Saturday, August 16, 2008

50 Greatest Books - Principia Mathematica

Principia Mathematica

Globe and Mail
August 15, 2008

The scope and originality of Isaac Newton's Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) make it seem like a prophecy delivered from a mountaintop rather than a textbook in mathematical physics penned by a reclusive Cambridge professor.

To be sure, the Principia did not come out of the blue. Its central ideas came to Newton beginning in 1665, when an outbreak of the plague forced the university to shut down. The young scholar, still in his early 20s, returned to the family home in Lincolnshire.

Over the next 18 months, he laid out the laws of mechanics, developed a new branch of mathematics (which we now call calculus), began his investigations of light and colour and deduced the law of gravity.

And he kept it all to himself.

The notebooks and papers containing Newton's revolutionary ideas collected dust in his study for more than 20 years, until astronomer Edmond Halley urged him to publish. The massive text was finally printed in 1687, and met with universal acclaim — at least, from those who could decipher its message.

While Newton was surely a product of his time — he had devoured Galileo's dynamics and Descartes' mechanical philosophy — the Principia was a great leap forward from anything that had come before.

In its dense pages, Newton analyzes motion in a resistive medium, calculates the speed of sound, explains the irregularities in the moon's orbit and works out the physics behind the ocean's tides. He even uses the Earth's true shape (our planet is slightly "bulged" at the equator) to explain the "precession of the equinoxes" — the gradual wobble of the Earth's axis in a 26,000-year cycle.

And then there was the insight into gravitation. Allegedly inspired by a falling apple, Newton came to see that the same force could pull a falling body to the ground and hold the moon in its orbit — a force whose strength could be calculated with mathematical precision.

Newton used this "law of universal gravitation" to compute the orbits of all the planets, and even the motion of comets that sweep past the sun along highly elliptical (or even parabolic) paths.

There could no longer be any doubt that celestial and terrestrial physics were as one; the same rules applied in the heavens as on Earth.

Again and again, Newton took seemingly unrelated phenomena and found the unifying principles that underlie them — always with the calculations to back him up. Galileo's claim that nature was "written in the language of mathematics" was now firmly established.

There were, of course, unresolved problems: To some philosophers, the idea of a force acting over a distance seemed like more like magic than science.

Indeed, Einstein would later describe gravity as a warping of space itself rather than a force. It would also fall to Einstein to correct the Principia's assumption of "absolute" space and time, which had served as a foundation for Newton's mechanics but are now seen to have their limitations.

And now, the confession: I have not actually read the entire Principia (though I've read many portions of it in modern translation, and own a lovely 1960 edition).

In fact, hardly anyone in more than 100 years has actually read it. Even physicists have great difficulty with the book: In his calculus, Newton used complex geometrical representations which have since given way to more elegant notational systems. (Newton would later say that he had made the text purposely difficult so as to ward off "little Smatterers in Mathematicks" — likely a jab at rival Robert Hooke.)

So we honour the Principia not for its prose, but for the world view that it represents — what Nobel Prize-winning physicist Steven Weinberg has called "Newton's Dream" — the quest "to understand all of nature, in the way that he was able to understand the solar system, through principles of physics that could be expressed mathematically."

If you can't quite wrap your head around the Principia, you can take comfort in an anecdote — probably apocryphal — about a pupil in Newton's day who had similar troubles.

Watching the great man pass by in his carriage, the young student supposedly quipped, "There goes the man that writ a book that neither he nor anybody else understands."

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