The h Bar - 2016-08-21 (page 1 of 5)

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12:01 AM

@ACuriousMind

I'd like to draw your attention to this answer of yours

20

A: How does gamma-gamma pair production really work?

Quantum field theory does not offer a description of "how" its processes work, just like Newtonian mechanics doesn't offer an explanation of "how" forces impart acceleration or general relativity an explanation of "how" the spacetime metric obeys the Einstein equations. The predictions of quantu...

I agree mostly with what you said.

However, I think it's a bit reductionist to say that QFT doesn't tell us anything beyond scattering probabilities.

While I understand the idea that theories are only about producing predictions of experiments, I disagree with it.

Consider two theories which both give the same predictions for experiments; perhaps consider normal QM and one of the many more esoteric flavors.

How does one choose between these theories?

There are many ways! We can go on the basis of complexity, generally favoring the theory which is simpler.

We could try to pick one which seems to give a better intuition. We could even pick one which seems more likely to be extensible, an often underappreciated factor in physics theories.

Furthermore, and maybe more importantly, interpretations of theories matter. A lot.

Being able to think about time dependent Hamiltonians as an expansion in the number of scattering vertices (a.k.a. the Dyson series) is useful even if, as you always say, physics is not fundamentally a perturbation series.

Similarly, lines of electric field are a useful construct, even if they don't really have anything to do with the real-life outputs of electromagnetic theory.

@dmckee I support something like this rather strongly.

Remember all the hubbub about low quality posts, and that "experiment" we did about it? I think one of the root causes for all the trouble is that we're all afraid to down-vote.

Incidentally, I also think that if we were all to upvote more, we'd be less miserly with our rep and ready to downvote more too.

@dmckee i dont really think itd make a difference, unless your saying it cost the downvoter 3 pts

12:32 AM

@DanielSank Well, it does tell us more, but that "more" - like the derivation of the LSZ formula, or Goldstone's theorem, or any other non-scattering QFT effect - is not amenable to storytelling. I can tell you that particles "split into virtual particles", or that "gauge bosons eats broken symmetries", but without understanding the formal meaning behind these notions it doesn't tell you anything.

@DanielSank Maybe you like this answer of mine better in its tone, then

However, my "reductionism" and my insistence that perturbative descriptions are not fundamental come from my frustration with the fact that the people freely using "virtual particles" or "excitations of the field" without backing it up with the corresponding math usually don't tell you that they're using a perturbative notion with limited applicability, and make it sound as if these notions are somehow the fundamental core of quantum field theory

In particular, it's dangerous to teach those "interpretations" before teaching the actual thing - just look at all the confused questions about virtual particles, or the rubber sheet analogy of GR, or any other popular analogy for explaining a complicated topc we get

And the comparison with "lines of electric field" is really not applicable here: the field lines do have a clear, rigorous definition - that of regions of equipotential - and what you're told about them - that charges follow them - is completely and rigorously true.

they're not an approximation, and they're not usually imbued with meaning that simply don't follow from the theory

That is different for all those "interpretations" of quantum field theory.

@JohnRennie In my opinion, a little bit of lower tone in the sake of the clarity can be less harmful, as the pent-up anger.

12:49 AM

@user507974 No, he's saying it should cost the downvoted 3 points. Currently, one upvote on an answer needs five downvotes to have zero rep gain for the poster. There are people who just post bad answers, yet slowly but steadily gain rep although almost all of their posts have more downvotes than upvotes. Changing the zero-net-rep ratio from 5:1 to 3.33:1 would help make that more difficult.

@ACuriousMind Posts with negative vote count tend to disappear. Questions with negative votes, but having upvoted answer, will serve as a long-term sign that you made a mistake. And both of them produce a significant psychological pressure. While the -1 own rep is not a real problem - first, it is small, second, you will get them back if the post is deleted. I think these additional effects make the downs so bad, and not the -2 rep loss.

@peterh There are posts that get a few downvotes and a few upvotes. That gets the author positive reputation.

However, if you get +5 and -5 on an answer, in my estimation, this means the answer is really bad or that the question was bad.

^that

@ACuriousMind I understand and I agree with everything.

Yes, teaching interpretations first can be a really big problem. However, I think that in most cases the real problem is not the ordering of interpretations versus theory, but the fact that the real theory is never explained.

I think the obvious flow of learning is basic idea -> theory -> revisit basic idea and refine

The middle step is often left incomplete and the third one entirely absent.

@DanielSank It is true. But, as far I know, a +5/-6 answer will later disappear and you lose the rep. Maybe we can consider a +5/-5 as a border case.

1:00 AM

@peterh To be honest, without examples we're both just pissing into the ocean.

@peterh Have a look at this query that selects users with a high percentage of negative score answers.

4

The "ocean" here is the ocean of discussion on site policies, all too often carried out without any evidence for the various contributors' opinions.

In particular, look at the answer score distributions of the highest rate offenders.

@ACuriousMind THANK YOU for providing some data!

If your score distribution looks like a bell curve centered at 0, you should not have thousand reputation points.

6

1:03 AM

^ That

@DanielSank Thank @EmilioPisanty for producing it ;)

Thanks, @EmilioPisanty!

@user507974 Not the person casting the vote. The one receiving it. To most people it would make little difference. They have few downvotes on posts that are not deleted.

@peterh Answers are not automatically deleted for having a low score.

@ACuriousMind I see in you in the future a "data scientist" or "senior data analyst" by a Big Company, fighting a desperate crusade against the specifications and the docs lacking the rigor and precision :-)

Question with negative scores and no positively scored or accepted answers are reaped eventually, but bad answers to good questions can remain around indefinitely. As can bad answers that the OP accepts.

1:05 AM

@peterh Yeah that, or maybe just a future in being a reasonable scientist who backs up what he says with data?

@dmckee Ugh, that's the worst.

I once wrote a nice answer debunking a perpetual motion machine and the OP accepted someone else's wrong answer. Then, despite rather lengthy discussion in the comments, refused to switch the acceptance because they just thought I was wrong.

I was actually somewhat vexed.

@DanielSank When someone asks about perpetual motion, your prior for them not asking in good faith sadly should be much higher than for other topics :P

@DanielSank I know. Not becuase it matter that much in the greater scheme of things, but it's just so pigheadedly wrong.

@DanielSank Well, it is also possible :-)

I like to remain just a tad optimistic when people ask about perpetual motion machines because sometimes people aren't referring exactly to the same definition as physicists for it

sometimes they just mean that term for a frictionless (or rather very low friction) device that takes in more energy than they expend, the people asking this are just not as good energy accountants as us

given the general level of education of the public i wouldnt be suprised if many misidentified a dam generator as a perpetual motion machine

@dmckee Ok, thanks. But I don't see too many old posts with negative vote count. Something eliminates them.

@user507974 Some decades ago I've heard about physicists-enthusiast cooperation trying to make de facto perpeetum mobile from vacuum energy. They were relative active, despite that they were categorised by the mainstream physics as pseudoscience. They disappeared.

1:27 AM

@peterh Well we all know those exist :p

I like the youtube channels that purposefully make fake "zero point energy" machines

with hidden wire/batteries, et cetera

@ACuriousMind oh I don't know... My highest score ever is on a perpetual motion machine question.

1:42 AM

@NeuroFuzzy ok ok :-) Btw, zero point energy is that the energy eigenvalues of the Hamilton operator don't always include 0. And, the vacuum energy has various calculations between nearly 0 and $10^{120}$ and nobody knows, what is the truth. But these two seem to me nearly unrelated.

@ACuriousMind SE don't like complexity...

My algorithm in the case of a VtC is this: I try to imagine a HQ answer to it what I would vote up. If I can, I vote for "leave open".

2:13 AM

@dmckee Not quite accurate. That applies only to closed questions, cf. meta.stackexchange.com/questions/5221/…

From what I can tell, even a downvoted question with a downvoted unaccepted answer, even with no upvotes on either, will remain on site unless it's closed.

@DanielSank link?

@ChrisWhite You defended? That's awesome stuff. I'll hopefully catch up soon enough.

@EmilioPisanty Hmmm ... yep. You're right.

@DanielSank No worries. It has made me (even more) unpopular with certain sections of the site, though.

1 hour later…

3:44 AM

4

Q: Brownian motion moving nano/micro coils inside a magnetic field

Following experimental setup. We take copper coils which are small enough to be subject to brownian motion. We combine those coils with some other material to make them about as heavy as the liquid we submerge them in (same weight per volume) so they would neither all gather up at the top nor bo...

thermodynamics magnetic-fields brownian-motion

In fact, @dmckee, you wanna see an example of pigheaded wrongness, look there ^

4:27 AM

this reminds me back into feynmans research on trying to extract work from the environment, basically he tried to design a ratched motor of sorts that would spin in a direction due to fluctuations in the atmosphere. ANybody ever find his formal explanation why that failed?

5:00 AM

@JohnRennie You're late.

Overslept today - got up at 05:30 :-)

Well I'm up with cohomology

It's addictive

I have a conjecture

@JohnRennie Interesting theorem: removing a point does not change orientability of a manifold

5:22 AM

Does a non-orientable manifold necessarily contain loops that cannot be shrunk to a point?

@JohnRennie Yes, a nonorientable manifold must be not-simply connected.

Do you want the proof?

@0celo7 No it's OK.I wouldn't understand the proof anyway :-) I was wondering if this could be related to your conjecture.

@JohnRennie oh no my conjecture has to do with integrals of cohomology classes

I was just mentioning a neat fact I discovered

Ah OK, the non-changing of orientability is already an established theorem.

Yes

5:25 AM

It seems intuitively obvious, though no doubt there is a fiendishly complicated proof.

One can show that removing a point does not change the cohomology groups, and one can use cohomology of the tangent bundle to orient

Basically

I haven't worked out the details

Sounds fiendishly complicated to me

@JohnRennie A manifold is orientable iff its tangent bundle is orientable as a bundle. Every vector bundle over a simply connected base is orientable.

The first thing is easy to prove, the second "fiendishly complicated."

@JohnRennie Something interesting and "easy" to prove is that the tangent bundle is always orientable as a manifold.

BTW did you move the XRD to the other PC?

No, a colleague has been using it nonstop.

@JohnRennie Listening to some Lil Jon, it's certainly interesting.

2002 Crunk

5:32 AM

My current favourite album is Your Wilderness by The Pineapple Thief. However it's prog rock so you would absolutely hate it :-)

ach, where is the German when you need him

I'm feeling so stupid this week

me too

@JohnRennie do you know what Crunk is

:: John reaches for Google ::

crunk
krəNGk/
noun
noun: crunk; plural noun: crunks

1.
a type of hip-hop music characterized by repeated shouted catchphrases and elements typical of electronic dance music, such as prominent bass.

5:38 AM

The trouble is that I've always been fairly chilled, and as old age sets in I'm getting positively glacial.

what

Music made by angry young men as a way of venting their anger doesn't really appeal.

I'm one of the chillest people around

Hey John, apparently the metal heads of this generation would probably have been the classical music crowd of previous generations

what?

5:40 AM

@user507974 Well I used to listen to Sabbath and Zeppelin when I was 12.

The next generation along listened to Iron Maiden

Literally don't know any of that

And the next to Guns and Roses

Then nu metal

I think young men have always listened to loud raucous music of some form.

Closest I've gotten to Guns and Roses is a feature/sample on Jay-Z's Blueprint 2

...

I'm not a huge G&R fan, though they have done a few great tracks

I'm a calm white nerd and all I listen to, basically, is gangster rap.

Huh

5:42 AM

There were some psychological studies done on the mental profiles of music listeners. Metalheads (including heavy metal) and classical music listeners basically came out to the same psyche profile

Oh and hardcore techno

Oh well

@0celo7 what type of techno?

@user507974 hardstyle, rawstyle, hardcore

the way you described it i guessed as much, though i still dont really know what hardcore is (or if it has any relation to nightcore)

give a link

I can link some good hardcore

Angerfist - Retaliate - HQ Official

@JohnRennie you will probably not like this

5:46 AM

nightcore usually has a major emphasis on upshifting the frequencies of the song (so high pitch singers is always universal), so its stylistically all over the place

@0celo7 there's (almost) no music I actively dislike, as in I'd get up and turn it off. But you're right, that isn't my favourite style of music.

@JohnRennie Challenge accepted.

Terrorcore coming up.

OMG what have I done? :-)

man, looks like the genre for nightcore has changed alot since i was listening to it (its been like 4 years) old nightcore: youtube.com/watch?v=Gld-19Ttn2M and youtube.com/watch?v=6SCQyBcHeDg

I don't know when this shit was made

So I won't say early

5:49 AM

new nightcore: youtube.com/watch?v=F6GMVUrVLNc

fuck

Strangle And Mutilate (Negative A & Counterfeit Remix) - Angerfist

this is actually horrible

before actually trying to open this, I LOVE THE TITLE

Listening now ...

@0celo7 so this is hardcore?

@user507974 yes

I don't think what I posted is terrorcore.

It's just terriblecore.

5:51 AM

kinda reminds me of some industrial but way more active

Industrial can have some really good music if you dont get unnerved by the vocals

Asphyxia - Self Deception

those vocals are unnecessary.

the song would probably be a tad too bland without them, not sure what type of vocals would fit though

@JohnRennie If you don't want to turn that off, you're a liar. Or deaf.

If that's not bad enough, I have the worse song ever made ready.

Which one, Strangle and Mutilate?

Yes.

5:55 AM

Putting offensive lyrics on a track is nothing new.

I don't care about the lyrics

The music is actually terrible

I can't tell the difference between good techno and rubbish techno

Ah

this is a bit closer to what i meant by industrial and hardstyle being a bit similar youtube.com/watch?v=aMtrQ8O7HhA

I have Torture, Murder, and Cannibalism which is actually very good.

But the lyrics are unnecessary.

very good hard techno:

Chris One - Sin City (Phuture Noize Remix) [HQ/HD]

5:57 AM

that last song i posted i remember being my research jam back when i was doing intern work at caltech

the drop at 2:35

oh god

@0celo7 so this is dubstep (rolls eyes) yay

no

dubstep is completely different

Great lyrics

dubstep is not techno

5:59 AM

Rage Against The Machine-Bullet in your head

@0celo7 just opened song, ok yea this is hardstyle right?

@user507974 very hard hardstyle

i liked the tonal progression at 1:20...

hardstyle has changed so much over the years

@JohnRennie what genre is this supposed to be

I think Rage Against the Machine pretty much created their own genre.

6:02 AM

oh, back to cohomology

i feel like the only place where this type of music might now get made is the UK

If you haven't heard their first album you might want to give it a listen. It's not your usual sort of music but it's pretty angry.

(rise against the machine that is)

But they kind of petered out after the first album

@JohnRennie i think i may have the polar opposite of this musically if you want to hear it

6:03 AM

@JohnRennie I don't like angry music.

Gangster rap isn't angry?

Yes, but that's not why I like it

And actually modern rap is very chill

Future is basically R&B

Drake is basically R&B

Not gangster rap, granted

i like a bit of tupac and eminem, thats like almost it in rap

Tupac was a gangster

he was more than that with his music though

at least sometimes

6:04 AM

@JohnRennie What I mean is that I don't like angry music as a rule.

@0celo7 do you like anti angry music then?

@user507974 Depends on the context

Most hardstyle is euphoric, hardly angry

But let's have JR decide...

i give you the antithesis of angry music youtube.com/watch?v=tQsC5IEXDag

JR decides he likes this sort of thing:

Hawkwind - Master of the Universe

But that won't be to many people's tastes :-)

Angry?

Rebourne - Leaving

6:07 AM

@JohnRennie when i see that title i immediately think youtube.com/watch?v=EyoutEHpPAU, the internet has ruined heman for me

@JohnRennie this isn't even bad

@JohnRennie lyrics are a bit muddy but i definitely wouldnt say i dislike this song

@user507974 The Hawkwind album predated the cartoon by 11 years!

still

@0celo7 so far 30 seconds i like this more

then again my favorite electronic music is trance so that makes sense

I hate cohomology

wtf does it mean for fibers to be "homotopic"

6:14 AM

man, you can tell that a genre has changed when you search it on youtube and now instead of it all being music playing with pictures of anime girls in the background its now music with pictures of real girls in the background

same homotopy type?

do they mean diffeomorphic

6:40 AM

@JohnRennie Would you like to sample some wonderful electronica?

@DanielSank go on then :-)

@JohnRennie Excellent. First, a short introduction.

First, there was Argentina. Then Germans went there with an instrument called the bandoneon. With this instrument, the Argentine dance known as tango became what it know it to be today.

Then Gotan Project got hold of tango and turned it into the greatest genre of music ever known: tango nuevo.

Observe: youtube.com/watch?v=2oZc2b-VDMU

As electronic music goes that's not especially electronic ...

It's lovely, no?

Here's my favorite by them: youtube.com/watch?v=0Otelte6m5Q

It takes a while to get to the vocal part, but it's worth it.

If you don't want to up and leave Britain and go spend the rest of your life with a Spanish woman in Sevilla after listening to that song, you're not a heterosexual male.

:: John experiences a crisis of sexuality ::

6:45 AM

Well wait, did you get to the vocals in the second song already? Seems unlikely.

Crisis averted?

Alright, give me seven minutes and four seconds and I'll listen to the whole thing. The sacrifices I make ...

It's not a sacrifice.

Your life is about to improve considerably.

You wouldn't happen to understand Spanish, would you?

1 hour later…

8:05 AM

@DanielSank spain does seem like a far more interesting place to visit than britain. I mean between staying up until 3 am and a 2pm nap these are my people

@BernardMeurer if you think make is bad, try building anything beyond "hello world" on the web.

@DanielSank how about he just tries to make a list of what he should use to make things on the web

html php css sql javascript xml ajax asp jquery flash(though thats dying slowly)

for the record really digging lebertango

8:49 AM

@Ocelo7 No, they mean homotopy equivalent.

Why should fibers be diffeomorphic ?

9:15 AM

@DanielSank Yeah, that's not great. I usually just refer them to Feynman's ratchet explanation in the Messenger Lectures

Richard Feynman Messenger Lectures at Cornell The Character of Physical Law Part 5 The Distinction of Past and Future

@DanielSank No, that's not quite right. Nuevo tango is along the lines of Ástor Piazolla (cf. the original Libertango). What you're describing is Neotango.

Also, moving to Sevilla is a terrible idea if you want a voice like that - you're looking for Buenos Aires or Montevideo.

Anyways, neotango is awesome. Here's some more cool stuff from that corner:

Otros Aires - Allerdings (live)

Otros Aires - Milonga Sentimental.

Electrocutango - Retrolonga

Also @JohnRennie, try the above

9:43 AM

Guys, I'm really derping hard, how did i find the right BC for this condition sketchbin.com/?id=f2e5fa

i know the solution is suppose to look like that shape I drew but I keep screwing up on the values for E and F

right BC coefficients*

in case it wasnt clear the BC is $C(r_1)=C_l ; C(r_2=1cm)=0$

@user507974 well, what did you try? It's not that complicated so I'm not sure what to say without knowing what you did.

(derpy mistakes are okay in chat)

so if I plug in at r_2 the ln term goes to 0 right

leaving only F = 0

then you plug in for $r_1$, and solve for E and you get $E= \frac{C_l}{\ln r_1}$

@user507974 ohhh, that's $C(r) = E\ln r + F$? I thought it was $C(r) = \frac{E}{nr} + F$. Anyway.

First things first, the argument of a logarithm has to be dimensionless. You can't do $\ln r$, it has to be something like $\ln \frac{r}{r_0}$ where $r_0$ is some reference distance.

So, no, we don't know that the log term goes to zero at $r = 1\ \mathrm{cm}$.

Not unless that's your reference distance.

10:01 AM

@DavidZ what exactly do you mean by reference distance

Some constant with the units of distance

It has been recently revealed that my tenancy to things not of my primary interest is very low
For example, for physics projects, my limit is 1 year before database dryness does me in (this is the ONLY reason that my interest of chemistry is greater than physics)
The major reason I like synthetic chemistry oriented research despite my curiosity and using computational methods to explore a system is because the tangibility help offset the database dryness
The issue is, however, many chemistry and physics professors have pointed that I am less proficient in synthesis and more proficient in co…

so i guess quick rundown of problem, picture radioactive material in a shell and a barrier, I'm solving for the steady state concentration within the shell assuming that the shell is 1 cm and at the end of that shell the concentration should be treated as 0

@DavidZ no info necessarily about r1 but r2 is defined like that, would that qualify as a reference distance?

I see... you could make the reference distance $r_2$, in principle.

Let me say this: is this for an assignment or something? I mean, is there a fixed correct answer someone else has derived that you have to reproduce? Or are you just doing it for yourself?

im trying to redo part of a test from last year im pretty sure i got wrong =)

mainly because of this BC shenanigans

10:07 AM

Ah, then in that case you have to be given the reference distance. If you don't use the same value of $r_0$ as the grader, you won't get the same answer.

I'd guess 1cm is implied as reference

OK then. It really should be explicitly given, but we can go with that.

So the formula you should be working with is $C(r) = E \ln(r/1\ \mathrm{cm}) + F$.

F still equals 0 then right

Well, yeah, if you plug in $r = 1\ \mathrm{cm}$ then you find that $F = 0$.

But I don't think you should be plugging in $r = 1\ \mathrm{cm}$. If you do, that means that $r_1 = 0$ and you know what happens when you try to take the logarithm of $0$.

yea

so clearly im doing something derpy, basically by inspection im pretty sure the final form should be a constant minus a constant*log

10:15 AM

The fact that you're using a log formula suggests that this is based on some kind of cylinder

yep, cylindrical shell

Then $r$ is distance from the center of the cylinder

yea

saying anything particular about the concentration inside the shell isnt in the scope of this question and would lead to messy time dependency stuff like in this paper ncbi.nlm.nih.gov/books/NBK230519

Sure, so?

i like enrichment but my compulsion to finish and not leave it hanging is great

i can see why the method i did is wrong, but should I just plug in $r_1$ and $r_2$

then try plugging in 1cm at the end

(or rather 1cm/1cm)

10:22 AM

I'm not quite sure what you mean

You can certainly do the problem without plugging in any numbers, just in terms of $r_1$ and $r_2$, if you want

starting with BC $C(r_2) = 0 = E \ln(r_2) + F$ one get $F = -E \ln(r_2)$

Remember you can't have $\ln(r_2)$, it has to be $\ln(r_2/r_0)$

@peterh : IMHO the important thing to appreciate about the chart is that is that upvotes won't make a wrong answer right, and vice-versa. Science is not a democracy. The important thing to do is look at the individual answers. Ask yourself is this wrong? and if so, why. If you can't say why, ask why there's six downvotes.

@DanielSank : electric field lines are a misleading construct. It's the electromagnetic field.

so with the $r_1$ BC you get $C(r_1) = C_l = E \ln{\frac{r_1}{r_0}} - E \ln{\frac{r_2}{r_0}}$

My approach for something I am unfamilar:
See downvotes: Explain to myself why it is wrong, or showed it is actually right or something in between
See upvotes: Explain to myself why it is right, or showed it is actually wrong or something in between

The key is to cross reference a lot regardless on what the votes said

10:28 AM

or $ C_l = E \ln{\frac{r_1}{r_2}}$

oh ok, i see whats happening now

i think

so that makes $E = \frac{C_l}{ \ln{\frac{r1}{r2}}}$

Yeah, makes sense

leaving $C(r) = \frac{C_l}{ \ln{\frac{r1}{r2}}} \ln(r)$

Hi guys! A scalar field propagator can be expand in terms of delta distributions? Something like $\Delta_F(x-y) = (something)*\delta^{4}(x-y) + …. $ ?

@user507974 Don't forget $F$

Also don't forget that $\ln(r)$ isn't valid!

what would be the right way to define r as unitless to not deal with that headache

10:34 AM

Well, IMO the right way is to keep the units, because they help you catch errors. But if you really want to write things like $\ln(x)$, you would have to define $x = r / r_0$ for some fixed reference distance $r_0$.

here they've been the source of a lot of errors though it seems...

so finally I have $C=C_l \ln{\frac{r-r_1}{r_2}}$

Here your failure to use units has been the source of some errors ;-)

if i cancelled everything well

Not really. But you would have noticed something wrong with your formulas a lot earlier if you'd been paying attention to units.

@user507974 That's not what I get

which i dont think i did

yea

ah

i accidentally did something screwy with the ln denominator

is there a better simplication then $C=\frac{C_l}{\ln{\frac{r_1}{r_2}}}(\ln{\frac{r}{r_0}} - \ln{\frac{r_2}{r_0}})$

10:42 AM

Yeah that's more like it

or rather $C=\frac{C_l}{\ln{\frac{r_1}{r_2}}}(\ln{\frac{r}{r_2}})$

yeah

nothing better right

"better" depends on your purposes, but that's pretty well simplified

OK, now that that's done I've got to take off for now

thanks

gl

10:58 AM

@JohnDuffield I think it is mainly ideological difference to make the things easier to understand in the high school. The main problem with it, that high school math often doesn't contain vector fields, although they are easy, somehow the education ministries find more important to learn meaningless poems of centuries long dead poets.

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