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7:00 PM
Sometimes it's literally just because it's convenient to be able to represent points by numbers
 
@BalarkaSen Yeah, $2^{2n}-1$ is always a multiple of three, I did the proof for $4^n - 1$ last week
 
thermal conduction too...for fast shm
 
Like [gonna butcher the maths here] you can make all the axes of a 3d space imaginary, but different numbers, so the imaginary part of multiplication of two points gives you the cross product
 
Now what I don't know is whether divisibility by three implies the tiling
 
@BernardoMeurer True (good observation), but is your formulation equivalent to my problem?
 
7:01 PM
I don't know yet
 
@Phase You know... I think I'll stick to believing and not understanding you there :P
 
Well, the tromino is symmetric
 
@CooperCape let $i^2 = j^2 = k^2 = ijk = -1$
you have pretty much all you need
 
Hmm, I am not sure
 
its not commutative so left and right multiplication arent equivalent
 
7:02 PM
Right...
 
@JohnR: Are you around?
 
in fact its anticommutative
so ab = -ba
 
@Kaumudi.H yes ...
 
$$\neg \text{hot}(\text{man})$$
 
Oh boy... how exciting.
That's wild
 
7:02 PM
Fine ill stop talking : p
 
@JohnRennie I messed up my laptop, big time.
 
@BalarkaSen How do you like that? :P
 
@BernardoMeurer How about a 1x3 rectangle? # of squares there is 3, which is divisible by 3.
 
@Phase Nah it's interesting you just lost me at 'so the imaginary part of multiplication of two points gives you the cross product' cause I'm not sure how that is a thing but thanks anyways yano...
 
@Kaumudi.H unless you dropped it in the bath or out of a window it's unlikely to be irretrievably broken ...
 
Sid
7:03 PM
@Kaumudi.H Get a new one
 
well refer back to my previous message
i j and k are unique imaginary numbers
 
Right.
 
@BalarkaSen Sure, but you proposed a square, not a rectangle :P
 
since ijk = -1, ij = k, as kk = -1, and you can derive the other info for the table from that
 
@BernardoMeurer I rate this meme a shaq/10
 
7:04 PM
right okay.
 
theres groups in further maths right?
 
@BernardoMeurer Well, a square with a hole. But it does constitute a counterexample to your claim that if the number of squares is divisible by 3 it can be tiled by L-shaped trominoes, right?
 
@Phase Since the last two times you mentioned further maths, for reference, I still don't take further maths ;)
 
@BalarkaSen Yeah, that is true
 
@Kaumudi.H do you want to switch to Hangouts to avoid the chatter about tiling problems?
 
7:05 PM
And I think not iirc
 
I am mystified
I'll tell A. this one
Maybe she knows how
 
Coolio
 
Nice problem, thanks
 
@CooperCape just get FP textbooks
Decision maths sucks
 
It's also enlightening to do it for $n = 1, 2$ by hand
 
7:06 PM
Nice, I got loads of grid paper :P
 
lololol
 
n=1 is trivial
 
Yup
 
n=2 not so much
 
@Phase Ehh I roughly know what each textbook covers and I sort of swing in and out of the topics at random intervals.
 
7:06 PM
But still I can see it
 
Mhm
 
@CooperCape if I can give you any advice at all from my limited experience
Get a structure as soon as you can dont just learn bits and pieces
It will fuck you over in the long run
 
Maybe I have to smoke trees to solve this one
 
yeah I spent a lot of time un-messing up my knowledge of the A-level physics course over the past few months due to doing that.
 
When you're done with your A levels and if you're bored in the Intermediate time
It's my recommendation to pester 0celo7 with constant messages until he gives you a book list
 
7:08 PM
@Bernardo It's basically quick maffs.
 
@BalarkaSen Get a snapchat
 
@Phase or blocks me... I wonder wots first...
 
So I can provide you with daily memes
I have some real good shit
 
I'll bug him for a list for you if that becomes the case : P
 
@Bernardo Make a discord and send those over to me
 
7:09 PM
Bah
That's too much work
 
lol
 
I send them in the morning to everyone
lol
 
I once adressed an important person as "Dead Mr. X" rather "Dear Mr. X"... — peterh yesterday
@peterh Glad to know I'm not alone
 
@SirCumference Was that in an email or something? My friend emailed a uni admissions tutor I was applying to "What's poppin Val, where the links at".
 
@BalarkaSen @BernardoMeurer
3
Q: Nested integral: volume of a right simplex

DanielSankConsider the integral $$I_n \equiv \int_{t_1=0}^T dt_1 \int_{t_2 = t_1}^T dt_2 \cdots \int_{t_n = t_{n-1}}^T dt_n \, .$$ I suspect the result should be $I_n = T^n/n!$ but would like to prove it. Doing the $n^\text{th}$ integral gives \begin{align} I_n &= \int_{t_1=0}^T dt_1 \cdots \int_{t_{n-1}=t...

 
7:16 PM
Nice, someone finally made it using induction
 
@DanielSank Nice
@BalarkaSen We are noobs
We got rekd trying
 
I actually proposed an answer using Fubini
Maybe I can post it
 
Yeah, it's just interesting that you don't need to use Fubini.
 
I am a lazy ass
@DanielSank True
 
@BalarkaSen Post. I will upvote.
 
7:17 PM
@BalarkaSen Only answers using theorems created by people this tall can be used
 
By the way, that simplex integral comes up when you deal with time ordered operators.
 
@DanielSank Did you see my charger in the conference room?
@DanielSank Also, I was laughing alone in my exam this morning thinking of the email w.r.t to backpack that was left there
 
@BernardoMeurer I'm not in the office. Working at home today.
 
@DanielSank Ah, alright
 
@BernardoMeurer I sent it. It was awesome. Kunal responded saying "Oh, thanks that's mine."
 
7:22 PM
@DanielSank LOLOLOL
That reminds me I have to email him
@DanielSank You home cause of the smoke & ash?
 
@DanielSank whut
 
@EmilioPisanty Only git users understand the joke
 
@BernardoMeurer I'm a git user
much as you might not like that
 
u r a git h8r
 
@BernardoMeurer I don't hate git
 
7:26 PM
@EmilioPisanty I found a backpack left at work yesterday evening after Bernardo and I finished working on something. I looked inside to see if I could identify it. I figured I'd send a group email to the effect of "Someone left a blue backpack containing x, y, and z at work."
 
I do think it's overrated and that git evangelizers do a lot of things that actively hurt its cause, but I don't hate git
 
So I went to itemize x, y, and z.
I found a laptop, a sock, and a conference name badge.
 
@DanielSank a sock?
as in, a sock puppet?
 
So I sent the group an email: "There is a blue backpack containing a laptop, a sock, and a conference name badge reading <name of coworker> in the conference room".
A different coworker than the one named in the badge replied "Oh, thanks Dan that's mine", which was funny.
 
@DanielSank yeah, that's a bit bizarre
 
7:28 PM
Oh, by the way:
 
have a star, good sir
 
Why, thank you!
Did you read it?
 
@DanielSank didn't read the author intros
 
Do modern physicists (meaning set remove cranks) care about the idea of multiple universes, or does such a notion belong to philosophy?
 
did read the rest
@Narcissusjewel the statement "there exist smart people that are generally recognized as not-cranks and that have wide recognition as field experts in several branches of physics, who both care about the idea of multiple universes and who think it's probably true" is true
 
Anonymous
7:36 PM
@Narcissusjewel Well, if you consider Greene to be a non-crank
 
whether all modern physicists care, that's a different matter
 
@EmilioPisanty Sure, I wasn't careful. I was leaving that to you lovely folks.
 
@SirCumference :-)
 
Where can I read about such a thing from a non pop-science perspective?
 
@EmilioPisanty comments? Good/bad?
how to improve...
 
7:38 PM
@DanielSank well, the mission statement sounds like the blog will be something the internet would benefit from having
 
I heard a good argument about the acceleration of expansion of space getting larger than the speed of light at points so some galaxies that were in the observable universe at some point in the past may not more be in the observable universe anymore. I don't know the authenticity of this argument though
 
I don't particularly care about audiophilia
 
@EmilioPisanty I don't either, but I like signals ;-)
 
past a certain reasonable level of audio equipment quality, I don't really hear the differences / care that much about them
 
These escaped objects should form the "other universes", whatever that means, or so I heard
 
7:39 PM
I expect that I'll start caring about audio equipment soon though.
 
Anonymous
@BalarkaSen Yes, that's quite a well established argument
 
Anonymous
I don't the math behind it. But I read it in many places
 
Anonymous
Perhaps even Wikipedia discussed that
 
@Narcissusjewel scientificamerican.com/article/… as an example
@DanielSank is that a healthy thing to be doing?
wallet-wise, I mean
 
@EmilioPisanty Sure.
 
Anonymous
7:43 PM
@BalarkaSen Hmm, wouldn't that just be a part of the universe, beyond the observable universe?
 
I have a real job. I'm not planning to go crazy, maybe just acquire nice speakers etc.
 
I mean, kinda like the advice that Japanese people give not to become a Wasabi connoisseur unless you have deep pockets
 
Anonymous
I'm not sure your second statement is true @BalarkaSen
 
@EmilioPisanty hahaha haven't heard that one.
 
... but then again, yes, you're the guy with the cushy industry job, aintja
 
7:44 PM
^
 
@Blue I mean, the functional definition of universe is the observable universe.
 
I don't plan to go nuts. The only thing I spend too much money on is vintage video games.
 
@DanielSank that is a reasonable way to spend money
 
Agreed
That's why I do it.
 
7:45 PM
have you bought a lego Saturn V yet?
 
wut
no
how to do?
 
Anonymous
@BalarkaSen I don't think so. en.wikipedia.org/wiki/Observable_universe and en.wikipedia.org/wiki/Universe. Astronomers normally consider the universe only to be the observable portion. But as far as theorists are concerned, pretty sure, no
 
it's already gone out of stock once, if you want one you should order soon
as in, damn soon
 
@Blue shrug
 
Anonymous
String theory has a notion of multiverse too, I think. You could ask ACM :P
 
That's cool, but I could get a good condition Mega Man 4 for that much money.
 
@DanielSank indeed, but a Mega Man 4 isn't a meter-tall user-assemblable sculpture of the largest rocket flown by mankind
 
Yeah, as Blue suggests, that's not the definition I was hoping to be used. My friend was talking about escaping the heat death of the universe by moving to another universe. I wondered if the candles (universes) were all burning out together (dying to entropy), or if we can move to another candle and light it nice and fresh.

(Motivated in part by the [in my opinion excellent] short story 'The Last Question' by Asimov)
 
True, but it is an episode in one of the greatest video game series of all time.
 
(Before considering this though, it'd make sense to find out what the notion of other universes could even mean. Hopefully determining if there is moral reason to assume that these have to start at the singularity or something.)
 
Anonymous
7:56 PM
@Narcissusjewel Wikipedia has a nice article on multiverse. You could start with that. Most of what I know about this is from "The Book of Universes" by Barrow
 
Anonymous
I have forgotten many of the details tbh
 
Anonymous
But that is a real nice book
 
@DanielSank ¯\ _(ツ)_/¯
 
8:31 PM
@DanielSank I have posted my tome.
 
8:48 PM
I am trying to derive the relation $A = A_o e^{-bt/m}$ for damped harmonic motion.
I have reached $m\dfrac{dv}{dt}= -kx -bv$. What do I do next? Anyone?
$A= A_o e^{-bt/m}\sin(w't+\delta)$ **
 
Anonymous
@Abcd That's a second order differential equation. There are standard ways to solve it. Just google
 
@Blue Couldn't find the derivation on google.
 
Anonymous
That's not possible.
 
Anonymous
8:55 PM
I'm getting bombarded with 100s of results by Google.
 
@BalarkaSen I have read, appreciated, and upvoted your tome.
 
Thanks!
 
Oh, you are telling me methods to solve differential equations @Blue.
 
Anonymous
@Abcd Yes
 
I was searching for the derivation of the above equation because there's introduction of lot of variables while solving it.
As there was in the case of SHM and Angular SHM.
So even if I solve the differential equation, I'll not reach the standard result.
 
 
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