The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)

Part II. Hope and Monsters

Chapter 19. From Earthworms to Angels

If the thinkers of the seventeenth century had been content to see God as a superbly talented artist and craftsman, their homage might have taken a different form. Instead they looked at the marvelous sights revealed by the telescope and microscope and found new support for their favorite doctrine, that God was a mathematician.

They believed it already, thanks largely to their discoveries about the geometry of the cosmos, but they saw the new evidence as proving the case beyond the least possible doubt. In part this was because of the new sights themselves. Seen through the microscope, the least imposing objects revealed a geometer’s shaping hand. One early scientist wrote an astonished hymn to grains of salt, which turned out to be “Cubes, Rhombs, Pyramids, Pentagons, Hexagons, Octagons” rendered “with a greater Mathematical Exactness than the most skilful Hand could draw them.”

But the renewed emphasis on God-the-mathematician came mostly by way of a different, stranger path. One of the seventeenth century’s most deeply held beliefs had to do with the so-called great chain of being. The central idea was that all the objects that had ever been created—grains of sand, chunks of gold, earthworms, lions, human beings, devils, angels—occupied a particular rank in a great chain that extended from the lowest of the low to the hem of God’s garment. Nearby ranks blended almost insensibly into one another. Some fish had wings and flew into the air; some birds swam in the sea.

It was a fantastically elaborate system, though it strikes modern ears as more akin to a magical realist fantasy than a guide to everyday life. Purely by reasoning, the intellectuals of the seventeenth century believed, they could draw irrefutable conclusions about the makeup of the world. Angels, for example, were as real as oak trees. Since God himself had fashioned the great chain, it was necessarily perfect and could not be missing any links. So, just as there were countless creatures reaching downward from humans to the beasts, there had to be countless steps leading upward from humans to God. QED.

That made for a lot of angels. “We must believe that the angels are there in marvelous and inconceivable numbers,” one scholar wrote, “because the honor of a king consists in the great crowd of his vassals, while his disgrace or shame consists in their paucity. Thousands of thousands wait on the divine majesty and tenfold hundreds of millions join in his worship.”

Each link had its proper place in the hierarchy, king above noble above commoner, husband above wife above child, dog above cat, worm above oyster. The lion was king of beasts, but every domain had a “king”: the eagle among birds, the rose among flowers, the monarch among humans, the sun among the stars. The various kingdoms themselves had specific ranks, too, some lower and some higher—stones, which are lifeless, ranked lower than plants, which ranked lower than shellfish, which ranked lower than mammals, which ranked lower than angels, with innumerable other kingdoms filling all the ranks in between.

In a hierarchical world, the doctrine had enormous intuitive appeal. Those well placed in the pecking order embraced it, unsurprisingly, but even those stuck far from the top made a virtue of “knowing one’s place.” Almost without exception, scholars and intellectuals endorsed the doctrine of the all-embracing, immutable great chain. To say that things might be different was to suggest that they could be better. This struck nearly everyone as both misguided—to attack the natural order was to shake one’s fist at the tide—and blasphemous. Since God was an infinitely powerful creator, the world necessarily contained all possible things arranged in the best possible way. Otherwise He might have done more or done better, and who would presume to venture such a criticism?

As usual, Alexander Pope summarized conventional wisdom in a few succinct words. No one ever had less reason to endorse the status quo than Pope, a hunchbacked, dwarfish figure who lived in constant pain. He strapped himself each day into a kind of metal cage to hold himself upright. Then he took up his pen and composed perfectly balanced couplets on the theme that God has His reasons, which we limited beings cannot fathom. “Whatever is, is right.”

The great chain had a long pedigree, and from the beginning the idea that the world was jam-packed had been as important as the idea that it was orderly. Plato had decreed that “nothing incomplete is beautiful,” as if the world were a stamp album and any gap in the collection an affront. By the 1600s this view had long since hardened into dogma. If it was possible to do something, God would do it. Otherwise He would be selling himself short. Today the cliché has it that we use only 10 percent of our brains. For a thousand years philosophers and naturalists wrote as if to absolve God from that charge. “The work of the creator would have been incomplete if aught could be added to it,” one French scientist declared blithely. “He has made all the vegetable species which could exist. All the minute gradations of animality are filled with as many beings as they can contain.”

This was also the reason, thinkers of the day felt certain, that God had created countless stars and planets where the naked eye saw only the blackness of space. God had created infinitely many worlds, one theologian and Royal Society member explained, because only a populous universe was “worthy of an infinite CREATOR, whose Power and Wisdom are without bounds and measures.”

But why did that all-powerful creator have to be a mathematician? Gottfried Leibniz, the German philosopher who took all knowledge as his domain, made the case most vigorously. The notion of a brim-full universe provided Leibniz the opening he needed. Leibniz was as restless as he was brilliant, and, perhaps predictably, he believed in an exuberantly creative God. “We must say that God makes the greatest number of things that he can,” Leibniz declared, because “wisdom requires variety.”

Leibniz immediately proceeded to demonstrate his own wisdom by making the same point in half a dozen varied ways. Even if you were wealthy beyond measure, Leibniz asked, would you choose “to have a thousand well-bound copies of Virgil in your library”? “To have only golden cups”? “To have all your buttons made of diamonds”? “To eat only partridges and to drink only the wine of Hungary or of Shiraz”?

Now Leibniz had nearly finished. Since God loved variety, the only question was how He could best ensure it. “To find room for as many things as it is possible to place together,” wrote Leibniz, God would employ the fewest and simplest laws of nature. That was why the laws of nature could be written so compactly and why they took mathematical form. “If God had made use of other laws, it would be as if one should construct a building of round stones, which leave more space unoccupied than that which they fill.”

So the universe was perfectly ordered, impeccably rational, and governed by a tiny number of simple laws. It was not enough to assert that God was a mathematician. The seventeenth century’s great thinkers felt they had done more. They had proved it.

The scientists of the 1600s felt that they had come to their view of God by way of argument and observation. But they were hardly a skeptical jury, and their argument, which seemed so compelling to its original audience, sounds like special pleading today. Galileo, Newton, Leibniz, and their peers leaped to the conclusion that God was a mathematician largely because they were mathematicians—the aspects of the world that intrigued them were those that could be captured in mathematics. Galileo found that falling objects obey mathematical laws and proclaimed that everything does. The book of nature is written in the language of mathematics, he wrote, “and the characters are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”

The early scientists took their own deepest beliefs and ascribed them to nature. “Nature is pleased with simplicity,” Newton declared, “and affects not the pomp of superfluous causes.” Leibniz took up the same theme. “It is impossible that God, being the most perfect mind, would not love perfect harmony,” he wrote, and he and many others happily spelled out different features of that harmony. “God always complies with the easiest and simplest rules,” Galileo asserted.

“Nature does not make jumps,” Leibniz maintained, just as Einstein would later insist that “God does not play dice with the universe.” We attribute to God those traits we most value. “If triangles had a god,” Montesquieu would write a few decades later, “he would have three sides.”

Newton and the others would have scoffed at such a notion. They were describing God’s creation, not their own. Centuries later, a classically minded revolutionary like Einstein would still hold to the same view. In an essay on laws of nature, the mathematician Jacob Bronowski wrote about Einstein’s approach to science. “Einstein was a man who could ask immensely simple questions,” Bronowski observed, “and what his life showed, and his work, is that when the answers are simple too, then you hear God thinking.”

For a modern-day scientist like Bronowski, this was a rhetorical flourish. Galileo, Newton, and the other great men of the seventeenth century could have expressed the identical thought, and they would have meant it literally.