Saturday, April 25, 2009

Newton v. Leibniz, semi-official transcript

What follows is a shadow of the proceedings of the Monday, March 30th trial reenactment, Newton v. Leibniz, performed by my Calculus I class. There is paraphrasis, but I've tried to preserve the most important passages as perfectly as I can. I know that I managed to catch several of the juiciest lines verbatim.

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9:05 -- 9:07. Leibniz's lead attorney (played by Kent) makes his opening argument. "We plead with you that you look past Newton's fame and popularity, and merely focus on the facts."


9:07 -- 9:08. Newton's lead attorney (played by Silas) makes his opening argument. "We will prove our case through an analysis of our client's paper on infinite series, and we will call John Collins and Henry Oldenburg as witnesses attesting to his character."


9:08 -- 9:32. Leibniz's team mounts a defense. The first witness on behalf of Dr. Leibniz is Ehrenfried Tschirnhaus (played ably by Omar). He testifies to the upstanding character of his friend, and to his mathematical talent.

Tschirnhaus: "I knew him well. We met in 1665, and he visited in 1666. I worked with him further, on mathematical projects. He assisted me in my work on catacaustic curves (involving a geometric form of calculus) and natural philosophy. He was a profoundly good mathematician. He was also an honest man. Though he may have been given the opportunity to plagiarize, he didn't take advantage of this opportunity."

Newton's attorneys have nothing to ask in cross-examination.

The second witness called to the stand is a noted historical and mathematical expert (played by Olaf), who testifies as to the differences between the two scholars' mathematics works.

Leibniz's counsel: "So Newton and Leibniz used different techniques?"

Witness: "Yes."

Leibniz's counsel: "Is it likely that their methods were developed separately?"

Witness: "Yes."

Newton's counsel [in cross-examination]: "What, specificallyt, leads you to believe that the methods are different?"

Witness: "Though Newton's work [on calculus] was performed in the years 1665 and 1666, he didn't publish his work until after [Robert] Hooke died. Leibniz had no exposure to Newton in that time."

Newton's counsel [after a good deal of conversation with ihs client and colleague]: "If Leibniz had seen a manuscript of Newton's, is it reasonable that he would have stolen Newton's work?"

Witness: "Yes, reasonable. He did see Newton's work, though it didn't relate to calculus."

Newton's counsel: "Did Leibniz see those papers? Did he use them?"

Witness: "I don't know for certain."

The third witness called in Leibniz's defense is Leibniz him(her)self (played impeccably by Francine).

Leibniz's counsel [holding Exhibit A, a diagram of Leibniz's derivation of infinitesimals]: "Is this involved in your derivation of calculus?"

Leibniz: "Yes."

Leibniz's counsel: "Can you explain it, please?"

Leibniz: "This illustrates my formulation of calculus through the use of infinitesimals."

Leibniz's counsel: "When did you perform this work?"

Leibniz: "The work was completed by 1675."

Leibniz's counsel: "Is it true that you were in London around that time?"

Leibniz: "I was indeed visiting John Collins in 1676. At that point he showed me a copy of Newton's De Analysi, but I didn't take any notes on it."

Leibniz's counsel: "Why were you holding off on publishing your own work?"

Leibniz: "The Holy Roman Empire was a tricky place to publish at that time. Catholicism was on the outs, and I didn't want to do anything to draw attention to myself."

Newton's counsel now begins their cross.

Newton's counsel: "The word 'infinitesimal' appeared in Newton's work in 1665, did it not? Are we to believe that you got no information from Newton's manuscript?"

Leibniz: "I can't prove that I hadn't stolen from Newton, but I ask that you take me on my word that I did not do so. Infinitesimals are integral [no pun intended] to calculus, so the word should appear. On the other hand, I came up with the word 'calculus.' Moreover, many of our terms are different, like 'fluids' and 'fluxions.' After all, I'm not going to call it a duck if it's an infinitesimal triangle."

Newton's counsel: "Would there have been time for you to have found a new route to calculus, given the time delay between your reading my client's work and your publication of your own? Or maybe you changed the date on some of your manuscripts?"

Leibniz: "Why would I do that? Absolutely not."

Newton's counsel: "Could you have, though?"

Leibniz: "I don't date all of my notes, so I can't be sure of when they were created."

Leibniz's attorneys call their final witness, Sir Isaac Newton himself (played by Knut, who shows outstanding mastery of Newton's work on calculus).

Leibniz's counsel [holding a diagram illustrating Newton's derivation of the Fundamental Theorem]: "Do you recognize this?"

Newton: "That looks like my rate of change method. I began my work in 1665, and published it in 1704. In 1687 my first publication appeared."

Leibniz's counsel: "Why did you wait so long to publish?"

Newton: "I was afraid of criticism, as usual, and I wanted to touch it up."

Leibniz's counsel: "Did my client come to the Royal Society in 1711 to plead his innocence?"

Newton: "Yes."

Leibniz's counsel: "You don't think that your position as President made you a little biased?"

Newton: "..."

Newton's attorneys begin the cross-examination of their own client.

Newton's counsel: "You were the President of the Royal Society. Don't you think that's quite an honor?"

Newton: "That is the case."

Newton's counsel: "When did you say you began your work?"

Newton: "In 1665."

Newton's counsel: "What did this work concern?"

Newton: "It was on fluxions and fluids. And rates of change, with infinitesimals."

Newton's counsel: "And this work was done in 1665?"

Newton: "Yes."

Newton's counsel: "Did you do anything else prior to 1687 that Leibniz might have seen?"

Newton: "No, but I wrote letters to Leibniz that contained veiled references he could have pieces together."

Newton's counsel: "You claimed to be able to calculate the tangent to any curve?"

Newton: "Yes. I referred to that in my letters."

Newton's counsel: "Is it reasonable to assume that Leibniz saw your letters and plagiarized your work?"

Newton: "Definitely."

Newton's counsel: "Thank you, Sir Isaac Newton."

Leibniz's attorneys ask a single question in redirect:

Leibniz's attorney: "The Presidency of the Royal Society is a position of power, correct?"

Newton: "Yes. I had excessive power in that regard."


9:32 -- 9:38. The court recesses for a brief break. After the break Newton's side mounts an offensive.


9:38 -- 10:02. Newton's attorneys present their case. The first witness called to the stand is John Collins (played astutely by Mary Ellen).

Newton's counsel: "You and Sir Isaac Newton are colleagues, correct?"

Collins: "Yes, since 1670."

Newton's counsel: "Can you describe Sir Isaac?"

Collins: "He's peculiar, but brilliant. He has a sensitive soul. He's very averse to criticism and often withdraws into depression."

Newton's counsel: "Would you call him vindictive?"

Collins: "No."

Newton's counsel: "Is he honest?"

Collins: "Yes."

Newton's counsel: "Perhaps the most honest person you've known?"

Collins: "Not more honest than my mother, but Newton's definitely up there."

Leibniz's attorneys begin cross-examination.

Leibniz's counsel: "You were personally involved in Newton's promotion to the Presidency of the Royal Society, correct?"

Collins: "Yes. I voted for him."

Leibniz's counsel: "And you were partly responsible for introducing Leibniz to Newton's work?"

Collins: "Yes, I got them together. I had no idea that Leibniz would plagiarize Newton, though."

Leibniz's counsel: "You're positive that Leibniz plagiarized?"

Collins: "Yes. We have the letters proving it."

Leibniz's counsel: "Have you seen Leibniz's techniques?"

Collins: "I've seen his methods, and some of them look different, but that doesn't take away from the fact that he saw Newton's work."

Leibniz's counsel: "Are you aware of the publication dates that show my client's work appeared before Newton's?"

Collins: "It was publicly distributed work, even if it wasn't formally published."

Leibniz's counsel: "How well do you know Leibniz? How would you describe him?"

Collins: "He's brilliant."

Leibniz's counsel: "Brilliant enough to come up with calculus on his own?"

Collins: "Yes."

Leibniz's counsel: "If he could develop calculus on his own, why steal it from Newton?"

Collins: "That's a good question!"

The next witness to take the stand on behalf of Newton is Henry Oldenburg (played by Kevin).

Newton's counsel: "What is your relationship with Newton?"

Oldenburg: "I'm the Secretary of the Royal Society. I've been in frequent correspondence with him, and have had many personal interactions with him."

Newton's counsel: "What is Sir Isaac's character?"

Oldenburg: "He's easily discouraged by criticism from other people. He's never satisfied with his method, and he always tweaks his experiments over and over to make sure he's got it right."

Newton's counsel: "I read about that. When he was working on On Optiks, he deformed his own eye to learn how it would effect his vision." [At this point, for the only time in the trial, Silas broke character: "No kidding. I read that. It was insane."]

Oldenburg: "I pushed Newton to publish. I talked with him often as a friend and not as a scientist. He was kind of withdrawn. At one point he dropped out of correspondence for 19 months. But I personally saw his work develop in his letters."

Newton's counsel: "When was this?"

Oldenburg: "In the early 1670s, I think."

Newton's counsel: "Was the manuscript available by 1675?"

Oldenburg: "Yes."

Newton's counsel: "Would it have been available to Leibniz?"

Oldenburg: "Well, he was elected a member of the Royal Society in 1670."

Newton's counsel: "Was he a big name at that time?"

Oldenburg: "Yes."

Newton's counsel: "As big, intelligent, important as he was, does that mean he wouldn't plagiarize?"

Oldenburg: "It's possible."

Leibniz's attorneys begin their cross:

Leibniz's counsel: "Newton showed Leibniz documents pertaining to calculus. Why did you encourage this?"

Oldenburg: "I wanted to help further knowledge in mathematics. It was unfinished work, but Leibniz requested to see it.

Leibniz [from his/her seat at the defense team's table]: "I did not request that!"

Me [as presiding judge]: "Order."

Newton's counsel [on redirect]: "The issue, Mister Oldenburg, is not that Newton shared his work, but rather than Leibniz plagiarized it, correct?"

Oldenburg: "Correct."

Newton's team calls their final witness, Isaac Barrow (played enthusiastically by Bernice).

Newton's attorney: "How did you meet Sir Isaac Newton?"

Barrow: "It was 1667, in an optics lecture I was giving. He was a geometry student. It was in the early 1670s when I saw his work on calculus. He took a lot of scorn and criticism. He was concerned about his work, since it was not concrete like geometry was."

Newton's attorney: "As a professional thinker, if you had ever published a paper in which you'd made use of another's work, would you acknowledge the other in your work?"

Barrow: "Yes. To not do so would be plagiarism."

Newton's attorney: "Knowing Newton as you do, would Newton have accused Leibniz of plagiarism if he'd not been guilty of it, if he'd merely collaborated with Newton's full knowledge of it?"

Barrow: "No, and he would have been happy with Leibniz if he'd given credit where credit was due."

Newton's attorney: "Is it possible that Leibniz used Newton's work as a stepping stone to complete his own?"

Barrow: "Yes."

Newton's attorney: "And Newton would have been all right with this had Leibniz given him credit?"

Barrow: "Yes, there'd be no argument."

The defense had no questions for Barrow.


10:02 -- 10:04. Leibniz's team offers their closing argument: "Both of these men invented calculus, and invented it by different means. As a remark, note that the two men never met face-to-face, never collaborated, and neither likely knew what the other looked like. I would also like to point out that Newton used fluxions and fluids and not infinitesimals, and we have never accused Newton of stealing the ideas of another."


10:04 -- 10:06. Newton's team offers their closing statement: "Sir Isaac Newton, President of the Royal Society. Undeniably both of these men have great minds, but the point of this trial was to establish whether ot not Gottfried Leibniz stole Newton's work. Newton began his work prior to Leibniz's beginning his own work, and this work was available to Leibniz, so it could have been done. Leibniz saw Newton's manuscripts, and there's no way he could have ignored what he'd seen."

***

The things I like best about this re-enactment:

1. The students' robust preparation: every single one actively involved in the court proceedings showed they'd practiced their roles carefully and had mastered the material they'd be asked to discuss.

2. The students' arguments: while the Leibniz team did all they could to drive a wedge between the two scholars' methods (no doubt hoping the jury would be convinced they were different enough to have been, undeniably, developed independently), Newton's attorneys focused on the character of their client, arguing (more subtly at times than at others) that he was a trustworthy man, honest and upstanding, surely incapable of making false accusations of plagiarism.

3. The students' performances: with only one or two (understandable!) exceptions, none of the students broke character, and every one offered sterling deliveries.

Coming up next: in their own words, students' reactions to the activity, and a little commentary of my own.

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