## Potpourri

==> Following Bryan Caplan’s lead, I talk about the long-term results of TARP.

==> Be careful, kids: My son was telling me matter-of-factly that this scientist Hooke was a bastard (not his actual term) etc. etc., and I interrupted to ask, “Did you get this from a *Cosmos* episode?” He said yes. Then–relying on this guy’s withering account–I warned my son that apparently there were a lot of problems with the history of science as rendered by this show. The most serious blunder, I told him, was that Tyson claimed authoritatively that Newton developed the new calculus in the Principia, when in fact historians of science have argued for decades about why Newton *didn’t* use it, instead relying on geometry.

My son was startled by this, chiefly because he had told things he learned in Cosmos to the kids in his school. (I was pleasantly amazed that that was his reason for being glum.) In an exercise to discover truth, my son and I wanted to independently see whether in fact Newton never used calculus in the Principia. We decided it was much more nuanced than the blogger made it seem. E.g. from a 2007 publication titled, “Did Newton use his calculus in the Principia?”:

Abstract

A question that is often formulated by people interested in the history of mathematics is: Did Newton use his calculus in the Principia? This question comes very naturally to mind, since Newton discovered the calculus of fluxions before writing the Principia. It is just obvious to think that Newton had employed the calculus in order to mathematize his natural philosophy. However, very little trace of calculus techniques is to be found in the Principia, which are mostly written in ‘geometric style’. On the other hand, some propositions of the Principia are framed in a geometric language which appears to be very easily translatable into calculus concepts. Thus our question is very tricky.

As a matter of fact, the question of the presence of calculus in the Principia has been debated since the 169Os, when Fontenelle stated that almost the whole work is about the differential calculus. The question played an important role in the muddled context of the priority dispute with Leibniz. Since then the opinions of mathematicians and Newtonian scholars have been very contradictory and our question seems still to be waiting for a definite answer. In order to achieve an understanding of Newton’s use of calculus in his mugnum opus, we have to consider the exchange of information between a restricted group of adherents to the Newtonian school.

So, I will give Tyson (and his writers) the benefit of the doubt on this one. From further investigations, it seems that Newton used the idea of a limit of shrinking geometric shapes, which one could plausibly say is, or is not, calculus.

==> This economist debate about Hank Aaron is really interesting. I first agreed with Tyler Cowen that Nate Silver had left something important out of his analysis, when Silver wondered, “What if Hank Aaron had never hit a home run?” But then Scott Sumner convinced me that Cowen’s critique was churlish, and that Silver’s method was perfectly fine for this sort of thing.

Then, I couldn’t stop myself from reading the comments at Scott’s post, where people went nuts over Barry Bonds vs. Babe Ruth. This was my favorite from W. Peden (which I’m slightly editing to maximize the punchline): *“On baseball: like most Brits, I know next to nothing about baseball, but I think most of the stats people are quoting are very misleading. I looked up a site called shadowbaseballstats.com and it pointed out that, due to changes in the sport, Barry Bonds had 100,000 home runs in [the original] terms.”*

Not the only false history this Cosmos show is popularizing!

http://armariummagnus.blogspot.com.au/2014/03/cartoons-and-fables-how-cosmos-got.html

Also, isn’t your kid a little young for his playground talk to revolve around 17th century mathematicians? I’m pretty sure when I was his age we mostly talked about boogers.

You mean you didn’t calculate the trajectories of spitballs (or boogers)?

Actually a real shadowbaseballstats would presumably show either Bonds having fewer or Ruth having more, runs than the official stats.

Actually a real shadowbaseballstats would presumably show either Bonds having fewer or Ruth having more, runs than the official stats.Why? The analog is to price inflation, right? Shadowstats says that (price) inflation would be a lot higher today, if they calculated it the way they did back in the 1980s.

So, if we calculated home runs today the way we did when Ruth was playing, Barry Bonds would have way more…

“From further investigations, it seems that Newton used the idea of a limit of shrinking geometric shapes, which one could plausibly say is, or is not, calculus.”

But that is exactly where these ideas stood *right before* Newton and Leibniz developed calculus! That is the very point: he went back to immediately pre-calculus math to do the Principia. Of course, the math of limits *right before* calculus contained many ideas “very easily translatable into calculus concepts”: that’s right: they were ripe for “calculisizing”. In short, this guy confirms my point. And anyway, Tyson claimed he developed calculus *in* the Principia, which is nonsense: it was developed years before.

I can think of a reason why he would use just geometry. To prove it can be done without calculus, so no-one could even allege a debt to Leibniz. Pride.

Or it’s part of a secret conspiracy. I await he next Dan Brown.

Or he just wanted to write for a wider audience.

In latin, in an edition few could afford. Could be, seems unlikely.

Gene Callahan wrote:

In short, this guy confirms my point.No, Gene, I’m sorry, and this makes me hesitant to fully trust your other claims on history of science stuff.

When someone has a paper published in a journal that says “Thus our question is very tricky.” and you say, “He confirms my point,” when your point was that it was well-known among historians of science that this question had a definitive answer, then I can’t trust you to tell me what the field has to say about this.

It sounds like I could poll the historians of science, and 35% of them could say, “I think Tyson’s claim is defensible,” and then you would say, “They really don’t believe that, they agree with me, let’s probe a little deeper into why they think that.”

Note, I have no problem Gene if you want to say, “Anybody who thinks the calculus was in the Principia is a moron.” But you went further than that, and told me with confidence that nobody in this niche would believe that; that Tyson’s claim was patently absurd.

Gene let me make sure you understand my reaction to your latest comment. This guy’s abstract says,

“A question that is often formulated by people interested in the history of mathematics is: Did Newton use his calculus in the Principia?”Later he says,

“Since then the opinions of mathematicians and Newtonian scholars have been very contradictory and our question seems still to be waiting for a definite answer.”So to defend your stance, I don’t want you to tell me, “This guy confirms my point.” No, you have to say, “This guy is completely full of crap, I can’t believe this paper got published, let me google and see what this ‘journal’ is, because that’s nonsense.”

Do you see what I mean? Either he is totally wrong with his statement above, or you need to be a little more nuanced in teling people how awful Tyson’s mistake in the Cosmos show was.

“It sounds like I could poll the historians of science, and 35% of them could say, “I think Tyson’s claim is defensible…”

No! 0% would say it is defensible. Tyson claimed he INVENTED calculus in the Principia. He invented it 20 years before!

And the calculus used in the Principia was NOT what he invented.

The only reason you don’t think that paper confirms my point is you have no idea what is at issue here!

Gene blogged that the howler was claiming the PM was where calculus was introduced. I assume that means was Newton’s first comprehensive explication of it. If Tyson made that claim it’s a howler. Gene’s link is an odd choice of references for vindication, since a direct link to someone discussing Newton’s earlier work on calculus seems simpler. But it does vindicate Gene.

I am trusting you both Tyson did make that claim. I really cannot take him so don’t watch.

Here you go:

https://blogs.otago.ac.nz/emxphi/2011/10/newton-and-the-case-of-the-missing-calculus/

A friend in college once told me that the area of a triangle is half the base times the height (we already knew this part), which in essence is the integral of the line from the bottom left corner (origin) to the top right corner. Half the square area is the triangle, integral of y=x (in the case of a square) is 1/2x^2. I was never told this in public school.

From your link:

Hmmm, that doesn’t sound too likely.

https://archive.org/details/newprinciplesgu00wilsgoog

Robins published in 1742 which was 60 years after Newton’s Principia, but Robins did use Fluxions to solve the same laws of motion and gravity for a parabolic trajectory. Robins had also written about Fluxions earlier in 1735 and it is know that Robins spent a lot of his early life studying Newton’s work.

What’s more, in the modern context, pretty much all equations of motion are solved using Robins’ method, although the concept is often explained to students geometrically.

http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Robins.html

There’s a biography of Robins, suggesting that he he was perfectly familiar with both the algebraic approach and the geometric approach, and clearly would have been quite comfortable translating between them.

It is true that in the Principia, Newton did not use the algebraic language and symbolism that is nowadays used in calculus. And it is true that Newton wrote the Principia in the same geometric language that his predecessors used, using limits of geometric magnitudes going to zero much like the ancient Greeks did. But it’s not correct to say that what he conveyed using the language of geometry was just what his predecessors knew. Look at the theorems of calculus proved in the beginning of book I:

http://en.m.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookI-I

These results are clearly beyond the work of Fermat, for instance.

Now what is true is that the second fundamental theorem of calculus is never explicitly invoked in the work, which is why there was a priority dispute between Newton and Leibniz, because Newton hadn’t actually published any work stating the theorem at that time. But there is some scholarship arguing that Newton at least implicit discusses the first fundamental theorem, for instance in evaluating the rate of change of area in the context of using Kepler’s second law to prove the first.

You don’t assert that the PM was where Newton introduced calculus though do you Keshav?

I think Gene’s claim of vindication is oddly roundabout. If there is debate that PM used calculus then it can hardly be where it was introduced, and if people who think he didn’t use calculus wonder why not, then one may infer it was known earlier, QED. Easier to just link Wikipedia on Calculus or some other source with dates before 1684. But it is correct nonetheless.

“The most serious blunder, I told him, was that Tyson claimed authoritatively that Newton developed the new calculus in the Principia, when in fact historians of science have argued for decades about why Newton didn’t use it, instead relying on geometry.”

It gets even better. Archimedes is the earliest known inventor of calculus. It is referred to as “The Method.” He didn’t publish it because he was afraid of being publicly shamed. Why? Because most mathematicians of his day explained everything in geometry, and Archimedes couldn’t show it geometrically.

Because of this, mathematics was set back 2000 years.