvet dark. I remember feeling small, but with my back against grass and the warm earth under me, I don’t ever remember feeling lost. The world as I knew it had concrete foundations. I believed it immovable and unshakable. And for many centuries, most of humankind held a similar view. Aristotle claimed as much in 355 B.C.E.[CE1] : “In the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts.”[i] Aristotle’s universe had no creator; it preexisted all things: an I HAVE BEEN rather than the great I AM. But Aristotelian ideas would be used by Christian Medieval and Renaissance astronomers to build complex mathematical systems for understanding the cosmos as a purpose-built machine. This universal clockwork—the mathematics, even the numbers—they claimed, proved the presence of an intelligent creator. They were unlikely heroes of “new philosophy” on their quest to find order in the numbers, and a divine God within the Machine.
French technology theorist Paul Virilio, known for his work on engineering accidents, reminds us that all technology invents its own destruction. “When they invented the railroad, what did they invent?” he asks: “An object that allowed you to go fast, which allowed you to progress—a vision a la Jules Verne [. . .] But at the same time they invented the railway catastrophe.” Taking this as the end position, and the history of mechanics, order, and power as the starting line, I wrote a book about our need for control and our capacity for chaos. It’s called Clockwork Futures. I’ve mentioned it before, a book that strikes a balance between the two impulses in a series of paired chapters:
Part One: CHAOS | order
1 | The God of Mathematics
2 | Clockwork Boy and the Mother Machine
Part Two: DARKNESS | light
3 | Catching Lightning in a Bottle
4 | Into Dark Country
Part Three: PRIVATION | Industry
5 | The Scientist and the Engineer
6 | He Who Powers the Future
Part Four: ANARCHY | Control
7 | A Wrench in the Age of Machinery
8 | Of Acid and Accident
It ends with a fifth part, about death and immortatlity, and all the while writing, I felt there was yet more beneath the surface. It’s like a basilisk’s egg; contained within are desire and dread. Humans fear and want a lot of the same things, somehow; it’s led to scientific breakthrough but also climate crisis, medical miracles but also holocausts. Here is an excerpt from my first chapter of that book. It’s the closest I’ve come to articulating the dread-tech of mankind, and still doesn’t really capture it’s essence. Possibly, it takes fiction to do that.
In the book’s introduction, I suggested that the earth was old and technology new. David Wootton, a historian used to taking the long view, explains that tool-making humans have been around for about 2 million years, with Homo sapiens (our own particular brand of human) arriving about 200,000 years ago, pottery 25,000 years ago, and agriculture between 12,000 and 7,000 years ago.[ii] George Shattuck Morison described these “ages” of men, too, from his lecture of 1896. He calls them the “three periods of savagery, followed by three periods of barbarism,” with the taming of fire as the initial precondition—fire led man from the first to the second stage, the weapon from the second to the third, and so on until we arrive at written language and “civilization.”[iii] Despite our long history, written records have existed for only about 6,500 years, and modern technological and scientific innovations of the sort we’re talking about occupy only the last 400.[iv] Four hundred years: just less than twice the age of the United States Declaration of Independence, a good 125 years after Columbus stumbled into North America, a bare slip of time. Wootton rightly calls the world we live in today “box fresh”;[v] Science as we know it was “invented” between the discovery of a new star in 1572 and the publication of Newton’s Opticks (on light) in 1704. [vi] What Morison described as the “new epoch” is the crescendo of a movement forty generations old, heralding the end of “old buildings, old boundaries, and old monuments, and furthermore of customs and ideas, systems of thought and methods of education.”[vii] Ironically, in 1664 a man named Henry Power claimed almost exactly the same thing: “Me-thinks, I see how all old Rubbish must be thrown away, and the rotten Buildings be overthrown, and carried away with so powerful an Inundation. These are the days that must lay a new Foundation of a more magnificent Philosophy.”[viii] An English physician and one of the first elected Fellows of the Royal Society, Power felt that he, too, stood on the heaving deck of a brand new epoch. You can only move forward, never back; the wave of change will come. Both men were right about that, but the story can’t begin in the shining future with its gleams of promise. It starts in the stench and decay of those “rotten buildings” at the dawn of the seventeenth century, and mankind’s firm conviction that no new knowledge existed.[ix]
Imagine a city, circa 1600: Animals were slaughtered and the entrails and blood left to seep in straw, home to flies and larva and all manner of bacteria. Light came from guttering animal-fat candles, foul smelling and sooty. Close living and no plumbing meant human and animal excrement mixed in streets. Science writer Edward Dolnick describes London as particularly crusted and bleak, but even the palace of French king Louis XIV only cleared its corridors of feces once a week.[x] Today, we may argue over sexing public restrooms, but until fairly recently there were no public facilities, and in fact no toilets, at all. Pests were naturally everywhere—from the rat down to the louse. Even “romantic” writing included reference to the ubiquitous flea (most famously John Donne, who attempts to woo by reference to the mixing blood in the insect’s gut). Skin disease, rot, and various infections scabbed over the bodies of urban dwellers, rich or poor. Country folk fared only marginally better, their bodies broken under heavy manual labor. War and religious tumult, from the Thirty Years War in Germany to the English Civil War, meant that national governments existed in flux and instability. And to make matters worse, the Black Plague swept across Europe in deadly waves from the fourteenth century to the devastating outbreaks of the 1650s–60s. Medicine stood mostly helpless under the onslaught, and too often the cure killed as fast as the ailment. It could not have been a great comfort to think God was in his heaven and all was right with the world. It was, however, the only comfort going. The educated man before 1600, says Wootton, would have believed that the earth remained fixed and still, and all else revolved around it, and that God was minutely involved and interested in man.[xi] Man’s only recourse in this deeply flawed but fixed little world was to that same God, whose ways he little understood, but who nonetheless provided the answer to all questions. Even death. The world was just so because God ordained it, and mathematics could prove it.
The Mechanics of the Universe
Nicholas Kratzer arrived in England in 1516, bringing with him the latest ideas in mathematics and astronomy (something that made him a favorite in the court of infamous Henry VIII.) A Renaissance man in the literal sense, he believed the “secrets of the universe could be unlocked with precision engineering”—but that’s not all. As Dr. James Fox points out in the BBC TV series A Very British Renaissance, Kratzer made good on his word. He crafted small, intricate, unbelievably accurate sundials (one with a dial on nine sides), and in so doing “harnessed” the sun itself. Here was the grand design, rendered sensible, miniature, mechanized. And it proved to his eager patrons that all was right and orderly: In the beginning, there was God, and God created the heavens to revolve around the earth. And since Kratzer engineered the dials to be timed for England’s particular place on it, the sun rose and set right over king and court as the center of their world. Nothing in the divine clockwork suggested otherwise, and Kratzer’s friend, collaborator, and fellow German Hans Holbein further solidified this orderly understanding with his painting The Ambassadors. [Fig 1] Fox, a Cambridge historian with a particular interest in art, takes the time to reveal the work’s somewhat mystical symbols: a table with celestial materials on top (many of which were tools Kratzer used in his study of the heavens) and earthly matters on the bottom (including human means of entertainment, like the lute). The painting, like Kratzer’s clocks, contained the heavens and the earth, summing up the celestial bodies for human scale consumption. Aristotle and those who followed, like Claudius Ptolemy in 100 C.E.[CE2] , were no longer just men who thought deeply about the cosmos; they were part of a system that, nearly two millennia later, served as the structure undergirding everything, from the King and Court, to the religious centers, to men and women out in the muck and mire of daily existence. But the system wasn’t without its problems.
If you looked carefully at the night sky, and you did so every night for a year, you would notice something unusual. Stars and planets don’t just spin around the visible hemisphere, sliding along the horizon in a predictable way. Instead they appear in odd quadrants at different times of year—and to the careful observer, especially one who believed all of these heavenly bodies were spinning around the earth, the movements would seem erratic and out of order. Given that the precision and permanence of the cosmos offered just about the only succor in the dying world, the anomalies had to be figured into the system. The astronomer Ptolemy tackled this puzzle in the second century. Taking it as unquestionable truth that the sun went around the earth, he theorized planets must move in something called “epicycles” or miniature circles while on the big loop or “deferent” around it. But an intrepid and stalwart star watcher might notice something else amiss too. Planets and stars appear to speed up and slow down. Now what? Ptolemy wasn’t discouraged. He decided that half the epicycle runs counter to the deferent, which makes it appear that things change speed or reverse direction. He even took it a step further by inventing a point called the “equant,” meaning Ptolemy moved the observation point explicitly off the center to account for variation. If that sounds confusing, it should. The system worked on mathematical principles that are not terribly easy to explain. You can model them, however, and Giovanni de’ Dondi created a complex gear-work called the astrarium in Padua in the 1380s to demonstrate exactly how the solar system, as Ptolemy understood it, functioned. In order to answer the need for mathematical precision, Ptolemy gave rise to the concept Kratzer would later take for granted: we live in a universe that operates like a clock. The mathematics was correct. But the model, with its assurance of a constant and predictable universe, was wrong.
In 1572, a new star appeared. The discoverer, Tycho Brahe, used trigonometry to show that what he saw through his telescope, a brilliant star that could be seen with the naked eye inhabited the heavens, not the corruptible lower spheres.[xii] Who among us would be so lucky? New stars are rare phenomena—an earthbound explorer might only view one in a thousand years. But for it to appear in the “unchanging” cosmos at a time when demons still caused ill winds and witches were still burned (along with those who challenged deeply held views), this nova signified terrifying portents. Why was it there? How was it there? Was the world ending? Brahe spent the next fifteen years observing the heavens and measuring the immeasurable, though he never entirely questioned that the Earth remained stationary. That was left to another: Italian astronomer, mathematician, and engineer Galileo Galilei. The ill-fated Galileo wasn’t the first to see the flaw in the Earth-centered design, just the first to run afoul of the Inquisition (a series of offices of the Catholic Church charged with combating heresy and prosecuting heretics). Renaissance mathematician Nicolaus Copernicus made arguments against Ptolemy in the 1500s. He published De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) just before his death in 1543 and ushered in a true “paradigm shift”—a radical shift in thinking that some have credited with the dawn of the “Scientific Revolution.” But the new system did not make waves; it didn’t even capture the attention of the Church until six decades later, when Galileo was condemned for holding Copernican beliefs. Timing, as they say, is everything.
Suggesting that we weren’t at the center of the universe and that years of careful modeling had to be thrown out the window wasn’t winning Galileo any friends, but it had less to do with stars and planets and more to do with heresy—or contradicting the Church and its doctrine. Galileo’s problems begin in 1611, a full sixty years after the death of “scientific” clockmaker Nicholas Kratzer. They end with his formal interrogation in 1633 (for eighteen days), the threat of torture, and house arrest, under which he died in 1642. The contest is often reduced to religion versus science, but it’s actually far more complicated and more interesting. The cosmos, like the nine-sided sundial, supported the unquestioned mechanism of order, but also of authority. The Inquisition expanded its scope of influence in part to assert its authority over the Protestant Reformation, which began when Martin Luther nailed his “Ninety-Five Theses” to a cathedral door. A few years later, Henry VIII asserted his own authority by abolishing the Catholic Church in England and becoming a rule unto himself. The struggle over who has the power to give orders and make rules informs the backstory of all the conflicts to follow, including the English Civil War, which cost King Charles I his head and ushered in Puritan rule, which itself ended in violence—some of it posthumous (Oliver Cromwell was exhumed so he could be hanged). Regardless of personal faith or conviction, the 1600s would have seemed out of order indeed, nothing stable, nothing secure.
We fear chaos. We should. It speaks of confusion, disorder, mayhem. Chaos seeped from diseased bodies and sloughed from rotten timbers, but with Galileo’s ideas came a chaotic threat to the very cosmos above, the dwelling of God, and all the systems that had been built upon their unchanging nature. Today, with our general understanding of a constantly expanding universe, with our quantum physics and string theory, our acceptance of earth’s insignificance in the vast reaches of space, it’s hard to imagine the earth-shattering effect of new knowledge. But consider again what it meant the first time you heard it, when you wrapped your child-mind around the idea that Earth hurtled through space at a 1,080 miles per hour—or that the sun, which appeared to rise and set, actually stood still as we spun around and around. Imagine the foundation of belief crumbling from beneath you, and not only you, but a whole generation. When the Copernican system finally supplanted the Ptolemaic, it required new visions, new mathematical models, new means of reproducing that original desire for precision. In the process, “magic numbers” took on new significance, and empirical evidence new meaning. But something else emerged at its very birth, and from the same grisly throes. A dark twin, a doubt: a dread that the world had no foundations after all, that even religion may be faulty and untrustworthy, crept forth with the first questions of the empirical mind. Who would order the universe afresh? The coded language of the cosmos would be deciphered by three men, independently: Johannes Kepler, Isaac Newton, and Gottfried Wilhelm Leibniz. Together, they imposed an order never thought of before, making the heavens and the earth alike mathematically legible.
Or so we hope(d).
“Grandfather Clock is a creature of logic and precision [. . .] He allows neither change nor error.”
—S. M. Peters, Whitechapel Gods
I said fiction sometimes tells the story best.
In S. M. Peters’s modern steampunk novel Whitechapel Gods, the world isn’t running like clockwork, it’s run by clockwork—by Grandfather Clock, an austere, joyless, rule-keeper of logic and precision, and Mama Engine, whose creative, reproductive power is also fiery destruction. Oliver (the vaguely Dickensian hero of Peters’s novel) struggles against the Whitechapel Gods, but also against his own physical nature. A kind of steampunk loom-breaker, Oliver intends to bring the system down by use of his own body. The scene screams at us, visceral and violent: wires and spikes pierce Oliver’s flesh and coil under his ribs. This is communion with the “father,” and he “succumbed without struggle, though the relentless pounding wounded him in ways he did not know he could be damaged.”[i] Oliver’s great achievement is also his great fear—he loses awareness of himself, even as he destroys his god in the wasteland district of Whitechapel.
Maybe the fictional novel says best what I so-often struggle to communicate. The crisis we face now—climate, viral, political—they are not new. They are old, like the earth. But our capacity for destruction has outgrown us. Technology gets away from you. It’s not that machines become sentient and destroy humankind, but that we use tech to destroy ourselves. The line between miracle technology and murder technology is a fine one; the line between the machinery and our own bodies equally difficult to parse. And fiction still tells it best.
The end of Peters’ book offers hope, but a of a strange kind. The hero intends to bring the system down by use of his own body. The scene screams at us, visceral and violent: wires and spikes pierce Oliver’s flesh and coil under his ribs. This is communion with the “father,” and he “succumbed without struggle, though the relentless pounding wounded him in ways he did not know he could be damaged.”[xiii] Oliver’s great achievement is also his great fear—he loses awareness of himself, even as he destroys his god in the wasteland district of Whitechapel.
I want to return, for a moment, to the dark void of night we’ve all faced at one point or another in our lives. Growing up, as we have, in an age where the exposure of nature’s secrets is a necessary part of education, we can miss the significance of the great and wondrous beyond, the mystical realm of gods and demons and sorcerers. Steampunk aficionados resist being considered “fantasy” or “escapist,” but that prefigures these as negative terms.
For Newton and his contemporaries, “science” infused natural philosophy with mystery and made room for flights of fancy. Kepler wrote fiction, Newton practiced alchemy and apocalyptic code-breaking, and Leibniz believed that dogs might be trained to speak. They all lived with contradiction, believing that God ordered the world and spoke in mathematical proofs that we could decipher and use to study the natural as well as the celestial world, and also believing in a great host of things we today would call fantasy and superstition. Like them, we have both a desire for and dread of the unknown. Because of them, we believe those secrets are discoverable, and while we might not think in terms of magic numbers, it’s the numbers that made this possible.
There is still hope in the world, still a chance to walk back from the edge.
[i] Aristotle c.355 B.C.E. On the Heavens I, 270b1; quoted in John Deely. Four Ages of Understanding. Toronto: University of Toronto Press, 2001. (79)
[ii] Wootton, David. (3)
[iii] Morison, George Shattuck, 1896. (1)
[iv] Wootton, David. (4)
[v] Wooton, David. (4)
[vi] Wootton, David. The Invention of Science. New York: Harper, 2015. (1)
[vii] Morison, George Shattuck, 1903. (130)
[viii] Power, Henry. Experimental Philosophy (1664) quoted In Wootton. (1)
[ix] Wooton, David. (74)
[x] Dolnick, Edward. Clockwork Universe. New York: Harper, 2011.
[xi] Wooton, David (6)
[xii] Wootton, David. (13)
[xiii] Peters, S. M. (2008-02-05). Whitechapel Gods (Kindle Locations 5435–5436). Penguin Publishing Group. Kindle Edition.