The h Bar - 2017-03-12 (page 3 of 4)

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6:01 PM

would the volume of a cylinder using the rectangular cross section of the cylinder be $\pi r c$, where $c$ is the cross section (as opposed to $\pi r^2 h$)?

because the cross section would be $hr$, so you'd multiply that by $\pi r$?

@heather The $r$ and $c$ would be variable (a function of distance from the central line). And the volume of a rectangular element would be $cdx$ (taking $x$ to be distance from central line). How did you get $\pi rc$?

To find the whole volume you'll need to integrate within proper limits

@2017 by rearranging the normal calculation for volume of a cylinder. $hr$ is the cross section, $c$.

it isn't volume of a rectangular element.

@heather Wait, what is $r$ ?

@heather Yes, you are correct.

@2017 radius of the cylinder.

@ACuriousMind okay. my dad did it some other funky way, apparently, so I'm too late, but oh well.

now, how to prove that is true...

6:08 PM

@heather Uh, you already did

@heather Oh yes, that does make sense

When you said rectangular cross section I thought of something like:

@ACuriousMind well I thought so, but my dad said I didn't.

user image

^The second one

@heather You said that the cylinder has volume $\pi r^2 h$, so with $c = rh$ the volume obviously becomes $\pi r c$. What is there left to "prove"?

@ACuriousMind i don't know, my dad wanted to show it using calculus. I think I'm just going to leave this problem, because he has his own answer.

@2017 oh, I see =)

6:11 PM

Well, there is a calculus way to compute the volume of the body traced out by a revolving surface but that's just completely ridiculous overkill if you already know that the volume of the cylinder is $\pi r^2 h$.

And even if you don't, that's much more easily derived by considering the area of the circle times the height.

that's what I thought.

Sometimes, I feel amazed that the Greeks derived the formula for volume of sphere without any calculus!

how do you derive the formula for the volume of a sphere using calculus?

@heather By considering elementary discs. There are other methods also..

oh, in terms of the Greeks, wikipedia says

> Archimedes first derived this formula, which shows that the volume inside a sphere is 2/3 that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.)

Cavalieri's principle, interestingly enough is seen as a step toward integral calculus

6:16 PM

@heather From a modern viewpoint, you'd just go to spherical coordinates and integrate over the unit ball, but that of course first requires you to figure out the volume element in spherical coordinates.

The three dimensional case of cavalieri's principle is

> 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.

@heather Right! That was a pretty amazing deduction in my opinion :-)

Here's the explanation Wikipedia gives. I must admit, I don't really follow the argument =)

@heather Which step do you not follow?

There isn't much to it - compute the crosssectional area of a cylinder minus a cone and a sphere, observe they are equal at every height, conclude by Cavalieri that their volumes are equal.

Cavaliers?

Are we doing measure theory :D

6:22 PM

i'm going to go over it again and sketch it out this time.

Just sit with a pencil and paper...you'll figure it out :)

(Hope you know Pythagoras theorem)

$a^2+b^2=c^2$

where $c$ is the length of the hypotenuse and $a$ and $b$ are the lengths of the two legs

Right, you know it...^

you can derive it then!

Okay, got to go now!

bye bye people :)

have a good day @2017

interestingly enough, however, I don't follow how the pythagorean theorem is used.

@heather For the hemisphere: Since the cross-section is a circle, the area is $\pi s^2$ where $s$ is the radius of the circle. Now You use Pythagoras to express $s$ in terms of the radius of the base $r$ and the height above the base $y$.

6:31 PM

@ACuriousMind I posted a message earlier today and I'm wondering if you have any comment:

9 hours ago, by Danu

Sounds pretty cool but I don't think I've ever seen anyone use this bicomplex.

ah, okay

i will try to derive that now.

Hi, anyone can help with meson decay modes?

@Danu How much have you seen of mathematical classical field theory anyway? :P I've seen at least the jet bundle language, organizing the methods applied to it as a "variational bicomplex" may be not general, but the nlab page linked contains enough references, doesn't it?

suppp

I wonder how it differs/what its advantages are in comparison with the principal bundle stuff

6:42 PM

@Danu What "principal bundle stuff"?

The question isn't about gauge theories as such

And it's asking for the geometric formulation of configuration space, which you usually don't do even if you have bundles - you don't conceive of the "space of all sections of the bundle" as a geometric object in its own right

That answer is saying that if you want to do a geometric formulation of field configuration space, you don't use the ill-behaved space of sections but the better-behaved jet bundle.

Of course you do talk about the spaces of sections of the bundles

SW theory is precisely the study of those sections up to gauge transformations

@OBE, hello

@Danu ...yes, sure. But talking about the space of sections is different from conceiving of that space as a geometric object. Is it anything more than a set in the formulation you're thinking of?

The main focus is on those configurations that solve the SW equations, but you can also consider the space of configurations up to gauge and say something about that, if one is so inclined

random question @ACuriousMind

6:46 PM

Yeah, it is a lot more. We proved something about its homotopy type, etc @ACuriousMind

with probabilities, in quantum mechanics, can't they be negative or even imaginary? or are they always just normal positive numbers between 0 and 1?

@Danu Okay, I can see that it's a topological space. Is it more?

That is, once you divide out the gauge group. Without doing that, it's a pretty boring space. For instance, for SW theory it's just the space of connections (an affine space) times the space of positive spinors (a vector space).

Because geometric formulation, to me at least, means more than having a topological space.

@ACuriousMind Well, the SW invariants for instance are homology classes of this space.

6:48 PM

@Danu That doesn't make it anything more than a topological space

Could anyone post a comment onto this Physics.SE question

27

Q: Is the light from the Sun the same as the light from a bulb?

I'm arguing with a friend of mine on whether the light emitted from the sun is of the same type of that emitted by a bulb. Her insistent ignorance is laughable, unless I'm wrong... She's talking about how light from the bulb is "artificial" ... I've tried explaining that that makes no sense, an...

visible-light electromagnetic-radiation frequency sun

I'm not saying you can't do interesting things with this, I'm saying this is not what most people would accept as a geometric formulation

with a link to this EE.SE question. Similar question about LED light.

2

Q: Do standard white LEDs produce a full spectrum of light?

At places like Radioshack, small (and sometimes large) LEDs are available that are labeled to be "white". This is a link to a Radioshack page for such an LED: http://www.radioshack.com/5mm-white-led/2760320.html#q=white%2Bled&start=2 Does a light like this produce a full spectrum of light, such ...

(I haven't got commenting provilege on Physics.SE myself.)

@ACuriousMind What I'm saying is that the raw configuration space isn't interesting. I just told you it's a product of an affine and a vector space.

So what's there to say, really?

@heather A probability is a probability, it can't anything but a non-negative real number. There are probability amplitudes that are imaginary or complex,

@Danu Ah, I might also agree with that. The point of this bicomplex or the jet bundle is not to be interesting, I think - it's just to provide the analogue to the geometric formulation of classical point mechanics.

Whether you can discover interesting things from the geometric properties of this analogue I don't know, but that also wasn't the question.

6:52 PM

I guess that what I'm getting at is---let me preface this with "I know I'm going to sound like a naysayer"---that it seems really unnecessary to talk about "higher prequantum geometry" for this purpose.

You can formulate the Lagrangian/Hamiltonian as functionals on the configuration space just fine, as far as I can tell.

@NickAlexeev done

@heather Hi

@ACuriousMind Thank you!

@ACuriousMind and I don't suppose these probability amplitudes are what would result from squaring the qubit's state? or is that the probability?

@Danu For what purpose? Neither the question nor the answer give any purpose for this formulation

I think if you want to know whether there are interesting results hiding here that are inaccessible to other formulations or at least more difficult to obtain, then you'll need to ask a different question

6:57 PM

I guess...

When someone asks "What is the principal bundle formulation of gauge theory?" I wouldn't launch into an explanation of instantons or such things, either, I'd just lay out the actual formulation.

@heather I don't know what you mean by "squaring the state"

Silver linings in Rimworld : My last surviving colonist just went in a rage

But on the other hand

He can't hurt anyone else

Hallöchen.

he just goes around very angry

@ACuriousMind Probably means taking the inner product with itself

6:59 PM

Given two states $\lvert \psi\rangle,\lvert \phi\rangle$, the probability amplitude to find $\psi$ in the state $\phi$ is $\langle \psi\vert \phi\rangle$ and the probability is $\lvert \langle \psi\vert \phi\rangle\rvert^2$.

Oh except he got into an argument with a boar and the boar won

So basically he's dead

I know not of what you speak :)

Talking to yourself again? ;)

Oh man.....

@Danu Well, that's at least a chance for intelligent conversation ;P

I kid, I kid

7:00 PM

lmao

What does lmao mean?

hehe

idk dude

@ACuriousMind the second bullet point here is what I'm referencing

What does idk mean?

7:01 PM

i don't know = idk

@heather that's not squaring the state.

@heather I understand, thanks.

@OBE no, it isn't, I'm sorry

Laugh my ass off = lmao

f?

7:03 PM

function?

@heather What you're squaring there are coefficients, not the state itself. And $\lvert \alpha\rvert^2$ is a probability, so it will always be a non-negative real number between 0 and 1 if you've done everything correctly.

okay, dumb question #2: why do you need to do $|\alpha|$? can't you just do $\alpha^2$?

@PhysicsGuy yes lmaf is basically a function times lma which are scalars. you can basically write it at $l m a \cdot f(x)$ to be more clear

because squaring it keeps it from being negative anyway?

@heather $\alpha$ is a complex number.

7:04 PM

Someone's learning basic QM here.

so...? oh, duh

::facepalm::

I am going to fix that probability function now

well technically you can be sloppy and just write it like that

Why the caps in obe now?

idk

to emphasize that it's O. B. E. not obe.

so if I do that properly, I shouldn't need to convert it back to a real number - or maybe python will be grumpy

7:06 PM

@skullpetrol I'm guessing he's a big boy now :P

LMAO

@ACuriousMind yes exactly

Google says that idk also means "I don't care"

:D

@PhysicsGuy that's idc

7:07 PM

Care =/= k

I know.

But Google never lies.

show pics

you have 30 seconds

to rule out any real quick photoshop

@SirCumference xd

Do you really think that I would photoshop a picture just to prove you that idk does also mean "I don't care"?

depends

on?

7:10 PM

it depends how much you kare

Ok, I don't find it. But I am sure that I read it somewhere.

Maybe you're right.

maybe

I think you guys are arguing over something not really important =)

Yes.

Acronyms are important @heather ;-)

7:13 PM

How's your work on propability functions going on?

I fixed the error @PhysicsGuy

thanks to @ACuriousMind =)

@Danu @ACuriousMind I have something super duper exciting to tell you but I'll tell you in like 7 months.

...why'd you bring it up now unless you want us to ask?

so I don't forget

That's illogical.

7:15 PM

I won't remind you

Write it down somewhere.

I wanted it to be logged that I said that 7 months ago.

Let's start with the definition of what a function is? @heather

and this isn't a joke or attention seeking thing. I'm working on something really cool I will show you guys in about 7 months.

@OBE Imagine today to be October 12th 2017.

Now tell us.

7:16 PM

it's not done.

What is it about?

secret

Some NSA thing?

no?

Btw. Is the NSA reading this right now?

7:17 PM

A gf?

why would that be important for danu and acm to know?

dafuq?

Just a wild guess pal

lol

why would it take 7 months to reveal that

@skullpetrol something that takes something in, changes it according to a rule, and spits out the solution is the intuitive definiton

I can pull out Halmos for the more mathematical description

Nah, that's good enough.

Didn't they give you a definition in algebra?

Have you done a chapter on introduction to functions? @heather in school

7:23 PM

@skullpetrol, sure.

What definition did they give you?

basically the one I said up above.

they never really gave a rigorous one.

rigorous isn't always useful

Depends.

Something that is always useful is vital, right?

7:46 PM

Not giving gifted students at least a semi-rigorous definition of what a function is not right imho.

it depends what they want to do

They're gifted.

I am new to quantum physics and I why read that electrons can take only 1 , 2 or 3.... photons energy. Nothing like 1/2 photon & so on. This explains Photoelectric effect & Bohr theory. Now can a free electron take 1/2 or a fraction of Photon energy. Can anyone please help

what

8:01 PM

i think he's talking about electrons moving between energy levels and absorbing energy or emitting photons.

@skullpetrol eh, not really. we're accelerated by a grade or two, but that just means we started a year earlier in elementary school according to some random tests and teacher input. there are certainly people in my class who are gifted, but i am not among them.

besides, they're teaching a curriculum put together for kids who take it when they're supposed to. it's the same thing. just being accelerated doesn't mean the class is any different.

@Slereah if you referred to me then - I was asking that electrons can take energies of integer number of photons like 1 photon . They cannot take energies equal to half a photon . We use this in explanatinon of Photoelectric effect and Bohr theory. But then in Compton effect the electron takes a fraction of Photon energy

Have you taken Pre-Algebra: an accelerated course? @heather

I've taken half of 6th grade math, half of 7th grade math (this was in 6th grade) and then jumped straight to Algebra I in 7th. This year I'm taking Geometry. 6th and 7th grade math were I guess basically pre-algebra, just a little more watered down.

but it wasn't accelerated at all.

I see.

next year I'll take Algebra II, and then in 10th grade I can start taking whatever I want, so I'll be taking AP prob and stats, trig, and precalc, and then in 11th grade AP Calc I and II, and then apparently I can take college classes senior year. It should be fun =)

(if you're wondering how it all fits in, the answer is the wonders of block scheduling.)

8:17 PM

No AP physics?

@Shashaank do you know what $e^{ix}$ is?

Yes I know that....

@skullpetrol oh, I was just going through math

over the course of 10th and 11th, I'll be taking Chem I, AP Chem, AP Physics I and II, and astronomy.

@heather What is block scheduling?

@Shashaank Sounds like you want to have a look at Compton scattering.

@ACuriousMind instead of a bunch of short periods (7 to 9 40-50 minute periods) you have longer "blocks" (3 to 4 multiple hour periods). This compresses a class into a semester instead of a full year, which allows you to take two math classes in a year, even though one might have the prerequisite of the other.

So, for example, AP Calc II has as a prerequisite AP Calc I. Each would normally take a full year, but because of block scheduling, each only takes a semester, so I can take both in a year.

Semester long classes only take a quarter in block scheduling. (The time to take a class is generally halved.)

8:31 PM

@heather Hm, does this mean you don't take some classes you would otherwise take or do you spend more time in school as a result?

no, you take the same general amount of classes, and the school day is about the same length (as far as I know)

I have trouble seeing how changing the portioning of time is supposed to shorten the total time a class takes

the period is longer, so more material is covered. the class therefore is compressed into a semester instead of a year.

How does a 3 hour block cover double the material three one hour lessons would cover?

That doesn't make much sense to me

@ACuriousMind Yes I had studied Compton scattering recently. And I knew that ( by the photo electric effect and Bohr theory that electrons cannot take a fraction of a photon energy) . But here they are taking a fraction of Photon energy. So I wanted to know that electrons cannot take fraction of Photon energies when they are in energy levels only or also when they are free. Because they are

Is it only in energy levels that an electron has to absorb a whole photon

8:39 PM

@ACuriousMind I don't know that I get double in long blocks, but I certainly spend some time in each class period reminding the students where we'd got to and intimating what we'll be working on next time. Long blocks mean less time spent on that kind of framing.

@Shashaank Well, you should think of Compton scattering more like the electron absorbing the incident photon briefly and then emitting a photon with a different wavelength

On the other hand, few people can actually stay 100% on for three hours, so I do have to structure long classes to allow for some shifting of mental gears.

@dmckee Yeah, I get that there is some increase in efficiency, I just can't believe it's this big

@ACuriousMind 2 hour block vs. 1 ~1 hour period.

that's in a day.

there's a block class every day (as I understand it, though again, I've never actually done it, this is just what I've been told/have heard)

@heather Well, but if a single 1 hour period is replaced by a 2 hour block, then you are just spending more time on the subject and this has nothing to do with the scheduling as such - you'd get a comparable increase if you just added an additional 1 hour lesson to your plan

8:45 PM

As dmckee mentioned there are diminishing returns with longer blocks.

well, yeah @ACuriousMind

but the school day hours are fixed

@ACuriousMind Thanks For clarification. I never thought that. Its not in the book also that I am referring. Just one thing. That an electron can absorb only a photon and not take its fraction of energy is universally true in Quantum mechanics ( whether the electron the be in an energy level or be free).

Because one answer on stack exchange said that electrons ( by the quantum theory) absorb a photon only when in an energy level and can take its fraction of energy ( without the remitting ) when it's free .

so this is a way for students to be able to take (say) multiple math classes in a year without problems with prerequisites.

@heather But then you have to drop another 1 hour lesson from your plan to fit the 2 hour block in!

I.e. you are not taking some class you otherwise would

Like biology :-)

Which I didn't see on your list?

8:49 PM

i don't know @ACuriousMind - it seems like I was able to fit in a comparable number of classes.

@skullpetrol yeah, I'm not taking biology. i'm just not particularly interested in it, it's not required to graduate highschool, and the college I want to go to requires only two years of science, and I've got that covered without bio =)

Has this shown up on this chatroom yet?

31

A: Is it ok to upload joke papers to arXiv?

There is a long tradition of posting joke papers to arXiv on or around April Fool's Day, especially in astro-ph. Examples: Superiority of the Lunar and Planetary Laboratory (LPL) over Steward Observatory (SO) at the University of Arizona On the utter irrelevance of LPL graduate students: an unb...

I don't get it - if this achieves double the learning speed without increasing the net time students spend in school and without decreasing the variety of subjects they can take, why would you have non-block scheduling at all?

Sounds like a free lunch, doesn't it?

@EmilioPisanty Not until now

David's found quite a list

8:53 PM

I do recall having seen some of these papers before, though

and still managed to miss my two favourites

> The authors have always conceived of the CMB as an elderly lesbian Tea-Partier; this perhaps says more about them than it.

@ACuriousMind hehehehe

What?

^my 0celo impression :-)

9:29 PM

@ACuriousMind Please ban the bully.

@heather What is AP Calc I/II?

Back in my day it was AB/BC.

basically AB/BC I guess. Covers the same stuff.

(as far as I know)

@ACuriousMind I have no idea

American schooling isn't exactly known for its logical setup.

9:54 PM

Are you @0celo7 calling me a bully? :P

10:06 PM

lol, I hope that person has read the arXiv TOS and realizes that it is totally NOT ok to upload joke papers

How about papers generated by computers?

just because it has happened doesn't mean it's ok

if they find out you've done something like that, they will revoke your privileges

Finding out is half the battle :-)

You bet I am

:(

10:11 PM

You're no s h o g, but still

I dunno, I think it's important to take arXiv seriously

it's well on the way to replacing traditional journals, in my field anyway

I apologize @0celo7 if I seem that way to you.

I'll try not to in the future.

Tradition will not give up easily @BenNiehoff

AccidentalFourierTransform

to defy the laws of tradition is a crusade only of the brave

For example this very network has been black listed by some.

which network?

AccidentalFourierTransform

10:21 PM

this very.

Stackoverflow/Stackexchange /math overflow

blacklisted from what exactly?

Having any association with.

Asking or answering questions etc.

blacklisted from what, though?

or, by whom?

by some

10:35 PM

some what?

Administrators.

did everyone forget how to write a complete sentence?

@skullpetrol Administrators of what? Try to form a complete sentence that explains who has blacklisted what and why.

Bernardo Meurer

@ACuriousMind I blacklisted you

Basically, if they catch you here you're toast.

10:37 PM

lmao

That's all I can say.

Oh, that's what the gunmen that shadowed me last month were for!

Perhaps.

@BernardoMeurer, could you answer a quantum computing question so I can make sure I'm not being stupid?

Bernardo Meurer

@heather Much like ZFC cannot prove it's own consistency, I'm afraid I cannot prove or disprove your stupidity

But ask away

10:42 PM

if I have some code that looks at a control qubit and based on it applies another gate (NOT, Pauli-Z, Hadamard, whatever) how do I handle the case where the control qubit is neither in the |0> state or |1> state?

Bernardo Meurer

You mean if the qubit is on some combination of |1> and |0>?

yes.

Bernardo Meurer

Hm, well I don't know

Assuming the qubit is in a superposed state, then "checking" it's state to apply a gate ruins the fun

Which is why IIRC crafting "quantum" algorithms is so hard

cause you can't look

It's like those couples who commit to only have sex after they get married

interesting (strange) analogy.

@BernardoMeurer true - I'm not really sure how else to do it.

Bernardo Meurer

@heather Lots of finger crossing I guess

10:56 PM

@BernardoMeurer no need to use that sort of analogy

Bernardo Meurer

@DavidZ Oh come on, what's wrong with that? I can say the word "sex"?

@BernardoMeurer What's wrong with it is that you made an unnecessary reference to sex. Don't do that.

Bernardo Meurer

@DavidZ Is there a rule against references to sex?

Can you give me an objective reason why that comment was out of bounds?

I just did.

Bernardo Meurer

As far as I can tell that doesn't go against the "Be nice" policy, and so there's no reason for you to come here and give me crap for it

10:59 PM

I think the question here is why is mentioning sex a problem, not whether or not it is unnecessary.

Bernardo Meurer

^

this is the kind of stuff I'm talking about @BenNiehoff @ACuriousMind

It is unnecessary to talk about food, for example, but people still talk about it.

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