Tazerenix (u/Tazerenix)

Tazerenix commented on How to Study Mathematics (2017) math.uh.edu/~dblecher/pf2... · Posted by u/ayoisaiah

jayhoon · 9 months ago

Interestingly, this guide states that the intuitive understanding of maths is only suitable at the school level but not for the university.

In his recently published book "Mathematica: A Secret World of Intuition and Curiosity", David Bessis argues that the intuition is the "secret" of understanding maths at all levels.

Not sure what conclusion to draw from here, but my (rather dated) experience with university maths tells me that the intuition is a powerful tool in developing the understanding of the subject.

Tazerenix · 9 months ago

This is related to Terence Tao's notion of the stages of mathematical rigor.

As Tao puts it, the value of intuition becomes much higher in the post-rigorous stage once you have sufficiently developed your technical skills.

https://terrytao.wordpress.com/career-advice/theres-more-to-...

Tazerenix commented on Mourning and moving on: rituals for leaving a career (2014) franceshocutt.com/2014/09... · Posted by u/luu

prof-dr-ir · a year ago

As another 'mainsteam' academic with relevant expertise I think this comment is spot on.

I would like to add that Sabine's video on her academic experience was quite a tragic thing to watch. If her allegations are true then the behavior of her PhD supervisor was completely outrageous.

She also did seem a bit too dreamy-eyed about academia. Sure you can criticize everything you want, but she never seemed to have understood that tone of voice still matters. Academics are busy people with emotions, and not likely to engage with someone whose claims appear to have more loudness than substance.

Tazerenix · a year ago

I certainly am not making any comments about her experiences for sure! Academia is difficult and full of terrible stories, and its not surprising that it causes many people to become exceedingly bitter and contrarian (Peter Woit is famously of the same ilk as another string theorist critic who fell out of academia like Sabine).

Unfortunately a chip (even a legitimately earned one) on ones shoulder about the bad parts of academia doesn't save you from being criticized for being crank-y.

Tazerenix commented on Mourning and moving on: rituals for leaving a career (2014) franceshocutt.com/2014/09... · Posted by u/luu

roel_v · a year ago

Not to highjack this topic, but she was recommended (like to many others of you no doubt) quite a bit in my Youtube feeds over the last few months; and the first few videos I watched seemed to be solid enough. Yet as I watched a few more, I couldn't shake the feeling that she's so out of left field that she's not just a 'quirky renegade' anymore, but rather a quack who dresses up her quackery with just enough 'real' physics to make it all sound very convincing. (By that I don't mean that she says factually wrong things, but that her conclusions or extrapolations from established facts seem to me, well, outrageous). However, I don't know enough physics to be able to tell if this is a correct feeling, and the Youtube comments are, as usual, one big fanboy fest, which is true for any large enough channel - even those of flat earthers and similarly delusional content).

So my question is - just how serious should she (and others like her, who denounce 'mainstream' academia as much as those other fringe groups who go on and on about the corruption of 'mainstream' media) be taken? Anyone have an opinion on this?

Tazerenix · a year ago

As an expert in at least some of the things Sabine makes videos about (string theory), Sabine is a contrarian who, if you are not otherwise an expert on what she is talking about, it would be best to avoid.

Sabine, like many contrarians, takes advantage of the fact that there are smart and convincing criticisms of many mainstream ideas, and she does her best to rely on those criticisms. However like all contrarians she presents a biased and exaggerated view of things in order to stoke engagement, and unless you are an expert it can be difficult/impossible to determine whether the view she is giving is balanced.

This is a classic issue with string theory critics, because string theory has many legitimate problems with it, but many of the critics are intellectually dishonest and you probably shouldn't listen to their criticisms on principle (but even I must admit it's quite hard to find good quality intellectually honest criticism of string theory which is digestible, so these contrarians tend to be the only loud voice).

In Sabine's case it is not so bad, because it is clear from some of her other positions that she is basically a crank. MOND and superdeterminism are basically crank physics at this point but she supports them purely because she is a contrarian. On this evidence alone you should not trust anything she says on any other subject, otherwise you're falling for a kind of Gell-Mann amnesia.

Tazerenix commented on Galois Theory golem.ph.utexas.edu/categ... · Posted by u/mathgenius

mbivert · a year ago

> I'd be interested in any recommendations for math history tomes like that.

Not a book, but FWIW, I've enjoyed a few videos from Norman Wildberger's "Math History" playlist[0]. Interestingly, he has a unconventional view of infinite processes in mathematics, a point of view that used to be common about a century ago or so.

I'm sure knowing some amount of history is useful, but there must be a limit to how much of it is practically useful though.

https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL55C7C8378...

Tazerenix · a year ago

Wildberger is a crank

Tazerenix commented on Goodsteins theorem en.wikipedia.org/wiki/Goo... · Posted by u/dedalus

Tazerenix · 2 years ago

A theorem which is true in every model is provable by Godel's completeness theorem. Since this theorem is true for the standard model of the natural numbers but not provable, it follows there are nonstandard models of the natural numbers for which it is false.

That is, there are models of Peano arithmetic which contain all of the natural numbers we know and love, and some other ones on top of that and there are some Goodstein sequences using those extra "non-standard" natural numbers which do not terminate at zero.

https://en.wikipedia.org/wiki/Non-standard_model_of_arithmet...

Tazerenix commented on What is a zero refractive index material? skullsinthestars.com/2023... · Posted by u/_Microft

Kranar · 2 years ago

To be clear there are numerous explanations for why light slows down in a medium and they are almost all incorrect in one way or another.

This video uses the explanation that light interacts with electrons in a medium which causes the electrons to produce an electromagnetic wave whose interference pattern changes the phase of the light wave, kicking it back.

The problem is that an interference pattern can never change the speed of a wave, it can change the phase of the wave and adjust it, but that won't explain how light passing through a medium takes longer to traverse that medium than light travelling in a vacuum.

I don't know of a visualization or explanation that captures why light slows down in a medium, and the video linked is still a good way to get a sense of what's happening, but it's worth knowing that there is still a great deal being left out of that explanation.

It is nevertheless better than explanations involving the absorption an reemission of photons or that light bounces around within the internal structure of a medium. Both of those explanations manage to explain how light takes longer to pass through a medium but fails to explain how light keeps a consistent direction as opposed to scattering randomly.

The explanation in the video manages to explain how light maintains a consistent direction but fails to explain how light will actually take longer to pass through a medium compared to a vacuum.

Tazerenix · 2 years ago

The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the electromagnetic field, the pure electromagnetic wave gets transformed into a phonon, which is a combination of electromagnetic and mechanical oscillation within the medium (and therefore has speed <c, depending on the particular properties of the medium). When the phonon subsequently leaves the system, those traveling oscillations induce a new self-propagating wave on the other side, sending the light on its way as usual.

Tazerenix commented on UHZ1: NASA telescopes discover record-breaking black hole chandra.si.edu/photo/2023... · Posted by u/raattgift

dmix · 2 years ago

What are some possible explanations or implications of this?

Tazerenix · 2 years ago

One of two things:

Either what we know about black hole formation is basically complete (it goes gas -> star -> black hole -> accretion + collisions) but the environment in the early universe was sufficiently different/dense that parameters which rule out the formation of supermassive black holes now were different. Maybe there were many intermediate black holes just in the millions of years after the big bang and things were still close enough together that accretion could happen and collisions were "likely" at the rate needed to form SMBHs after just a billion years. If that is true we might expect to see many many active galactic nuclei as we get better telescopes and look further back, depending on how quickly such black holes formed.

The other option is there is a mechanism of black hole formation that bypasses the above chain which we understand. People talk about supermassive stars, gas clouds collapsing directly into black holes, or primordial black holes that existed due to essentially random distributions of density moments after the big bang causing some regions of space to collapse into massive black holes which then persisted. Such things are far more difficult to observe, but could be inferred if we don't see many many active nuclei as we get better telescopes but all other indications of the accuracy of the big bang + inflationary theory hold true.

Tazerenix commented on UHZ1: NASA telescopes discover record-breaking black hole chandra.si.edu/photo/2023... · Posted by u/raattgift

digging · 2 years ago

Quick summary:

We've spotted strong evidence for a supermassive black hole (of the kind that tend to sit in the center of galaxies like ours, which contains Sagittarius A*) in an extremely distant galaxy - one that formed within the first half-billion or so years of the galaxy.

What makes this important is that we've seen increasing evidence that supermassive black holes (SMBHs) exist earlier than we've expect if they were born from the deaths of massive stars and slowly accumulating mass in the way "typical" black holes today do.

This black hole is apparently very good evidence that these early SMBHs did not form from star collapse but may have formed from gas clouds collapsing directly into black holes. Finding support for this alternative model could lead us to new possibilities in physics.

Tazerenix · 2 years ago

Also important to note that the process of stellar collapse and then black hole accretion takes absolutely enormous amounts of time to collate a large amount of mass together. It's also an extremely energetic process, you would expect to see very bright black holes if millions of solar masses of matter were infalling creating very large and bright accretion disks. We do see some active galactic nuclei but not that many. There's just no way there was enough time for this to happen in the early universe, or really even after a measly 14 billion years (i.e. seeing these young supermassive black holes is challenging for the stellar collapse theory, but the theory was already pretty challenged).

Not to mention if supermassive black holes were being formed by accretion, you would expect to see many intermediate mass black holes (1000-1000000 solar masses) everywhere, but we see almost none.

Tazerenix commented on Linear Algebra Done Right – 4th Edition linear.axler.net... · Posted by u/__rito__

resource0x · 2 years ago

>... rather than relying on the crutch of intuition from Euclidean space

Euclidean space is not a good crutch, but there are other, much more meaningful, crutches available, like (orthogonal) polynomials, Fourier series etc. Not mentioning any motivations/applications is a pedagogical mistake IMO.

I think we need some platform for creating annotated versions of math books (as a community project) - that could really help.

Tazerenix · 2 years ago

On that of course I agree, but mathematicians tend to "relegate" such things to exercises. This tends to look pretty bad to enthusiasts reading books because the key examples aren't explored in detail in the main text but actually those exercises become the foundation of learning for people taking a structured course, so its a bit of a disconnect when reading a book pdf. When you study such subjects in structured courses, 80%+ of your engagement with the subject will be in the form of exercises exploring exactly the sorts of things you mentioned.

Tazerenix commented on Linear Algebra Done Right – 4th Edition linear.axler.net... · Posted by u/__rito__

lll-o-lll · 2 years ago

Or, you know, mathematics can be viewed as a powerful set of tools…

Somehow I seem to remember getting through an engineering degree, taking all the optional extra math courses (including linear algebra), without there ever being a big emphasis on proofs. I’m sure it’s important if you want to be a mathematician, but if you just want to understand enough to be able to use it?

Tazerenix · 2 years ago

> I’m sure it’s important if you want to be a mathematician, but if you just want to understand enough to be able to use it?

This book is for people who want to be mathematicians.