AUTHOR: ISAAC NEWTON
DATE: 1687
Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy; often abbreviated to simply the Principia) is a three-volume work that introduced Isaac Newton’s law of universal gravitation and his three laws of motion. It became a lynchpin for the entirety of modern scientific thought and has remained a staple text, even after Einstein’s General Theory of Relativity and the emergence of quantum mechanics undermined its claims to universality.
Born in Lincolnshire, England, in 1642, Newton was one of the most formidable polymaths of his day, making numerous notable contributions across a range of fields. He was a key figure, for instance, in the development of telescopic lenses, laid the framework for infinitesimal calculus and even spent a significant amount of time on alchemical studies. But it was the Principia that raised his name into the echelons of the truly great scientific thinkers.
In his elucidation of his three laws of motion, he became the first to comprehensively account for the movement of objects through space using theoretical mathematics. The first of these laws is the law of inertia, which states: ‘An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.’ His second law establishes that acceleration is produced when a force acts on a mass. The larger the mass, the larger the force required to accelerate it. His third law, meanwhile, says that for every action, there is an equal but opposite reaction. With a few strokes of his quill (he wrote his text in Latin, as was customary for academic texts at the time), Newton thus established the foundations of modern mechanics.
GRAPPLE WITH AN APPLE
The quasi-legendary status of the circumstances of Newton’s gravitational revelations in the Principia was famously encapsulated by Lord Byron, who wrote in Don Juan: ‘When Newton saw an apple fall, he found / In that slight startle from his contemplation … / A mode of proving that the earth turn’d round / In a most natural whirl, called “gravitation”.’ Byron also proved himself something of a prophesier in the verse, when he predicted that the discoveries of Newton – ‘the sole mortal who could grapple, / Since Adam – with a fall – or with an apple’ – would ‘full soon’ see steam-engines conduct man to the moon!
Yet, arguably, his theory of universal gravitation had an even greater impact. Fundamentally, it sought to show that all things are attracted to all other things in space by virtue of an invisible force. It describes how any two masses attract each other with a force equal to a constant (the gravitational constant) multiplied by the product of the two masses and divided by the square of the distance between them.
Quite how he arrived at this insight is a mystery shrouded in legend. One popular version of the circumstances is that it came to him as he sat beneath a tree and an apple fell on his head. But it is now largely accepted that the story, though greatly appealing, is apocryphal. Nonetheless, it is by no means beyond the realms of possibility that he was at least in part driven towards his startling conclusion by witnessing a similar scenario. Seeing an apple being ‘pulled’ from a tree towards the earth, he might well have pondered why it always took the route downwards to the earth and did not, say, fly upwards into space or in some other direction altogether.
Regardless of how he arrived at it, the theory at last explained why things move as they do – on earth and in space. Among other things, it provided the longed-for mathematical proof of the veracity of Copernicus’s heliocentric model. In devising his thesis, Newton also made plentiful use of Johannes Kepler’s planetary observations. As Newton would memorably put it: ‘If I have seen further, it is by standing on the shoulders of giants.’ Yet, he was under no illusion that he had hit upon a ‘theory of everything’. ‘Gravity explains the motions of the planets,’ he observed, ‘but it cannot explain who set the planets in motion.’
The Principia emerged from a much shorter paper, ‘De Motu’ (‘On Motion’), that Newton composed in 1684 after the astronomer Edmond Halley asked for his help in solving some problems of orbital dynamics. While the kernels of the three laws of motion were contained within it, it did not however address the subject of universal gravitation. But once the Principia emerged, Newton was elevated to superstar status in the scientific firmament.
Lucrative public offices came his way, as did a knighthood. But there would be controversies too. In particular, he ended up in an unseemly spat with the German philosopher and mathematician, Gottfried Wilhelm Leibniz, over which of them was the inventor of calculus. Both men spent years developing their systems, although Leibniz was the first to go public with his discoveries. It is now widely agreed that Newton had in fact developed his calculus earlier than the German, but that both arrived at their results entirely independently. Not even Leibniz’s death in 1716 could snuff out the bad blood. The affair would hover in the background of everything Newton did until his own death in 1726.
It is Principia, though, that stands as his masterpiece and secures Newton the place in history that he craved. Alexander Pope wrote him a moving epitaph: ‘Nature and nature’s laws lay hid in night; / God said “Let Newton be” and all was light.’ More than two hundred years later, Albert Einstein – the man whose own work forced a fundamental reconsideration of Principia – confirmed his enduring legacy: ‘Newton’s age has long since passed through the sieve of oblivion, the doubtful striving and suffering of his generation has vanished from our ken; the works of some few great thinkers and artists have remained, to delight and ennoble those who come after us. Newton’s discoveries have passed into the stock of accepted knowledge.’