The h Bar

user228700

4:01 PM

Hey @JohnRennie: Quick question. Where do you stand on the debate "Language helps us know feelings" vs "Feelings are feelings, and we can have them, even if we don't know the words to express them".

John Rennie

@Kaumudi I don't have a view. Sorry if that isn't very helpful, but I'm the ultimate pragmatist and tend to regard discussions like this as too vague to be interesting.

user116211

0

Q: Double Exponential Function and Growth of the Human Population

I read a paper: "The Hyperexponential Growth of the Human Population on a Macrohistorical Scale", doi:10.1006/jtbi.2001.238 In the first part they show that the growth of the human population follows the differential equation: $\frac{dN}{dt}=kN^2$ The solution by simply integrating is $N(t...

user116211

How is it even related to physics?

user228700

@JohnRennie Okay, fair enough.

John Rennie

4:18 PM

@MAFIA36790: Dude! You just took out the reference details I added!

user116211

No. Is it ._.

user116211

But I didn't do anything ;/

John Rennie

physics.stackexchange.com/posts/290833/revisions

user116211

WTH ;/

user116211

Okay, so we were editing it simultaneously.

user116211

4:20 PM

But then, the system would have prevented me to make the edit, won't it?

0celo7

4:40 PM

@MAFIA36790 $\overline{\bigcup A}=\bigcup\bar A$ for finite unions?

@ACuriousMind too

user116211

I saw some post on this; let me check...

user116211

1

A: $ \overline {\bigcup_{n=1}^ \infty A_n}=\bigcup_{n=1}^ \infty \overline A_n \cup \bigcap _{m=1}^\infty \overline {\bigcup_{n=0}^ \infty A_{m+n}}$?

Since $$ A\subset B\implies \overline{A} \subset \overline{B} \quad \text{and}\quad A_n\subset \bigcup_{n=1}^{\infty}A_n $$ for any $n$. So we have $$ \overline{A}_n\subset \overline{\bigcup_{n=1}^{\infty}A_n}\quad \text{and}\quad \bigcup_{n=1}^{\infty}\overline{A}_n\subset \overline{\bigcup_{n=...

0celo7

It is a yes or no question

I don't need a proof

user116211

sey

David Z

5:00 PM

Anyone care to double-check that the suggested edit here isn't correct? (it replaces $1/r$ with $1/(2r)$ in the last equation)

John Rennie

5:14 PM

@DavidZ see page 1 of this article. It agrees with the edit.

@dmckee I have an embarassingly simple question about particle decay if you have the time ...

@DavidZ but this article agress with you. Now I'm confused.

Obliv

@mafia do you know if the change of variables for the riemann integral works for any transformation? (affine, linear, etc)?

i thought no at first but math.stackexchange.com/questions/267267/… uses a parabolic function

(below littleO's answer)

0celo7

5:34 PM

@Obliv should work for any diffeomorphism

Why would you ask him and not me :(

Obliv

@0celo7 because you usually give me answers that I have to google

0celo7

But they're always correct

Obliv

but they're also incomprehensible :[

which is no fault on you.

0celo7

x squared is not a diffeonorhousn

Lol

Was expecting spell check to save me there

Obliv

lol

David Z

5:38 PM

@JohnRennie One has to be careful about what operator one is defining. If you check the math in my answer, though, it should be internally consistent...

Obliv

@0celo7 why isn't x^2 a diffeomorphism? its inverse is differentiable, no?

0celo7

It doesn't even have an inverse.

Obliv

@0celo7 what about x^3

0celo7

Inverse isn't differentiable

Obliv

it is though @0celo7

0celo7

5:44 PM

If it's differentiable, give me the derivative?

(1/3)x^(-1/3)

For which x?

all but <0

What?

for x > 0

5:46 PM

That's wrong

It's for all x not zero

Which means it's not differentiable

Obliv

oh right its' cube root not square

@0celo7 are you on your phone

just making sure

0celo7

Yes

Obliv

okay going to stay away from tex. by that reasoning you just provided, 1/ax isn't differentiable at x=0 does that mean the inverse function, for g(x): x \to ax, f^-1 : ax \to e by ax*(1/ax) is not a diffeomorphism?

idk if that was comprehensible @0celo7

0celo7

I can't make sense of that.

You need to look up what an inverse is, I think.

But I'm not sure if that's what the issue is.

@Obliv ?

Obliv

6:03 PM

@0celo7 nvm I just fucked up the definition of an inverse just then. was thinking of real numbers lol ax * e/ax retrieves identity e

0celo7

Who calls the number 1 e?

Danu

@ACuriousMind o/

Obliv

it's more general. anyway the reason I asked is because I wasn't sure if the new integral of the transformed function would retrieve the same sum @0celo7

0celo7

More general? What?

Obliv

it's not always the case we're talking about (R^n,*) @0celo7

but in this case we were so i shouldn't have used e over 1

0celo7

6:08 PM

What else would you be integrating on?

Obliv

yeah okay I get it dude @0celo7

Obliv

6:34 PM

@0celo7 how are inverses of multivariable functions defined/found usually?

Danu

@Obliv Look up the inverse function theorem.

0celo7

@Danu That thm hardly "finds" inverses...

@Obliv Trial and error.

Obliv

8:00 PM

bounds would change accordingly for $x = r\cos \theta$ and $y = r \sin \theta$

waiit somethings missing 1 sec

0celo7

What are you babbling about

Obliv

okay so finding the area of a circle using $f(x,y) = x^2 + y^2$, $G(r) = \sqrt{f(x,y)}$ $\int \int_E G(r)\pi dr^2 = \int \int_E f(x,y) \pi (dx^2+dy^2) = \int \int_G f(r\cos \theta,r\sin \theta)~r~ dr~d\theta$

I'm just seeing if they're all the same. going to test it now

okay that was a fail.

0celo7

8:49 PM

@Obliv sigh, what are you doing?

heather

hello

@BernardMeurer, DST starts next week.

@Mew, I think we can keep the post it is at +3 right now

0celo7

!!!!

$p(\bar A)=\overline{p(A)}$ if $p$ is closed?

yes, if it's continuous too

heather

9:07 PM

@JohnRennie, sadly, I'll still have to walk to the bus stop in the dark even with DST...

0celo7

Nice

Almost half-way done with topology homework

Shing

9:26 PM

that's mind blowing

quantamagazine.org/…

Is This What Quantum Mechanics Looks Like?

►

2

MetaEd

@Shing Yeah, that popped up in my news feed a couple of days ago. Really interesting.

heather

Wow. i found out about this cool thing called spritz that helps you read faster. I was reading a wikipedia page at 300wpm! Dunno how well it works in terms of understanding what you read, but you certainly read faster.

It's just something you drag to your bookmarks bar and click on to activate. it highlights certain key letters in words so you can read them basically instantly.

vzn

9:41 PM

in toy models of QM, Jan 26 '15 at 21:58, by vzn

superclassical/ emergent QM, recent developments, rough outline/ overview/ leads / Tmachine blog

0celo7

@heather proof?

heather

@0celo7, proof of what?

0celo7

If you could, prove that a perfect map preserves second countability

heather

what? huh, I'll look into it.

perfect map...*(::frantically googles::)*

4

Q: Being second countable is invariant under perfect mapping

Firstly, I will give the definition of perfect mapping: Let $f$ be a closed mapping from a topological space $X$ to another topological space $Y$. We call it a perfect mapping if for every point $y \in Y$, the subspace $f^{-1}(y)$ of $X$ is compact. My question is this: If $X$ has countabl...

general-topology

@0celo7

0celo7

that proof is cheating

I already found it

heather

9:45 PM

@0celo7, how is it cheating

@vzn, quickly skimmed your article, looked interesting. as an aside, with QM biology have you heard of that book by Schrodinger that talks about it?

0celo7

Schroedinger was a crank

dmckee

@JohnRennie I've got a few minutes.

heather

@vzn, What Is Life, from 1944, is what it is called

0celo7

Jesus

When did he die?

heather

Schrodinger?

0celo7

9:49 PM

yes

heather

1961, that's supposed to say from 1944 =P

0celo7

aha

heather

yeah

January 4 1961 aged 73 according to Wikipedia

Quantum biology

Quantum biology refers to applications of quantum mechanics and theoretical chemistry to biological objects and problems. Many biological processes involve the conversion of energy into forms that are usable for chemical transformations and are quantum mechanical in nature. Such processes involve chemical reactions, light absorption, formation of excited electronic states, transfer of excitation energy, and the transfer of electrons and protons (hydrogen ions) in chemical processes such as photosynthesis and cellular respiration. Quantum biology may use computations to model biological interactions...

What Is Life?

What Is Life? is a 1944 science book written for the lay reader by physicist Erwin Schrödinger. The book was based on a course of public lectures delivered by Schrödinger in February 1943, under the auspices of the Dublin Institute for Advanced Studies at Trinity College, Dublin. The lectures attracted an audience of about 400, who were warned "that the subject-matter was a difficult one and that the lectures could not be termed popular, even though the physicist’s most dreaded weapon, mathematical deduction, would hardly be utilized." Schrödinger's lecture focused on one important question: "how...

@vzn, see above, and also a copy of the book here (it is public domain, I think).

0celo7

@heather you need to scare your parents into getting you a phone.

heather

@0celo7, but anyway, what is wrong with the proof?

0celo7

9:53 PM

I have a plan

heather

@0celo7, I'm nervous already, but go ahead

0celo7

I'm going on a date in 2 minutes...not enough time. We'll discuss later.

It's a terrible plan, honestly.

heather

Okay, well, good luck on the date.

0celo7

@heather Maybe not a "date"

heather

Oh?

1006a

9:56 PM

Hi, I have a question about terminology which I think I'm supposed to ask here...

0celo7

@heather we've been together for a while, don't know if it's still called a date

Anyways, you need to find a stupid boy who likes you and you

*dont

Ok this plan is worse than bad

Forget it

1006a

Here rather than the main site, I mean. I'm looking for a very short explanation of "why the sky is blue"—like two or three words. Something like "Rayleigh scattering" or "diffuse sky radiation" would probably work, but if at all possible I'd like it to rhyme with conclusion. What I'm wondering is, would "short wavelength diffusion" or "sunlight diffusion" or something else ending in diffusion be a reasonable choice? Many thanks if anyone has any thoughts on this!

heather

@0celo7, just a sidebar, I'm a nerd. Nerds aren't exactly high on the "date" list so I'm not sure there is a boy who likes me. But, anyway, have fun on the not-date date. =P

rob

@1006a "Air is blue"

1006a

@rob Hmm, it would probably convince my 6-month-old, but it doesn't rhyme ;-)

Also, I'm looking for something that won't someday haunt me in "I knew my mom was an idiot when I offered her nursery rhyme up in science class and was laughed out of the room"-type stories

rob

10:05 PM

@1006a A nice explanation on an ugly web page: amasci.com/miscon/miscon4.html

So you're writing a nursery rhyme about why the sky is blue, and you're hoping to rhyme with "conclusion"?

1006a

Yes, basically.

It's actually a kind of nonsense song I sing to the baby, so really just for me, but...I get hung up on these kinds of details.

rob

"Air is blue / I love you / doot-de-doo / (raspberry noises on belly)"

I don't know that "diffusion" is the right word to describe the scattering of light by the atmosphere, even though the scattered light is "diffuse." That's an interesting language quirk that may be particular to my brain.

1006a

@rob Yes, I'm basically wondering whether physicists would use the term diffusion this way. In a non-technical context, it's a pretty good substitute for scattering, but my physics instruction pretty much ended with AP physics in high school so I don't know whether it works in context.

rob

10:21 PM

"Diffusion" seems to me more like it describes a process where the spreading-out material interacts with the medium many times. However I think that light from the sky has usually only scattered once, which is why the light from the sky is polarized.

1006a

Ah. To my non-technical ear, if something (like skylight) is diffuse then it probably has been diffused and therefore it ought to be possible to talk about its diffusion. But if that won't work, I can always fudge the rhyme between "radiation" and "conclusion". Many thanks for indulging my questions!

user218912

i don't like the way physics is taught in undergrad i'll just do math instead and learn physics on my own time.

Sanya

11:01 PM

@DavidZ are there any transcripts of the last chat session by the way?

David Z

@Sanya no bookmarked transcripts that I know of, but you can always find it in the room transcript

vzn

@heather hi thx for tip, havent read that book yet, on my to-read pile, its semifamous for some reasons...

Sanya

@DavidZ ok :) I thought maybe they get saved separately ...

David Z

@1006a no, I wouldn't. I guess you could jump through some hoops to do it, but it's unnatural.

Sanya

thanks

David Z

11:13 PM

@Sanya Whenever there's a chat session of particular importance, e.g. to something we're doing on meta, I'll bookmark it, but in general I don't bother. You can always bookmark it yourself, though. Anyone with chat privileges can choose a section of the transcript to make a bookmark.

Transcript for