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The Calculus Wars (What the Conspiracy!)
26 Plays2 years ago
M schools Josh in the mud-slinging history of calculus!
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Josh is @monkeyfluids and M is @conspiracism on Twitter
You can also contact us at: podcastconspiracy@gmail.com
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Transcript
Introduction and Film Discussion
00:00:00
Speaker
Pumpkinhead. Sorry? Pumpkinhead. The film with Lance Henriksen. You were trained to recall in the last bonus episode was Pumpkinhead. No. Yes. You sure?
00:00:14
Speaker
Pumpkinhead is a stone-cold Lance Henrickson classic, I'm pretty sure I'd remember that one. Well look, a patron got in contact to say it was Pumpkinhead, and frankly, who are we to question the wisdom of the most beautiful people in the world? Who indeed, Pumpkinhead. She's not really off my game. Sorry, isn't this a What the Conspiracy Week? Aren't we meant to be double-bluffing each other over the topic here? I think that joke has truly and utterly run dry.
00:00:39
Speaker
Yeah, fair enough. Ah, Pumpkinhead, Stan Winston's directorial classic. His three sequels, you know, two of which are filmed in none other than Booker Reston, one of which stars Doug Bradley, Mr. Pinhead himself. The thing I like best about the first Pumpkinhead film is that I will have a prologue and then immediately cuts to a shirtless Lance Henriksen doing work outside as the caption, the present appears. And it's not entirely clear if the present is telling us that we've now moved ahead in time or simply if the shirtless site of Lance Henriksen is a gift to us all.
Podcast Introduction and Patron Perks
00:01:26
Speaker
Hello, you're listening to the podcaster's guide to the conspiracy. In Auckland, New Zealand, I am Josh Addison, and in Zhuhai, China, we have associate professor of philosophy, and the last voice any of us will hear before the end, Dr. M. R. Xtenteth. Which means you should be worried that what you're listening to now...
00:01:37
Speaker
subtle, subtle nuanced filmmaking there that I think, um, I don't know what to say.
00:01:44
Speaker
is the end. And are you prepared? I don't think you are, Nigel. If you're not called Nigel listening to this podcast, please stop now. We don't want to know about it. This is Nigel's last message.
00:02:00
Speaker
Yeah. In regards to that opening sketch, I think the first thing to say is that Em wrote it. The second thing to say is how dare you, how dare you suggest that I would not be able to remember the name of pumpkin headlamps in one of London.
00:02:17
Speaker
who gave you this film. Honestly, I'm insulted and offended quite frankly. I'm obviously, you are a patron of ours and therefore one of the most beautiful people and quite frankly, I can't stay angry at you, but nevertheless, pumpkin head for God. So you might as well say, oh, did you know that Lance Henriksen isn't aliens? Have you ever heard of that obscure indie number? Honestly, good God. Anyway, so I looked through the IMDB. It turns out the film I was thinking of is called It's In The Blood.
00:02:44
Speaker
from 2012 it's not a good film it's hopefully not a film any of you have seen because it's not a good film and that's that's all there is to say but in fact this is gonna be nothing to our listeners anyway because this is all about a reference that came up in the bonus episode last week so maybe we should just stop talking about it completely
00:03:02
Speaker
But this does point out, if you do want to find out about the weird things we talk about on those bonus episodes, you should consider becoming a patron. Because it's not just conspiracy theory stuff we talk about, but actually, often the bonus episodes start off as being conspiracy theory related, and then become conspiracy theory adjacent.
00:03:22
Speaker
and then doesn't even really mention conspiracy theories but becomes a... Remember that film we watched back in 1998? You know, the one with the actor? Yeah, you know, that one. It had a farm in it and maybe an alien spaceship that crashed into it. You know, it was probably one of the extra films. I mean, you know, you remember it. Yes, and generally I do.
00:03:45
Speaker
Oh, and just talking about the extra films, what a weird sequence of films they turned out to be, related really only by name, and not really by anything else. No, no, yes. I've seen the first one, I'm pretty sure I've seen the second. The thing is, you wouldn't know the second one. No, I wouldn't know it was the sequel, unless you actually looked at the VHS cover.
Weekly Theme: Conspiracy Guessing Game
00:04:07
Speaker
Anyway, this is about the conspiracy week, and it is Em's turn to hoodwink me.
00:04:14
Speaker
if you can. So unless you have anything else to say, shall we move things along? We shall indeed. Let's move on over to Want the Conspiracy with a jazzy, jivey beat. It's time to play Want the Conspiracy.
00:04:40
Speaker
Okay, Josh, this week we are going back to school, which is the only hint I'm giving you for the three perennial questions of when the conspiracy, where the conspiracy, and what the conspiracy. So Josh, when does this conspiracy take place? Well, back to school, you say. So at least it's presumably post the advent of school.
00:05:09
Speaker
which puts it sometime in the last, what, 2,000 years? Not really giving me a lot of help, quite frankly. I'm going to say, specifically, 1983. August, August 1983. Mmm. Specific, you say. Specific. All right, where does this August 1983 conspiracy take place? Well, clearly in a school. Where are the most schools in the world?
00:05:37
Speaker
I don't know. America has the most universities, so let's say the Grand Dog USA. You're not going to get more specific than that? No. I mean, really? OK. No, I'm going to go generalist. I'm just going to say the American continent, anywhere in North or South America. Interesting. All right. So really, well, relatively specific for the whim. Very vague to the where. I'm now quite curious to know how specific, vague or ambiguous the what is going to be.
00:06:07
Speaker
Ah, we'll see here, I've got you figured out. You said back to school as the hint, which seeks to sort of steer me into the, into the realms of education. But I know you're actually about to say, back to the future, and quickly just change your mind slightly. So it's going to be some sort of a time travel slash movie starring Christopher Lloyd and Michael J. Fox themed conspiracy.
00:06:32
Speaker
i see right through you that takes place in august 1983 somewhere on the continental americas yes interesting so i have to say your gambit and your specific gambit about the when very very wrong very very wrong because we're talking about the term of the 17th and 18th centuries right is that different from august 1983
00:06:59
Speaker
ever so slightly. Now the where is Britain and the Holy Roman Empire as Germany was called back in those days. So basically looking somewhere between London and Hanover. Right, neither of which are in the wider American continent I'm given to understand.
00:07:21
Speaker
not even on the loosest definition of what counts as American soil. And the what is the development of calculus calculus, I'm sure that was involved in the sum of the calculations behind the development of the flux capacitor and back to the future too. So I'm calling that calling that a win.
00:07:40
Speaker
Well, actually, in that respect, you're right in some sense in that Isaac Newton talked about flexions and indeed his development of differential calculus was based upon his flexion calculus. But it turns out that flexions and flux capacitors are related by four letters and virtually nothing else. Like I say, I claim a win. So tell me about conspiracy theories and calculus.
00:08:08
Speaker
All right, so what do you know about the history of the development of calculus?
The Calculus Controversy: Historical Insights
00:08:14
Speaker
Oh gosh, less than I used to. I studied calculus at high school. I used to be able to do it, but my calculus muscles have atrophied over time, what with not having any application for them in my everyday life. Didn't, didn't, didn't, old Hypatia of Athens, wasn't she on her way to developing calculus before she got killed? And if she had
00:08:39
Speaker
the course of human history could have gone completely differently. So I think there is something to that. I know that there's an awful lot of talk about what Hypatia may or may not have done in Alexandria as a proto-mathematician in the sense that we call mathematics now, because of course there wasn't the kind of formalism we have in mathematics.
00:09:02
Speaker
in the ancient world and certainly her being almost erased from history is one of the great tragedies of the development of philosophy over time. Did you actually see the film Hypatia? The Rachel Weiss one? Yeah. Oh no I never did.
00:09:18
Speaker
quite interesting, takes a lot of liberties with the story of Hypatia. But at the same time, most histories take fair liberties with the story of Hypatia because we've had to kind of reconstruct her history and what we think she was working on. Given the aforementioned erasure, erasure, erasure, erasure, erasure from history.
00:09:43
Speaker
All right, so you don't have any idea of the controversy over who developed calculus then? Not particularly. It was one of those things where it would have been one of those things where the people coming up with it like to write in code and all that sort of stuff, so people didn't steal their ideas.
00:09:58
Speaker
I assume. There seem to be a lot of that going on. So basically there are two people who discovered calculus independently of Egypt. Other, in the United Kingdom, or Britain, or England, you have Isaac Newton, who is infamous for stabbing needles in his eyes, and over in the Holy Roman Empire have got free to be able to have lagnets.
00:10:21
Speaker
who is famous for being very, very cantankerous. And they both kind of came up with the idea of differential calculus around about the same time, because civilization was basically primed for calculus to emerge at that point. These aren't people who are sitting isolated in rooms, inventing mathematical systems from whole cloth,
00:10:44
Speaker
These are people who are going, oh, all of these new exciting developments in mathematics suggest a particular lacuna. And so they are working independently of each other, although independently here is a very, very conditional term, developing calculus and then discovering
00:11:03
Speaker
that the other person has developed calculus as well, leading to accusations that ideas have been stolen or that plagiarism has occurred. Now here's a fun fact.
00:11:16
Speaker
I'm going to talk about two figures who are alive at the same time, who are in correspondence with each other, one of which actually visits the other's country, two men who get into a big epic mudslinging fight about who invented calculus, and it turns out they never met face to face. So it's like a sliding door situation, except this is telling calculus.
00:11:42
Speaker
and also has no trend. Or, you know, involves a multi-pass in a civilization that doesn't require multi-passes. Now, I just need to test your calculus knowledge here. So a trainer is travelling south from Britain might station to Papakura at 40 kilometers an hour.
00:12:01
Speaker
an hour. Meanwhile, Lord Morrissey Morrissey is walking along the tracks from Papacurra to Brissow Mart at three kilometers an hour. Assuming continuous motion, how far away from Papacurra does his lordship meet his fate? Yes. Good answer. All right. So as I say, the standard story is Leibniz and Newton independently arrived and invented calculus using their own formulations and notations.
00:12:29
Speaker
in the 17th century. So you've got work occurring towards the end of the 17th century and then a controversy that starts to occur in the 18th century. Now this is the epic age of mudslinging.
00:12:44
Speaker
So people like to talk about the end of the 17th century as being the golden age of academic mudslinging. People liked to accuse other people of doing bad things and then responding in kind. And what's interesting about this particular age is that there are a lot of mudslinging matches going on.
00:13:06
Speaker
in the academic world of Europe at that time, and that also led to people basically ignoring each other's work in order to maintain the sense of national pride. Newton and Leibniz were both natural philosophers,
00:13:23
Speaker
And they were engaging in a lot of correspondence. We have the papers of both Newton and Leibniz in libraries now, so we can kind of see what they were writing to one another. We can also see what they were working on at different points in time.
00:13:41
Speaker
And initially their correspondence is relatively friendly, but starts to get quite confrontational, especially when they start accusing each other of stealing each other's ideas. And one of the reasons why Newton and Leibniz end up getting kind of offside is that Leibniz was very much a mechanist. Leibniz was of the belief that the world works in a really quite mechanical fashion.
00:14:09
Speaker
And he found Newton's idea of gravity to be just ever so slightly occultic. Occultic? Because of invisible forces. Yeah, action at a distance seemed like Newton was proposing a going back to supernaturalism or mysticism as a way of explaining things about the world, and that wasn't the direction the sciences were taking at that time.
00:14:34
Speaker
How did they account for gravitational effects? Was it ear pushing down on us or something?
00:14:40
Speaker
Yeah, so you'd have notions of centripetal forces or centrifugal forces, the idea of like attracts like, so the kind of resurrection of Aristotelian notions, the idea of action at a distance, which we now take to be a fairly standard mechanical process in a deterministic universe, did really seem quite mystical, and given that new certain
00:15:05
Speaker
was trying to turn lead into gold the entire time in a search for the floss of the stone. You can kind of see that if you knew what else Newton was up to,
00:15:15
Speaker
You might go, I mean, this gravity thing does seem like a little bit of a cultic nonsense. Are you quite sure this is the fundamental and foremost natural philosopher of Britain, someone who believes that gravity is action at a distance? I mean, I mean, that's the kind of thing that Pope would say.
00:15:36
Speaker
Okay, so was this the start of the falling out between the two? Or did this spark an argument between them? Or was this nearly the first in the long string of things? We can look at two dueling theories here. The first is that Leibniz plagiarized the work of Newton. Then we're going to look at the claim that Newton stitched Leibniz up knowingly.
00:16:04
Speaker
And they both have some degree of secrecy and conspiracy. One of them is going to be incredibly conspiratorial to the point where if you had a button you could press that went dun dun dun, you'd be pressing dun dun dun like it was going out of fashion.
00:16:23
Speaker
So let's start with the more prosaic one. This is the thesis that Leibniz stole Newton's idea of calculus. So calculus emerges as we say turn of the 17th and 18th centuries when Leibniz publishes his first work on differential calculus
00:16:48
Speaker
He's immediately accused by the supporters and friends of Isaac Newton of Platerism. And this is because Leibniz produces a paper on calculus.
00:17:04
Speaker
and now in 1684 so 1684 is when he publishes nova methodus pro maximus et minimus or a new method for maxima and minima as well as tangent which is not obstructed by fractional or irrational quantities so this is the first formal publication
00:17:24
Speaker
of calculus in the Western world. The problem is Isaac Newton had written a paper on calculus back in 1669. Right. Had this been distributed wide enough that it's conceivable Leibniz could have read it? So here lies the issue. So Newton writes his paper in 1669 and then refuses to publish it. Ah, one of those, yeah.
00:17:51
Speaker
he didn't like publishing anything. So the Principia Mathematica is his major work. He publishes at the age of I think of 66. So he spends most of his youth
00:18:06
Speaker
writing and investigating the natural world, writing papers are, but refusing to publish them. And we know from correspondence with his friends, they are encouraging him to publish all the time. Isaac, you've got to get these ideas out there. Isaac, you should really release this paper. Isaac, you're a member of the Royal Society. Why not publish this in the journal the Royal Society runs?
00:18:33
Speaker
And he would just refuse to publish. And we don't know why. There's no explanation as to why Newton was publication a verse. But we know that he was. He simply was not going to publish these small papers. He was working on his magnum opus, the Principia Mathematica. And then once the Principia is produced, he starts doing things like the optics and the like. So we start to publication, create very late in life.
00:19:00
Speaker
Now we have the papers he wrote now. We also know that he was sending those papers around his friends.
00:19:09
Speaker
but he wasn't sending them to many friends. We think there are probably less than 10 mathematicians in the United Kingdom that he, I don't know why I keep calling it the United Kingdom, I don't think the United Kingdom is as negative. I think I should just be talking about Britain and that way it can be vague as to whether Britain contained other elements other than England. He's sending his papers to friends in Britain
00:19:36
Speaker
but less than 10 mathematical friends. But the suspicion is that those friends gave Leibniz access to Newton's unpublished work. Right, but only a suspicion?
00:19:53
Speaker
Well, we've got some circumstantial evidence. So a copy of one of Newton's manuscripts had been sent to, I'm going to really, really butcher a German name, Unfried Walter von Schauhausen in 1675. So this had been sent by whatever counted as the post back in those days to a colleague in Germany. And later that year,
00:20:22
Speaker
this particular mathematician was working with Leibniz. So it is possible that if the German held a copy of Newton's manuscript
00:20:35
Speaker
And then he took that copy of the manuscript to a meeting with Leibniz. Leibniz might have seen it. Right. And in 1676, so a year later, Leibniz visits London because Leibniz traveled quite a lot.
00:20:53
Speaker
And he was working with John Collins and Henry Oldenburg, who were close friends of Newton, and they were members of the Royal Society. And they might have shown him the same manuscript by Newton, a copy which was possessed by at least one of them. Right. Do we also... We must have records, though, of when Leibniz was doing his work, though.
00:21:21
Speaker
Yeah, so here are my issues. So I was about to say the other bit of incriminating evidence here is that Leibniz and Newton were corresponding by letter with frequency and Newton at one point describes his calculus in one of the letters to Leibniz. But yes,
00:21:40
Speaker
As I mentioned earlier, we do have a fairly good corpus of the papers written by both Leibniz and Newton. And so we can track the development of both Newton's development of calculus and Leibniz development of calculus.
00:21:58
Speaker
And at every single point where Leibniz might have seen the work of Newton, we can show that he's already done the relevant work a few years prior. And this brings us into a kind of interesting notion of primacy here, because it is the case that Leibniz published first on calculus. It is also the case that Newton invented calculus first.
00:22:26
Speaker
But in a sense, because Leibniz independently came up with calculus a decade or so later, and then was the first person to publish it, we can say that Newton first invented it, but Leibniz was the first person to actually formally publish on that work.
00:22:46
Speaker
And he appears to have come up with calculus independently of any of the work Newson had done. And this kind of gets us into a really interesting cultural distinction here because these days there's a rush to publication. You want to be the first to be on record with an idea. But in the 17th century,
00:23:07
Speaker
as long as you were known to have worked on a topic, which is to say that you wrote on the topic and you had reliable witnesses who had seen that you had worked on the topic, that was often seen to be sufficient to be the originator of an idea. I mean yeah we see that all the time with
00:23:29
Speaker
inventions as well, even going back a couple of centuries or rather than rush to publish it would be the rush to patent because we know there are there are types of examples of an idea whose time has come where you'll see multiple people working on the same thing and developing them independently. But you know, one person, the Wright brothers were the first ones to actually make it to powered flight, even though there were people all around the world, including Richard Pierce here in New Zealand.
00:23:58
Speaker
It's not like they were copying off of the Wright Brothers' plans, but they were all working on the same thing. The Wright Brothers got there first, and lots of other things. Who was it? The radio? Wasn't Marconi and a bunch of other people working on radio at the same time? There's heaps of cases of that, so I assume in the academic world it would be similar.
00:24:17
Speaker
Or at least it is similar these days, but yes. Interesting that it wasn't always the case. The other example of course is Tesla versus Edison working on what is the most effective way to transfer power over a distance to allow you to pump electricity into homes.
00:24:37
Speaker
And in that case, they both come up with rival hypotheses as the best way to direct current versus alternating current. And then, of course, get involved in a mudslinging match of the most epic proportions, which led to Edison electrocuting elephants.
00:24:54
Speaker
Only he didn't. We've talked about that in our episode of this before. Given I have such a low opinion of Edison, I would just rather prefer to believe he actually did electrocute those elephants. There was a good chance he electrocuted dogs, or at least worked with someone who electrocuted dogs and didn't have a problem with it. I can't remember exactly how it worked, but yes. The other one,
00:25:18
Speaker
A little bit different, of course, is Darwin and Mendel, where Darwin's coming up with his theory of natural selection, evolution by natural selection, without any idea of genetics. So he knows that traits are passed on from one generation to another, but has no idea by the mechanism how. At the same time, Mendel is developing genetics, and the two would work together nicely, but they weren't actually aware of each other. And it wouldn't be until sometime later that people actually stuck the two of them together to come up with a grand synthesis.
00:25:47
Speaker
It probably doesn't help that Mendel was a monk working in a monastery. Really, really interested in pea plants.
00:25:57
Speaker
Now that's making me think of a gritty reboot of Breaking Bad set in a monastery, but Mendel's not working on pea plants, he's working on the evolution of pea. Which for non New Zealand listeners, pea is the term we use for pure amphetamine back home. So meth basically.
00:26:20
Speaker
Right. Something probably freely available to Newton and Leibniz, quite frankly. They were all on cocaine back then, weren't they? They did enjoy a good old snifter, if you know what I mean.
00:26:36
Speaker
where they got across on the microphone, I have no idea whatsoever. So Newton's supporters basically accused Leibniz of plagiarism. Leibniz had access to Newton's papers, even they claimed if Leibniz had independently come up with calculus initially,
00:26:58
Speaker
he was then borrowing the more advanced work by Newton. So one of the theories goes that, yeah, Leibniz was working on calculus. It was only when he saw Newton's mathematical work that he worked out there was a simpler way to do it, that he was then able to finalize his calculus. Because of course, the kind of notation we use for calculus is not Newtonian. Newtonian calculus turns out to be
00:27:25
Speaker
slightly more complicated than it needs to be. Leibniz notation is the one that we use in the here and now because it's a much simpler way to do a very complicated thing and I still don't know when Lord Morrissey Morrissey is going to hit his fate Josh. Have you worked it out yet? Tea time. Proper time for an Englishman to meet his maker.
00:27:46
Speaker
Also a good answer. Now it also doesn't help that Leibniz had been accused of plagiarism before. He had claimed to have come up with a method of differences for numbers in series, but people had worked out that someone in France had actually already generated this idea.
00:28:05
Speaker
which caused Leibniz huge embarrassment. I believe it's one of the things that made him leave London the first time he visited. He was able to acquit himself by displaying his private notes by going, look, I can show that I didn't copy anyone's work. My diary entries kind of show that I've been working on this for quite some time. But the fact that he'd been accused of plagiarism in the past was used by Newton supporters in him around
00:28:34
Speaker
about this time. Now a consequence of all these claims of plagiarism was actually put back British mathematics by about a hundred years.
Impact of the Calculus Dispute
00:28:47
Speaker
How so, if Newton was supposedly the guy who was on the money? Because the British wouldn't use Leibniz notation. And it turns out the Europeans were. The Europeans go, oh, this new calculus, because other Europeans didn't really care about the national pride of the British. They're going, well, we've got this new idea. It's been written up in an article or a book.
00:29:12
Speaker
We can use it to solve a whole bunch of differential issues. Let's go full steam ahead and engage in wacky mathematical work. And the British way we are, we're not using Leibniz notation. We're going to use Newton's much more complicated notation instead.
00:29:30
Speaker
And that led to a situation where British mathematicians were unable to use the work of the European counterparts because of the difference in the way they were resolving their problems using different notation, and also being steadfast in refusing to use that notation for about a hundred years, which meant that they were using a much more difficult system
00:29:55
Speaker
to look at differentiation, and that caused them quite a lot of backsliding in the mathematical world. Who would have thought that Britain's opposition to how things are done in Europe would end up having horrible negative consequences for them? I know you'd almost think that there's a lesson in that today, although I'm not quite sure what it is. No, no, it's a mystery.
00:30:18
Speaker
So yeah, our first claim is that Leibniz stole the work of calculus from Newton with claims of plagiarism, and whilst there's secrecy involved here,
00:30:34
Speaker
There's not really a conspiracy. It's simply Newton supporters accusing Leibniz of doing something untoward and the grim consequences of that. So instead, let's move to the much more conspiratorial aspect of the story, the claim that Leibniz was stitched up by Isaac Newton.
00:30:57
Speaker
some sort of a some sort of a reverse sting operation or something where you do the one of those ah you've done exactly what I wanted you to do and now it's made it look like you plagiarized even though I know you didn't that sort of thing well I mean there's going to be an element of that to the story so as said in 1684 Leibniz publishes Nova Methodist Pro Maximus et Minimus and
00:31:22
Speaker
It turns out that, yes, Newton had actually developed calculus earlier. It also turns out that Leibniz had developed calculus earlier. So he publishes Nova Methodus Pro Maximus et Minimus in 1684. It actually developed the system described in that piece nine years prior, but it's had never got round to writing it up. So like Newton, Leibniz was kind of sitting on an idea and go, well,
00:31:52
Speaker
When I get time, I'll write this particular thing up. But on the publication of Nova Methodist, Pro Maximus et Minimus, Newton, who's in correspondence with Leibniz, as previously mentioned, kind of gets in touch to go, hey, I already invented that, please give me credit. And Leibniz, who as mentioned before, was quite cantankerous, was going,
00:32:16
Speaker
Yeah, I'm not going to give you credit for A, work I've never read, although as Newsom points out, I actually did describe some of the system to you in a letter, although Leibniz goes at that point, well, yeah, sure, but I'd actually already worked it out by that point, so I kind of ignored that. And also Leibniz going, I'm not giving you credit for work you haven't published.
00:32:37
Speaker
I mean, you can say, oh, I came up with this idea a few decades before you did, but you didn't actually publish it anywhere. So how would I know that? Which seems a fair point. But as said, Leibniz is cantankerous. So Newton publishes The Optics, and Leibniz writes an anonymous review of it, an actor, yeah,
00:33:06
Speaker
Eriditorium. So erudite, so Ecto eriditorium, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite, erudite. I should just do the whole
00:33:30
Speaker
I see the name of your journal. In which he insinuates that Newton's calculus came after Leibniz. So this is an anonymous review of a work by Newton written as if it's by a kind of
00:33:48
Speaker
neutral third party observer, and he just slips in that he thinks that, as the anonymous reviewer, that Newton's calculus came after and didn't precede Leibniz's work.
00:34:02
Speaker
the equivalent of setting up an alternate Twitter account these days. Basically, yes. Now, it's not clear that Newton was aware of this review, but in 1708, a fan of Newton, John Keel, wrote a paper on the laws of centripetal force, which was published in the philosophical transactions of the Royal Society, so the Royal Society's journal,
00:34:30
Speaker
Now academics today complain about the period between submitting a piece and then getting a piece published. It turns out this problem has been around for a long time because Keel writes his piece in 1708. It doesn't get published until 1710.
00:34:47
Speaker
And in this particular paper, he claims that Newton invented calculus and doesn't state explicitly but really insinuates that Leibniz stole the idea from Newton. Right. So is this where the claim was made public first? Had people been
00:35:08
Speaker
muttering about it before this, or...? So it seems like it had been muttered, but it had never kind of been written down. And Leibniz takes exception to this, because this has been published in the foremost journal in the English-speaking world at the time, the Philosophical Transactions of the Royal Society. So he makes a complaint to the Royal Society, saying, look, one of your members
00:35:35
Speaker
has claimed that I stole the work of Isaac Newton. I can show that A, I was the first person to publish on this topic. And B, even if it turns out that this Isaac Newton fellow who claims that he wrote his work down well before I did, I can prove that I came up with this idea independently. And also by the way, I was the first person to actually publish on this topic.
00:36:03
Speaker
So he appeals to the Royal Society in Britain to basically censor John Keel. And so the President of the Royal Society appoints a committee to investigate these allegations. Now Josh, who do you think was the President of the Royal Society in 1710? My guess would be Isaac Newton.
00:36:27
Speaker
It was indeed Isaac Newton. So Isaac Newton, who is having to investigate a claim that his foe Leibniz came up with the idea of calculus first, has been asked to investigate this claim and appoints a committee to investigate the allegations. What do you think happens next?
00:36:53
Speaker
I assume the committee finds entirely in Isaac Newton's favour. You're kind of right, in that it is true the committee produces and endorses a report saying that Leibniz
00:37:09
Speaker
concealed knowledge of prior relevant work they don't actually the report doesn't actually say he plagiarized the work it simply says that Leibniz is guilty of concealing knowledge of prior work but crucially this report was not written by the committee
00:37:27
Speaker
This report was written by Isaac Newton. So, Isaac Newton points a committee of his friends, presents them with a fate accompli, this is what you're going to find. You just need to sign and endorse the documents. Here's a document, give it a stamp, give it a signature, and we're going to release it.
00:37:50
Speaker
So coincidentally, the Royal Society concludes in 1715, could take some a while to engage in this investigation, that Leibniz was concealing knowledge of the work of relevant achievements of other researchers, like say the president of the Royal Society, Isaac Neusen, based upon claims such as, well, you know, some of Neusen's friends visited Leibniz in Germany
00:38:19
Speaker
and had letters of Newton's describing the calculus. And when Leibniz visited London on previous occasions, he was in the presence of particular works of Newton and may well have copied their contents down. We're not saying he plagiarised it. We're simply pointing out that he should be aware that other people came up with ideas first.
00:38:44
Speaker
I wonder, so what do these friends think of this? Like they're sort of being accused of wittingly or unwittingly being collaborators in this plagiarism, although I suppose if there was a bunch of them then they could each think, oh he must mean another one, another person was the one who
00:39:03
Speaker
went and spilled the beans to Leibniz. The claim here is not that these people secretly gave Leibniz on the slide. I guess, oh, have a look at this particular thing here. So we know all mathematicians doing mathematical work. We're carrying around our mathematical papers. No one's even aware that Leibniz is working on these particular issues. So we're just sharing information with one another as colleagues are likely to do. And that's where they go, look,
00:39:32
Speaker
They're not making that claim that Leibniz was engaging in plagiarism. They said, you just should recognize that Newton got here first and you knew it. You knew Newton got here first because you've seen the evidence he was working on this topic before you came up with the idea. So they don't need to think that they've done anything wrong. They just need to think that Leibniz has abused their friendship.
00:39:57
Speaker
Right, okay. I assume Leibniz took this very well with a cheery disposition. Well, he dies one year after the report was released. That's an extreme reaction. Yeah, I actually don't know much about the death of Leibniz. I'm assuming it isn't based upon stress and anxiety. I'm assuming it's based more upon the fact that we're talking about people in the 17th and 18th century with both deplorable lifestyles and also deplorable living conditions.
00:40:27
Speaker
But yes, the report comes out, Leibniz dies. People become aware after that point that Newton was actually the author of the report. Leibniz's death didn't stop Newton from continuing to litigate the claim that actually his fame had been defamed by Leibniz's publication.
00:40:49
Speaker
So even after Leibniz's death, Newton was trying to get people to say that Leibniz was in the wrong and had not been recognising prior work. So it turns out dying wasn't enough to stop this feud. Newton was going to continue to litigate this for a long time afterwards. Now it is recognised
Independent Development of Calculus
00:41:11
Speaker
that actually calculus was developed independently by two different people. It's actually quite possible it's been developed by more than just two people, but only two people have kind of got to the point of publishing and then fighting about it. Anyone else who may have been working on the issue might have gone.
00:41:29
Speaker
I don't really want to get involved in that. I might just stay quite quiet about this. But yes, it actually seems at least in the case of Newton's campaign against Leibniz, we have an actual conspiracy in that Newton has asked to investigate
00:41:49
Speaker
insinuations concerning himself decides to appoint a committee to investigate those insinuations or allegations, writes the report himself, gets his colleagues in the Royal Society to give it the imprinture as if an actual investigation has gone on,
00:42:10
Speaker
and then present that as being a proper investigation as commentators on the feud point out. They don't even go so far as to ask Leibniz, can we see the evidence you've got to show that you at least independently came up with calculus? No, it's a
00:42:28
Speaker
It's a fate accompli. It's a Moscow show trials situation. Well, we're going to do a fair and independent investigation. Who's actually working on it? Well, Isaac Duesitos, of course, he's writing a book. We're not going to admit that Newton wrote the report. We're going to pretend it was actually written by the commissary and that information doesn't come out for quite some time.
00:42:49
Speaker
right so i mean i guess asimov got the last word there asimov i keep saying i keep thinking of the wrong isac well i mean no but it's true asimov did get the last word because he helped lived newton and light and Leibniz through the trick of being born after they were dead yes yes no sorry but newton newton got the last word so uh did Leibniz have any supporters who were still sticking up for him after his death or was that kind of the end of it
00:43:19
Speaker
Well, the funny thing about this is it's very much a feud in Britain. It's really not a feud elsewhere. As I say, the Europeans, as if the Europeans are one homogenous people, the mathematicians working on continental Europe, well, Leibniz's work is easier to use and
00:43:39
Speaker
we've got a written down formally published one. So Newton's work occurs several years afterwards, at which point mathematicians in continental Europe are already using Leibniz notation. So really, in continental Europe, people are going
00:43:58
Speaker
No, we're just going to use Leibniz's stuff. And the fact that the British are so adamant, you must recognise Newton as being first. And mathematicians in Europe are going, you know, we don't really have this national pride thing. It doesn't really end up being an issue anywhere other than the UK, as far as I can tell.
00:44:19
Speaker
No, I suppose that makes sense, yeah. Yes, I can imagine the rest of the people who didn't have any skin in the game going, well, this one's already here, oh, Newton did it first, okay, yep, good for Newton, yep, I agree, I can see how they're the same. Anyway, back to the one we were already using, yeah.
00:44:33
Speaker
Now, you might go, well, you know, maybe Newton did come up with it first, but his notations really, really ornate. This Leibnitzian stuff is much easier to use. And as I say, when we were taught calculus at school, we were taught to use it in Leibnitz notation. Yes, in fact, I'd heard the phrase Leibnitz notation a long time ago, and never really put to, or at least didn't, at the time I learned Leibnitz notation, I didn't know who Leibnitz was.
00:45:01
Speaker
So yeah, it didn't actually mean anything to me. It was just what it was called. And of course, neither of us actually remember enough calculus to be able to make a sophisticated two plus two, but calculus inspired joke. I remember quadratic equations. I can't remember how differential equations work. I remember I used to understand them.
00:45:24
Speaker
but I don't anymore. I remember I used to be able to do Laplace transformations, which, is that how you turn a differential equation into a quadratic equation? Something like that. But I never got Fourier transformations. Those are just bizarre and yet actually genuinely useful if you do any sort of work with waveforms or electronics or what have you.
00:45:45
Speaker
I'm more of a furry transformation kind of person these days. I'll say. So, have you any more to tell me about this feud between your Newtons and your Leibniz's? Or if we come to the end?
00:46:01
Speaker
Well, the only thing I'll say now is that actually one of the best bits of evidence we have now for why it has to be a case of independent discovery is it turns out the motivation for why they were working on their individual calculus projects are quite different.
00:46:20
Speaker
So Newton was interested in what's called a cinematic approach. So he was working on his theory of flexions, which was the notion of the fundamentals of instantaneous change. So he was interested about
00:46:35
Speaker
objects in movement and solving the calculations required to work out how moving parts work. Was Leibniz was actually kind of interested in the analytic approach. He was using geometry and going well look if we if we take shapes and do transformations to shapes how
00:46:54
Speaker
how do we do those transformations? So the actual fundamentals as to how they got to their idea of all calculus solves these problems come from almost opposite end of the mathematical spectrum. So there really wouldn't be any point in Leibniz cribbing the work
00:47:14
Speaker
of Newson, or Newson trained to adapt the work of Leibniz into their own work, because they're approaching the problem from very different directions. Hmm, I guess that makes sense then. I just like the word Fluxion, quite frankly, that's the one thing I'm going to be taking away from this episode. Well, and so you should. So finally, when does his lordship meet his fate on the train tracks from Papakura to Brittomart?
00:47:42
Speaker
What time did the train leave again? It was midday. Let me check my worked example. Actually, I never said. Right. I never said. In that case. Because the question I asked was how far away from Papakura does his lunch at Mrs. Fate? Yeah. Right.
00:48:01
Speaker
I would say it was three kilometers an hour he was walking. Yeah, and the train's traveling at 40. Quite slow for a train. It is kind of. I would say, what's the distance between Papakura and... I don't care. I'm just going to make up an answer anyway. So I'm going to say 300 meters. 300 meters? That's... I mean, I'm no number weighing expert, but I mean, 40 kilometers an hour.
00:48:30
Speaker
I'm not even just non-number weighing expert, I cannot say the word hour. I'm not a number weighing expert, nor can I say the word hour, but if his lordship is travelling at three kilometres an hour moving north from Papakura, and he meets his fate 300 metres away from the station,
00:48:52
Speaker
with a train travelling at 40 kilometres an hour going south. You're basically saying that Papakura and Britomart are right next door to one another? I'm saying I am plucking numbers out of thin air. The only thing I will say definitely is that when he meets his fate will be sometime in August of 1983.
00:49:14
Speaker
Interesting. I see how you've tried to risk you that. You see how you tried to risk you that, except... Oh, I don't say there's no Britomart station in 1983, but of course, your what was a time travel conspiracy, wasn't it? Exactly. How do they time travel in Back to the Future 3? In a DeLorean with a flux capacitor. No, by train, you idiot! By train! Pushed, but there was pushing a DeLorean with a flux capacitor.
00:49:40
Speaker
Yeah, but then there's a flying train in the final scene. I think it was the flying train afterwards, yes. No, I see. I get where you're going. I should have picked up on that. Yeah. It all makes sense. This is from the person who doesn't even remember the film Pumpkinhead. Die, we'll dance on your grave. Yours and everyone else's who insinuates I might have forgotten Pumpkinhead. With the kind of cough you've got, I'm expecting I'll be dancing on your grave any day now.
00:50:03
Speaker
It's almost gone. It's just an occasional cough. Like your life, it's almost gone. Fair enough. Do you have an actual answer? Did you plug those figures into a differential equation? God, no. No? Okay, right. Good. Then I'm safe in plucking a number from thin air. Are we done? I have to say, even plucking number three from thin air, 300 metres, is obviously wrong. It's just so obviously wrong.
00:50:30
Speaker
Interesting fact about me, I have no head for distance. I don't understand distances at all. You can you can ask me, like, like, if it's far enough away that I can imagine pacing it out in meters, I can work it out. But any further than that, and I just do not have a clue distances mean nothing to me. It's a brain. I know. I want to test this hypothesis. How far away is China from New Zealand?
00:50:57
Speaker
You could tell me it's a thousand miles, you could tell me it's ten thousand miles, I would believe you. The figures mean literally nothing to me.
00:51:06
Speaker
All right, so I just want to test this slightly further. So if I said that China is eight kilometres away from New Zealand, that would go... That's probably not correct, because eight kilometres is... I don't know how far it is, but I know it's within Auckland. 200 kilometres? How long is New Zealand? New Zealand's about...
00:51:28
Speaker
isn't New Zealand about, it's longer than 200 kilometers long. So I guess no, we're not in China yet. So I can, if I have a known quantity, I can maybe do a little bit of figuring around, but just simply in absolute terms. I'm just imagining that in your head. No, you're going right. If I can just work out how many New Zealand. Exactly. That is exactly the only way I would be able to work it out. Yeah. Oh, I had no idea that you have this distance-related issue.
00:52:00
Speaker
just, I don't know, it just doesn't mean a thing to me. Well, we've both learned something today. You've learned about the controversy about the invention of calculus. And I've learned that you measure every length by a standard unit, aka how many or how much of a proportion a New Zealanders between two points. True fact, true fact.
00:52:22
Speaker
So I think, I think, how far away is New Zealand from China? Do you know? I actually have no idea. This is not a case of my not knowing distances. This is just my just not caring about the distance. Okay, so anyway, anyway, we've come to the end of an episode. But before we go, we do, of course, have to say thank you to our wonderful patrons, even the ones who make slanderous accusations about my film knowledge.
00:52:47
Speaker
And we love our patrons so much that every week we record a bonus episode for them. And this week, we're going to be talking about a recent BBC podcast about conspiracy and all manner of COVID wackiness. You've listened to the whole thing, have you? I haven't had every 10 to 15 minute episode. Yeah.
00:53:06
Speaker
Yeah, so we'll talk about that, basically. I wonder if I'll tell you the name. It's called Death by Conspiracy, question mark. If you wish to know what we thought about the Death by Conspiracy. So Josh, could you say that in a British accent? A British accent? Because I think that's a very New Zealand way of saying Death by Conspiracy, question mark. How would a Brit say it? Let's say Death by Conspiracy. Death by Conspiracy?
00:53:33
Speaker
Midlands Death Boy Conspiracy. You are. And now on BBC2, Death by Conspiracy. By Conspiracy? Anyway, that's what it's called. It has a gratuitous question mark located in your minds. If you want to know what we heard about, what we thought about that podcast, if you haven't, if you've listened to that podcast, if you haven't listened to that podcast and want to hear us tell you about it so you don't have to listen to it,
00:53:59
Speaker
Tune in for that episode, which you can if you're a patron, if you'd like to be a patron, specifically so that you can listen to that one episode. Go to patreon.com and search for the podcaster's guide to the conspiracy, and good luck to you for doing so because you also get to listen to all the older bonus episodes. If you don't want either of those things, then just carry on. Carry on as you were. It's all good.
00:54:25
Speaker
Yep. Carry on you wayward son or daughter or child. Someone who's in between. You wayward child. You redheaded stepchild. Exactly. So to all the redheaded step children out there I would simply choose to sign off
00:54:42
Speaker
in the method of saying goodbye. Flexion! I prefer that to Durango, to be honest. You've been listening to Podcast's Guide to the Conspiracy, hosted by Josh Addison and M. Denter. If you'd like to help support us, please find details of our pledge drive at either Patreon or Podbean. If you'd like to get in contact with us, email us at podcastconspiracy at gmail.com. Oh, actually, I'd like you to go on.
00:55:09
Speaker
Tell me more about Pumpkinhead. That was me going on. I don't know. It's a film. He's in it. He summons a demon to do stuff and then realizes that he probably shouldn't have summoned the demon and spends the rest of the film trying to unsummon the demon. Have you actually seen any of the sequels? No. No. And I now kind of feel that I should watch three and four, the ones that were filmed in book rest, because A, I want to see how well they've managed to make
00:55:37
Speaker
Bucharest, a metropolitan area of Romania, look like redneck cities in the United States. And also, because I was looking at the cast list and going, yep, every single name in this cast, other than Doug Bradley and Lance Henriksen, is a very Romanian name. And I just want to see small town Hixville accents.
00:56:02
Speaker
on Romanian actors. I mean, Romanian actors are very good at pretending to be anything. But I mean, because I mean, given so many of those straight to DVD films were made in Romania, so prophecy four and five were filmed in Bucharest, although I think they were actually set in Bucharest, they can get around this. But no, I just want to watch Romanians pretend to be small town Americans, summoning, summoning demons.
00:56:34
Speaker
Sounds like good times. Good times. And drinking flame beer with Lance Henriksen.