Is God a Mathematician_ - Mario Livio [50]
On 15 April 1726 I paid a visit to Sir Isaac at his lodgings in Orbels buildings in Kensington, dined with him and spent the whole day with him, alone…After dinner, the weather being warm, we went into the garden and drank thea, under the shade of some apple trees, only he and myself. Amidst other discourse, he told me he was just in the same situation, as when formerly [in 1666, when Newton returned home from Cambridge because of the plague], 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? Assuredly, the reason is, that the earth draws it. There must be a drawing power in matter: and the sum of the drawing power in the matter of the earth must be in the earth’s centre, not in any side of earth. Therefore does this apple fall perpendicularly, or towards the centre. If matter thus draws matter, it must be in proportion of its quantity. Therefore the apple draws the earth, as well as the earth draws the apple. That there is a power, like that we here call gravity, which extends its self thro’ the universe…This was the birth of those amazing discoverys, whereby he built philosophy on a solid foundation, to the astonishment of all Europe.
Irrespective of whether the mythical event with the apple actually occurred in 1666 or not, the legend sells Newton’s genius and unique depth of analytic thinking rather short. While there is no doubt that Newton had written his first manuscript on the theory of gravity before 1669, he did not need to physically see a falling apple to know that the Earth attracted objects near its surface. Nor could his incredible insight in the formulation of a universal law of gravitation stem from the mere sight of a falling apple. In fact, there are some indications that a few crucial concepts that Newton needed to be able to enunciate a universally acting gravitational force were only conceived as late as 1684–85. An idea of this magnitude is so rare in the annals of science that even someone with a phenomenal mind—such as Newton—had to arrive at it through a long series of intellectual steps.
It may have all started in Newton’s youth, with his less-than-perfect encounter with Euclid’s massive treatise on geometry, The Elements. According to Newton’s own testimony, he first “read only the titles of the propositions,” since he found these so easy to understand that he “wondered how any body would amuse themselves to write any demonstrations of them.” The first proposition that actually made him pause and caused him to introduce a few construction lines in the book was the one stating that “in a right triangle the square of the hypothenuse is equal to the squares of the two other sides”—the Pythagorean theorem. Somewhat surprisingly perhaps, even though Newton did read a few books on mathematics while at Trinity College in Cambridge, he did not read many of the works that were already available at this time. Evidently he didn’t need to!
The one book that turned out to be perhaps the most influential in guiding Newton’s mathematical and scientific thought was none other than Descartes’ La Géométrie. Newton read it in 1664 and re-read it several times, until “by degrees he made himself master of the whole.” The flexibility afforded by the notion of functions and their free variables appeared to open an infinitude of possibilities for Newton. Not only did analytic geometry pave the way for Newton’s founding of calculus, with its associated exploration of functions, their tangents, and their curvatures, but Newton’s inner scientific spirit was truly set ablaze. Gone were the dull constructions with ruler and compass—they were replaced by arbitrary curves that could be represented by algebraic expressions.