James Burke, a BBC TV host, science popularizer, and creator of the fantastic "Connections" TV series said this about it:
The Principia provided such an all-embracing cosmological system that it stunned science into virtual inactivity for nearly a century.It also kicked my butt, completely and utterly. In "Ground truthing" I talked about my experience with Galileo's proof that the path of an artillery ball is a parabola. I was forced to confess that "it turned out to be hard. I never did really figure it all out". Principia is literally proof after proof after proof, all of them as hard to handle as Galileo's proof or, in some cases, harder. And there are hundreds of them. One reason for this is that Newton's proofs are in the same geometric style as the one Galileo used. But on top of that Newton added in other elements that make his proofs hard to follow, elements like a primitive version of Calculus.
I am not going to inflict any of that on you. Instead I am going to do two posts on Principia. In the first post (this one) I am going to talk around it. I am going to give some historical perspective, background, and observations on what was going on and how Principia fits into the bigger picture. In the second post I will go into what is actually in Principia.
And, of course, I didn't actually read Principia. It's in Latin. What I read was a book with a very long and convoluted title. In full it is: ISAAC NEWTON - THE PRINCIPIA - Mathematical Principles of Natural Philosophy - THE AUTHORITATIVE TRANSLATION. The author credit is "by I. Bernard Cohen and Anne Whitman assisted by Julia Budenz". This book also includes A Guide to Newton's Principia by I. Bernard Cohen. The Guide runs 370 pages (Principia itself is 575 pages long) and is critical to making any sense of Principia. This book came out in 1999. Before it came out the only English translations of Principia were either one done over 250 years ago or a "modernized and revised" version of the 250 year old translation that came out in the 1930's. Let's start with a little history.
Newton was born in 1642 and died 84 years later. He was born into a minor British noble family. At that time science was done by "gentlemen of leisure" who didn't have to earn a living. They did science as a hobby or for the betterment of mankind rather than as a paying job. This was an accurate description of Newton. He got a degree from Cambridge University in 1665 and promptly headed for home because the Great Plague was sweeping the country. And it was especially dangerous in urbanized areas like the town and University of Cambridge. During the next two years, and for perhaps some time after that, he did his seminal work in science.
This included inventing Calculus, careful studies of Optics (the properties of light) and what we would now call Celestial Mechanics, understanding the laws that govern the motion of heavenly bodies. He then returned to Cambridge where he was elected a member of Trinity College and took over the "Lucasian" chair in mathematics there. As a result of Newton's association with the chair, holding the Lucasian chair is now considered the most prestigious position a mathematician can hold. Stephen Hawking, the renowned physicist, held it for thirty years and only relinquished it relatively recently.
But in general Newton fairly quickly moved away from science and mathematics and pursued other interests. He had a long standing interest in Alchemy and was considered an expert. He also spent more time and energy on theology than he ever did on science. Again, in his time he was considered an expert on the subject. He also moved into politics. He served two different terms in Parliament and was appointed Master of the Royal Mint, a political appointment. He did maintain a connection with science to the extent of spending more than two decades as president of the Royal Society. But he spent most of his time and energy at that point on politicking and little on doing science. Like many men of his time, he did almost all of his significant scientific work while he was a young man.
Although he had done the underlying work years ago he didn't publish Optics until 1704. There was also a substantial delay between when he did the work and when he published Principia. The first edition came out in 1687. A revised edition came out in 1713 and a second revision came out in 1726, shortly before his death. Why the delays?
The short answer is that he had to be goaded into publishing. He was very secretive. The best way to get him to publish was either to tell him that someone was about to publish something Newton thought he had invented or to tell him it was long past time to score points against one or more of his rivals.
The rules on who got credit for a scientific advancement were just being worked out in Newton's time. The modern "he who publishes first gets the credit" method came about later and was partly a response to the damage done by feuds involving Newton. He was a glory hog. Much of his glory was justified. He was a great mathematician, a great theorist, and a great experimentalist. Consider that he invented Calculus (mathematics), invented "Newton's law of Gravity" (theorist), and using the results from a brilliant set of experiments laid much of the foundation for the study of light and optics (experimentalist). Nevertheless, he was stingy when it came to giving credit to others and greedy when it came to taking the credit (often singular credit) for himself. Consider Calculus.
Calculus was in the air when Newton invented it. If is based on two then recent developments in mathematics, the study of "infinitesimals" and the study of "limits". Both of these concepts were developed by others and Calculus couldn't exist without them. But Newton applied them effectively, developing a number of important methods for doing Differential and Integral Calculus. So did Leibnitz, a German mathematician. Both developed Calculus at the same time and both did it pretty much independently of each other. And Leibnitz did the better job. The Calculus we use to day is the Leibnitz version. Some corners of engineering cling to the Newtonian version but no one else does.
So the real story was that it was in the air. Both Leibnitz and Newton got to it at about the same time but Newton was "all in" to make sure he got all the credit and Leibnitz got none. Since by this time he had the political connections, which he made adroit use of, for a long time he got all the credit, at least in the English speaking world. A fairer reading of how much credit should be allocated to who had to wait until many years after his death.
He was also involved in a big fight with the Descartes of "I think therefore I am" fame. Newton was not interested in Descartes' philosophical musings. What he was interested in was his theory of gravity. It was based on something called vortexes. If you haven't heard of this before it is because Newton totally destroyed Descartes' vortex theory in Principia. Newton got and richly deserved full credit for this. In this case he beat Descartes fair and square. And he did such a good job of it that today only people interested in Descartes or in the history of science have even heard of the vortex theory of gravity.
But there was a down side. Descartes invented Cartesian Coordinates and what we now call Analytic Geometry. Because he was having a fight with him, Newton wouldn't even consider using the methods of Analytic Geometry in Principia. That makes what he did far harder to follow. And the techniques Newton deployed in Principia are extremely hard to use. The same technique done using the methods of Analytic Geometry are much easier to understand and much easier to actually make use of. And the ultimate irony is that Calculus and Analytic Geometry go together like ham and eggs. One big reason we now use the Leibnitz version of Calculus is because he had no problem with Analytic Geometry. And it was easy to adapt his methods so they could be seen as extensions to standard Analytic Geometry methods.
In modern Calculus we characterize Integral Calculus as a method for "finding the area under a curve". How do we define "area"? We do it in terms of Analytic Geometry concepts. What does "under the curve" mean? Well, you set the problem up using the methods of Analytic Geometry and . . . The same thing is true with Differential Calculus. Here we want to find "the slope of a curve at a given point". These are all concepts that are fundamental to Analytic Geometry. In short the methods Newton demonstrated in Principia ended up being put to practical use in an Analytic Geometry context and often using the Leibnitz form of Calculus.
And it is perhaps worth noting that Newton succeeded in achieving the results he did in spite of the fact that he was using ill suited geometric methods not because of it. That makes his achievement all the more impressive.
Let me give you another example of how petty Newton could be. At the time the Royal Navy had a serious problem called the "longitude" problem. They needed a method for determining the longitude of a ship so it could avoid crashing into rocks or getting lost when visibility was poor. The British government put up a 20,000 pound prize (equivalent to millions today) for the first person to solve the problem. And the problem boiled down to figuring out how to construct a portable high precision clock.
It was solved by John Harrison who invented the "chronometer", a precision pocket watch. Newton was on the committee in charge of awarding the prize. Harrison jumped through all the necessary hoops to prove his device actually worked. But Newton didn't want to give him the money. Why? Because he was a regular bloke and not a member of the nobility. That's just petty. Harrison had done the job and the money was not coming out of Newton's pocket.
So much for Newton. I am now going to move on to Principia itself.
It was published at time of transition. Descartes' Analytic Geometry was such a big improvement over the previous geometric method that science in general quickly abandoned the latter for the former. The mathematics of science quickly started looking modern rather than ancient. So in a sense Newton lost that battle as well as the battle over the mechanics of how Calculus should be done. But he won the war. To this day scientists speak of "Newtonian Mechanics". This is shorthand for any system of mechanics that ignores Relativity and Quantum Mechanics.
In a very real sense Newtonian Mechanics describes how the world of ordinary distances and speeds works. Quantum Mechanics is quite different from Newtonian Mechanics. But for the most part Quantum Mechanics deals with the world of the very small, the world of atoms and subatomic particles. Relativistic Mechanics (mechanics that includes Relativity) is quite different from Newtonian Mechanics. But for the most part Relativistic Mechanics deals with the very large, the world of stars and galaxies, and things going very fast, speeds near light speed. The world we mostly live in, the "middle distance" world, works pretty much the way the mechanics Newton invented says it works.
One thing puzzled me until I read the book. Why did it have such a special place? The answer goes back to those hundreds of proofs. Newton supplied answers and methods for everything. He didn't just prove the main thing. He provided methods for calculating this, that, and the other thing. He considered things from multiple angles. He pretty much said all there was to say about the subject areas he delved into. So in case after case after case he reduced the situation to "But -- oh wait. He covered that too." His analysis was so broad and complete that there was little left to add.
The result was that when it came to calculating the orbits of heavenly bodies or how to navigate space probes, for the most part it is all in Principia. It took more than a hundred years for the state of the art of telescopes and other instruments for observing the heavens to get precise enough to find something that wasn't where it was supposed to be. It turns out that the orbit of Mercury is not exactly where Newton said it was supposed to be. The discrepancy is very small. And this "Mercury problem" was one of the problems that Einstein's Relativity theories ended up solving.
The state of the art has gotten a lot better since. So it is now relatively easy to find situations where Newtonian Mechanics gives an answer that is just a little bit wrong. The signals from GPS satellites include a relativistic correction. Without it GPS receivers would spit out "you are here" answers that are slightly wrong. Back in the day navigation errors could cause ships of the British Royal Navy to crash into rocks in the fog. We live such high precision lives, often without realizing it, that there are some situations where Newtonian Mechanics gets an answer that is dangerously wrong. If left uncorrected it is big enough to, for instance, cause a car to crash into a lake or an airplane to miss its runway.
These tiny errors are often detectable now because we can measure billionths of a second and distances far smaller than the diameter of a Hydrogen atom. In Newton's day they couldn't measure anything accurately enough to reveal any difference between the answer Newtonian Mechanics gives us and the one the modern theories would. And Newtonian Mechanics is far simpler and easier to deal with than Relativistic Mechanics or Quantum Mechanics. And most of the time in most situations Newtonian Mechanics gives us an answer that is accurate enough for our day in day out needs. And that's why scientists and engineers still study Newtonian Mechanics.
Mostly what Principia did was be convincing. It was easier for scientists of the period to deal with it because they were familiar with the "geometric" approach Newton used. And Newton was completely honest. He decided to write the book with the expert in mind. It is the exact opposite of a "for dummies" book. That made it completely inaccessible for normal people of the day. But it also made it completely convincing to the experts of the day. And they were quick to accept it and to embrace it. And they convinced the normal people of the day that what Newton said in Principia was true.
This was important for reasons that people who live today can understand. Newton had some things to say that went against many beliefs that were strongly held at the time. It helped that Newton was widely seen as a "good Christian" and a theologian of note. Because some of these beliefs were based in religious orthodoxy. It is important to remember that not long before this Galileo had gotten into very serious trouble for saying things that the Church did not approve of. But Newton got little or no push back about this sort of thing. And one reason was the near universal opinion of experts that the constructs Newton laid out in Principia were convincing and compelling. Back then experts were seen more as experts and not people pushing one agenda or another. Sadly, this is not true today.
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