Mathematics - 2017-05-09 (page 3 of 5)

Fargle

19:02

By Erdos, no string of consecutive positive integers will be a perfect square.

Daminark

Hey everybody!

DarthVader1056

@Fargle By no string you mean product? Can you give a link

Fargle

@DarthVader1056 Yes, I mean product, my bad. renyi.hu/~p_erdos/1939-03.pdf

(quadratfrei = square-free)

Sha Vuklia

"The dot-product with the normal vector of the surface kills all non-radial contributions."

"kills"

aren't physicists amazing creatures? :P

DarthVader1056

@Fargle Oh thanks a lot, the paper seems elementary enough to be read. Thanks again man.

Fargle

19:05

No problemo! I learned something today.

Astyx

Annihilates would be more appropriate, or perhaps exterminates. @ShaVuklia

Sha Vuklia

lol :P

Daminark

19:21

Lol I say "kill" all the time

Actually in the REU there was this one time where I talked about how you'd "kill" off the term, and Laci was like "Kill is not an arithmetic operation"

Sha Vuklia

yea, but this was an official text written by a physicist :P

Daminark

Kek

Ohai @Steamy

SteamyRoot

ohi

Sha Vuklia

@Steamyyy !!:P

I'm always happy to see you, because we are neighbours :P

Astyx

Some choose to live in harmony with terms, others chose to declare war on them

SteamyRoot

19:23

Hahaha, so we are ^^

Daminark

Yeah, I dunno, I guess we're just... not on good terms

Sha Vuklia

SLOW CLAP

Daminark

Woo ('-')/

Hey @Semi!

Semiclassical

hi

Sha Vuklia

@Semi! I actually just needed you for something, but it got solved in the physics chat:P

Semiclassical

19:26

@Astyx I prefer 'annihilates' because in physics we talk about creation/annihilation operators in quantum mechanics.

lol

Daminark

"And then we sentence this mathematical object to capital punishment"

Sha Vuklia

We will even destroy its entire family (of functions)

Semiclassical

e.g. $x+\frac{d}{dx}$ annihilates $e^{-x^2/2}$.

SteamyRoot

I've heard people talk about "kill" often in maths too

Usually, they're the same people who refer to variables or constants by "this guy" and "that guy"

Daminark

@Steamy I do that

Sha Vuklia

19:28

yea I just like to make fun of physicists, just to feel a bit like a mathematician again :P @Steamy

SteamyRoot

And you end up with classes where "this guy kills that guy..."

Alessandro Codenotti

I had a professor even use "defungere" regularly for terms which got simplified and the like, which is the archaic version of "to die" in Italian, I can't really translate it in English though

Daminark

Hai @Alessandro

Semiclassical

@ShaVuklia Oh, did you figure out the envelope business? I can give a simpler explanation.

Alessandro Codenotti

Hi @dami

Sha Vuklia

19:29

@Semi to be honest, I left that for today:P I've been reading on surface integrals and I'm now doing electromagnetism. The envelope business is vibrations and waves, which I'll do maybe tomorrow or the day after

SteamyRoot

"defungere" already existed in Latin :D

Sha Vuklia

or actually

I'm not doing much now anyways

Daminark

And lol that's always amusing when these itsy bitsy mathematical objects are (presumably violently) killing each other off

Sha Vuklia

I'll do that then as my last thing for today

let me reread what you wrote @Semi

Semiclassical

Actually, let me try something else first.

There's a better explanation than the one I gave.

ok?

Alessandro Codenotti

19:30

@SteamyRoot a lot of latin words survived unchanged in modern Italian

Sha Vuklia

yea sure!

Semiclassical

So, you had $x(t)=e^{-\gamma t}C\cos(\omega t+\phi)$.

Evinda

Is there a general methodolgy to find solutions of a differential equation of the form $y''(x)+p(x) y'(x) +q(x) y=0 $ ?

SteamyRoot

Completely unchanged? :o

Semiclassical

Now, here are two questions which sound similar but aren't the same.

SteamyRoot

19:31

It always seemed to me like the "tail" of words had undergone rather significant changes

Akiva Weinberger

I tend to just use "goes away," I think

Or "disappears"

Semiclassical

One: At what times does $x(t)$ achieve its max/min values, and what are those values?

SteamyRoot

But, maybe it's not the same with verbs... do they (nearly) always end in "ere" in Italian too?

Sha Vuklia

those are the roots of $x'(t)$?

Akiva Weinberger

(Hm, sounds like a euphemism they'd use in a dystopia)

Semiclassical

19:32

Right.

Sha Vuklia

I forgot their values, but you gave them yesterday

Daminark

@Steamy "nearly always" meaning measure zero? :P

Sha Vuklia

one sec @Semi

Semiclassical

Two: If I pick a certain time and consider different phase angles, what's the max/min values possible?

Astyx

Now I'm imagining Daleks going around variables shouting "Exterminate! Exterminate!" - thanks

Alessandro Codenotti

19:33

Most Italian words have latin roots, but most words were changed a bit

Sha Vuklia

lol here they are :P

Alessandro Codenotti

@SteamyRoot the infinite tense of every verb in Italian ends with either "are", " ere" or "ire"

Sha Vuklia

@Semi uhh let me think

Semiclassical

To see why that's worth thinking about, consider the following picture

SteamyRoot

@AlessandroCodenotti I see...

This almost makes me want to study languages again.

Alessandro Codenotti

19:35

Sometimes I think I should start studying/practicing my German again, weil ich fast alles vergessen habe

Sha Vuklia

@Semi hm, intuitively, I would think the max/min values are still the same

Semiclassical

Alessandro Codenotti

da ich, maybe?

Semiclassical

So if I look at, say, t=2, then I'll get very different values depending on what $\phi$ is.

Sha Vuklia

yes

Semiclassical

19:35

The question is what the range of values is.

Akiva Weinberger

@AlessandroCodenotti Interesting. In Spanish, it's "ar", "er", or "ir".

Sha Vuklia

well if we can shift $\phi$ as much as we want

we just get the "actual" max and min value?

Akiva Weinberger

(No love for "or(e)" and "ur(e)", apparently)

Semiclassical

Well, that's not entirely obvious.

Alessandro Codenotti

@AkivaWeinberger we strongly like vocals at the end of words

Semiclassical

19:37

The two questions are in fact different, but to see that it's helpful to actually do the math.

SteamyRoot

They're mostly interchangeable

Semiclassical

For that, we should think of $x=e^{-\gamma t}C\cos(\omega t+\phi)$ as a function of $\phi$ not of $t$.

Akiva Weinberger

(@AlessandroCodenotti "Vowels", not "vocals")

Semiclassical

We pick a value of $t$ and ask how big it can be as a function of $\phi$.

Fargle

@AkivaWeinberger Latin's verbs were all "are", "ere", and "ire" (with there being two types of "ere" verbs depending on whether the first "e" is long or not; they conjugate differently)

Alessandro Codenotti

19:37

@AkivaWeinberger Woops, it looked wrong, thanks

Sha Vuklia

well, if $t$ is fixed, then we find the appropriate $\phi$ such that $\omega t+\phi=k\pi$

for some $k$

Semiclassical

Then $\frac{\partial x}{\partial \phi}=-e^{-\gamma t}C\sin(\omega t+\phi)$, which vanishes when $\sin(\omega t+\phi)=0$.

Yep.

Daminark

@Alessandro I've definitely gotten that vibe. I used to know a few words of Sicilian back in Brooklyn (a kind that I'm pretty sure is not spoken much anymore) and I remember thinking that it was interesting how the language had a lot of vowel endings

Semiclassical

Equivalently, if the sine vanishes, then the cosine is $\pm 1$.

Akiva Weinberger

In Hebrew, all the infinitive verbs start with "L"

Sha Vuklia

19:39

right

Semiclassical

Hence if we plug that $\phi$ back into $x$ we get $x=\pm e^{-\gamma t}C$.

Daminark

Hey @Mike!

Interesting @Akiva

Sha Vuklia

yea, I agree

Semiclassical

With that in mind, let's add that to our plot from before:

Mike Miller

hi

Daminark

19:40

How's it going?

Semiclassical

Mike Miller

it's ok

Sha Vuklia

alright

Balarka Sen

i need to do stuff but am unable to force myself to

Semiclassical

Now, if you compare the expression we just got with the one you quoted above, what's the difference?

Daminark

19:42

in Palpatine's voice doit @Balarka

Sha Vuklia

the one that I quoted is always smaller than this one?

Semiclassical

Right.

Balarka Sen

i know 0 star wars

Semiclassical

To see why, let's zoom in on one of those oscillations

Sha Vuklia

so we took two derivatives?

one with respect to $t$, and one w.r.t. $\phi$

Balarka Sen

19:44

I can try to say that in Mystery Man's voice, just for kicks.

Daminark

Lol I've only seen episodes 4 and 5, though they're pretty good, would recommend watching if you need a break from stuff

Mike Miller

Oh, you've finally watched Lost Highway?

Balarka Sen

@MikeMiller That was the first Lynch movie I ever watched. Did I forget to tell you?

SteamyRoot

That's the one with Rammstein music isn't it?

Mike Miller

yup

Sha Vuklia

19:45

(btw it's 21.45 here, and I'm at the university library that closes at 22.00, so I maybe have +- 8 minutes left @Semi)

Semiclassical

@ShaVuklia Yeah. Moreover, with one we held time fixed and varied phi, whereas we did the opposite with the other.

What you can notice from that is that the envelope curve isn't actually intersecting the maximum. It's hitting a bit to the right and below of it.

Sha Vuklia

so the envelope curve corresponds with fixed time?

you pick the max phase for a fixed time?

Semiclassical

Eh, it's more subtle than that. Let me describe it for here.

Balarka Sen

it's also how I got introduced to Outside (the beginning and ending track is from that album) :P

brilliant movie anyhow

Semiclassical

The reason is that, while the peak is the max value over time for that value of phi, it's not the max value of x over different phases at that time.

Jason Bourne

19:47

@ShaVuklia You talk to Waiting? I think Waiting accidentally put me on ignore. Could you let her know about it so that she can unignore me? Thanks.

Daminark

@BalarkaSen That was intense

Semiclassical

If I were to slightly decrease the phase, the other curve would peak a bit earlier and therefore have a slightly higher value at the other curve's peak.

Balarka Sen

@Daminark I have to do stuff but I am in your house right now.

Semiclassical

Jason Bourne

@ShaVuklia You call her him? LOL. OK, you can call her whatever you want.

Semiclassical

19:49

like that.

Daminark

gulps @Balarka

Semiclassical

The blue curve has a slightly different phase (larger, actually---I had it backwards) and it overshoots yellow curve's peak value.

Balarka Sen

the scene scared the shit out of me because i watch movies with headphones in

Sha Vuklia

@Semi uhm I just don't really see where the shift comes from mathematically:(

Balarka Sen

that laugh tho

Alessandro Codenotti

19:50

@Daminark look at a random wiki page in Italian and see how many words end with a vowel :P

Semiclassical

Well, mathematically I'd say it comes from the fact that if you differentiate w/r/t phi, you only differentiate the cosine part of x(t). but if you differentiate w/r/t time, then you have to use the product rule because e^{-\gamma t} carries time dependence at well.

Balarka Sen

Lynch manipulates his scare scenes too well

Jason Bourne

@ShaVuklia I talked to Waiting a lot in this chat under different accounts in the past. =) That was long before you appeared.

Semiclassical

@JasonBourne She's had a bunch of different ones over the years.

Astyx

Is waiting the one who keeps changing her username ?

Sha Vuklia

19:51

@Jason oh right, I just assume genders :P

Jason Bourne

@Semiclassical Just like me. =)

Daminark

Right?

Semiclassical

Whereas I just stay the same :P

Daminark

I may watch that movie

Alessandro Codenotti

I've seen lost highway in a small cinema and enjoyed it, ereaserhead on the other hand was rather terrible, or maybe I just don't understand surrealism

Daminark

19:52

@Alessandro If you want to know game theory you'll need to start learning that

Balarka Sen

i should watch eraserhead

Sha Vuklia

@Jason can I ping her another day then? because I don't want her to read that I assumed her gender XD

Semiclassical

Aaanyways. That picture in some respect illustrates the issue: The envelope curve doesn't pass through the max value of the yellow curve.

Alessandro Codenotti

@Daminark what

Mike Miller

watch blue velvet

3

Sha Vuklia

19:53

@Semi haha I'm soo sorry.. I wil have to read this slowly

Semiclassical

mmkay.

Sha Vuklia

I'm also slightly stressed because the library is about to close

Alessandro Codenotti

@BalarkaSen I wouldn't suggest it to be honest

Sha Vuklia

I'm sorry

Daminark

Game theory uses surreal numbers! (Conway-style)

Semiclassical

19:53

No worries.

Sha Vuklia

really, usually I can keep up

but here I just don't see it

I promise I will come back to it :P

it was not for nothing :P

Jason Bourne

@ShaVuklia OK. I assume you are the beautiful girl in the picture, so I will call you "she". My real name is not Jason Bourne, but it is one of my favourite movie characters. =)

Semiclassical

It doesn't help that you have to really zoom in on these pictures.

Sha Vuklia

yea but especially the closing of the library is making me stressed :( @Semi

like, I can't concentrate

Semiclassical

Gotcha.

Daminark

19:54

@JasonBourne That's not your real name??? gasps in betrayal

Semiclassical

Read it when you have a chance, then.

Sha Vuklia

@Jason oh haha, cool!:P and thanks:)

I'll ping her tomorrow, ok?

Jason Bourne

@MikeMiller I am surprised you watched that movie, LOL. I watched it too. I also watched Blue Car and Blue Desert.

Balarka Sen

@MikeMiller Yeah you recommended it. I got it in the very top of my list :)

Sha Vuklia

yes I definite will, @Semi I appreciate it a lot that you wanted to dive into this with me

Semiclassical

19:54

np

Balarka Sen

@Alessandro Hmm. Why did you not like it?

Sha Vuklia

see ya @all!

Jason Bourne

@Daminark My username also used to be Will Hunting and James Bond.

Balarka Sen

Is it because of the heavy surrealism, the plot, the body horror, or something else? Just curious.

Semiclassical

If it doesn't make sense later, there's another example I can give. Buuuuut another time.

Daminark

19:55

I was counting on your identity being those characters and having shifted around

Astyx

Bye sha

Semiclassical

night.

Sha Vuklia

sure! @Semi bye!

Daminark

See you @Sha!

Jason Bourne

I don't think Blue Velvet is suitable for @BalarkaSen. It's quite a blue film, LOL.

Balarka Sen

19:56

i have seen worse

Jason Bourne

I am just really surprised MM recommends it. It's the kind of movie only I watch.

Balarka Sen

we all like david lynch, that's all :)

Jason Bourne

@BalarkaSen I recommend Blue Car.

Daminark

makes joke about those who don't like him being lynched

Alessandro Codenotti

@BalarkaSen absence of structure, absurd and disturbing imagery mostly, which are both trademarks of surrealism, so I guess the first option is the right one

Jason Bourne

19:58

I like Blue Car because I am in love with Agnes Bruckner.

Almo

wait a minute. Blue Car. when was this released

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$Mathematics$ Mathematics