What Isaac actually asked the apple.

Yesterday on my twitter stream people were retweeting the following quote:

“Millions saw the apple fall, but Newton asked why.” —Bernard Baruch

For those who don’t know, Bernard Baruch was an American financier and presidential advisor. I can only assume that those who retweeted it did so because they believe that it is in some way significant. As a historian of science I find it is significant because it is fundamentally wrong in two different ways and because it perpetuates a false understanding of Newton’s apple story. For the purposes of this post I shall ignore the historical debate about the truth or falsity of the apple story, an interesting discussion of which you can read here in the comments, and just assume that it is true. I should however point out that in the story, as told by Newton to at least two different people, he was not hit on the head by the apple and he did not in a blinding flash of inspiration discover the inverse square law of gravity. Both of these commonly held beliefs are myths created in the centuries after Newton’s death.

Our quote above implies that of all the millions of people who saw apples, or any other objects for that matter, fall, Newton was the first or even perhaps the only one to ask why. This is of course complete and utter rubbish people have been asking why objects fall probably ever since the hominoid brain became capable of some sort of primitive thought. In the western world the answer to this question that was most widely accepted in the centuries before Newton was born was the one supplied by Aristotle. Aristotle thought that objects fall because it was in their nature to do so. They had a longing, desire, instinct or whatever you choose to call it to return to their natural resting place the earth. This is of course an animistic theory of matter attributing as it does some sort of spirit to matter to fulfil a desire.

Aristotle’s answer stems from his theory of the elements of matter that he inherited from Empedocles. According to this theory all matter on the earth consisted of varying mixtures of four elements: earth, water, fire and air. In an ideal world they would be totally separated, a sphere of earth enclosed in a sphere of water, enclosed in a sphere of air, which in turn was enclosed in a sphere of fire. Outside of the sphere of fire the heavens consisted of a fifth pure element, aether or as it became known in Latin the quintessence. In our world objects consist of mixtures of the four elements, which given the chance strive to return to their natural position in the scheme of things. Heavy objects, consisting as they do largely of earth and water, strive downwards towards the earth light objects such as smoke or fire strive upwards.

To understand what Isaac did ask the apple we have to take a brief look at the two thousand years between Aristotle and Newton.

Ignoring for a moment the Stoics, nobody really challenged the Aristotelian elemental theory, which is metaphysical in nature but over the centuries they did challenge his physical theory of movement. Before moving on we should point out that Aristotle said that vertical, upwards or downwards, movement on the earth was natural and all other movement was unnatural or violent, whereas in the heavens circular movement was natural.

Already in the sixth century CE John Philoponus began to question and criticise Aristotle’s physical laws of motion. An attitude that was taken up and extended by the Islamic scholars in the Middle Ages. Following the lead of their Islamic colleagues the so-called Paris physicists of the fourteenth century developed the impulse theory, which said that when an object was thrown the thrower imparted an impulse to the object which carried it through the air gradually being exhausted, until when spent the object fell to the ground. Slightly earlier their Oxford colleagues, the Calculatores of Merton College had in fact discovered Galileo’s mathematical law of fall: The two theories together providing a quasi-mathematical explanation of movement, at least here on the earth.

You might be wondering what all of this has to do with Isaac and his apple but you should have a little patience we will arrive in Grantham in due course.

In the sixteenth century various mathematicians such as Tartaglia and Benedetti extended the mathematical investigation of movement, the latter anticipating Galileo in almost all of his famous discoveries. At the beginning of the seventeenth century Simon Stevin and Galileo deepened these studies once more the latter developing very elegant experiments to demonstrate and confirm the laws of fall, which were later in the century confirmed by Riccioli. Meanwhile their contemporary Kepler was the first to replace the Aristotelian animistic concept of movement with one driven by a non-living force, even if it was not very clear what force is. During the seventeenth century others such as Beeckman, Descartes, Borelli and Huygens further developed Kepler’s concept of force, meanwhile banning Aristotle’s moving spirits out of their mechanistical philosophy. Galileo, Beeckman and Descartes replaced the medieval impulse theory with the theory of inertia, which says that objects in a vacuum will either remain at rest or continue to travel in a straight line unless acted upon by a force. Galileo, who still hung on the Greek concept of perfect circular motion, had problems with the straight-line bit but Beeckman and Descartes straightened him out. The theory of inertia was to become Newton’s first law of motion.

We have now finally arrived at that idyllic summer afternoon in Grantham in 1666, as the young Isaac Newton, home from university to avoid the plague, whilst lying in his mother’s garden contemplating the universe, as one does, chanced to see an apple falling from a tree. Newton didn’t ask why it fell, but set off on a much more interesting, complicated and fruitful line of speculation. Newton’s line of thought went something like this. If Descartes is right with his theory of inertia, in those days young Isaac was still a fan of the Gallic philosopher, then there must be some force pulling the moon down towards the earth and preventing it shooting off in a straight line at a tangent to its orbit. What if, he thought, the force that holds the moon in its orbit and the force that cause the apple to fall to the ground were one and the same? This frighteningly simple thought is the germ out of which Newton’s theory of universal gravity and his masterpiece the Principia grew. That growth taking several years and a lot of very hard work. No instant discoveries here.

Being somewhat of a mathematical genius, young Isaac did a quick back of an envelope calculation and see here his theory didn’t fit! They weren’t the same force at all! What had gone wrong? In fact there was nothing wrong with Newton’s theory at all but the figure that he had for the size of the earth was inaccurate enough to throw his calculations. As a side note, although the expression back of an envelope calculation is just a turn of phrase in Newton’s case it was often very near the truth. In Newton’s papers there are mathematical calculations scribbled on shopping lists, in the margins of letters, in fact on any and every available scrap of paper that happened to be in the moment at hand.

Newton didn’t forget his idea and later when he repeated those calculations with the brand new accurate figures for the size of the earth supplied by Picard he could indeed show that the chain of thought inspired by that tumbling apple had indeed been correct.



Filed under History of Astronomy, History of Mathematics, History of Physics, History of science, Myths of Science, Newton

12 responses to “What Isaac actually asked the apple.

  1. Michael Weiss

    Bernard Baruch was an American financier and presidential advisor

    Quite right, or at least Bernard Baruch thought he was. Supposedly, President Truman once said:

    I’ve never understood why Bernard Baruch prides himself on being an “advisor to presidents”. I can tell you, all presidents get way more advice than they can use.

  2. Michael Weiss

    On the subject of what actually inspired Newton’s work on gravitation, I recently watched a TV show “Comet Encounter” (about ISON); in it, the historian Patricia Fara claimed that the path of comets served as a much bigger impetus for Newton’s theory than the apple.

    Of course, an entirely reasonable response would be, “How does she know?” Indeed, reconstructing trains of thought is a dicey business, even when done by the original discoverer after a few decades.

    The “back of the envelope” calculation must have played an important role in causing Newton to lay topic aside, but I remember reading speculation (by Chandrasekhar, I believe) of another issue: the apple/moon calculation assumes that the earth can be replaced by a point-mass at the earth’s center, at least for gravitational purposes. This proposition apparently took Newton some time to verify.

    • After Flamsteed succeeded in convincing Newton, who was at first sceptical, that two comets were in fact one and the same comet orbiting the sun they did indeed play a very central role in developing his universal theory of gravity. This is also why Halley invested so much time researching historical observations of comets leading to his legendary paper of 1705. The discussion of comets takes up one third of Book III of Principia, the actual book on the universal theory of gravity.

  3. Will Thomas

    This is a tangent, but on the “animism” of Aristotle, for a while I’ve liked C. S. Lewis in The Discarded Image (93-4):

    “The question at once arises whether medieval thinkers really believed that what we now call inanimate objects were sentient and purposive. The answer in general is undoubtedly now…. If we could ask the medieval scientist ‘Why, then, do you talk as if they did,’ he might (for he was always a dialectician) retort with the counter-question, ‘But do you intend your language about laws and obedience any more literally than I intend mine about kindly enclyning? Do you really believe that a falling stone is aware of a directive issued to it by some legislator and feels either a moral or a prudential obligation to conform?’ We should then have to admit that both ways of expressing the facts are metaphorical. The odd thing is that ours is the more anthropomorphic of the two. To talk as if inanimate bodies had a homing instinct is to bring them no nearer to us than the pigeons; to talk as if they could ‘obey laws’ is to treat them like men and even citizens.

    But though neither statement can be taken literally, it does not follow that it makes no difference which is used. On the imaginative level it makes a great difference whether, with the medievals, we project upon the universe our strivings and desires, or with the moderns our police-system and our traffic regulations. The old language continually suggests a sort of continuity between merely physical events and our most spiritual aspirations. If (in whatever sense) the soul comes from heaven, our appetite for beatitude is itself an instance of ‘kindly enclyning’ for the ‘kindly stede’.”

    I think this is a really interesting observation on the different kinds of continuities between earth and the heavens in the Peripatetic and Cartesian-Newtonian philosophies.

  4. Bernard Baruch became involved in matters of science when he was asked by Truman to develop and present a plan for the international control of atomic energy to the United Nations in 1946. His so-called ‘Baruch Plan’ came to be hated by scientists (such as Oppenheimer and others) who had developed earlier proposals for atomic arms control. In the traditional historiographies Baruch often takes much of the blame for the failure to institute control over the atomic bomb in 1946.

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  6. Cleon Teunissen

    Independent of whether any fruit was involved, I find the following aspect interesting.

    In the Principia Newton provides a demonstration (Proposition LXXI) that all the way down to the surface of the Earth its gravity is the same as if all of the Earth’s mass is concentrated at the Earth’s geometrical center .

    It is my understanding that Newton stated to Halley that it was only during the composition of the Principia that he had devised that proof. I assume that statement by Newton is true.

    So, if Newton did a calculation in 1666, what conclusion could he possibly draw? Well, if he got a mismatch then the most plausible supposition was that the inverse square law does _not_ hold down to the surface of a celestial object.

    Today it’s ingrained knowledge that the inverse square law holds at all distances, but in Newton’s time it was a big leap. It’s quite counter-intuitive, without proof you’re not going to believe it.

    Thony, you write that decades later a more accurate figure for the size of the Earth allowed a more accurate calculation. A calculation with that Earth size gives a good match, providing corroboration for the idea that the inverse square law holds at all distances.

    So, that’s why I’m not interested in any garden produce dropping by. It’s the history of Proposition LXXI that I would like to know more of.

  7. This is discussed in Chandrasekhar’s Newton’s Principia for the Common Reader. Apparently John Couch Adams (co-predictor of Neptune) was the first to make this speculation as the reason Newton did not pursue the results of the apple calculation for so long.

    In a letter to Halley (20 June 1686), Newton wrote:

    I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found last year, have suspected it did not reach accurately enough down so low; and therefore in the doctrine of projectiles never used it nor considered the motion of projectiles.

    Thony wrote:
    Being somewhat of a mathematical genius, young Isaac did a quick back of an envelope calculation and see here his theory didn’t fit! They weren’t the same force at all!

    Actually, Newton wrote (in a memorandum in the Portsmouth collection, written perhaps in 1714) that his apple/moon calculation “answer[ed] pretty nearly”. (Of course, Newton didn’t call it the apple/moon calculation.)
    On the other hand, Pemberton, in the preface to the 3rd ed. of Principia, wrote that Newton’s computation “did not answer expectation”.

    So it’s probably impossible ever to know why Newton put these matters aside from 1666 to 1679. Probably both the faulty calculation and the logical gap later filled by Prop. LXII played a role.

  8. Oops, two typos in my last post. The second occurrence of “projectiles” in the quotation from Newton’s memorandum should be “heavens”, and for Prop. LXII read Prop. LXXI. (Actually LXXV is the one Newton mentions.)

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