The real Newton
NOVA: Everybody has an image of Newton, the guy who got hit on the head with an apple and dreamed up the universal law of gravitation. Is there any truth to this?
Buchwald: I doubt that an apple is what stimulated him to get the idea. The story behind it, of course, is that he was lying in the garden there, and instead of thinking about girls, he was thinking about the moon and how it goes around the Earth and so on. And an apple falls, and the story goes that bang, he suddenly has the idea that the same thing that's making the apple fall is what's holding the moon in its orbit. Then he does a calculation to see whether the mathematical behavior, the acceleration, as it's known, of the moon as it orbits around the Earth would fit with the fall of the apple if you assume that it falls at a certain rate. In other words, he's already got the whole ball game in his hands. I don't believe it.
So how do you see Newton? I mean, who was Isaac Newton?
Well, these were, of course, the very early years in which science itself was forming as a discipline. The idea of doing experiments, the idea of taking measurements and what you did with them afterwards, what a laboratory was and what you should do in one, and how you should put it all together with mathematics were really in many ways new. Not that there weren't elements long before that. You can go back to antiquity and find Ptolemy, the great astronomer, handling things mathematically and doing observations. But there were a lot of new things about Newton.
For instance, it's pretty clear that he had the most sophisticated way of handling data, at least that I know about, in the 17th and early 18th centuries. He treated data very much the way scientists much later treated data. To give you an example, if you're an astronomer and you observe the position of a star and you observe the position of a star again, you're going to get different numbers every time because people aren't perfect. Well, what do you do with all those different numbers? Nowadays, really since the end of the 18th century, you take what's called an average. You put them all together with this mathematical procedure.
But almost nobody did that until the middle of the 18th century except Newton. He was extremely sophisticated in the handling of data. This is a major part of the novelty and the difficulty of his science, because he puts that together with a deep and profound understanding of how to build a mathematical structure. Almost nobody at the time was able to penetrate deeply into what he had done there, in part because he never really talked about it. These are the kinds of things that he did but never really discussed.
So the way I see it, he is the exemplar of a profoundly new way [of doing science]—mathematically based, grounded in the generation of laboratory data, and the handling of complex data in a very concerted way. You can recognize a lot of the present in Newton, and you can't in most other people in the 17th and early 18th centuries. So to me he represents in some ways the birth of the very ethos of quantitative science.
You started to talk about calculus. For the uninitiated, what exactly is calculus and what does it allow one to do? And what was Newton trying to solve that brought him to invent the calculus?
Newton was interested in solving mathematical problems that had gripped people. This was a guy who adored computation of every kind. Among the things that you can see if you open his manuscripts, for instance, is there are places where you'll find he's calculated logarithms out to 50 places and things like that. Not because he needed it, but because he liked doing it. I mean, it was a pleasure to him to do that sort of thing. He was an unusual sort, obsessive, but gripped by the power and the beauty of sheer computation. I think that was a driving force behind what he did.
"Once he was onto something, he worked at it and worked at it and worked at it until he could solve it or until he had to give up."
And when he hit a problem he couldn't solve, he bounced it off other related problems and saw relationships between them that other people had never seen before. So the mathematical structure really emerged in that sense within the boundaries of what were already intrinsically interesting mathematical problems. Not because he needed something to solve the orbits of the planets.
But calculus has very practical uses today. In what way does it?
Well, calculus is about finding the behavior of continuously changing things. Like, for example, when a rock falls, its speed is continuously changing, and you may want to find out the distance that it's traveled or how fast it's going at a given point. The calculus is adapted to continuous change—not jumps, but continuous change—and that raises a lot of philosophical questions that people addressed as well. But it has practical application in the sense of being useful for the solution of problems of that sort.
Now, preeminently, problems of that sort are the problems of mechanics, and among the problems of mechanics are, of course, the motion of the planets. When Newton produced the Principia, he deployed a form of the calculus in order to figure out the relationships between the orbits of the planets, the forces that keep them in their orbits, and indeed what kind of paths they could use. In the absence of the calculus, these problems are, if not unsolvable, close to being unsolvable. So he needed that structure in order to produce the famous Newtonian mechanics itself.
When he did his alchemy, was he doing it to gain knowledge for knowledge's sake? Or was there some driving quest to understand truth or whatever? Did he have an aim in this, do you think?
Well, he was a complicated man, and you can't reduce things to single motivations. Lots of things clearly motivated him. For instance, once he was onto something, he was gripped by it and he worked at it and worked at it and worked at it until he could solve it or until he had to give up. In other words, it was the quest to reach a solution, to break the problem, that gripped him. It's the same kind of thing that motivates scientists today in very much the same way, only he was maybe more extreme and successful than many.
But when you say solve this thing, what is it?
Well, there were many different things. In the case of the mathematics, he wanted to solve the problems that were out there that other people had treated and that he saw relationships between. When he found that the shape of the sun in the prism wasn't what it should be, [he asked] why is that so? He was driven to figure this out, to probe it, to push, to monkey around, whether he was playing around with prisms in a laboratory or whether he was sitting there with his quill pen and his paper and trying to calculate. This was really the same kind of activity. It was a quest to solve whatever problem it was that he came upon in his voluminous and voracious reading, things that were floating in the air. Same in the alchemical laboratory. He was seeking for methods of transmutation, of course, and he thought he could make progress where other people hadn't. In the end he didn't, but he spent an awful lot of time trying.
Were there connections between his scientific accomplishments, his work in early chemistry, and his work in religion? Or were these all separate endeavors?
No, no, I think they were connected but in complicated ways. I think that, first of all, they were connected at a certain level in the way he thought about how to handle information—how to deal with it, how to work with it. His techniques of working on these things were all the same. There was also an underlying belief that all of these things must be connected, because the world was, after all, created by God. God is not irrational. There had to be a logic underlying all of these things. That was a profound belief that he had, a belief derived from a deep-seated religious conviction. Now, there were plenty of others around, particularly by the 19th century, who didn't need that religious conviction to believe that a rational order underpins the universe. But Newton did.
Setting the standard
Why is the publication of the Principia held to be such a crucial event?
Well, the Principia is objectively a work of profound mathematical insight. And I would argue that anybody in the late 17th century who was capable of reasoning at that level (and there weren't many but there were several) would have recognized the brilliance of what he had done, even though they might quarrel with the basis of the mechanics underlying it, as both [the Dutch mathematician Christiaan] Huygens and [the German mathematician and philosopher Gottfried] Leibniz, his two greatest contemporaries, did. Here he had put together the mechanics of the world with the most profound and advanced mathematics available.
"Except in the rarified world of general relativity, the Newtonian system still reigns."
It set a standard and a structure that anybody choosing to work in that area subsequently had to meet. It was an almost impossible standard to meet, but it was nevertheless something that did set a structural standard. After, say, 1710 or 1715, you would no longer get people who would be taken profoundly seriously—that is, who would invent stories, so to speak, about the world—without attempting to bind it in some way to a mathematical structure that led to results that could be compared with observation. This was something that the Principia provided and that ever after was a desideratum, something that is necessary for scientists to work towards.
Did many people even understand the Principia?
Very few people could understand what this thing was about, but a lot of people could see that there was something important in there. Even some really smart people couldn't figure out the novelty of what was being done in there. In particular Huygens and even Leibniz, when they first ran into this thing, didn't really understand what he was doing. Now, they would argue with him later on about other things in it, and eventually they did understand it, but very few people could.
You know, there weren't tens of thousands of students taking calculus at universities in those days. It was very hard to understand, and moreover, this was very arcane stuff. I mean, after all, what was the point here, right? What were you going to do with this stuff? It was purely abstract. Eventually it had some practical results, and Newton had some in mind eventually. But initially it was very abstract.
What is Newton's legacy today? Why are we still interested in him 300 years later?
Well, I think it's reasonable to say that Newton both represents and, in fact, was the founding father in a certain sense of the form of experimental, quantitative science that has ever since become the way in which we do things. He's not the only one; there are many others as well. But I think the dimensions of his accomplishment are really in almost every respect unparalleled in all of these various aspects.
Now, you could find people who did magnificent things in other areas, and even areas that Newton worked in, like Huygens or Galileo. But I think that in terms of the influence that he had, the impact, the way in which it eventually changed the practice of science, both for good and some might say for bad as well, are a part of Newton's legacy. Certainly in England at the Royal Society and elsewhere as well, science did change very radically under Newton's tutelage.
Of course, since really the 1920s and 1930s, we have had an image of a certain basic divide in science—well, really in physics—between what we call the classical world and the quantum world. Interestingly enough, the classical world, if you ask physicists today, usually includes relativity, and the quantum, or non-classical world, is about the strange behavior of particles.
But it's also generally thought that there is a major divide between mechanics as done before Einstein and mechanics after relativity, after, say, 1905 or thereabouts. That divide is often expressed as being represented by the difference between the Newtonian world and the Einsteinian world. And there is some truth to that, that is, that Einstein's innovations do make many of the claims that you might have made in using the mechanics before Einstein incorrect.
"Was he a nice guy? No, he probably was not."
On the other hand, it is also the case, as historians of relativity will tell you—especially general relativity, the theory of gravity—that one of the most important factors in what lead to the particular form of general relativity that Einstein produced was the necessity of figuring out how to get Newton's world out of it.
That's not the way we usually think about it, I guess.
No. No, but what I mean is it was an essential requirement that by choosing certain specific values for all of the various parameters that went into the general relativistic, complicated equation, you had to be able to get the Newtonian system out. And in that sense, the Newtonian system, except in the rarified world of general relativity, which doesn't have that much of an effect on most things, the Newtonian system still reigns. (Although it is the case that we've become so accurate today with GPS systems that they must take account of general relativity—non-Newtonian effects—so our world today is in a fair number of effects quite realistically non-Newtonian.)
Final question: Newton was not always a nice guy, I guess you could say. Can you tell me about that? What was he like?
Well, that's a very interesting question. Of course, it's trying for a historian to try and get behind that. There were all sorts of stories that would emerge later on about Newton. Was he a nice guy? No, he probably was not. He led a very self-confined, solitary existence. He didn't seem to care that much, at least in his youth, about other people. He certainly didn't, at least until the 1690s, have any significant relationships with anybody else.
A book written by a now deceased historian, Frank Manuel, tried to probe the psychology of Newton. [See A Portrait of Isaac Newton, Da Capo Press, 1990.] Manuel was convinced, maybe not incorrectly, that Newton's whole persona was formed when his father died before he was born and he was then brought up for three years by his mother. And his mother then married the Reverend Barnabus Smith. He was an older man, I believe in his 60s at the time, and Smith did not want the little boy around the house. So Newton had to stay back at Woolsthorpe Manor, taken care of by his grandmother, I believe, while his mother would see him relatively infrequently. Eventually, Barnabus Smith died and she came back.
But Manuel would argue that this had a very profound effect on the young Newton. It must have had some effect on him because, after all, he was a three-year-old boy when his mother vanished from his life all of a sudden. That cannot have had a good effect on him. And he was not an easy young guy, so the story goes, later on in life. But this is speculative. These psychological things are very difficult to know. But I think there's enough evidence to show that this was not, generally speaking, a man who at least until the 1690s you wanted to spend an evening drinking with. I think there's no doubt about that whatsoever—not that he didn't drink, because he did. But he could not have been very pleasant company on the whole.