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# Newton’s Apple

## Brian Koberlein

13 June 2013

You probably know the story of Isaac Newton. He was sitting under an apple tree when he saw an apple fall to the ground. This inspired his idea of universal gravity. There’s long been some debate as to the truth behind this tale. The story comes most famously from *Memoirs of Sir Isaac Newton’s Life* by William Stukeley in 1752. Earlier mentions appear in works of Voltaire and Robert Greene. Whether true or not, it is a story we love to tell. It portrays Newton as a genius with a revolutionary insight.

Newton’s genius is hard to deny. In many ways one can divide our scientific understanding of the world into pre-Newton and post-Newton. But ideas in Newton’s theory were not entirely unique to him, and the true power of Newton’s theory wasn’t realized until after his death. The genius of Newton’s work was not the originality of the ideas, but that these ideas were integrated into a cohesive theoretical framework.

What we now call Newtonian dynamics can be summarized in four simple rules. The first three are known as Newton’s laws of motion: a moving object will continue at the same speed and direction unless a force (push or pull) acts on it, a force applied to an object will cause the object to accelerate (change speed) in the direction of that force, and forces happen between two objects. The fourth is his law of universal gravity, that there is a gravitational force between any two objects with a strength that decreases proportional to the square of their distance of separation. These rules were presented in his *Principia* (or *Mathematical Principles of Natural Philosophy*) in 1687. Newton didn’t quite express them in this way, but the modern versions encompass his versions.

Newton’s first law is also known as the law of inertia, and it parallels the idea proposed earlier by Galileo Galilei and Christiaan Huygens. Rene Descartes proposed a similar idea, stating that bodies have a natural state of rest or motion, and that their tendency is to stay in that state. Descartes also predates Newton’s second law by noting that an object will only change its state when a force is applied to it, though Newton’s version is more refined, and presents a geometric description of an object’s change of motion under force. Newton himself doesn’t present his first two laws as new ideas. In fact in the *Principia* he states that they are “accepted by mathematicians and confirmed by experiments of many kinds.”

His third law was unique, and actually contradicted earlier works, such as that of Descartes. Newton expressed his third law not as an equality of forces, but rather that due to the forces between two objects their motion was in proportion to each other. So if a light object and a heavy object were to collide, for example, both would move in proportion to their mass. In contrast, Descartes thought that a lighter object could never move a heavier object.

Newton’s idea of an inverse square force for gravity wasn’t entirely original either. The inverse square relation had been demonstrated for gravity in the mid-1600s by Ismael Ballialdus, and Huygens proposed a similar idea for the circular planetary orbits. Robert Hooke went so far as to accuse Newton of plagiarism for the idea.

This gets us back to the story of Newton’s apple. In the story, Newton arrives at the idea of universal gravity from his own insight, inspired by the drop of an apple. But it may be that Newton was also inspired by the earlier work of Hooke. There is still debate on how much Newton owes his idea to Hooke.

Newton once wrote that he saw further by standing on the shoulders of giants. While it is certainly true that Newton’s seminal work is derived from the earlier work of others, that shouldn’t diminish his work. Even if we consider all of his laws as largely derived by others, what Newton had that they lacked was the mathematical prowess to explore their consequences. To that he added a philosophical approach that moved us toward a modern scientific perspective.

But I’ll save that for another time.