Celebrating Sir Isaac Newton's Principia

There are some books so important that they revolutionise science. For physics, the pivotal text is Sir Isaac Newton’s Philosophiæ Naturalis Principia Mathematica - the Mathematical Principles of Natural Philosophy - which was published in this month in 1687. So to celebrate its 331st anniversary, Izzie Clarke visited another important scientist, Professor Lord Martin Rees, to find out about the Principia and the man behind it…

[In background]

Martin - So you're doing something on Newton and the Principia?

Izzie - Yes yes...

Martin - I’m Martin Rees, Astronomer Royal and Professor at Cambridge University.

Izzie - Now the Principia was first published in 1687. And it was essentially the foundations of classical mechanics. What exactly did it entail?

Martin - Well it was a wonderful mathematical achievement, and he used immense mathematical talents to codify lots of ideas about the laws of motion and gravity, and his book the Principia is famously in three parts. The first gives his famous laws of motion. The first is that everything continues in its state of rest or uniform motion, unless something pushes it, as it were. The second said that if something is acted on by a force then the amount by which it accelerates depends on that force and on its mass. And the third law said that if something pushes, there's a pushback, so what's called action and reaction are equal opposite. So those are the actual laws but what’s impressive is the way he use mathematics to apply those laws, particularly to the orbits of the moon and planets.

Izzie - Now those laws of motion may take you back to your high school physics lessons. But why are these so important?

Martin - Well, of course, until that time we didn't really understand. I mean, the laws of motion which were believed by most people since classical times were those of Aristotle, which were that everything stopped moving unless you stop pushing it. And that of course is true of most things. But nonetheless Newton realized that, in practice, if something is not moving in a steady way, something is pushing it, or something is dragging it

Izzie - and that something would be a force. So that's part one of the Principia covered. The second discusses how bodies move under gravity and resisting forces. And the third applies Newton's theories of gravity to detailed problems, like the motion of the moon and planets.

Martin - Well of course he was the first person to realize that the force that makes the apple fall and holds us on the ground, is the same as the force which holds the moon in its orbit around the Earth, and the earth in its orbit around the sun. And he was also the first to show in detail how these orbits worked. Of course it was known that the orbits were not perfect circles, that they were ovals or ellipses. He didn't understand why. And I suppose the most famous single achievement of Newton in the Principia was to show that if the force of gravity obeyed a so-called inverse square law, which means that it falls off by a factor of four if you go twice as far away, inverse square law, then that force will cause an orbiting body to move in an ellipse, where the source of the gravity has a focus. And so he actually showed that this inverse square law force explained why the orbits had the shape they do.

Izzie - Have you ever tried to read the Principia?

Martin - Well it's not an easy read, and in fact it's interesting that Newton didn't want it to be an easy read. We must accept that he was probably one of the greatest scientific intellects of all time, but he was a deeply unpleasant character really. He was solitary and reclusive, and in his later years he became really very vain and vindictive, and we perhaps should recognise him for his works, and not for his character.

Izzie - Yes, so definitely quite a controversial character. You mentioned he was a recluse. Do you think part of that is to do with the fear of someone might take these ideas from him?

Martin - Well he was deeply concerned about priority and that's why he had longtime disputes, but of course what was special about him was not only his brilliance, but his power of concentration. In fact someone asked him how did he succeed in solving these very difficult problems about gravity and inverse square law, and his reply was ‘by thinking on them continually’. He did night and day and there are all these anecdotes about how he forgot to eat his meals etc. and continued. This was particularly the case in the two years when he was writing his Principia. And of course remember it was written in Latin and there were later editions, and then there were English translations and French translations, and it became a book which was probably not understood by many people, but it became seen as an archetype for how we can actually understand and see patterns in the world. And this led to the idea of a sort of clockwork universe, which could in principle be understood by mathematical formulae.