Tuesday, November 09, 2010

Newton v. Leibniz, Section 1

Below is a (rough) transcript of my first section's rendition of the Newton v. Liebniz trial!


[Court is called to order at 8:00 a.m.]

Leibniz's lead. As our opening argument, we should indicate we are stating that Leibniz did not plagiarize Newton's work. There were letters written between Newton and Leibniz, but the colleagues were as much to blame for the debate as the characters themselves.

Newton's lead. Let us begin by saying we are accusing Leibniz of plagiarizing Newton's work on two separate occasions. We are here to make sure Newton gets primary credit for his discovery.

Judge 1. Prosecution may call the first witness.

Newton's lead. Henry Oldenburg, please come to the stand. Mr. Oldenburg, have you ever shown Leibniz any of Newton's work.

Oldenburg. Indeed. He visited in 1667 and then I showed him Newton's work.

Newton's lead. Which work?

Oldenburg. I believe it was Epistola prior and Epistola posterior.

Newton's lead. These were geometry-based, the building blocks for calculus, right? Could Leibniz have seen the beginnings of calculus here?

Oldenburg. I believe so.

Newton's lead. That is all. Thank you.

Leibniz's lead. Why do you say that it's "safe to say" Leibniz saw the work?

Oldenburg. He did look over it: it's got information concerning binomial series, curves, etc.

Leibniz's second. Did you read it yourself before giving it to Leibniz?

Oldenburg. Yes.

Leibniz's second. Didn't they have different methods?

Oldenburg. Yes, they were different in notation, in the end.

Leibniz's second. Didn't Newton also encode his work?

Oldenburg. Yes.

Newton's attorneys. Objection! That was a different letter.

Judge 1. Sustained.

Leibniz's second. That is all.

Newton's lead. Call John Collins, please. [Collins takes the stand.] Isn't it true that you also showed Leibniz some of Newton's work?

Collins. Yes. In 1667, the Royal Society was in recess at the time, and I wanted Leibniz to see how great British scientists were. He looked at my work and at De analysi, on which he took notes.

Newton's lead. He took these notes back to Germany.

Collins. Yes.

Newton's lead. He could have developed this into calculus, correct?

Collins. I can't say directly, but it's possible. I never told Newton that I'd shown his work around, either.

Newton's lead. Sketchy.

Collins. I guess. I felt bad about what I'd done.

Newton's lead. The beginnings of calculus were there, in De analysi, correct?

Collins. Yes. Leibniz could have gotten information that inspired him in this work.

Newton's lead. Indeed, Leibniz could easily have discovered calculus from this work? No other questions.

Leibniz's lead. So you're saying the you showed Leibniz Newton's work. How do you know what Leibniz knew before this?

Collins. Since the early 1670s Leibniz had been in touch with me. Leibniz had been writing to me and to Oldenburg asking about mathematical ideas. We didn't give him any real information; we only gave him methods. He sent us information, as well, but none of us sent complete information.

Leibniz's second. Do you know why Newton didn't publish his work right away?

Collins. I pushed him to publish, but he wouldn't. He was shy, and he had been burned: he'd published a work on optics and had been embarrassed, so he was reluctant to publish until his critics died. Moreover, after the Great Fire nobody published for a long time. Mostly, though it was because of public criticism. There's clear evidence, though, that he has priority. I don't know if you could call it plagiarism.

Leibniz's second. Was Newton angered by Leibniz's publishing first?

Collins. Personally, I was dead at that point. But I know that the colleagues were the one who had the most beef.

[There is grumbling from the Leibniz people.]

Newton's second. We call Leibniz to the stand. We hear that you were not popular with your employees.

Leibniz. That is all hearsay.

Newton's second. Didn't you have business schemes that ended in failure?

Leibniz. No.

Leibniz's lead. Objection!

Judge 1. Sustained.

Leibniz's lead. I have Leibniz's response to the allegations. [He reads from a formal statement which indicates that it would be too much trouble for him to respond formally to every point.] To me, this says that even though he's being attacked, his integrity is such that it drove him to continue his work rather than respond to specious claims.

Newton's second. Didn't Leibniz have a hard time corroborating his work, and he had a hard time indicating his sources. How do you respond to that?

Leibniz's second. We have no response to that. Is this line of questioning relevant.

Judge 1. Sustained! The sort of allegations being made by Newton's side are immaterial to to the case at hand.

[There is grumbling from the Newton bench.]

Judge 1. Any more witnesses for Newton?

Newton's lead. We call Newton to the stand. Mr. Newton, are you the sole originator of calculus?

Newton. With no doubt.

Newton's lead. When did you start work?

Newton. 10 years before Leibniz...about 1665 or 1666.

Newton's lead. This had to do with "fluxional calculus," correct? It was very unwieldy and hard to understand at that time. But could not Leibniz simply clean it up, make it more efficient, and claim it as his?

Newton. Yes.

Leibniz's second. Is it not true that Leibniz received your letter after he created his own method of calculus?

Newton. He received the letter in 1666, and he hadn't published anything at that point.

Leibniz's second. But he had developed his method.

Newton. There's no proof.

Leibniz's lead. [Reads statement on Leibniz's development of calculus before publishing, indicating the elegance of Leibniz's notation.]

Newton. I would say he changed my notation, but that he stole my ideas.

Leibniz's second. What proof do you have that he took your notation and changed it?

Newton. No response.

Leibniz's second. Nothing further.

Judge 1. Any further witnesses for Newton?

Newton's lead. We call Barrow. Mr. Barrow, you knew when Newton came up with calculus, correct?

Barrow. Correct. I was very close to Newton, and I suggest that he become Lucasian Professor at Cambridge after I left that position. He showed me a lot of his work.

Newton's lead. What was he doing then?

Barrow. In a letter in 1666, he announced his binomial theorem, just a decade before Leibniz published his work on calculus. I know also that Newton had developed De analysi before Leibnis published.

Newton's lead. So it's fair to say, based on your testimony and the others', that Newton clearly developed his work ten years before Leibniz, and because of the fire and because of personal reasons (Newton's a shy man), Newton was leery of critics.

Leibniz's second. Don't the letters between Newton and Leibniz talk about the different methods the two men came up with.

Newton's lead. Objection: those letters were privy only to Newton and Leibniz.

Judge 1. Sustained, unless you can show the substance of these letters.

Leibniz's second. [Reads from a 19-page letter from Newton to Leibniz indicating his method of fluxions, written in code.] Did Leibniz know how Newton came about his calculations?

Barrow. Both of these men are incredibly intelligent, and either could have deciphered the code and understood the work. Both were moving along the same path, in the same direction.

Leibniz's second. They moved along the same path, different methods?

Barrow. But the question is who developed it first; second discovery counts for nothing.

Judge 1. If there are no further witnesses, let's take a brief recess.

[The court is in recess for five or ten minutes.]

Judge 1. The court is called back in session. Leibniz's side may begin their defense.

Leibniz's lead. We would like to call Ehrenfried Tschirnhaus. How would you describe Newton's character.

Tschirnhaus. I didn't know know Newton well.

Leibniz's lead. How would you describe Leibniz's character?

Tschirnhaus. I knew him well. I met him in 1675 in Paris, and we developed a rapport, both professional and personal.

Leibniz's lead. Could you go into greater detail?

Tschirnhaus. Leibniz had great integrity, and these attacks are groundless. He allowed me to study unpublished works by great philosophers, and it helped me along professionally. Also, after we left Paris and went our separate ways, we kept in touch. If I were working out a problem, I'd write to him for advice, and he was always willing to help me out.

Leibniz's lead. So the Newton team is trying to distort the view of Leibniz?

Tschirnhaus. Indeed.

Newton's lead. Are you not also biased in this regard, being a close friend of Leibniz?

Tschirnhaus. True.

Newton's lead. Does the defense have any neutral parties to testify on their behalf?

Leibniz's second. We call Jacob Bernoulli to the stand. Could you please tell us the difference between Leibniz's work and Newton's work?

Jacob Bernoulli. I'd be delighted. Let it be known up front that whatever work these two men had was not entirely original. It all contained bits and pieces of work men prior to them had been working on, like Wallis. The work on infinite series had been done long before. It was these two men, though, who really went to work in solving problems with calculus methods. The differences were in the ways they handled things like infinite series, and in the ways their work was capable of doing different things. Newton's work, only shared in code, didn't give a clear-cut method for solving problems, but Leibniz was the first to give it a solid algebraic method. Newton's work in the '60s didn't have this foundation, but Leibniz's work on infinite series did. The clearest indication that Leibniz's work was original came in 1675: Leibniz could actually find closed sums of infinite series, whereas Newton could only find approximations. Leibniz took two years to develop this method. In fact, in 1677, after Leibniz shared his work with Newton in a letter and Newton looked it over, that's where the problems began.

Leibniz's second. So the correspondence began after they had both developed their methods?

Jacob Bernoulli. Leibniz had developed his method, but Newton had yet to formalize his method. Principia did not contain anything new, even though Newton knew of Leibniz's methods.

Leibniz's second. Could we not say that Leibniz did not plagiarize Newton's work?

Jacob Bernoulli. Yes.

Leibniz's second. No further questions.

Newton's lead. Didn't Newton's work precede Leibniz's?

Jacob Bernoulli. Yes, but he had yet to develop a systematic method, which is necessary for dealing with things like integration. He had the foundation of his work down, and he could solve a few problems, but he hadn't developed his work to the extent that Leibniz had. Moreover, Leibniz, like Newton, was a very intelligent man, and was able to discover these ideas on his own.

Newton's lead. When was it that Leibniz had developed his method?

Jacob Bernoulli. It was in the 1660s. My brother Johann and I were among the first to work with Leibniz and make use of his methods.

Newton's lead. But when did Leibniz first publish his work?

Jacob Bernoulli. I believe it was in 1675. It was not uncommon then to have such long gaps in communication.

Newton's lead. I just find it strange that Leibniz had gone to London to see Newton's work just before he begins his later-published work.

Jacob Bernoulli. But you can't say he wasn't working on developing calculus during that time. The letter from Collins in 1673 was more of an update on British mathematics at the time, it's not like it was singularly about Newton. To say that Newton was the centerpiece of that work would be to misconstrue it. So, yes, there was information in that letter Leibniz may have used, but Newton's work didn't lead to a particular method. Leibniz could not have discerned Newton's method from his work.

Leibniz's lead. We call Johann Bernoulli. Mr. Bernoulli, can you tell us about the problems you sent to various mathematicians?

Johann Bernoulli. First of all, hail Leibniz! I should be up front about things: in 1696, I submitted a problem which could only be solved by those who really knew calculus. The problem was out there for six months without being solved. A year later, finally, there was a response from Newton ["that bloody British!'].

Leibniz's lead. Do you have any evidence in support of Leibniz?

Johann Bernoulli. In 1684, my friend and colleague found a method for solving certain differential equations. [He writes on the board: "dx n = n xn-1."] This formula was given in Acta eruditorum before Newton had determined it, two years later.

Leibniz's lead. Do you have any more evidence in support of Leibniz?

Johann Bernoulli. Indeed. I can't understand why Newton would impugn the character of a man who attempted to unify philosophy and science.

Newton's lead. How did his attempt to unify Protestantism and Catholicism go?

Johann Bernoulli. He was unsuccessful. But he had many interests, he tried to diversify his interests. He had good intentions, but most of his work was mathematical and philosophical.

Newton's lead. Here's a quote regarding Acta eruditorum and Principia. [Read quote.]

Johann Bernoulli. Can I respond in the form of a question? Which equation is now used by scientists and engineers?

Newton's lead. The one you've written.

Johann Bernoulli. So!

Newton's lead. It's a cleaner form, no doubt. But Newton did develop fluxional calculus, much earlier. There's enough time in there for Leibniz to take this work and polish it up.

Leibniz's second. Objection: doesn't plagiarism require publication?

Judge 1. Sustained.

Leibniz's second. It's a legal impossibility: Newton's work never appeared in print.

Johann Bernoulli. The moral of the story is: "don't be shy."

Judge 1. Any more witnesses? No? Closing statements?

Newton's lead. Newton's impact has been profound. Newton has been knighted; Leibniz has not. Newton's Principia is a foundation of science; Leibniz has no such counterpart. Newton's formulas concerning gravity and planetary and tidal motion, and his laws of motion are all used today. Newton is a genius: he singlehandedly developed physics, whereas Leibniz failed at many practical endeavors. How could Leibniz have developed calculus while Newton, scientific genius, did no precede him? This seems strange to me. Leibniz plagiarized.

Leibniz's lead. Leibniz was also a genius, as was Newton. There is also considerable evidence for the originality of Leibniz's work. Moreover, as we've seen, Leibniz's methods are those currently in use today, and his notation is superior and current. This was developed independently from Newton's work. It's also important to point out that the Royal Society itself cleared Leibniz of the charge.

Judge 1. As the statements have been given, we are now adjourned. The jury may deliberate.

[UPDATE: After five minutes of deliberating, the jury returns its verdict.]

Jury foreperson. We find that Leibniz is not guilty of plagiarism: the charge is insubstantial.

No comments: