The h Bar

1:38 AM

@Mr.Feynman because learning a programming language is technically the easy bit, especially if you already know one language. Knowing how to churn numbers, on the other hand, is a lot more difficult to teach.

@Amit I think this is very irresponsible advice. Just because the syntax looks similar does not mean anything; the basic syntax is the easiest part of a language to pick up, and is pretty useless as an indicator of proficiency. The fact of the matter is that, if your large C++ codebase looks like C, you are doing something wrong.

@Amit what are you even on about. You first linked about IFM, which is barely linked to quantum zeno; I'm not even bothering to attack the zeno v.s. frozenness, but frozenness or not has nothing to do with weak measurements. Can you, like, not turn into another RR?

@Arjun Oh no, things can be bad even without the fudging of results. You can have a serious research field produce a lot of great output, e.g. useful insights, great methodology, produce interesting experiments, but then be utterly non-commercialisable and thus almost no industrially useful output. Yet, you definitely also know that modern academia kinda always want to link themselves to industrial money. Then there will be a huge pressure to produce papers that sound amazing but

either assumes some unicorn thing, or is decades into the future to apply, or is actually a known dead-end some other way else.

Even bullshit can be nuanced, ok

Slereah

6:31 AM

Modern day programming is mostly about knowing how to deal with the gigantic mass of frameworks around programming anyway

all the bloody pipelines for the various bits

123

Hello Everyone...

Ryder Rude

6:48 AM

hi

Slereah

naturallyInconsistent

7:10 AM

lol

Amit

9:07 AM

@naturallyInconsistent It wasn't an advice, what advice? I said knowing C makes it easier to start learning these other languages, and I didn't suggest you shouldn't learn them well

@naturallyInconsistent i am not here to satisfy you

@naturallyInconsistent I also would like it better if you do not speak to people like a spoiled & condescending brat

But I won't really expect that because you are free to act as you want within the chat rules

naturallyInconsistent

9:32 AM

@Amit In no part of that comment of mine is there any suggestion, whatsoever, that you should be satisfying me of any form or kind. If you cannot realise that there is something else being an issue, that is very much on you. I mean:

Sep 11 at 15:06, by ACuriousMind

@RyderRude I find it very revealing that you consider the literal truth of your statements to be an irrelevant detail, and I'm done with this conversation.

@Amit And the record stands for itself, whomever is the one seems to be "like a spoiled & condescending brat"

Amit

Just so that won't come across as an ad hominem, I'll define precisely what I mean by those words.
Spoiled and condescending behavior: immediately attacking a person that makes a wrong or inaccurate statement, in a manner that questions his intelligence or honest intention *rather* than pointing his mistake in a nice and respectful manner.
It's spoiled because it gives the impression that the person cannot contain the fact that sometimes people will make statements he disagrees with / finds as wrong. It's condescending because he feels no hesitation to reply to such statements in a hurtful …

Ryder Rude

9:50 AM

several people have already complained against naturallyinconsistent's behavior

John Rennie

Take it easy guys. naturallyInconsistent is a little more more brusque than I would be but he's also been very helpful to lots of people.

naturallyInconsistent

"... the person cannot contain the fact that ..." does not parse properly, but there has been quite many evidence in this chat alone that I'm ok with disagreements. Even if it comes purely down to disagreements, I'm not sure how expressing that is somehow "spoiled"; rather, what I have said there is a set of really mild challenges: you could have supplied, in overall, some linkages between the topics, or gone into detail, namely, talked about 1) IFM -> zeno 2) frozen -> weak measurements.

Amit

@JohnRennie I'm not complaining / asking anyone to change their behavior. Just to be clear

naturallyInconsistent

Instead, you chose to go all defensive and prickly. I quote from Cambridge dictionary:

> A spoiled child is **allowed to do or have anything that they want,** usually so that they behave badly and do not show respect to other people.

emphasis theirs.

Amit

If my definition doesn't "parse" that's too bad. I don't feel there's a need to explain my critique any further. If there's anything in it, I'm sure you've understood. And if not -- it is not a matter of clarification but rather perhaps of wanting to understand, and I'll say no more about it.

naturallyInconsistent

10:01 AM

@JohnRennie Thank you, much appreciated.

qwerty

10:17 AM

walks in with pizza gif

anyways, I just dug up a paper I didn't understand from about 8 years ago, i wasn't kidding when I mentioned it takes me years to figure things out lol. at this rate I'll finally understand QM and QFT when I'm like, 95.

it'll be great!

naturallyInconsistent

@qwerty This happens to us all. Don't be too hard on yourself. What is the topic that caused the confusion?

qwerty

@naturallyInconsistent I think I'm just slow to pick up on the real... fundamentals. sometimes I just circle around a topic for months-years and it just takes a particular wording, or a particular book to make it all click

into place

a bit like a step function.

naturallyInconsistent

@qwerty Most of QFT is like that too. Especially since the standard treatments are sooooooooo precarious.

qwerty

I found a paper I was reading on the noether theorem, and two books. nothing to really discuss yet, I've only just started reading.

naturallyInconsistent

anyway progress is a yay yay

qwerty

10:24 AM

@naturallyInconsistent I actually begged to sit in on a undergraduate QM course during my postgrad studies because I felt I never learned it properly when I did do my undergrad. I did really well, and then still never managed to pick up any QFT/particle physics. I'll learn it one day!! right now I'm really into Lie groups and symmetries and all that. I think I can make good progress this time.

the quote from ACM's page ""Once we have bitten the quantum apple, our loss of innocence is permanent." - Ramamurti Shankar"

i'm waiting to taste the apple properly

I think there's sometimes a few keystone concepts with things; if you dont understand the foundations you don't internalise the knowledge and understand how it all fits together into a narrative

@naturallyInconsistent whats your preferred treatments? everyone just says peskin and schroeder but im not convinced. I've also got Dirac's principles on my to-read list for QM; i started on it and liked it a lot.

naturallyInconsistent

10:40 AM

@qwerty Pesky and Shredder is absolutely unreadable. They were experimenting with the shortest route to churn out Feynman diagram crunchers, and that experiment is a tremendous failure. There is no hope to understand QFT by straight up ignoring all the prerequisite basics and going straight to QED.

But P&S's renormalisation bits are surprisingly ok

Dirac's two books on QM are quite nice to read. Ideas from a begone era. But don't read his QFT stuff, because he was trying a lot of random ideas bashing against the problem and getting nowhere.

There are some really beautiful theorems in Dirac's QM books. Very much enjoyable.

qwerty

@naturallyInconsistent a million times better than griffiths, gasoworicz,eisenberg+resnick and all the books i was suggested in my undergrad!! I actually got the idea to try dirac on qm since i liked his GR book so much.

naturallyInconsistent

I really think you are similar to meow, as in, we want to know why we walk the particular path. If you agree with this sentiment, keep Anthony Duncan's Conceptual Framework of QFT in mind. It is quite a difficult read too, but at least the dead-ends are pointed at all the important places.

@qwerty oh, that means you really need the rigour? I'm the opposite; I need the handwavy basics e.g. from Griffiths, first. But it is ok, the suggestions thus made are all rigorous.

anyway, tada, it is time for the whole weekend's worth of partying. I'm getting too old to be partying like this, but gotta make up for lost time

qwerty

@naturallyInconsistent thank you!! I will get it now and try not to forget about when I eventually try to pick up qft properly

@naturallyInconsistent hmm, I would say I need concepts and rigour/details? I dont like handwaving, like in the old soviet style of lecturing. where everything is just approximations and pulled from thin air. I need things built up consistently.

I didn't learn GR from Dirac; I didn't understand it at all when I first read it, but it was really good when I felt like I had "mastered" the concepts of GR to some extent. I learned mostly from Hartle, D'Inverno and MTW; but the absolute basics I learned in high school through an illustrated children's book on GR. it was amazing and I still love it - it somehow wasn't handwavy at all, despite being for kids.

@naturallyInconsistent enjoy your partying!!! never too old :)

nickbros123

12:04 PM

@Mr.Feynman as sillygoose mentioned, a lot of quants are phd physics or math, But I have always wondered what it was that they were actually doing. mostly data collection / sorting I suppose, and cleaning etc. ML seems pretty interesting in its own right, but again, question arises, academic ML or like, making something useful immediately, like an app?

qwerty

@nickbros123 afaik quants do a lot of financial modelling? from what ive heard theyre far too highly paid for it to be routine data sci tasks.

nickbros123

I see. I still lack clarity on what exactly it is that they do. Maybe I should do an internship at a hedge fund xD. Its funny because I really want to make some money, but at the same time im kind of repulsed by non-academic jobs.

basically I would love to be bruce wayne. Then I can just retire and invest all my time on books

3

qwerty

@nickbros123 theyre not known for being ethical jobs. i think theyre very picky with who they hire as well, they do a lot of screening/testing and there's an air of exclusivity around those places that im not fond of.

nickbros123

@qwerty just to be clear, are you talking about academia or hedge funds?

or both

qwerty

12:21 PM

@nickbros123 quant finance lol. but yes, academia can be downright snobby with the wrong crowd too.

nickbros123

what you said also holds in academia lol

some institutes in my country hire "internal" candidates for tenure-track posts, and publish the flyer for like, 1 day or something, just because theyre required to. Completely opaque process.

qwerty

welllll, i mean we're in physics not in say medical science so when it comes to ethics at least we're mostly only hurting ourselves and maybe higher ideals and not like, torturing rats or burning the amazon or whatever

Ryder Rude

@qwerty this term can be confused with quantum finance

qwerty

@nickbros123 oh yeah that happens everywhere not just academia. its not ideal.

Silly Goose

1:13 PM

@qwerty unless you worked on creating the atomic bomb (among other things)

qwerty

touche

naturallyInconsistent

@qwerty sadly, no treatment of QFT can meet that demand, because we still can't prove them enough to satisfy ourselves, let alone the mathematicians. But you might want to learn some analytical approximations before QFT because then you can appreciate that renormalisation isn't total bullshit.

@qwerty I really really really hated when a prof tried to teach from Hartle, and I had to deal with the trainwreck. Wald for theoretical physicists, Schutz for almost everybody else, and MTW for those who really like long and detailed expositions.

Silly Goose

@qwerty if you are already learning lie/representation theory i find it grounding to think of quantum fields as transforming under irreducible representations of the restricted lorentz group. this at least gives you something of a definition of a quantum field.

qwerty

@naturallyInconsistent lol maybe I need a qm+qft book illustrated and written for young children alongside the hardcore books in that case. like pairing tea and biscuits... one sweet and one bitter haha.

Silly Goose

then you can consider all permissible quantum fields (under that definition) and then figure out what sort of poincare invariant actions you can write down. then you have a QFT

that is all just framework though. computations im not sure about

naturallyInconsistent

1:22 PM

@SillyGoose that is what he wants first. To have a sense of bearing

The whole "Let's find out what wave equations are Lorentz invariant in the first place" is the Lie groups, Weyl and Wigner and Van Der Warden routes, and they are obviously the correct way to go.

@qwerty im writing one, but it might be 3 decades out in the future...

zooming out for partying again lol tada

qwerty

@naturallyInconsistent oh noooooo. i couldn't stand schutz!!! at all! what's your criticism of hartle? i think it's mostly nice; a bit waffly at times. d'inverno was my biggest reference in undergrad I think. wald is... okay? more advanced, like i can admire his rigour and it was really useful as a reference but i wouldnt learn from it. MTW is a gem. great concepts overall, but can be hard to find stuff in it.

@naturallyInconsistent you're spot on! but it's she, for the record :)

Claudio

does anybody know the name of this ex user whose current username is
user346? I see many of his answers/comments in some of the most advanced topics and questions ever posted on this site, so I guess he might be some kind of professor/known scientist?

maybe ACM knows him

qwerty

@SillyGoose thank you! but im just starting out with lie groups, so i dont have a big intuition yet. maybe it will be a good background for picking up qft later on then :)

Silly Goose

lie/representation theory seems unavoidably foundational to qm and qft

Claudio

it is it is :P

qwerty

1:29 PM

@naturallyInconsistent ok definitely link it and tag me in 30 years, i'd still be interested for sure haha.

@SillyGoose ooooooh so maybe that's why they never clicked for me on a deep level. actually I had trouble with bras and kets until I learnt covectors and vectors in GR. apparently its weird to learn gr before qm makes any sense...

Silly Goose

but at the same time one is left wondering that lie/rep theory is not really the full story

@qwerty yes i am not sure how people understand QM to a sufficient level without knowing some representation theory

Claudio

I'm one of them

Silly Goose

although strictly speakign the covector vector business belongs to the realm of linear algebra

Claudio

although I don't think my level of knowledge is satisfactory enough for a person like @SillyGoose

qwerty

@SillyGoose yup it took me ages for lin alg concepts to click for me. the maths courses i did emphasised computation rather than concepts and it was a huge detriment

Silly Goose

1:34 PM

or maybe i should not use the word "understand" but more the word "has the ability to organize the information presented"

Claudio

hmmmm

Silly Goose

the addition of angular momenta was a very uninteresting and strange thing (for me) until knowing some rep theory

Claudio

also rotation operators for 1/2 systems,harmonic oscillator

Silly Goose

@qwerty linear algebra seems to be this way from the few data poinst i have. i am grateful for my linear algebra course, which was very much with a "pure math emphasis"

Claudio

in my uni, linear algebra is taught by math professors which is great

qwerty

1:38 PM

when I was a young student. early early on. I think a lot of my struggles came from not understanding maths terminology compounded with the way that physicists sometimes use shorthand terminology

so you get statements like, observables are operators

which only makes sense if you already know the theory

and the lecturers would never unpack it

Claudio

I think the biggest disadvantage is not learning how to write proofs, I know they have specific courses just for learning how to write proofs in pure math degrees

qwerty

(ctd.) I would never write statements like that myself, i feel like it's intellectually lazy and misleading. but i think im not the norm.

@Claudio hm, how come you say that? it's true that proofs worried me a lot as a student. but i can't say I've needed to write a proof as a (non-mathematical) physicist in theory.

Claudio

I know I never needed to do that either, but I think writing down 3-4 pages of computations and being able to neatly express your results in a few lines is a much needed skill

qwerty

@Claudio fair take

Claudio

I guess it goes back to organizing what you learn and then being able to expose in a crystal-clear manner

@SineoftheTime since you're a mathematician, I suppose you pose great value in writing neat proofs. Do math professors put emphasis on this aspect

qwerty

1:46 PM

@Claudio "Hobbits delighted in such things, if they were accurate; they liked to have books filled with things that they already knew, set out fair and square with no contradictions." - LoTR, Tolkien. I am a hobbit.

Claudio

lol that's a good quote

Ryder Rude

Saitama VS Superman - fan Animation | one punch man

►

ACuriousMind

3:17 PM

@qwerty The main problem with "mathematically careful QM" is that mathematically careful QM is just so full of subtleties that the physics courses would never get anywhere: look at how dense and large the main references for mathematical QM - Reed & Simon's books - are.

It can feel "lazy", but actually I think it's impressive how physicists have managed to set this up in a way where people who don't insist on rigor mostly can work with it just fine without worrying too much about this underbelly of functional analysis you would actually need to do it "right"

To someone like you (and me :P) who thrives much more in the way mathematicians tend to structure such understanding this is frustrating, but while it's taken me a while, I understand why it's often seen as necessary.

qwerty

3:46 PM

@ACuriousMind i definitely agree with your overall argument. but also, I think you're being very kind and generous in your overestimation of my intellectual/mathematical depth! I would absolutely love to be rigorous and mathematically careful. but I'm also talking about things like careful wording, especially for pedagogy, I think almost everyone but me would find rather more inane. but to me it might distinguish two different concepts that most physicists dont feel the need to distinguish

actually, I think it's sort of related to how physicists never want to distinguish between a function and the value of a function at a point

ACuriousMind

oh, I understand, I tell people to use proper terminology in this chat all the time :P

qwerty

in my notes I always say the cumbersome "observable property" rather than observable.

@ACuriousMind i just picked up a thin volume on mathematical qm last week, called "foundations of qm" by jauch. there's a nice quote in the intro: "The pragmatic tedency of modern research has often obscured the difference between knowing the usage of a language and understanding the concepts. there are many students everywhere who pass their examinations in qm with top grades without really understanding what it all means." im very excited to read it at some point.

ACuriousMind

I feel I know the name (and it's not just because there's a German TV presenter with the same name :P) but I don't know anything about the book

qwerty

4:05 PM

Josef-Maria Jauch

Josef Maria Jauch (September 20, 1914 in Lucerne – August 30, 1974 in Geneva) was a Swiss/American theoretical physicist, known for his work on quantum electrodynamics and on the foundations of quantum theory, and leader of the "Geneva School" of mathematical physics. == Biography == === Early life === Jauch was born on 20 September 1914 in Lucerne, Switzerland, the son of Josef Alois Jauch (a telegraph operator) and Emma Laura Rosa Jauch (née Conti). He had two older siblings: Adelheid Jauch and Emil Josef Karl Jauch. After his mother died in 1916, his father remarried, and a half-sist...

ive not heard of him before though

... well this is "fun". physics.stackexchange.com/questions/510537/…

Claudio

4:39 PM

Recommended by Polya and Pauli

he must've been a god or something

Sine of the Time

@Claudio do you mean in exercises or in general?

naturallyInconsistent

@qwerty Hartle starts with line element, i.e. throwing the metric at students and expecting them to understand stuff. That is just not any tolerable way to teach. None of the students understood anything, and I had to reteach the whole thing out of pity for them.

@qwerty That is just because it is technically more difficult; people are generally quite ok with doing handwavy stuff, and since you have trouble with that, your predicament is not toooo unexpected. There are a LOT of links in physics that are just not taught. Very deplorable state of affairs

@SillyGoose even more evidence that hoomans are silly drawing lines in the sand trying to separate topics

@qwerty Gilbert Strang, MIT OCW, is a good mix of both. Concepts, and then quickly some applications, then pure concepts.

@qwerty Extremely horrible. It is "We know from Sturm-Liouville theory that Hermitian operators are guaranteed to have complete set of eigenfunctions with real-valued eigenvalues; let's postulate that observables are such operators so then the resulting quantum theory is guaranteed to give physically sensible results."

@ACuriousMind truer words have never been composed.

qwerty

5:13 PM

@naturallyInconsistent this is really funny because I have always heard the take that qm is technically more difficult than gr but for me it simply wasn't? like I think I have a pretty decent conceptual understanding of gr, maybe not at a mathematical physicist level but ok. and my qm is definitely undergrad level.

and I think literally what you accuse hartle of sinning with, by throwing out a metric/line element... well, sort of isn't it the one key that unlocks pretty much everything else in gr?

I suppose you could motivate things better, with like the thought experiments and build up from there

ACuriousMind

@qwerty Einstein famously said the mathematicians made it so he didn't understand relativity anymore; conversely that must mean that mathematically-minded people don't really understand relativity when it is presented the physics way ;)

@qwerty people struggle with the linear algebra aspects a lot, especially because the physics texts often act as if all this is bespoke and complicated when plenty of statements are - at the level of rigor the physics texts are working at - just ordinary linear algebra

qwerty

@naturallyInconsistent you're completely right with that, though. I'm writing some notes on dynamical systems... and everything is linked. it's a lot of fun but I have no idea how I completed undergrad physics and there's so many gaps in my education wrt all the things I want to say and present in page one of my notes lol

naturallyInconsistent

@qwerty GR has an obvious realist underlying model; you don't have to break out of the worldview that would be familiar to Newton and Hamilton, that everything in that theory has a sensible physical interpretation. Quantum theory obviously is the opposite of that. Understanding QM requires realising that that worldview isn't everything.

Silly Goose

@qwerty im writing up a note on diffe g without reference to a metric yet :^)

naturallyInconsistent

@qwerty I am totally in agreement. But it is totally sinful to have students pass the only module on GR that they would ever get, that they had already spent their precious module credits that they could actually choose to invest (most modules are mandatory), and yet not even consider teaching them that parallel transport is a thing, covariant deriatives is a thing, Christoffel symbols are a thing (and how to quickly get them), Einstein's Field Equations are a thing, Schwarzchild metric...

Silly Goose

5:22 PM

though i am just trying to build up to differential forms. so I have I. Manifolds, II. Linear Algebra on Manifolds, III. Vector Bundles, IV. Differential k-Forms

qwerty

@SillyGoose don't at me with co-ordinate free everything, wedge products everywhere are still meaningless to ne

lol :p

ACuriousMind

@SillyGoose I mean, differential geometry is largely without a metric - the subfield of it that's specific to metrics is (pseudo-)Riemannian geometry

Silly Goose

is there a physicist way of describing precisely when sections are obstructed from existing

i don't mean just global sections. i mean sections generally (that are not just over a coordinate neighborhood)

qwerty

@naturallyInconsistent yeah he's very slow to get into it. I wouldn't follow chapter by chapter, you're right

ACuriousMind

@SillyGoose you'll have to be a bit more specific

physicists generally don't talk about "sections" and "bundles" at all, after all :P

Silly Goose

5:26 PM

naturallyInconsistent

@SillyGoose I'm not sure this ordering makes sense. Manifolds of inherent interest to physics, other than the trivial $\mathbb R^n$ and friends, have curvature, and then you don't get to do linear algebra on them that early. Instead, you have to have differentation defined first, and then you can go back to do linear algebra on their tangent bundles.

Silly Goose

this is the definition of a section that i am using

and then i suppose (1) restrict attention to differentiable ($\mathbb{C}^\infty$) sections and (2) maybe let's just talk about obstructions to global sections

ACuriousMind

@SillyGoose in that case your question is even more strange because for vector bundles the zero section always exists

Silly Goose

hm well excluding also the zero section

ACuriousMind

the non-existence of precisely what kind of section are you concerned with

naturallyInconsistent

5:29 PM

@qwerty the lecture module spent a tremendous amount of time on SR and on line element games, and then suddenly swerved into giving the Schwarzchild metric out of nowhere and computing the anomalous precession of Mercury. By the time I realised that the module was going that way, it was too late. I had to build everything myself in extreme time crunch.

Silly Goose

or i guess maybe i am interested in the existence problem in gauge theory. so not a vector bundle but a principal bundle

@naturallyInconsistent i have that under the manifolds section i think

ACuriousMind

@SillyGoose The non-triviality of the principal bundle is often encoded in the "gauge at infinity", see e.g. this answer of mine

Silly Goose

hm wait is non-triviality of the bundle a separate notion than existence of global sections though?

do they coincide for principal bundles?

ACuriousMind

for a principal bundle the two notions are the same

Silly Goose

oh i see

that is nice

ACuriousMind

5:33 PM

a principal bundle is trivial iff it has a global section

naturallyInconsistent

@SillyGoose Your notes leave it unstated, but I think your $U_i\subset M$ and $K_i\subset\mathbb R^n$?

@SillyGoose I don't know what you are doing there. I mean, if you already have $TM$, then $T_pM$ is clearly redundant. Your notation suggests that your vector bundle is the tangent bundle and nothing else, and certainly not a generic fibre bundle; are you making this suggestion at all? If you have $TM$, isn't $M$ part of it? So many questions!

ACuriousMind

@naturallyInconsistent The notation with $T$, usually reserved for the tangent bundle, is strange, but otherwise this tuple notation is the usual formal definition of a fiber bundle (cf. e.g. Wiki), where the tuple also contains the bundle, the base and the fiber, though one could argue the base and the fiber are already part of the bundle

naturallyInconsistent

@ACuriousMind uugh, was vaguely remembering that; that is definitely donkey years ago...

ACuriousMind

the reason is that even though the geometric intuition is that $M\subset TM$ in some sense (via the zero section, for instance), we make this formal definition before we have shown any of the properties of the bundle, and so for the projection map $\pi$ to make sense, the base and the bundle need to be separate objects in the definition

naturallyInconsistent

Also, partly because I only understood tangent bundle and not the generic fibre bundles, and the "how do we align the zeroes and axes everywhere on the manifold" was the show-stopper.

Silly Goose

5:45 PM

@naturallyInconsistent i wrote that $U_i \in \tau$, where $\tau$ is the topology of the manifold. the topology of the manifold is a subset of the power set of $M$, i.e. a subset of all subsets of $M$. this is a stronger condition than just $U_i \subseteq M$

since coordinate neighborhoods need to be open set w.r.t. the topology of the manifold by definition

(same for $K_i$)

@naturallyInconsistent oh yeah i am not generally introducing bundles in that note. though perhaps it should be changed to be so since it's not much mroe work

naturallyInconsistent

Since we are at this topic; I'd like to ask if it is that the Coleman-Mandula theorem implies that the fibres other than the tangent bundle necessarily has to be completely independent, i.e. the zero section on them has to be trivial? Like, that was the impression I got from one of your earlier answers to adjacent questions from meow.

ACuriousMind

@SillyGoose while correct, this is a bit un-idiomatic - most texts would simply write "$U\subset M$ open" instead of $U\in \tau$, it's a bit annoying for the reader to remember every time that your $\tau$ is a topology and hence you're talking about subsets

Silly Goose

@ACuriousMind i never know what topology people are referring to when they write $U$ is open!

hehe

naturallyInconsistent

@ACuriousMind yes; I kinda caught the necessity of the redundancy, but that, again, is years behind meow

Silly Goose

anyways for me it is good to keep track of all structures introduced. to explicitly write the topology and call the basic data of a manifold a topological space makes much more clear why a diffeomorphism needs to also be a homeomorphism--but this might just be me

ACuriousMind

5:48 PM

@SillyGoose ...but the definition of "open" is just that it's in your $\tau$, just a word instead of symbology

naturallyInconsistent

@SillyGoose That's the part that allowed meow to deduce that you wanted to mean that.

Silly Goose

@ACuriousMind but people never write what topology they actually mean, which bothers me :P. is it an arbitrary topology? the "usual" topology? etc.

and i think for physicists especially, open set does not induce the image of a topological space

ACuriousMind

@SillyGoose I don't understand the complaint - when people say "Let X be a topological space, $U\subset X$ open", then they mean that $X$ carries a fixed topology. It's very rare outside of specific situations that you want to discuss the same underlying set with two different topologies.

also, you almost never have a topology given in this form for a concrete example: Most topologies in practice are "induced" by some other construction, e.g. subsets of Euclidean space carrying the subspace topology, a metric space carrying the topology induced by the metric, etc.

Silly Goose

well i think objects like $\mathbb{R}^3$ are always assumed to carry the topology induced by the Euclidean metric, but before taking a course in topology this was quite confusing

because you might go through an entire textbook and never once find a mention of this assumption

so then you have to go looking onine and etc.

ACuriousMind

I mean, no one writes out the tuples from any of the other formal definitions, either

your linear algebra text will contain something like "A vector space is a tuple $(V,\mathbb{F},0,+)$ such that..." and literally one chapter after that every other theorem will start with "Let $V$ be a vector space"

Slereah

5:58 PM

Nobody writes topology explicitely for any set with more than ten elements

ACuriousMind

it's exactly the same with the definition of a topological space as a tuple $(X,\tau)$ and then everyone just saying "A topological space $X$..."

naturallyInconsistent

Sometimes formal notation gets so cumbersome that even mathematicians would bow to the pressure to abbreviate.

ACuriousMind

I don't understand why you would consider this confusing in the case of topological spaces but not, like, everywhere else :P

that the set carries the structure implied by saying it's a topological space or a vector space or whatever is, well, implied

and the word "open" makes it conveniently so that you never need to introduce a symbol for the topology on a space $X$ at all, you just say the set is open in $X$

naturallyInconsistent

@SillyGoose Surely you cannot have $M\ni p$ in one statement, and immediately have $p\in(U_i,\varphi_i,K_i)$ in the next statement. By the way you are using the notation, you clearly want to mean only that $p\in U_i$, so that then it can be acted upon by $f$

Slereah

@ACuriousMind it's a great notation if you need to talk about the forgetful functor tho

ACuriousMind

6:04 PM

it has its niches, sure

Slereah

> A Young diagram is a partition that wants to become a Young tableau.

naturallyInconsistent

In fact, you really mean that $\forall(p,f(p))\in M\times N\exists U_i\times V_j\ni(p,f(p))$ such that your final mapping thing is well-defined. And then you can be nice and make explicitly clear that when either $U_i$ or $V_j$ or both isn't unique, then the overlapping region has to satisfy consistency conditions.

naturallyInconsistent

6:25 PM

Also, I'm pedantic enough to use the opposite convention for the coördinate functions. Just like how sine cosine functions are extended to accept inputs outside of any choice of the principal range, whereas the arsin arcos functions generally are defined only to give you output only within the principal range, it should be $\varphi^{-1}:M\to\mathbb R^n$ that has the unique output, and $\varphi:\mathbb R^n\to M$ accepts redundant inputs

Claudio

6:38 PM

@SineoftheTime I guess in general

Sine of the Time

I'm not sure I've fully understood the question, but yes, there's emphasis on proofs, even if nowadays professors are less meticulous since there's less time to do all the details

plus, in subjects like real analysis, there's not enough emphasis on more "theoretical" exercises, but only on computational exercises

that's my opinion though

naturallyInconsistent

@SineoftheTime could you give an example of a theoretical exercise?

Sine of the Time

anything that does not involve a mere computation or an applycation of a formula

naturallyInconsistent

wouldn't an exercise asking for students to prove something then be an example?

Sine of the Time

6:54 PM

yes

naturallyInconsistent

thanks~

Sine of the Time

but this is not usually required

from the student I mean

and in the past people used to take more time but studying from diffent books/sources whereas nowadays in a lot of universities it's sufficient to study the notes of your professor

ACuriousMind

all my math courses had proof-type exercises

naturallyInconsistent

@SineoftheTime Has that changed? I mean, it used to be an EU thing that lecturers are expected to make notes for students to study from, whereas USA tended to use textbooks; the latter is preferable because the effort needed to publish books makes the overall learning experience much better than just random patchwork of notes. However, of course, price is also an issue.

ACuriousMind

I guess you could've usually qualified for the exam by just doing the computational ones and getting almost all of them correct, but that's not a good gamble to commit to

naturallyInconsistent

7:03 PM

@ACuriousMind actually, that ought to be a doable challenge---you know how maths department wouldn't even require you to use a calculator...

Sine of the Time

@naturallyInconsistent as far as I know, it has changed. In the past, you needed at least 3-6 months to prepare a single exam and professors used to say that you have to consult different books

naturallyInconsistent

sad

Such good culture, lost yet again

ACuriousMind

@naturallyInconsistent the notes vs. books thing is a double-edged sword: Sure, the average textbook might be better than the average lecture note, but the professor having to actively think about their lectures by writing the notes instead of just teaching a textbook in order might on average improve the quality of the lecture

naturallyInconsistent

true that.

Silly Goose

@naturallyInconsistent oh that is atypo thanks

ACuriousMind

7:05 PM

the worst of both worlds is of course lecture notes that are just copied at random from a book, but the best of both worlds is lecture notes following a book but improving on the presentation of the book where the lecturer thinks it's necessary

naturallyInconsistent

@SillyGoose mew mew~~

ACuriousMind

all the best lecture notes I've gotten had a preamble like "This is mostly based on X, but I think topic Y is better covered in Z, and chapter 7 is patched together from different sources because no one treats this properly"

naturallyInconsistent

@ACuriousMind no, no, the worst of both worlds is randomly put-together assortments of photocopies of fuzzy photocopies of lecture notes of a by-gone era, overlapping in parts and with slightly different proofs, and all sorts of inconsistent notation. Transparencies with cancellations. trauma resurrected

ACuriousMind

oh, sure, if the lecturer has completely given up the student have no chance :P

naturallyInconsistent

Oh wait, there is worse: The lecturer lectures from powerpoint, but is presenting not to any student. Eye contact is always to the ceiling. It is nowhere near Halloween. Yet even the most meticulous note-taker admits that there would be huge blanks because the lecturer's voice is the ultimate hypnotic cure for insomnia.

ACuriousMind

7:15 PM

I've never had any math or physics lecture presenting from a powerpoint

blackboards all the way

Sine of the Time

using powerpoints is a crime :(

Claudio

@SineoftheTime wait so your exams now require you to perform computations rather than on proof-based exercises??

Sine of the Time

@Claudio yes, in general that's the norm

Claudio

@ACuriousMind lol 1/5 of the courses I followed were on ppt

ACuriousMind

ew

Claudio

7:17 PM

and all of them were absolute trash

general opinion not mine hahaha

ACuriousMind

of course they were - the function of the blackboard is to limit the lecturer to the speed with which they can write, and to have to think about what they are writing

Claudio

@SineoftheTime I mean it's kinda sad, then again proof-writing always seemed to me like the most difficult skill to acquire

@ACuriousMind the slides were usually full of mistakes lol

ACuriousMind

of course there are good presentations using powerpoint, but it's far too easy to make a garbage powerpoint in any context; it's why at my workplace in most reviews powerpoints are banned and you have to actually do a live demo of the feature you developed

Claudio

lol

my professors dont have enough time on their hands

you can see the desperation in their eyes :)

naturallyInconsistent

I gave up LaTeX beamer slides after students kept clamouring for the board.

I mean, yes, I go a little too fast, but LaTeX looks nice...

ACuriousMind

7:23 PM

the children yearn for the mines, the students yearn for the chalk

Sine of the Time

@Claudio usually, there may be proof-writing problems in more advanced courses

naturallyInconsistent

they are mostly whiteboards here

Sine of the Time

like analysis 3

ACuriousMind

@naturallyInconsistent the math department here bought like 20 years of chalk supply when their favourite manufacturer was about to go out of business

Claudio

@SineoftheTime yeah I mean I suppose algebraic geometry doesn't sound too computational anyways :P Also what's your analysis 3?

we stop at 2 here in the phys department

Sine of the Time

7:25 PM

analysis 3 it's like what you call mathematical methods

Claudio

ah yeah functional analysis and so on I forgot

Sine of the Time

so in general: Normed and Banach spaces, L^p and Hilbert spaces, Fourier series and transform

it's an introduction of functional analysis basically

naturallyInconsistent

@ACuriousMind that manufacturer is back in business, relocated to another country.

ACuriousMind

possible, I don't remember the name

Claudio

jokes on you, we only do Fourier series and transform basically and some things on operators and infinite dimensional spaces

although we should be doing Banach, L^p,... but its just on paper

Sine of the Time

7:28 PM

you do only L^2 :)

naturallyInconsistent

@ACuriousMind It is Hagoromo. There is no other like it

Claudio

@ACuriousMind japanese chalk?

yeah that video got famous

Sine of the Time

@naturallyInconsistent OP chalk

naturallyInconsistent

@Claudio It is now in Korea

Claudio

that chalk looked like butter, I would eat it if I had some in my hands

Sine of the Time

7:30 PM

comment section of that video roasting the mathematicians for doing a video on chalks

Claudio

@naturallyInconsistent I guess hoarding chalk was a great move, they probably don't manifacture it the same way.

naturallyInconsistent

@Claudio made with edible materials

Claudio

Like that japanese ink that comes in blocks

ACuriousMind

@naturallyInconsistent ah, yes, looks like that was it

naturallyInconsistent

@Claudio it is the exact same recipe. The Korean buyer bought even the machines and shipped everything over.

ACuriousMind

7:31 PM

the timing fits, yes, this was somewhere around 2014

Claudio

@SineoftheTime lol, people can't understand the feeling of having good chalk in their hands

@naturallyInconsistent I dont believe them

naturallyInconsistent

@Claudio The people who have bought the new version confirm that it is just as good.

Claudio

I now fully believe this

naturallyInconsistent

Of course, only independent peer review is trustworthy

Claudio

@naturallyInconsistent well said my friend, well said

naturallyInconsistent

7:34 PM

whereas miao miao is already extremely insufferable with mah writing implements and so miao miao had better never get to touch Hagoromo. It will be instant addiction

ACuriousMind

Also, we haven't yet mentioned the main benefit of blackboards: It gives the students a minute or two of pause while the lecturer has to wipe the board

I remember I found this to be a crucial difference between school and university when I started studying: In school, the teacher would make a student wipe the board, in university, they wiped the board themselves.

Claudio

wrong: the best thing is the faces of students when the chalk cracks

that creaky sound, music to my ears

You can tell a good lecturer from a bad one by the way the wipe the board I think

naturallyInconsistent

@ACuriousMind are whiteboards not ok? </racism maximus>

ACuriousMind

I dunno, whiteboards are just soulless

Claudio

they use them at Oxford, like James Maynard

naturallyInconsistent

7:39 PM

they indeed are. The fumes are also ghastly. But then again chalk dust is also ghastly

ACuriousMind

also, there's always that one marker that doesn't write right, or the prof just grabs a marker with a horrible color because it writes the best, etc.

chalk just...works

Claudio

My department is so poorly maintained, I could bet the chalks are made out of asbestos

naturallyInconsistent

I was told that the nation ditched chalk because chalk dust is bad for lungs. That was a straight up fabrication. Lying liars

Claudio

@naturallyInconsistent people have allergies

naturallyInconsistent

@Claudio technically, that problem solves itself...

ACuriousMind

7:41 PM

also I think I hate whiteboards because some genius interior designer designed the office I work in with random surfaces that can function as whiteboards...but then there are other surfaces that are also white and flat and shiny and they are not whiteboards

naturallyInconsistent

@Claudio there's allergies to chalk???

ACuriousMind

I've had to call facility management several times so they could remove the markers from some surface I had mistaken for a whiteboard :P

Claudio

allergies? I think there are, I'm pretty sure Asthmatic people dont like it :P

naturallyInconsistent

@ACuriousMind summon baphomet. Someone needs to get a clue

Claudio

@ACuriousMind lol accidental vandalism

allergy to chalk = asthma :P

@ACuriousMind what about colored chalk

I hate it

ACuriousMind

7:44 PM

Sometimes it's fine, but mostly it's unnecessary

if you need color to make your concept on the board understandable you've already failed

Claudio

I had a professor who would use all different kinds of colors, she thought it would be a good idea, little did she know 50% of students couldnt see anything

naturallyInconsistent

on our side, there was a big new building that had these frosted glass functioning as whiteboards basically on every surface. i.e. you won't run out of whiteboard space and it is great. Spent millions on it. And then they had a silly scandal: they complained about them not being nice to erase, only to realise that they didnt know that there was a protective plastic layer they had to first remove...

Claudio

She was great, one of the bests I've had the pleasure to follow

ACuriousMind

(I have a variant of red-green color blindness so I've had to explain to many people not to use color as the only discriminant for something)

naturallyInconsistent

@ACuriousMind but, butt, Bryne's Euclid's Elements...

Claudio

7:46 PM

White chalk clears as per usual

@naturallyInconsistent lol

I gotta go back to studying lol its gotten late :) I love chalk

Arjun

8:12 PM

Exams are making me hate studying,like I couldn't think on a particular thing in depth for long hours..I have to quickly revise everything and not get stuck(cries in pain)

I have an exam today in like 8 hrs and I'm having a bad headache lol..I think I'm cooked

Ryder Rude

10:16 PM

@nickbros123 do u prefer reading books or publishing papers or both

@Arjun it will be fine...

fqq

11:35 PM

@ACuriousMind unfortunately quite common in the UK :/ they go "well" with the few hours of teaching they have

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