Also, it should tell you how long it is, or if it will play forever. That way you know when to stop it.

I think my real analysis professor has it out for us. At least with this volume of homework, he wants us to really, really, really understand measure theory.

https://twitter.com/neiltyson/status/551378648578916353?lang=en

NDT is a genius.

Is he still calling himself an astrophysicist? He hasn't published in over a decade.

There is simply no way somebody can continue to be a scientist and spend as much time interacting with the media as he does. On the other hand, people like Brian Greene are still putting out about a paper a year despite taking the time to talk to the media.

OTOH, maybe Tyson maybe simply thought astronomy was boring and wanted to pretend it wasn't by telling people so.

"Kids, go into astronomy like me. Then you can spend the second half of your life pretending to others that you didn't quit because science is painstaking work compared to goofing around with the media."

RJ, you gotta like, occasionally rein in whatever part of you just wants to do successive riffs on whatever your first reaction to something is. You get so far off the map and jump to wild conclusions. I guess that's fine if you're just having a cheeky conversation or trying to be funny, but blerurughhh...

What the hell do you know about this guy's intentions? Doesn't he see himself as a sort of popular educator? He certainly behaves like he sees himself as a popularizer of astronomy or the importance of science, not as a practicing, publishing astrophysicist. You can critique that if you want, but to go off into the weeds talking about him... quitting... doing real science... because it was too hard, and doing what he does now because he's lazy and wants to goof around with the media?

Isn't there room for some goofy, relatable scientist guy to transition into a PR/public educator TV guy role without you ****ting all over him for not writing serious research papers anymore?

I don't really care one way or another about Neil Tyson, but I just don't get where you're coming from with this.

You're right.

I need to slow down a bit and stop with the perpetual low rent Jon`C schtick (see what I did there). Actually, I just read this article a few minutes ago.

Are computers and the Internet making people a little bit autistic?
Is technology making today's kids a bit autistic?
Posted Nov 30, 2008



https://www.psychologytoday.com/blog/my-life-aspergers/200811/are-computers-and-the-internet-making-people-little-bit-autistic

I had been wondering how badly I'd been rubbing the rest of you guys with some of my posts. Sorry for enticing the rant from you, but at least know the point isn't lost on me. I know I have a problem. Actually maybe my generation kind of does, if that guy's article makes sense.

Shoulda been reading Marshall McLuhan rather than posting here

<-- the medium is the moron

That said, I still think it's slightly suspicious to listen too much to a man who tries to get people interested in science without actually being a scientist. (Edit: Not that he doesn't mean well, but who knows if we shouldn't simply be listening to other scientists instead? Although now that I think about it, a lot of what he seems to do is point people to the works of others scientists.) He might have other reasons for no longer practicing, and I suppose modern society sort of forces specialization, but I think it's not quite right for people to take Tyson as an authority on science to the exclusion of others who might be closer to the actual work at this point in his life (but see my edit).

Maybe this is the point though. He's not a genius, and that's OK, even if he makes cringy tweets from time to time. Probably was wrong for me to tear into him like that.

At the end of the day, the reason I post lots of plausible (or not-so-plausible) B.S. here is twofold:

1. Take my mind off whatever potentially difficult / complicated thing I'm trying to get done IRL
2. Entice others into saying something interesting (or be enticed myself by someone else)

I should slow down though.

I guess the pattern to my linking people's twitters is: social media is toxic, and let's peoples minor dumbass thoughts become public proclamations.

I hereby sentence you to 5 years in state prison for egregious crimes against apostrophes

But yeah I agree with that.

Marshall McLuhan

tl;dr we're all ****ed

Incidentally, Reid, I know I've treated you like trash on this topic, but since this is the "computer science and math stuff" thread, I would love to interest you in this post I made on somewhat the same matter at hand, in this very thread. I know that since I am not in a grad program, I am indeed a "pip squeak" before the collective intelligentsia of mathematics establishment as it exists today, but: from what I've gleaned from those greater than myself, I've come to appreciate what apparently is a minority view among mathematicians (although among the more problem solving oriented mathematicians I've interacted with, it is not quite as controversial a perspective to have as Cartier might seem to suggest). It's not necessarily in conflict with the majority view, either, but simply another angle to look at things, although I hope it might upset the degree of philosophical certainty through which you view the matter.

Anyway, I've quoted the interesting passage from the beginning of this very interesting essay by Pierre Cartier. Of course I don't want to appear the insecure name dropper desperate for approval, a la Koobie, which you've tacitly taken me for once I had provoked you into doing so, but: I honestly think what Cartier has to say is quite convincing (and the remainder of the paper is quite fascinating in content as well). I've tried to more or less take inspiration from it, at least in spirit, in everything I work on (which is admittedly mostly outside of mathematics, per se). Finally, I will mention that just looking at who the paper is dedicated to is a big hint about the aesthetic being depicted here.



(Emphasis in the original.)

[quote=Pierre Cartier]
To the memory of Gian-Carlo Rota,
modern master of mathematical magical tricks

[...]

The implicit philosophical belief of the working mathematician is today the
Hilbert-Bourbaki formalism. Ideally, one works within a closed system:
the basic principles are clearly enunciated once for all, including (that is an
addition of twentieth century science) the formal rules of logical reasoning
clothed in mathematical form. The basic principles include precise defini-
tions of all mathematical objects, and the coherence between the various
branches of mathematical sciences is achieved through reduction to basic
models in the universe of sets. A very important feature of the system is its
non-contradiction; after Godel, we have lost the initial hopes to establish
this non-contradiction by a formal reasoning, but one can live with a corre-
sponding belief in non-contradiction. The whole structure is certainly very
appealing, but the illusion is that it is eternal, that it will function for ever
according to the same principles. What history of mathematics teaches us is
that the principles of mathematical deduction, and not simply the mathe-
matical theories, have evolved over the centuries. In modern times, theories
like General Topology or Lebesgue’s Integration Theory represent an almost
perfect model of precision, flexibility and harmony, and their applications,
for instance to probability theory, have been very successful.

My thesis is:there is another way of doing mathematics, equally
successful, and the two methods should supplement each other and
not fight.

This other way bears various names: symbolic method, operational calculus,
operator theory... Euler was the first to use such methods in his extensive study
of infinite series, convergent as well as divergent. The calculus of
differences was developed by G. Boole around 1860 in a symbolic way, then
Heaviside created his own symbolic calculus to deal with systems of differen-
tial equations in electric circuitry. But the modern master was R. Feynman
who used his diagrams, his disentangling of operators, his path integrals... The
method consists in stretching the formulas to their extreme consequences,
resorting to some internal feeling of coherence and harmony. There
are obvious pitfalls in such methods, and only experience can tell you that
for the Dirac δ-function an expression like xδ(x) or δ′(x) is lawful, but not
δ(x)/x or δ(x)2. Very often, these so-called symbolic methods have been
substantiated by later rigorous developments, for instance Schwartz distribution
theory gives a rigorous meaning to δ(x), but physicists used sophisticated formulas
in “momentum space” long before Schwartz codified the Fourier transformation
for distributions. The Feynman “sums over histories” have been immensely
successful in many problems, coming from physics as well from mathematics,
despite the lack of a comprehensive rigorous theory.

To conclude, I would like to offer some remarks about the word “formal”. For the
mathematician, it usually means “according to the standard of formal rigor, of formal
logic”. For the physicists, it is more or less synonymous with “heuristic” as opposed
to “rigorous”. It is very often a source of misunderstanding between these two
groups of scientists.

[...]
[/quote]

The point of view also summarizes much of the one I had been trying to convey in this thread as well, which I also think we (at least silently) were butting heads on. It's not just something I made up as an undergraduate as an "idea about how mathematics should be done" that I should "outgrow", but simply a minority report I've stolen from a venerable member of Bourbaki itself.

(Originally, I came across this essay by reading it referenced in one of Doron Zeilberger's many infamous opinion essays).

Finally, I would like to point you to this post as a summary of my point of view here, as it pertains to Cartier's essay. I don't care to argue the points I was trying to make about just how sound set theory might be, or how fruitless it might have been to try so hard to make it so. Instead, I would like to draw your attention to the quote I inserted, from Oliver Heaviside, which I will reproduce here:
[quote=Oliver Heaviside]
In the preceding, I have purposely avoided giving any definition of 'equivalence.' Believing in example rather than precept, I have preferred to let the formulae, and the method of obtaining them, speak for themselves. Besides that, I could not give a satisfactory definition which I could feel sure would not require subsequent revision.[/quote]

And in particular:

tl;dr: people who are secretly "mathematical physicists" at heart can contribute just as much to mathematics as the "snobbier", more logically inclined (rather than heuristically or formally inclined) variety of mathematician, and that actually, a great deal of interesting mathematics was pioneered by people who couldn't care less about mathematical logic.

I don't mean to get hung up on the word axiom, but certainly, when physicists talk about the axioms of quantum mechanics, I very much doubt they understand the word in the same sense as modern mathematicians do when they speak of axioms of Euclidean geometry. Now, to be fair, when I brought up the possibility of the axioms being "wrong" (as Jon`C had suggested), I didn't necessarily qualify my use of the word axiom here, and indeed, perhaps I assumed the distinction didn't matter. But when Jon`C was talking about Euclidean space, and the choice of axioms that determined the fact that they might be working in Euclidean space (as they often do), well, certainly, those axioms are wrong, insofar as they lead to the wrong model of the universe. So really, what rubbed me the wrong way was that it seemed rather pedantic and condescending to hold onto this idea that it was wrong in any way to simply call axioms wrong in this narrow instance.

Also, what is mathematics if not geometry, and aren't physicsts the geometers of the universe who simply pay more attention to experimental results than the pure mathematician only typically does indirectly (through the benefit of the pioneering work of the mathematical physicist, actually)? We should give them credit for that, and admit that mathematicians have learned a ton from the efforts of their work, long before logic typically enters the picture (again, see the second part of the Heaviside quote as an example of this sentiment).

Also, I promise not to attack you for your views. And I don't even really care about the axiom stuff, that is just incidental. I am mostly just trying to get across my more general point of view, though this may help understand why I was adamant to the point of being uncivil before.

Of course I accept the possibility that you might simply disregard all of this as simply wrong, and that's fine too. I think I've said enough on this topic that if you don't particularly care for this viewpoint, I am OK with that.

Science outreach and advocacy is a job that desperately needs doing, and very few scientists have both the personality and media savvy in order to achieve it. I can pretty much guarantee that NDT has had a greater effect on his field by focusing on his advocacy work than he would have ever had by focusing on research.

And, also, noted non-scientist Bill Nye? Same thing.

Yeah, I kind of came around to that opinion. I think I took Reid's initial remark way too far there, heh.

The age of the polymath is long gone I guess. It is an inevitable fact of increasing specialization that the people who advocate for things may not actually do them all that much.

Well, this has perhaps always been true anyway.

Also, Reid, if you don't want to read all that egotistical non-sense I wrote about an hour ago, I would also be perfectly happy to accept a short "Jones, you're about 10 feet too far up your own ass for me to give you the time of day at this point".

Also, regarding the original Tweet:

He’s not even wrong.

An unhackable computer is absurd, but information security has a lot of low hanging fruit. Most companies are pretending that IS doesn’t even exist, let alone doing even the bare minimum about it. Improving that is where the money should be spent, not investigative work and international diplomacy to extradite foreign blah blah blah.

air gaps considered harmful to convenience

I don't doubt that the difference is in how we were using axiom, and I'm willing to accept that was the source of the whole debate.

Allow me to explain why that sentence sounds so wrong to me by making a comparison. Euclidean geometry as Euclid formulated it, before any of the axioms, starts as a Q-vector space. The axioms give a bunch of restrictions on what kind of geometric objects can be permitted, which in turn construct other numbers and extend your Q-vector space into one much larger. But, can Euclidean geometry work in reality? Well, no, because spacetime is curved. Therefore the Euclidean geometry axioms are wrong.

Now, let me compare that to the group axioms. The group axioms are a similar set of restrictions we apply to binary operations. We begin with a space of binary operations, and begin saying certain things are true a priori to begin cutting down the amount of objects that we permit. But, can groups exist in reality? Well, no, entropy is increasing, so inverse operations in the universe aren't possible. Therefore, the group axioms are wrong.

Does it sound absurd to say the group axioms are wrong because entropy is increasing? It should, because it is absurd. But neither example above are any different from a mathematical perspective. Axioms from a mathematical perspective have zero relation to anything we deal with in physics, and if you took the consequence of calling a set of axioms "wrong" because one application you came up with has inaccuracies, then math becomes reduced to one big set of statements made about wrong axioms. I don't think anyone can seriously argue that all of mathematics is formulated incorrectly on this basis. But that's essentially what the argument is, or at least how it sounds.

Also, as far as I'm aware, QM axioms are purely mathematical, as in bra-ket operator stuff. I'm not well versed in this so I won't speak on it, but I have a suspicion it would fall victim to the same problems if placed under the same scrutiny.

Hah, well, for what it's worth, this conversation is making me think Foucault's characterization of Cartesian and Kantian subjectivity is actually pretty accurate (or at least reasonable as an interpretation).

Dude, attack NDT all you want, but you lay off Carl Sagan, y'hear? I don't think I could handle that.

OK OK! I was wrong. Tell your sister, I was wrong.

I think you're mostly right here. Well, you're not wrong.

Actually, I began to write a very lengthy post in order to explain where I am coming from here, but I really can't bring myself to finish it, because even if you were to fully appreciate it, you are close enough to the truth already that I can't bring myself to go through with writing it just to give myself cancer.

An important thing to note on that section by Cartier: France is and always has been the epicenter for Bourbakian style mathematics, and that style never penetrated as deeply in other traditions, so it strikes me that his complaints are more particular to France than globally.

That's actually a really good point. In fact it also perhaps explains the highly polemical nature of the Vladimir Arnold essay I had linked to.

Now since we are on the topic of polemical essays, I have a much better one, which I have just read with pleasure this evening. It is quite scathing.

Turns out, sophmore differential equations course is hot garbage, and has been for at least a century.

I've heard that Professor Pugh at UC Berkeley, who actually does research in something related to differential equations, well, he doesn't even teach the standard content, instead making it an intro to dynamical systems.

Starting to read this, and wanted to comment on one section:



I think they're just trying to be funny, but.. this isn't true? At both my alma mater and the school I'm currently at, engineering math are sequestered off from "real math" which are pretty much reserved only for pure science majors.

Seemed like a fine text. I have never studied differential equations so I'm useless to give much commentary, but when I asked my mech engineer friend he said "we just solve them numerically", which as I understand it is how most people choose to do them.

In any case, updating the curriculum to avoid trickfinding and promote understanding core concepts is a worthy goal. I try to get my calculus students to reason through problems instead of trying to memorize, but even then problems that should be reasonable for calc 2 are easy to memorize, often the problems they're capable of doing but are actually hard depend on noticing some trick, so talking about homework with them is ~****ing annoying~ because if I don't see the trick, I'll be stuck myself. I'd rather talk about the Riemann integral or why the arc length formulas make sense, but nah.

Though, before the last exam, I really hammered into students that they should reason first about surfaces of revolution and think about why each part of the integral makes sense. I happened to grade that section on the exam, and my students did markedly better than the other prof's students. So I guess it works, which is nice to know.