Mathematics as Escape

Quotes from Edward Dolnick, The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, Chapter Twenty-One “Shuddering Before the Beautiful”

For the mathematically minded, the notion of glimpsing God’s plan has always exerted a hypnotic pull. The seduction is twofold. On the one hand, delving into the world’s mathematical secrets gives a feeling of having one’s hands on nature’s beating heart; on the other, in a world of chaos and disaster, mathematics provides a refuge of eternal, unchallengeable truths and perfect order.

When he was a melancholy sixteenyear- old, the modern-day philosopher and mathematician Bertrand Russell recalled many years later, he used to go for solitary walks “to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.”

“Of all escapes from reality,” the mathematician Gian-Carlo Rota observed, “mathematics is the most successful ever. . . . All other escapes—sex, drugs, hobbies, whatever—are ephemeral by comparison.”

Perhaps this accounts for the eagerness of so many seventeenth-century intellectuals to look past the wars and epidemics all around them and instead to focus on the quest for perfect, abstract order. Johannes Kepler, the great astronomer, barely escaped the religious battles later dubbed the Thirty Years’ War. One close colleague was drawn and quartered and then had his tongue cut out.’

Kepler spent six years defending her [her mother charged with witchcraft] while finishing work on a book called The Harmony of the World. “When the storm rages and the shipwreck of the state threatens,” he wrote, “we can do nothing more worthy than to sink the anchor of our peaceful studies into the ground of eternity.”

Newton had Cracked the Code

p. 36 ‘The picture of history was completely false, but Newton and many others had boundless faith in what they called “the wisdom of the ancients”. (The belief fit neatly with the doctrine that the world was in decline.) Newton went so far to insist that ancient thinkers know all about gravity, too, including the specifics of the law of universal gravitation, the very law that all the world considered Newton’s greatest discovery.

God had revealed those truths long ago, but they had been lost. The ancient Egyptians and Hebrews has rediscovered them. So had the Greeks, and, now, so had Newton. The great thinkers of past ages had expressed their discoveries in cryptic language, to hide them from the unworthy, but Newton had cracked the code.’

Scientists and History

p. 56-57 ‘Scientists tend to have little interest in history, even the history of their own subject. They turn to the past only to pluck out the discoveries and insights that turned out to be fruitful – Boyle, for instance,  is known today for “Boyle’s law”, relating pressure and volume in gases – and they toss the rest aside.

In fields where the notion of progress is indisputable, such disdain for the past is common. The explanation is not so much anti-intellectualism as impatience. Why study ancient errors? So scientist ignore most of their forebears or dismiss them as silly codgers. They make exceptions for a tiny number of geniuses whom they treat as time travelers from the present day, thinkers just like us who somehow found themselves decked out in powdered wigs.

But they were not like us.’

God-the-mathematician and Great Chain of Being

Chapter Nineteen From Earthworms to Angels

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.’

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.’

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.’

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.’

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 Royal Society of London for the Improvement of Nature

The Royal Society of London for the Improvement of Natural Knowledge, the formal name of this grab-bag collection of geniuses, misfits, and eccentrics, was by most accounts the first official scientific organization in the world.’

Science today is a grand and formal enterprise, but the modern age of science began as a free-for-all. The idea was to see for yourself rather than to rely on anyone else’s authority. The Royal Society’s motto was “Nullius in Verba,” Latin for, roughly, “Don’t take anyone’s word for it,” and early investigators embraced that freedom with something akin to giddiness.’

The world was so full of marvels, in other words, that the truly scientific approach was to reserve judgment about what was possible and what wasn’t, and to observe and experiment instead.’

“Books on the Second Coming were written by the score during this period,” one eminent historian observes, “and members of the Royal Society were preoccupied with dating the event.” They proceeded methodically, looking for hidden meanings in biblical texts or manipulating numbers cited in one sacred passage or another.’

If God were to relax his guard even for a moment, the entire world would immediately collapse into chaos and anarchy. The very plants in the garden would rebel against their “cold, dull, inactive life,” one Royal Society physician declared, and strive instead for “self motion” and “nobler actions.”

At another meeting in 1660, the Society gravely scrutinized a unicorn’s horn and then tested the ancient belief that a spider set down in the middle of a circle made from powdered unicorn’s horn would not be able to escape. (The spider, unfazed, “immediately ran out several times repeated.”)

Leeuwenhoek and sperm cells

‘Leeuwenhoek jumped up from his bed one night, “immediately after ejaculation before six beats of the pulse had intervened,” and raced to his microscope. There he became the first person ever to see sperm cells. “More than a thousand were moving about in an amount of material the size of a grain of sand,” he wrote in amazement, and “they were furnished with a thin tail, about five or six times as long as the body . . . and moved forward owing to the motion of their tails like that of a snake or an eel swimming in water.” Leeuwenhoek hastened to assure the Royal Society that he had obtained his sample “after conjugal coitus” (rather than “by sinfully defiling myself”), but he did not discuss whether Mrs. Leeuwenhoek shared his fascination with scientific observation.’