Oh my god, this is the first time I see Qmechanic replying to a physics question in the hbar

@Mr.Feynman my heart goes !!!!!!

@peterh yeah i think this is also pointing to smth relevant ab the points i made leading to this discussion. elementary education is indeed compulsory in the US, but there are a lot of factors that make it not accurate to say that education is free imo. for instance, my fellow students and i in [...]

[...] primary school could not go to school for days and some for weeks because there were lice outbreaks and the school policy was that students must be sent home if they have lice. the living conditions were so bad that this ended up being a cycle of lice outbreaks for more than a year. [...]

[...] did this happen in the richer neighborhoods and their schools? definitely not, and in the US schools are funded partially by the property tax of the neighborhood of the school and its forbidden to go to a public school outside of your district so even then id say that its not really accurate to say even this level of education is free. [...]

[...] what does it mean to say something is free when the quality of it depends on how much you pay for it? in similar vein, china requires everyone to to go primary school (and past that ofc), and the exams to get into schools at each stage are supposed to be based on merit. however, i have multiple friends who just paid to get into schools their scores werent good enough for. imo this is also not reminiscent of "education is free" and this is a country that is entirely separate from the [...]

US. i cant imagine that germany is free of these types of issues (or really any country) since they are intrinsic to a society with any sort of class divide, but id be happy to hear if it indeed was not a problem. i just dont really believe that "education is not free" is truly a US centric statement

i think it just reflects we mean different things when we say something is free.

im curious what you think in particular about this question "what does it mean to say something is free when the quality of it depends on how much you pay for it" @ACuriousMind (tagging since it's a response to your messages in the past convo but sorry if this is not proper)

One way of constructing Calabi Yau manifolds is to consider polynomials in projective spaces. E.g. A quintic in $\mathbb{P}^4$. What I am unable to understand is if a particular quintic corresponds to a particular CY fold, and changing the coefficients of the quintic corresponds to changing parameters of the CY 3-fold i.e. we get different CY 3-folds for different coeffs, then why does the Hodge number $h^{1,1}=101$ is associated with a CY 3-fold?

Is it not counting in some sense number of different CY 3-folds of the same type...here quintics in $\mathbb{P}^4$?

what is everyone's favorite proof

@RyderRude Cantor's diagonal argument is pretty cool

trying to figure out how to word something. namely: suppose you have fluid flowing out of a large tank through a narrow tube. i want them to use Bernoulli's principle to analyze the flow within the tank and use Poiseuille's law to analyze the flow in the tube

but bernoulli isn't applicable if there's viscosity, whereas Poiseuille's law relies on it

you know it is not applicable, yet you want to use it?

tbh it's more me trying to salvage a final exam problem from last year

i'd rather not start from scratch on it but

the more i look at it the more i think i have to

i've already had to scrap part of it b/c the old solution made a BS assumption

and if you don't make said BS assumption, the problem gets unreasonably hard

Yes; and the usual assumptions are extremely bad at fitting to actual experimental data

i could just tell them to ignore viscosity for that part i guess

morally i don't like it but

Part of the issue is that the boundary layer is actually going to be a mathematical singularity. Bender & Orszag, yes that book covering some mathematical details of renormalisation, mentioned this boundary layer nonsense

yeah

viscous vs non-viscous is a headache

Of course, IRL the quantum system will not actually have a singularity, but maths will be maths and the physics will approximate what maths says it should have

viscosity is weird in that it makes things mathematically both easier and harder

harder in that you can't appeal to Bernoulli's principle

easier in that viscosity helps prevent turbulence

@SirCumference yeah.. and Cantor invented his way of talking about infinities out of the blue

@RyderRude well that's kind of how mathematics works

you establish some axioms (which are ultimately up to what you intuitively want math to be) and then derive logical statements from them

if you want to reject some of those axioms, it'd be nonstandard but still perfectly valid

@SirCumference or realize that the axioms you picked are contradictory

@Semiclassical well, you usually try to avoid that

but there's a deep rabbit hole into establishing those axioms

try being the operative word :P

in any case, there's no "best" set of axioms. it comes down to preference

Cantor was nonetheless one of the most important contributors to set theory

@SirCumference i link this image way more often than i thought when i first saw it

smbc-comics.com/comic/know-your-linguistic-philosophies

lol

@RyderRude All this is to say that there's no such thing as a fundamentally true statement in math. You need to first define what is considered true (i.e. define your set of axioms), and that's something that indeed comes out of the blue. Everything after that is just a matter of finding logical consequences of those axioms

@SirCumference yes.i meant that that idea of infinity was out of the blue. there r other inventions that r not out of the blue ,. e.g. non euclidean geometry which is an extension of euclidean geometry

well, that would be an example of a logical consequence of axioms

when you're a set theorist like Cantor, you gotta work from the beginning of it all

i meant the axioms of non euclidean geometry r not out of the blue becuz similar axioms existed before

@Relativisticcucumber China follows probably a communist model. Most important characteristics is, that the state considers important the development of its citizens, so strong education is top prio. Beside that, there is a system of "protegee". That is an un-official pyramids of strong men and their followers, similar to the feudalism. For example, if you are a friend from the University of the director of your company, then you have some chance that this friend will call his friends at the

@Relativisticcucumber University where they have influence, and they trick that your son will be accepted there, even without enough points. That is, in theory, corruption, but former socialist countries work partially still on this way. As far I know, USA works very differently, there are "clans" or "clubs", mostly organized at the Universities, and these help each other. The former commie countries have pyramides of protegees.

usually, mathematicians invent axioms to abstract out a previously known idea... like group, set, topology, etc

I don't think Cantor invented infinity :P

like, everyone knows how collections of objects work. u just codify it and u hav got a set theory

He just demonstrated how infinity works under our usual set of axioms

@SirCumference infinity was a known idea, but levels of infinity is something no one knew intuitively

u cannot find levels of infinities in historical writings i bet

well, i'm sure somebody came up with the vague notion

oh

but yes, I assume no one had formally defined it before those kinds of developments in set theory took off

maybe someone had a vague idea

the idea that a boundless continuum intuitively feels "larger" that an infinite discrete set isn't too out there

depending on how vague it was, we could or could not call Cantor's work our of the blue

@SirCumference yeah... but in that sense, rational numbers feel equally larger

but it is the vague notion, yes

indeed, there is a lot surprising once you start formalizing the concepts

the idea that $[0, 1]$ is equinumerous with all the reals is one such surprising case, at least until you read the proof

yeah

or the idea that there are "more numbers" between 0 and 1 than there are integers on the number line

yeah. i wouldve expected these two to be equal

in any case i oughta head back to QM

later y'all

bye

@Relativisticcucumber As far I know, criminal law calls this "misuse of influence". That is, for example, if the director of a University misuses his influence to trick the entry exams, to help the son of his friend to get in. But that is the theory. Practice is that everyone "knows" where is the limit and they do not pass this limit. In the West, this limit is zero. On the East, it is not.

@Relativisticcucumber Btw, I have read a German elementary school math book. Imho, if the small kids really know these, then Germany has a strong math education. But I think it is more likely, that the kids learn only a small part of that.