Newton vs. Leibniz

In My Humble Opinion
1

I just finished reading The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World.

Excellent book, BTW. It’s so good I’ve gone back to Page 1 and am reading it again. :slight_smile:

The major takeaway from the book is that there were two mathematical/scientific geniuses in the 17th Century: Isaac Newton and Gottfried Leibniz. Newton was more narrowly focused in his endeavors, while Leibniz was involved in, well, everything. As someone once said, it’s as if he “Ate a library.”

Both men independently invented calculus. Newton did it twelve years before Leibniz, so I supposed he gets the prize for being the first to cross the finish line. But the notation we use today is based on the works of Leibniz, not Newton.

Starting with basic physical laws, Newton derived the mathematical framework of gravity, and proved a planet will assume an elliptical orbit. An incredible effort.

Both men were egotistical asses. Especially Newton. He had no wife, no girlfriend – no friends. He hated everyone. If he were alive today, he would hate you and hate me.

Between the two, my hat goes off to Leibniz. Not only was he the more “human” between the two (by all accounts, Newton was not “human”), but his brilliance in inventing calculus cannot be overstated. His approach to it was far superior compared to Newton’s, and it’s a tool that has been used countless times since. In addition, Newton was not kidding when he said he stood on the shoulders of giants… his work in Principia was completely based on the works of Galileo, Kepler, Hooke, and Descartes. He simply tied it all together. Interestingly, Leibniz understood the implications better than Newton himself. Leibniz knew it meant the universe operates perpetually and all on its own. Newton believed that God still had to intervene every now and then to put everything back in order.

2

Leibniz’s calculus is certainly superior to Newton’s, but other than that, the score stands firmly in Newton’s favor. Contrary to your assertion of narrow focus, Newton did very nearly everything there is to do in physics. Leibniz might have done more than him in math, but he didn’t leave nearly the impression on math that Newton did on physics.

I won’t dispute that Newton was not a person whom one would wish to socialize with, but that’s pretty low on my list of standards by which to judge historical geniuses. And I’m not sure how Leibniz rates in that regard, either.

3

Sounds like a great book and your OP is interesting.

Wasn’t Liebnez’ stock diminished somewhat because: pro-Newton/England vs. Germany sought to put Newton first? And also because Leibnez championed a “this is the best of all possible worlds” philosophy and was mocked by Voltaire as Dr. Pangloss in Candide?

4

I think Leibniz’s stock diminished primarily due to Newton’s effort to destroy him.

Leibniz wrote a polite letter to the Royal Society, asking them to examine the calculus controversy. Bad move on Leibniz’s part, because Newton was the president of the society. (Oops.) An “impartial” committee was formed and published a report. But the report was actually written by Newton, and (surprise surprise) it concluded that, not only did Newton invent calculus, but that Leibniz stole the idea from Newton. In other words, Newton figuratively stabbed Leibniz in the gut and then twisted it a few times. What an ass.

“If we evolved a race of Isaac Newtons, that would not be progress. For the price Newton had to pay for being a supreme intellect was that he was incapable of friendship, love, fatherhood, and many other desirable things. As a man he was a failure; as a monster he was superb.” - Aldous Huxley

5

Actually, integral calculus goes back to Archimedes. But it was hard to make that systematic without differential calculus and the fundamental theorem. But the real difference between the two is that Newton used it to revolutionize astronomy. Maybe I should say, change astrology to astronomy would be a better description.

In mathematics, it has often been observed that it is not the person who discovers a new idea, but the one who applies it and they are infrequently the same person. Newton was the exception. As for notation, we still often use Newtonian notation as when we write the simple DE as y’ = f(x,y). True, Leibnizian notation is often better. Neither man was ever able to give a satisfactory rigorous foundation for calculus. That was left for Cauchy, Weierstrass, and, around 50 years ago, Abraham Robinson.

As for personal qualities, why should I care?

6

Although this is no doubt partially true, it is also the case that Leibniz was far less published–much of Leibniz’ writings and correspondence was unpublished until the 20th Century, and even then, there are still volumes of significant correspondence that remain unpublished and only available to academic researchers. Judging both of them on their historical reputation is therefore unfair notwithstanding Newton’s alleged (and likely true) efforts to distort Leibniz’ contributions and work.

Newton’s work certainly does underpin virtually all of classical mechanics, both physical mechanics and optics, and his contributions to both analytic calculus and numerical approximation (although the common approximation method learned by that bears Newton’s name first and is learned by all engineers and physical scientists as their first introduction to differential approximation is actually more akin to the methodology that Joseph Raphson proposed). However, he was notably wrong in many regards, and his often utter refusal to consider contrary ideas and evidence left him stunted in potential. In contrast to a later pioneer in physics, James Clerk Maxwell, who discovered and integrated many ideas into a cohesive whole and gave credit where credit was due (sometimes to a fault), Newton, despite his famous quote about standing on the shoulders of giants, often failed to credit others as the genesis of his own notions. His infamous disagreements with Robert Hooke obscured the reputation of the latter for centuries.

One concept that Leibnez should be more remembered for and that is a fundamental part of physics today is his (and René Descartes’) notion of mathesis universalis, i.e. that all of science and nature should have a fundamental basis, the rules of which could be described by a coherent and self-consistent set of mathematical predicates and rules, from basic physics to biology and cognition. This was the first attempt to establish a true universal logic to all phenomenon instead of asserting supernatural or otherwise unrelated rules to different phenomena, and underlies all off modern dynamic systems theory.

Arguing which is “better” inevitably results in arbitrary distinctions; both are well known because of their lasting contributions (albeit often modified by the later work of others) and as contemporaries drew on a common base of prior knowledge as well as possibly influencing each other. Was Dick Feynman a better physicist than Murray Gell-Mann? Isn’t Steven Weinberg superior to both? What if we throw Pauling, Dirac, and Yukawa into the list? Even within the narrow field of fundamental particle physics, trying to identify a “best” or “most significant” is ultimately an exercise in personal preference and bias over any kind of objective evidence or rigorous criteria of “best”.

Stranger

7

Possibly. But you and I would still derive enormous benefit from what he accomplished.

A tiny fraction of humans, by dint of sheer genius and their contributions to science, art, literature, etc. are excused from the normal standards of personal behavior. Newton easily qualifies.

8

Newton was prickly, but hardly friendless. He had several friends, patrons and at least one man was either a very close friend or a lover.

I don’t think he was really that far out of the standards of behaviour for his time. He was imperious to those below him in the pecking order and syncophantic to those above him in a way that seems fairly dickish now, but was pretty standard for upper-class men at the time. Similarily, contentious priority disputes were pretty standard back then. Indeed, contentious priority disputes with Robert Hooke were pretty standard, Newton was only one of several people he tangled with.

And bachelorhood was actually a requirement of Cambridge faculty, and thus hardly strange.

9

Not disagreeing even, yet the qualifiers seem strange.
Scientific and intellectual life has necessarily evolved into small scholarly niches each devoted to a discipline,unshared across the worldly spectrum except in TED Talks, as opposed to the more communal and utopian scientific world of the renaissance — and I don’t think such obsequity to those above and arrogance to those below is unstandard in modern academe.

So the only modern comparison is the shared world of politics, where again weird deference ( Respectfulness is demanded ) and disdain for anyone poorer is now ingrained into the mental furniture of representatives, politician and upper civil servants in both the American and British political cultures, not to mention other such countries.

Nor would this have been limited then or now to the upper-classes
*Big fleas have little fleas upon their backs to bite them, and little fleas have lesser fleas, and so *ad infinitum
Tea Partyiers, the essence of the common people, are erratic in their sympathies to the less fortunate, and are admiring of the hard-working rich, whereas visiting back in Newton’s day, anyone will recall how a porter’s attitude aped the master of a household — and sometimes far extended it in snobbishness — and the reception depended entirely on the cloth on one’s back and the coins in one’s purse.
And probably the same servile behaviour throughout history.