Thursday, October 01, 2009

Liveblogging Newton v. Leibniz, Round 2

Below is the "transcript" of the Newton v. Leibniz trial, as enacted by my second section of Calc I studets. See here and, more recently, here, for accounts of other iterations of the same assignment.)

1:51: The court is called to order. Newton's attorneys make their opening statement: "There's a lot of controversy surrounding these two titans of the mathematical world. What we're here to do today is prove beyond reasonable doubt that Newton has absolute priority in the discovery of calculus, and that Leibniz did plaigiarize from Newton." And: "When somebody sees someone else's work and tries to make it their own, this is wrong and constitutes plaigiarizes."

Leibniz's opening argument: "When I came into contact with Newton's colleagues, I was first learning mathematics and didn't understand much of Newton's work. Leibniz subsequently developed my own work."

1:54: Newton begins his case; Johann Bernoulli is called to the stand.

"Is it true that you were the only one who thought well of Leibniz's work?"


"Then who else?"

"My brother Jakob, Ehrenfried Tschrnhaus, and hundreds of others in Europe and China."

"Did you deny writing a letter to Leibniz?"

"I don't recall."

There are no further questions for Johann Bernoulli.

1:56: A historical expert is called to the stand.

"What do you know about the Great London Fire of the 17th century?"

"It took out most of London, including printing presses."

"Did this affect the price of paper?"

"It did. It made paper more expensive."

"And because of the plague, weren't rags more often burned rather than being pulped for paper?"

"That may be true."

"Good. I am attempting to establish that Newton did not publish for reasons other than simply not knowing calculus."

There are no questions from Leibniz's team, and the historical expert is dismissed.

1:59: John Collins is called to the stand.

"What is your relationship with Sir Isaac Newton?"

"We met in 1676, through Isaac Barrow."

"Yes, in 1669."

"What were the contents of that letter?"

"It dealt with Newton's research. Not on tangents and curves, but earlier work."

"Did you copy this letter at all?"

"I don't believe so."

"Did you come into contact with Leibniz?"


"Did he see the letter?"

"He saw me in 1676 and he did see the letter at that time."

"Did he copy that letter?"

"I don't know, but I know Leibniz did see the letter."

Leibniz's team cross-examines: "We never received the entirety of the supposed letter. Do you know what we're talking about?"

"I know that when he came to see me, we talked about Newton's work."

"No further questions."

Collins is dismissed.

2:03: Henry Olderburg is called to the stand.

"Did you deal with Newton's writings and relay letters between Newton and Leibniz?"

"I did, in my capacity with the Royal Society."

"Were some of these letters rather cryptic?"

"I don't know. They were highly mathematical, including facts about the binomial theorem and other aspects of calculus."

[There is confusion from Leibniz's side of the courtroom: "how could one expect a 25-year-old not yet fully immersed in the world of mathematics to understand the convoluted mathematical writings of Isaac Newton?" "Do you have any questions for this witness?" "Not at this time."]

The witness is dismissed.

2:06: Newton's team rests. The court is in brief recess.

2:21: Court returns from recess, and Leibniz's team calls their first witness. Henry Oldenburg is called to the stand again.

"We have proof that there was a letter sent from Newton to you on October 24, 1676, that remarked that Leibniz had developed a number of methods, one of which was new to Newton (on power series). Is this true?"

"I'm not too sure. I might have seen such a letter, but I'm not sure."

Oldenburg is dismissed from the stand.

2:24: Johann Bernoulli is called back to the stand.

"Were you in contact with Isaac Newton?"

"Indirectly, yes."

"Did you ever receive a letter from him, talking about his calculus, and ways of coming upon calculus?"

"I did; I saw a paper he published. In Book 2, Proposition 10 of that paper, he made a mistake that I pointed out to my nephew, Nicolaus, who then corrected the error."

"This is after Leibniz had published his work on calculus, right?"


Cross-examination begins.

"What is the name of this book?"

"I believe it was his Principia."

"And this was not about calculus, was it?"

"I don't know."

"And who is this nephew? Do you have a copy of the book? Do you know what was in it?"

"It wasn't on calculus, it was more physics."

"What does his making mistakes about physics imply about his knowledge of calculus?"

"I merely want to point out that he's not infallible."

"No one's claiming that he's infallible. Not even the members of the Royal Society."

"But the Royal Society is claiming that he is the sole discoverer of calculus."

"Yes it is."

"But was Newton not on the board of the Society?"

"Yes, he was."

"Is this not a conflict of interest?"


Johann Bernoulli is dismissed.

2:31: Gottfried Leibniz is called to the stand.

"Do you know anything about Newton's development of notation, and his theories? And can you say more about your own notation?"

"Newton's notation came primarily from physics; he worked with vectors, velocities, speeds, and so forth. Whereas I, on the other hand, tried to use basic graph definitions. Newton did a lot of the same things, but his methods were harder. Furthermore, I tried to understand convergence of power series representations of functions, and he did not. Notationally, I used differential notation, whereas Newton used dots."

Cross-examination begins.

"Newton and Leibniz corresponded, is this not true?"

"Yes, but most of the time I learned of something from him only after I'd done it myself."

"So you did talk about mathematics, such as tangents and whatnot?"

"Yes, but Newton was concerned more with physical quantities."

"But even though you had your own ideas, the letters could have possibly helped you to expand on your work, is this not true?"

"Yes, because I'd often work through problems using both his work and your own?"

"Did you not admit in a letter to Conti that you were aware of Newton's work?"

"I did. But I'd already developed it on my own."

"Did the Royal Society not officially charge you with plaigiarism in 1715?"

"They did, but there was bias in that action."

"Do you have proof that you had discovered calculus first?"

"No, but I published first."

Leibniz is dismissed, and Leibniz's attorneys rest.

2:40: Newton's team gives their closing argument: "Keep in mind that what we're dealing with here is a very serious issue. Although there are dirty tricks played on both sides, the bulk of the evidence supports Newton's claim."

Leibniz's closing argument: "We're not claiming that Leibniz created calculus solely on his own, but only that he did not plaigiarize the work of Newton."

Fin. We'll see what they say tomorrow!

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