Tuesday, November 09, 2010

Newton v. Leibniz, Section 2

Aaaaaaand...Section 2!


Judge 1. We will begin with opening arguments.

Newton's lead. Thank you for being here today. I'm here today to ask you to give credit where credit is due. Newton was first by more than a decade, and he deserves this credit. We have proof that our opponent, though a great man, did in fact see some of Newton's work and did not give credit. We are here to get to the bottom of this case. Please recall that my client spent many years working on this material, and he deserves credit for it.

Leibniz's lead. We believe that our client is not guilty. He came to his theory of calculus based upon his own philosophy. Some describe him as a "universal genius." He is skilled in law, philosophy, and mathematics. We will here testimony to this end. Newton has a history of responding unhealthily to criticism, and that's why we're here today: Mr. Newton has it out for our client.

Judge 1. Newton: witnesses?

Newton's second. We'd like to call Isaac Newton to the stand.

Newton's lead. When did you begin working on calculus?

Newton. About 1665, right before the university closed.

Newton's lead. How much work did you put into it?

Newton. I spent two years getting the basics down. I worked hard.

Newton's lead. Did you develop it in service of some other scientific purpose?

Newton. I enjoy science and math as well, and I pursued math to help my scientific studies.

Newton's lead. You had a goal, then?

Newton. Yes.

Newton's lead. Why did you not publish?

Newton. As was stated, I was indeed leery of publishing. Moreover, there was a large fire which hampered publishing.

Newton's lead. It was difficult to publish, then?

Newton. There were difficulties.

Newton's lead. Who knew of your work?

Newton. Mr. Barrow, my mentor, and Mr. Collins, as well as Henry Oldenburg.

Newton's lead. So others knew about it?

Newton. Others knew.

Newton's lead. So Leibniz may have heard about it?

Newton. That's possible. My ideas on calculus came out about ten years before Leibniz's work.

Newton's lead. What is your opinion of Mr. Leibniz?

Newton. I believe he's intelligent, but I hope that he honestly came up with his own ideas on his own.

Newton's lead. Could just anyone have come up with calculus?

Newton. Not just anybody. There was a lot of work, regarding geometry and algebra.

Newton's lead. Many have referred to you as "the greatest mind of all time." What else have you done?

Newton. I worked on optics, color, and light, as well as in space...regarding the work of Galileo and others. My laws of motion are also important.

Newton's lead. Have you tried to destroy others' character?

Newton. Not really. I'm pretty much a homebody.

Newton's lead. Does fame matter to you?

Newton. Not really. I do what I do for the sake of the knowledge.

Newton's lead. You find these matters stressful. So why take this to court?

Newton. If Leibniz had simply given me credit, we could have avoided all of this.

Newton's lead. Thank you.

Leibniz's lead. Mr. Newton, to you believe that Leibniz plagiarized you?

Newton. I actually do not know that. This is largely up to the witnesses. I just want to be known as the first to study it.

Leibniz's lead. When, exactly, did you do your work?

Newton. I began in 1665, around February, as the records show. In 1669 and 1671 I wrote two papers which were not then published.

Leibniz's lead. In the first edition of your Principia you mention Leibniz, and his name disappears later.

Newton. I don't deal with the publishing matters, so I don't know.

Leibniz's lead. What did you discover?

Newton. Basically, the rate of change.

Leibniz's lead. It seems like a lot of your calculus is similar to that of Fermat. His work was not exactly right, but he was the first to discover his ideas, in the 1640s.

Newton. And why was he not considered the first?

Leibniz's lead. I don't know, but why can he not claim to be the discoverer?

Newton. I can't say. I can't say that Leibniz didn't work off of my work, and I can't say that he plagiarized. I just want credit given where credit is due.

Leibniz's lead. That's all I have.

Newton's second. We'd like to call Leibniz to the stand. When did you start your work on calculus?

Leibniz. In 1675.

Newton's second. So, after Newton?

Leibniz. Yes.

Newton's second. What's in the letters you exchanged with Mr. Newton?

Leibniz. There was no mention of differentiation, and that's what Newton's claiming I took from him.

Newton's second. So there was no influence on you?

Leibniz. None.

Newton's second. We believe Newton's colleagues will dispute that. We believe that you did not cite your sources when referencing my client.

Leibniz. I took rooms full of notes. and I can't be sure that I didn't have notes that should have been cited.

Newton's lead. What's your opinion of my client, Mr. Newton?

Leibniz. I believe he suffered from mercury poisoning.

Newton's lead. Did you ever work with chemistry?

Leibniz. No.

Newton's lead. So you didn't take as many risks as Newton did? Hmmm...did you ever credit the work of Newton which you saw?

Leibniz. I did see some information in his work.

Newton's lead. Why did you not give him credit?

Leibniz. I could ask the same of Newton: he took information from Barrow and gave no credit.

Newton's lead. What did you get from Newton's work?

Leibniz. I was only interested in infinite series, and I didn't find any information on this matter, so didn't feel it was worth citing.

Newton's second. Did you, indeed, plagiarize?

Newton's lead. Sometimes we do not cite people because we want people to believe that we did more original work than we had. Do you have something to hide?

Leibniz. I may have been influenced by Newton's work, but I did not steal his ideas. There is a difference between being influenced by someone and stealing their ideas.

Newton's lead. What is your nationality, Mr. Leibniz?

Leibniz. I am German.

Newton's lead. And my client is English.

Leibniz's attorneys. Objection.

Judge 2. Sustained. Relevance?

Newton's second. Getting back to the letters, why is it that you struck up correspondence with Newton?

Leibniz. I was interested in his ideas.

Newton's second. What kind of information did you get from these letters?

Leibniz. There was information on finding maxima and minima, but there was nothing which I could cite.

Newton's second. That's all we have for this witness.

Leibniz's lead. On the matter of the mercury poisoning, I should note that we can document this allegation, going to Newton's state of mind. I have another question for Mr. Leibniz, though. In one of the letters from Newton to Leibniz, he mentions his own "fluxional calculus," and Leibniz replied with a description of his own calculus. Why would he have replied at all, if he knew he was merely stealing Newton's ideas? The papers Leibniz wrote dealt with series, correct?

Leibniz. Correct.

Leibniz's lead. Why is this in dispute, then? ...

Newton's second. We would like to call John Collins to the stand. Mr. Collins, can you tell us about the relationship you had with Newton?

Collins. I was a publisher based in London, and carried on correspondence with many scientists both in Britain and on the Continent.

Newton's second. So you knew of Newton's work?

Collins. I knew of De analysi, for instance, and tried to get him to publish.

Newton's second. But he didn't?

Collins. He was a great thinker, but he was worried about criticism, after his experience with Hooke and Optics.

Newton's second. So Leibniz saw Newton's work?

Collins. When he visited, I showed him copies of De analysi.

Newton's lead. When did Leibniz visit England?

Collins. He visited Oldenburg, and he visited me in 1672 or 1673?

Newton's lead. Was he interested in Newton's work?

Collins. Yes, he was keenly interested. He asked questions about Newton. I knew he was carrying on a correspondence.

Newton's lead. What was his opinion of Newton?

Collins. Respectful. But Mr. Newton has his idiosyncrasies.

Leibniz's lead. You said that Leibniz got to look at Newton's De analysi, right?

Collins. Yes.

Leibniz's lead. But this paper dealt primarily with series, and not differentiation, right?

Collins. Nevertheless, Barrow thought the paper brilliant enough to give up his Chair to Newton.

Leibniz's lead. But Barrow was very interested in series, so of course he was impressed with Newton's work. Do you know anything about Robert Hooke?

Collins. We corresponded a bit.

Leibniz's lead. Did Newton's work have anything to do with Hooke's work?

Collins. Likely yes, given the interdisciplinary work we all did.

Leibniz's lead. It seems that Newton's work was very similar to that of Hooke.

Collins. Are you suggesting that Leibniz plagiarized off of Hooke? Or that both did?

Leibniz's lead. Nothing further from me.

Leibniz's second. One more question: were you aware of all of the convergent ideas at the time? You do realize that Hooke accused Newton of plagiarism?

Collins. You're referring to the optics paper?

Leibniz's second. Yes. There were a lot of ideas coming to a head then.

Collins. I agree.

Judge 2. We will now take a five-minute break.

Leibniz's second. We would like to call an historical expert. Talking about the idea of convergent ideas, can you indicate any other examples similar to Leibniz's and Newton's?

Expert. There were trends in advancement of these ideas. For instance, there was the Kerala School in India, where these ideas were put forward.

Leibniz's second. They had accurate calendars and were trying to compute the instantaneous motion of the moon, right?

Expert. Correct.

Leibniz's second. So these people, 300 years before Newton, invented some of the same ideas that would later become calculus? Is there any way this information could have gotten into the hands of Mr. Newton?

Expert. It was in a book, written in Sanskrit. It's still there, if you can read it.

Leibniz's second. And missionaries took this back to Europe? And they were schooled in mathematics. It was a possibility, then, that Newton could have deduced planetary motion from these texts, or at least been influenced by this?

Expert. This is possible.

Newton's lead. Is there any proof that Newton saw this work?

Expert. Not that I know of.

Newton's lead. So this is pure speculation?

Expert. It is possible.

Newton's lead. Is it possible that they plagiarized off of me?

Expert. I suppose.

Newton's second. Why are we arguing that Leibniz plagiarized off of Newton, if we could just as easily argue that they both plagiarized off of the Indians?

Expert. It was a very simple form of calculus, it could have done little more than influence people.

Newton's lead. 300 years is very different from 10. Isn't it more than coincidence, don't you think, that calculus was a simultaneous discovery?

Expert. It's odd, yes.

Newton's lead. Does Newton read Sanskrit?

Expert. Not that I know.

Newton's second. No further questions.

Leibniz's second. We call Johann Bernoulli. You are a prominent mathematician and long-time friend of Leibniz, yes?

Johann Bernoulli. I am his student.

Leibniz's second. What was his influence on you?

Johann Bernoulli. My father wanted to become a doctor, but after reading Leibniz's work, I became a mathematician.

Leibniz's second. This man changed your life?

Johann Bernoulli. Yes.

Leibniz's second. You expanded on Leibniz's work?

Johann Bernoulli. And Newton's. And I worked to spread their knowledge.

Leibniz's second. Was Leibniz smart enough to invent calculus himself?

Johann Bernoulli. No doubt. He could easily have come up with it himself.

Leibniz's second. No further questions.

Newton's second. We're not trying to argue that Leibniz did not make advances; we're trying to argue that Newton did it first. What can you say to this?

Johann Bernoulli. Newton's gravitational theories can be improved by using Leibniz's theories.

Newton's lead. The terms you're using sound similar to those used by Newton. Isn't it possible that Leibniz got these ideas from Newton?

Johann Bernoulli. Leibniz was able to use his methods to solve problems Newton posed.

Newton's lead. So Newton's work came first?

Johann Bernoulli. Newton did it wrong. I improved upon it using Leibniz's methods.

Newton's lead. You say that you love Mr. Leibniz.

Johann Bernoulli. Well, look at him!

Newton's lead. Don't you think you're a bit biased?

Johann Bernoulli. Yes: I'm his champion; I thought we went over this.

Newton's lead. Nothing further.

Leibniz's second. We call Newton back to the stand. Do you have any secrets you've kept as an adult?

Newton. No.

Leibniz's second. I have copies of a collection of your notes, and in them it was read that you studied alchemy and kabbalistic studies, and you hid this in order to avoid charges of heresy.

Newton. I like science, and I was curious. This isn't a secret.

Leibniz's second. So you weren't rather reclusive?

Newton. I admit to that.

Leibniz's second. But you ingested mercury?

Newton. Yes. What does this matter?

Leibniz's second. According to the Royal Society of London, you suffered two mental breakdowns?

Newton. Yeah. It was a rough time; I was somewhat stressed over the allegations Hooke made.

Leibniz's second. According to the Royal Society, your temper was extraordinary.

Newton. I had a temper, but it didn't affect my mathematical work.

Leibniz's second. But I believe that it affects your state of mind, and may lead to the reasons you raise the accusations you raise against my client.

Newton. Does this affect my mathematical work?

Leibniz's second. Doesn't this shed light on your view of his plagiarism, though? If he's found guilty of this charge, might it not destroy his reputation?

Newton. I agree he did something very good, but I only want credit where credit is due.

Leibniz's second. The work Leibniz published was only a small piece, though, and because this was simply a tiny result 10 years after his own discovery, might it be possible that he didn't think it necessary to cite his sources, especially since he might not even have been aware of the existence of those sources?

[General cross-talk and disorderly nonsense.]

Leibniz's lead. Between your work and Mr. Leibniz's, there are crucial differences, especially concerning integration. Your methods are very different, is that not the case?

Newton. This is correct.

Leibniz's lead. You used very different methods, so how can you claim that he plagiarized your work when his method was fundamentally different from yours?

Newton. It may be that he didn't plagiarize. I only claim that I did it first.

Leibniz's lead. Nothing further.

Newton's lead. They make a big deal out of your chemistry. Do you regret the work you did with chemistry?

Newton. No.

Newton's lead. Do you feel this work has harmed your judgment?

Newton. No, it does not.

Newton's lead. Do you believe this matter, all of this, is worth taking to court?

Newton. No. I'm only here because I believe there's an important case to be made here.

Newton's lead. Thank you, Mr. Newton.

Newton's second. You weren't intentionally sniffing mercury, right? Just to make this clear. You were studying this legitimately?

Newton. That is correct. But my mathematical work came early in my life.

Judge 1. It's time for closing arguments.

Leibniz's second. You heard a lot of evidence today, and the argument is essentially a matter of probability: is it likelier that my client stole his ideas from rough mention of "fluxions" and "fluents" or that he came up with the ideas on his own? There was a good deal of convergence in ideas during that era, and my client was certainly intelligent enough to come up with calculus on his own. Telescopes, logarithms...why not calculus? Our point is not to show that Newton stole his ideas from the Kerala School; it's to show that Newton may have come upon the same ideas at a different time in a different place. The maps of our ideas may look very similar, even though we've come upon those ideas separately from one another. Finally, consider that the notes Leibniz saw dealt only with a small chunk of calculus, nothing like the grand theory with which he later came up.

Newton's lead. We do believe that Mr. Leibniz did indeed plagiarize, with all due respect to his genius. We were unable to call sufficient witnesses to show what we've needed to show. Central to our argument is that Leibniz saw Newton's work, and didn't credit him as needed. Leibniz may have come up with some of his ideas independently, but he still needs to give credit for the ideas which he got from others, including Newton.

[The court recesses while the jury deliberates.]

Judge 1. The jury has reached a decision?

Jury foreperson. We find the defendant not guilty of the charge.

1 comment:

Anonymous said...

We put on quite the show. I thoroughly enjoyed it. Favorite part: "Witness, please don't interrogate the prosecutor."