A Brief Guide to the Great Equations (11 page)
There were some odd features of Newton’s account. Why, for instance, was the mass of a body involved in the gravitational force the same as the mass in the push-pull force described by
F
=
ma
? It didn’t have to be. Was this an accident? If so, it was an awfully strange accident. The answer to this puzzle would play a role in the development of general relativity over 200 years later. But in Newton’s time, one would have to think carefully to see it as a puzzle, so daring and dazzling was the sweep of Newton’s vision.
It was a deeply democratic vision. Gravity is a universal force, and it does not matter what a body looks like, nor where it lives in the universe, but solely how much mass it has. Galileo had universalized
things, and achieved insights, by turning all chandeliers into pendulums. Newton now universalized even more ambitiously by turning all bodies into attractors. Gravitation is all bodies, all the time, everywhere.
Newton’s equation of universal gravitation was hailed as the capstone of one of the most profound transformations of Western science. It led to Newton becoming the ‘gold standard’ against which scholars in other sciences compared the superstars in their fields. James Clerk Maxwell, for example, hailed Ampère as the Newton of electricity, while Alfred R. Wallace, Thomas Huxley, and others called Darwin the Newton of biology.
Diagram of Newton’s cannonball thought experiment illustrating the idea of an orbit. What would happen if one shot a cannonball horizontally from a peak that poked above the atmosphere? The more forcefully the cannonball is shot, the farther around the earth it will travel. With enough force, it returns to the peak, and follows the same path over and over again.
Moreover, Newton’s law of gravitation was often cited as the kind of law that a mature science required. François Magendie, in his classic textbook
Elementary Sketch of Physiology
(1817), lamented the absence from his field of ‘an intellect of the first order to come and discover the laws of the vital force in the same way Newton made known the laws of attraction.’
But the influence of Newton’s equation extended well beyond science – to education, philosophy, theology, and other areas of human culture. It also helped to change the very notion of ‘law’ itself.
In modern times, the concept of a scientific law has a specific meaning; it is something descriptive of nature and its behaviour. For example, in his book
The Software of the Universe: An Introduction to the History and Philosophy of Laws of Nature
, the philosopher Mauro Dorato from the University of Rome = calls a scientific law ‘a mathematical relationship between properties of physical systems.’
But it was not always that way. For the ancient Greeks, laws were not descriptive but
normative
, from the Greek
nomos
, the custom or behaviour of human beings. A law was an order that a ruler gave to subjects, who could then choose to obey or not obey. (For the nonhuman parts of the world, what we understand in terms of laws was then expressed in the idea of the thing’s characteristic nature.) Even as late as the seventeenth century, many scientists refused to apply the term ‘law’ to regularities in nature, insisting that it was no more than a metaphorical extension of social language to the natural world. But the growing appreciation for the clockworklike structure of the cosmos inclined others, such as Descartes, to describe creation as a juridical act by a supreme lawgiver. The difference between the human and nonhuman order is that the latter obey God unconsciously, while the former obey (or disobey) consciously.
Newton viewed the world in this manner. He saw himself as describing a universal principle that pervades the
entire
universe and affects
everything
in it, something whose influence is direct, immediate, and authoritative. The very universality of this principle, and the care with which Newton states that gravitation is not a property
in matter, was part and parcel of his view that he was describing the actions of a supreme lawgiver.
20
Newton’s matter is lifeless; it moves only when touched by a force. This got ‘out of God’s way’, to guarantee that the Creator had a free hand.
21
Newton’s mechanical view of the universe, as full of objects passively responding to forces from without, thus was not only consistent with a supreme lawgiver, but required it. How could there be laws and no lawgiver? As he wrote, ‘This most Elegant System of the Planets and Comets could not be produced but by and under the Contrivance and Domination of an Intelligent and Powerful Being.’ (That Sir Isaac Newton could have thought this regarding the origin of the solar system, which is now easily accounted for by the action of simple principles over time, makes us marvel at the outrageous hubris of those much smaller intellects today who are so confident that their inability to explain something’s origin means that this thing must have been the act of a god.)
Newton’s equation of gravitation gave an enormous boost to the inclination to view laws descriptively rather than normatively. The influence was reversed: natural language was now extended to the social world.
One of Newton’s assistants, the Royal Society member John Theophilus Desaguliers, composed a poem entitled ‘The Newtonian System of the World, the Best Model of Government.’ Desaguliers found in the Newtonian system, consisting of ‘the most regular Attraction of universal Gravity, (or attraction) whose Power is diffus’d from the Sun to the very Centres of all the Planets and Comets’ to be a ‘lively image of our System’ of government (the British), namely, ‘The limited Monarchy, whereby our Liberties, Rights and Privileges are so well secured.’ Thanks to this, he concluded, ‘the Happiness that we enjoy under His present MAJESTY’s Government’ is a sign ‘that A-T-T-R-A-C-T-I-O-N is now as universal in the Political, as the Philosophical World.’
22
But political theorists also began to use Newtonian language – so much so that it sharply influenced the modern conception of
democracy, as Cohen detailed in his 1995 book
Science and the Founding Fathers: Science in the Political Thought of Thomas Jefferson, Benjamin Franklin, John Adams, and James Madison
. All of the U.S. founding fathers read Newton, Cohen pointed out. Jefferson, whom Cohen describes as ‘surely the only president of the United States who ever read Newton’s
Principia
’, had several copies of the
Principia
in his library and Newton’s portrait on the wall; Franklin was so deeply impressed by Newton as a young man that he tried to meet him in London; Adams once cited Newton’s laws of motion in a political debate; and Madison wrote an essay comparing nature and human affairs.
Even the birth of socialism is tied up with Newton’s law. For the political thinker Henri de Saint-Simon (1760–1825), who was one of the founders of socialism, Newton’s law was not only the purest example of scientific thinking but also provided the model for creating a science of human social life, based on universal fraternity and collective organization. Saint-Simon once had a vision in which God disclosed to him that Newton sat at his right hand and decreed that the world should be governed by a committee called the Council of Newton. Its primary task, besides improving humanity – Saint-Simon is quoting God now – was to discover ‘a new law of gravitation applicable to social bodies.’ Newton’s equation was not just a key fact, but
the
key fact, unifying science and provoking the search for a law of social order that would work not merely between individuals and groups but also nations. Saint-Simon even criticized Newton for failing to turn gravity into an all-encompassing philosophical system.
23
The sooner humanity found this law and reorganized society accordingly, the sooner it would be liberated.
To be sure, Saint-Simon was a flamboyant character, and the kind of megalomaniac aristocrat – idealist, bad writer, idiot, and eccentric – with which early nineteenth-century socialism was amply stocked. But he was not alone. Other political thinkers, including Pierre Cabanis (1757–1808), Charles Fourier (1772–1837), and Giovanni Morelli (1816–1891), tried to apply the notion of gravitational attraction
to human life in holding that free, subjective, conscious individuals were nonetheless compelled by universal, deterministic scientific law – a notion that also influenced Karl Marx (1818–1883).
Newton’s equation of universal gravitation did more than quantify the attraction between objects, be they pebbles, spacecraft, or planets. Among other things, it inspired scholars in other fields – even political theory – to seek descriptive, mathematical, and universal laws. If the Pythagorean theorem was a proof that exhibited Proof, Newton’s equation of universal gravitation was a law that exhibited Law. In so doing, it not only altered our understanding of nature, but also our conception of science and human life.
The equation remains a symbol of the achievement of knowledge and rationality. In George Orwell’s novel
1984
, the final sign that protagonist Winston Smith (after accepting that 2 + 2 = 5) had fully capitulated to the thought police – had been thoroughly broken and ceased to think – is that he denies the law of gravity.
THAT APPLE
Then ye who now on heavenly nectar fare, Come celebrate with me in song the name Of Newton, to the Muses dear; for he Unlocked the hidden treasuries of Truth: So richly through his mind had Phoebus cast The radiance of his own divinity. Nearer the gods no mortal may approach.
Ode to Newton
What of the apple?
The story that Newton discovered universal gravitation after seeing an apple fall is one of the oldest and most familiar legends of science.
1
The incident is said to have taken place some time late in 1665 or 1666 at his mother’s orchard in Woolsthorpe, Lincolnshire, where Newton had retreated from studies at Cambridge to escape the plague. The story has long been dismissed as fiction, for several reasons. First, it seems just too theatrical to be true. Second, a cranky but influential early biographer named David Brewster doubted the story. Third, and most importantly, the story is just not how great revolutions happen. The causal force implied by the story – that seeing an apple fall created the law of universal gravitation in Newton’s mind, without much further analysis and reflection
– has to be false. As Newton’s biographer Richard Westfall observes, ‘The story vulgarizes universal gravitation by treating it as a bright idea.’
2
Yet biographers have found abundant evidence that the ultimate source is Sir Isaac himself, who told the story to several different people – including his niece (who passed it on to Voltaire) and to his friend William Stukeley (1687–1765). Here’s the version from Stukeley’s memoirs:
The weather being warm [Kensington, England, April 15, 1726], we went into the garden and drank tea, under shade of some apple-trees, only he and myself. Amidst other discourses, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth’s centre?
3
But we should still be skeptical. Why should this notoriously shy, secretive, and possessive person suddenly become garrulous, expansive, and giving about the origins of his greatest discovery? It doesn’t sound like the genuine Newton. Many writers and historians, in fact, suspect that it was not – that he was being devious, in an attempt to attack Hooke. For Hooke had claimed to be the first to come up with the inverse square law for gravitation, and had even once written a letter to Newton seeking Newton’s approval of the claim that he, Hooke, had come up with the law first. In telling this story, Newton was predating his discovery of gravitation to the 1660s, and thus removing the ground from Hooke’s claim. Such a deception sounds more like the genuine Newton, even if it is not the truthful Newton.
For the truthful Newton, the best we have is the following response he made when once asked how he made discoveries such as the law of gravitation: ‘By always thinking [about] them’, Newton said. ‘I keep the subject constantly before me and wait till the first dawnings open little by little into the full light.’
4
This rings far truer, and more closely resembles how other great discoveries are made, than the apple story. The dawnings involve more than seeing clearly, but conceptual shifts, transforming what he had inherited, and forging new things and new concepts. ‘The momentous discovery of universal gravitation, which became the paradigm of successful science, was not the result of an isolated flash of genius’, wrote I. Bernard Cohen, but a lengthy process involving the ‘transformation of existing ideas.’ Cohen added, ‘The discovery of universal gravity brings out what I believe is a fundamental characteristic of all great breakthroughs in science from the simplest innovations to the most dramatic revolutions: the creation of something new by the transformation of existing notions.’
5
An apple may well have played a role in Newton’s thinking of gravitation. But if it did, it served a similar purpose to Socrates’ pointing to the diagonal did to Meno’s slave – it helped him recast what he already knew of the problem in a new light, helping to transform that thinking in the process.