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Captain Bohemian
Captain Bohemian
4:01 PM
so you can't be granted a position there?
 
DanielSank
DanielSank
@JohnRennie That is arguable on both accounts.
 
Anonymous
@CaptainBohemian Yeah, I don't think so
 
Anonymous
The people involved are all from different places
 
Captain Bohemian
Captain Bohemian
maybe only principal investigators can get a position there. research followers can't.
 
Novalium Company
Novalium Company
4:30 PM
Hello wonderful peoeple. I'm reading (and almost finished) a book on how the structure of the DNA was found (by James Watson and Francis Crick) and there's a chapter which I don't understand clearly. It talks about how A-T and G-C bases bond with hydrogen bonding in a specific way but I don't really understand. After all, if I ask myself the question why A-T specifically bond together (and not A-G for example), I can't answer.
 
Secret
Secret
This is because (if I did not mix up the order of the two) A-T forms only 2 hydrogen bonds while G-C forms 3
 
Novalium Company
Novalium Company
Ok, but if I try to bond A-G, it should still work because there will just be one hydrogen unbonded, which I'm not sure if it's a problem?
 
Anonymous
You can simulate those compounds and check out the distances. A and G are Purines while C and T are Pyrimidines.
 
Anonymous
Base pair
A base pair (bp) is a unit consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA and RNA. Dictated by specific hydrogen bonding patterns, Watson-Crick base pairs (guanine-cytosine and adenine-thymine) allow the DNA helix to maintain a regular helical structure that is subtly dependent on its nucleotide sequence. The complementary nature of this based-paired structure provides a redundant copy of the genetic information encoded within each strand of DNA. The regular structure...
 
Anonymous
> Purines are complementary only with pyrimidines: pyrimidine-pyrimidine pairings are energetically unfavorable because the molecules are too far apart for hydrogen bonding to be established; purine-purine pairings are energetically unfavorable because the molecules are too close, leading to overlap repulsion.
 
Novalium Company
Novalium Company
4:38 PM
Hmm, got it. Thanks! Btw @Blue love your new pic :P
 
Anonymous
Heh :P
 
Anonymous
Thanks
 
Anonymous
It's from a childhood story book
 
Anonymous
(which I recently found after several years)
 
Novalium Company
Novalium Company
Also do the words purines and pyrimidines have any different meaning except to point to the corresponding nitrogenous bases in DNA, RNA...?
 
Anonymous
4:40 PM
Sure. They are a whole class of chemical compounds
 
Anonymous
A,T,G,C aren't the only ones
 
Novalium Company
Novalium Company
Uracil in RNA I suppose?
 
Anonymous
It's a pyrimidine derivative
 
Anonymous
Look up the structures
 
Novalium Company
Novalium Company
Ok then. How is uni going. High school started here :\
 
Anonymous
4:43 PM
LOTS of class tests ;_;
 
Novalium Company
Novalium Company
Same here ;___;
amazon.com/First-Song-Book-Anthem-Infinity-ebook/dp/B07HD2VQ9W Giving this bad boy a shot in the meanwhile.
 
enumaris
enumaris
hmmm
 
Anonymous
An ebook?
 
Novalium Company
Novalium Company
Oh yes, I have a kindle e-reader.
 
Anonymous
Ah. I don't read many books :P
 
Novalium Company
Novalium Company
4:47 PM
I didn't too, but I started a year ago and it's really nice. Gets you relaxed and 'out of this world'.
 
Anonymous
Are the modern Kindles worth buying?
 
Anonymous
I don't know much about the advantages of it over a normal tablet
 
Anonymous
@NovaliumCompany I can understand :)
 
John Rennie
John Rennie
@Blue Kindles have quite a small screen, so unless you make the font very small you don't see much of the text at a time.
 
danielunderwood
danielunderwood
I bought a refurbished fire tablet a few weeks ago and it's decent. Pretty bad as far as a tablet goes, but I only bought it to read ebooks, blog posts, and such
 
John Rennie
John Rennie
4:50 PM
I used a Kindle for a year or two but then switched to an eight inch tablet for reading books, and I find that far superior.
 
Novalium Company
Novalium Company
@JohnRennie Eyes don't hurt?
 
danielunderwood
danielunderwood
Yeah the screen is a bit small as well. I think they have multiple sizes though
 
John Rennie
John Rennie
@NovaliumCompany no, not at all. But you need to adjust the screen brightness to make it easy on your eyes.
 
Novalium Company
Novalium Company
Meh, I'm satisfied with the Kindle for now, but I can agree that the screen is not really big.
 
danielunderwood
danielunderwood
Also its app store is pretty bare unless you go through whatever effort to load the official play store
 
John Rennie
John Rennie
4:52 PM
@danielunderwood all the Kindles have fairly small screens. Amazon used to do a 10" Kindle some years ago but they discontinued it and now make nothing large than 6".
A shame, because if a 10" paperwhite Kindle was available I'd buy it in a moment.
 
danielunderwood
danielunderwood
Ahh I didn't know that. I think mine is either 7 or 8. It was a refurbished model from a couple years ago though
 
John Rennie
John Rennie
@danielunderwood The Kindle Fire tablet is completely different to the Kindle.
The Kindle uses an e-ink screen
 
danielunderwood
danielunderwood
Yeah I was talking about the fire. I'd be interested in one of the e-ink ones, but aren't you pretty locked down as far as what you can read?
 
Novalium Company
Novalium Company
lichess.org/XlbscNbc Anyone up for a quick chess (started playing a few days ago, I'm kinda addicted now :P )
 
John Rennie
John Rennie
@danielunderwood No, you can copy any book you want to the kindle. You just connect it to your PC with a USB cable and it appears as a USB drive. Copy the .mobi files across and away you go.
 
Novalium Company
Novalium Company
4:55 PM
 
John Rennie
John Rennie
Use something like Calibre to convert your e-books to mobi format.
 
Novalium Company
Novalium Company
@danielunderwood Be careful with the pdf files, I use some sort of converter when the file is not the right size for kindle, but it still looks ugly.
 
danielunderwood
danielunderwood
@JohnRennie but you have to have a proper ebook, right? Like no bootleg pdf textbook scans?
 
Emilio Pisanty
Emilio Pisanty
@DanielSank I dodged earlier 'cause I didn't have anything in mind, but now I do: youtube.com/…
 
John Rennie
John Rennie
@danielunderwood the Kindle will read pdf files, but they're a bit slow. They take a lot of processing compared to a MOBI.
But really I'd advise using a tablet. Ideally one with a 1080p screen.
 
danielunderwood
danielunderwood
4:57 PM
Like any pdf? Say you have a scan like this
I always thought there was no way to have something like that on kindle
 
Novalium Company
Novalium Company
If I have to honest, the only reason I bought a Kindle 5 was because it was relatively cheap (around 75$), it works good enough for now. But if you have the money, like @JohnRennie says, better get a tablet. :P
 
John Rennie
John Rennie
@danielunderwood My Kindle would read PDFs. Just copy the PDF onto the Kindle. I assume the more modern Kindles will too, though I don't know that for certain.
 
Novalium Company
Novalium Company
Ok, good evening everyone. I'll be going. Thanks for being such an awesome community <3
 
John Rennie
John Rennie
@danielunderwood you're in the US aren't you?
 
Anonymous
@NovaliumCompany Biya!
 
Anonymous
5:02 PM
75$ is somewhat reasonable if they give you internet access. Should be similar to an entry-level tablet
 
Anonymous
The Chinese tablets are actually doing very well these days in India
 
Anonymous
On the other hand, I bought an iPad this year in January but I hardly ever use it. The associated keyboard isn't good enough for fast typing and almost all the good apps are paid!
 
Anonymous
The stylus is apparently the only good thing about it, but I think they can improve on the body texture
 
Anonymous
It's way too slippery
 
Anonymous
(I was actually thinking of selling it off and buying some recent Samsung tablet instead)
 
Anonymous
5:08 PM
Nah, actually I'd prefer a laptop to a tablet I guess :P
 
John Rennie
John Rennie
@Blue a laptop is far better as a general purpose tool. But tablets are very good for reading on.
 
Anonymous
Yeah, I mean for someone who reads casual novels, etc tablets might be more useful. It's difficult to carry a laptop around. But I sit at my desk almost 12 hours a day, so not as useful for me
 
Anonymous
I feel cheated after having bought the extra keyboard though :P
 
Anonymous
It's the most useless thing ever
 
Anonymous
 
Anonymous
5:21 PM
The keys are soft as cotton balls. It's way faster to type using the on-screen keyboard
 
danielunderwood
danielunderwood
@JohnRennie someone starred that? But yeah I am
And regarding laptops vs tablets, I thought a surface would be neat. Turns out that it's neither a good laptop nor a good tablet
 
Anonymous
@danielunderwood The microsoft one?
 
danielunderwood
danielunderwood
Yeah
I do have a friend with one that seems to like it. I can't understand why myself
 
Anonymous
It was very expensive; at least 2-3 years ago - $3000 or something
 
Anonymous
I remembering window shopping one :P
 
danielunderwood
danielunderwood
5:30 PM
That must have been the desktop one or one of the ones meant for businesses unless there's a crazy price difference between countries
I was mainly talking about this one (well the past versions of it) microsoft.com/en-us/surface/devices/surface-pro/overview
 
Anonymous
 
Anonymous
Goddamn, this costs Rs. 479,999.00
 
Anonymous
6,641 $
 
Anonymous
"Microsoft Surface Book 2 (Intel Core i7, 16GB RAM, 512GB) - 15" "
 
danielunderwood
danielunderwood
I certainly hope that's a "we're the only offer on amazon, so it's crazy high"
Otherwise that's insane
 
enumaris
enumaris
5:33 PM
o.O
 
Anonymous
I think the costs are a bit higher in India, since a lot of the things are imported
 
Anonymous
But still, that seems a bit too much
 
Anonymous
> This laptop will also help you to go from one place to another, all you have to do start it and sit on it , may be that’s why it’s costing about $6000 price of a car 🚘
 
Anonymous
LOL
 
Anonymous
(in the review)
 
danielunderwood
danielunderwood
5:35 PM
lol
This was more of what I was thinking...still about twice the cost I'd expect amazon.in/Microsoft-Surface-KJR-00015-Integrated-Graphics/dp/…
 
Anonymous
@danielunderwood Ah, that looks reasonable
 
Anonymous
If it has a nice keyboard, I'd definitely go with that
 
Anonymous
instead of the iPad which costs around the same
 
Anonymous
HP also has some convertibles
 
Anonymous
I don't know how good those are
 
Anonymous
5:40 PM
 
DanielSank
DanielSank
@EmilioPisanty There is a certain pattern in the music you send me.
The vocals tend to be in Spanish and there's a trend of upbeatness.
 
Anonymous
> Sold both my kidneys and 1 of my eye to own it now i play vr games on it highly recommended
 
Anonymous
@AvnishKabaj Looks like you have a brother ^
 
Emilio Pisanty
Emilio Pisanty
6:00 PM
@DanielSank I am unsurprised by those features =P
 
Phase
Phase
6:11 PM
sup
 
ACuriousMind
ACuriousMind
6:34 PM
@Phase inf
 
Phase
Phase
6:45 PM
wow, typical man
minds always thinking about sets
 
Anonymous
@Phase Hi
 
Anonymous
Sep 15 at 19:04, by Blue
9 hours ago, by Blue
@user2646 $$\mathfrak{howzlife}$$
 
Phase
Phase
$$\mathscr{sick}$$
 
Anonymous
Aw
 
Phase
Phase
catch you on the $\mathfrak{flipside}$
$\mathfrak{narc}$
is chat usually this dead nowadays?
 
enumaris
enumaris
6:55 PM
$\mathfrak{negatory}$
 
Phase
Phase
hey @Blue is the pollution in India still pretty bad? I have someone telling me the rivers have been cleaned and that it's not super polluted and I'm pressing [x] to doubt pretty hard rn
@enumaris that is the weirdest y i've ever seen
 
enumaris
enumaris
$\mathfrak{y's}~\mathfrak{that}$
 
Anonymous
@Phase "rivers have been cleaned" - that's a funny claim, given that we have rivers stretching several 1000s of kilometers :P The pollution sort of depends on the area you live in. Near the Himalayan range in the North (near the source of the rivers) they are quite clean and you can even directly drink river water (it's basically molten water from the glaciers). It's further down the stream where the pollution begins ... esp due to the nearby industries
 
Anonymous
Maybe a certain area has been cleaned, but definitely not all.
 
Phase
Phase
Yeah idk, he's citing sources from Quora titled "positive tourism experiences in india"
I think I'm just gonna exit the argument
 
Anonymous
7:03 PM
You shouldn't get into arguments with people who cite Quora, in the first place :P
 
Phase
Phase
$\mathfrak{OOF}$
ok come on
those are meant to be O's
 
Curious Fish
Curious Fish
hi
 
Anonymous
@CuriousFish Hi, can may I eat you?
 
Anonymous
@SirCumference Still alive? :D Had any break-the-fast meal?
 
enumaris
enumaris
hopefully he broke-the-fast with a dinner
since Yom Kippur is over a sun down
 
Curious Fish
Curious Fish
7:17 PM
0_o don't eat me
 
Anonymous
Don't worry. I found some Nutella
 
Anonymous
Sparing you for today
 
Curious Fish
Curious Fish
Thank god.
Lol
Okay I'm leaving bye
 
bolbteppa
bolbteppa
7:33 PM
@vzn
@Everyone
Atiyah presenting a proof of the Riemann Hypothesis Monday twitter.com/HLForum/status/1042670700652318720 ???
 
Semiclassical
Semiclassical
Baez had a Twitter reaction which wasn’t encouraging, lemme find it
 
bolbteppa
bolbteppa
This is going to be insane if true
 
Semiclassical
Semiclassical
So my attitude right now is: if he’s actually succeeded, it’ll be splendid. But I wouldn’t hold my breath.
 
bolbteppa
bolbteppa
That's a very very very snarky comment, yikes
Links to this thread below
34
Q: What is the current understanding regarding complex structures on the 6-sphere?

jdcIn October 2016, Atiyah famously posted a preprint to the arXiv, "The Non-Existent Complex 6-Sphere" containing a very brief proof $S^6$ admits no complex structure, which I immediately read and realized I lacked the background to understand. The preprint inspired interest in KR-theory and a few ...

dg.differential-geometry at.algebraic-topology complex-geometry kt.k-theory-and-homology index-theory
 
Semiclassical
Semiclassical
Eh, snarky isn’t the right word imo
But it is rather bleak
It does rather read like that.
 
bolbteppa
bolbteppa
7:41 PM
10
Q: Atiyah's paper "Non-existent complex 6-sphere"

Max BorovkovI'm trying to understand the main idea of Atiyah's proof (https://arxiv.org/abs/1610.09366). Although there were discussions on MO year ago I couldn't find answers to my questions. Consider the isomorphism on the 4th page: "$KSp(\mathbb{R}^6) \rightarrow KR^{(7,1)}(pt) = \mathbb{Z}_2$" My quest...

dg.differential-geometry at.algebraic-topology complex-geometry kt.k-theory-and-homology
 
tarit goswami
tarit goswami
Atiyah claimed that he has used work of Dirac, I am curious about what he have used from work of Dirac to prove Riemann hypo
 
Anonymous
 
Anonymous
apparently
 
Semiclassical
Semiclassical
(I do remember hearing about the 6-sphere in the math chat at the time. I don’t know of the reception tho)
 
Anonymous
> The Riemann Hypothesis is a famous unsolved problem dating from 1859. I will present a simple proof using a radically new approach. It is based on work of von Neumann (1936), Hirzebruch (1954), and Dirac (1928).
 
Anonymous
7:44 PM
As for which exact part of it, we gotta wait I guess :P
 
Anonymous
(not that I'd understand it anyway)
 
tarit goswami
tarit goswami
@Blue thanks, are u sure from this paper of Dirac he has used something?
@Blue Yeah :p
 
Anonymous
@taritgoswami That's what most sources are claiming
 
bolbteppa
bolbteppa
This is a huge deal tbh
 
tarit goswami
tarit goswami
Does Riemann hypo has any impact in Physics?
 
enumaris
enumaris
7:53 PM
probably
but I don't know of any
 
Semiclassical
Semiclassical
It’s a huge deal if he’s succeeded
 
tarit goswami
tarit goswami
@Semiclassical Yeah it will help to understand distribution of primes in Mathematics more clearly
 
Semiclassical
Semiclassical
And I definitely take Atiyah saying he has a proof more seriously than most
But it’s still if, not when
 
Anonymous
41
Q: What does proving the Riemann Hypothesis accomplish?

MythioI've recently been reading about the Millenium Prize problems, specifically the Riemann Hypothesis. I'm not near qualified to even grasp the entire problem, but seeing the hypothesis and the other problems I can't help wonder: what is the practical use of solving it? Many researchers have spent ...

number-theory riemann-hypothesis
 
Anonymous
@taritgoswami There was this nice thread ^
 
Anonymous
7:56 PM
95
Q: Consequences of the Riemann hypothesis

Andrea FerrettiI assume a number of results have been proven conditionally on the Riemann hypothesis, of course in number theory and maybe in other fields. What are the most relevant you know? It would also be nice to include consequences of the generalized Riemann hypothesis (but specify which one is assumed).

nt.number-theory analytic-number-theory big-list riemann-hypothesis
 
enumaris
enumaris
I was under the impression the Riemann Hypothesis was one of the most difficult Millenium problems to solve
so this must be very radical :O
 
tarit goswami
tarit goswami
@Blue And I think there is a Cryptographic scheme using Riemann hypo, don't know proof will help to make it better or not :-(
 
Anonymous
In cryptography RH is already assumed to be true afaik
 
Anonymous
If someone proved it to be wrong that could have some effects I guess
 
tarit goswami
tarit goswami
there are thousands of paper states if Riemann hypo is correct , and the conclusions works pretty well
 
Anonymous
8:02 PM
Yeah, that's what I hear
 
Anonymous
@taritgoswami Where are you studying physics currently? (if you don't mind) Not a lot of places offer courses in QI at the undergrad level
 
Anonymous
From the "Goswami" title I suspect you're from WB?
 
enumaris
enumaris
8:17 PM
crap
forgot to charge my phone
now it's at 17%
 
Semiclassical
Semiclassical
Oof
 
enumaris
enumaris
if it dies, I'm gonna be so bored
existential crisis
 
Anonymous
Borrow a USB
 
enumaris
enumaris
I don't really want to walk around asking people for a USB-C...
 
Anonymous
You have an office chat group or group mail? ;)
 
danielunderwood
danielunderwood
8:19 PM
That's why I always have a cable for my phone in my work bag
Just stand up and yell at them all. Much more efficient than asking one by one!
 
enumaris
enumaris
hmmm
 
danielunderwood
danielunderwood
Or just think of the person with a pixel. At least that's the only phone I know of with USB-C
 
enumaris
enumaris
samsungs are USB-C
it's what I got
 
danielunderwood
danielunderwood
Or one of those!
I have a spare if you can manage to figure out teleportation
 
enumaris
enumaris
might be physically impossible...as a physicist, I can not condone such an undertaking
 
danielunderwood
danielunderwood
8:27 PM
What about "speed of light translocation"
should be fast enough and possibly physically allowable
Or just download one of those phone charging apps
 
enumaris
enumaris
according to the no-clone theorem there are limits to that
maybe I should put my phone in a microwave
hope that samsung installed that capability
I heard it only works on iphones, but you never know
 
danielunderwood
danielunderwood
Just better make sure they don't have any microwave detection strips
 
enumaris
enumaris
hmmm
 
danielunderwood
danielunderwood
Like they used to have water detection strips in case you dropped your phone in water and tried to warranty it
Side note: Those water strips aren't activated by acetone
 
enumaris
enumaris
I can take a look
 
danielunderwood
danielunderwood
8:30 PM
Side note 2: Acetone dissolves solo cups
(as well as a variety of plastics)
 
Anonymous
The new iPhones aren't waterproof?
 
danielunderwood
danielunderwood
Are any of the popular new phones waterproof?
 
Anonymous
There was one by Sony
 
Anonymous
 
danielunderwood
danielunderwood
huh neat!
 
bolbteppa
bolbteppa
8:42 PM
This is like all or nothing
He's risking his rep on this on purpose probably
 
enumaris
enumaris
I mean...dude's 90...the chances of dementia/cognitive decline is quite high...which may lead to lowered inhibitions
 
bolbteppa
bolbteppa
The whole 6-sphere thing adds to the drama
 
coniferous_smellerULPBG-W8ZgjR
coniferous_smellerULPBG-W8ZgjR
9:11 PM
I might reach 2k reputation in the next months. This will give me the power to edit without peer review, but I feel like a drunk driver with a train on the highway at full speed. is there a way I can still pass by peer review
to begin with, i am not a native english speaker, and I do try to edit sometimes
big problem there ^^
 
Semiclassical
Semiclassical
If he’s correct, it’ll be immense. If he’s wrong in an interesting way, that will be disappointing but perhaps not so disheartening.
The worst-case scenario is that he’s wrong in a boring/obvious way.
 
enumaris
enumaris
"Shouldn't there be a negative sign there?"
sits down
 
Kyle Kanos
Kyle Kanos
To the mod who declined my flag for protecting a particular question: had you bothered to read the link you provided, you'd see it explicit started that the protection capabilities for the 20k+ non-mods require the post to be 1 day old and have an answer by a user with <10 rep, so no I most certainly could not protect the question.
 
coniferous_smellerULPBG-W8ZgjR
coniferous_smellerULPBG-W8ZgjR
@KyleKanos I was told to flag the mod if you want his/her/its attention
I guess you can know who it is? if so, use @
 
Semiclassical
Semiclassical
For reference, the Scholze-Stix objection to Mochizuki’s argument sounds to me like: Mochizuki is wrong in an interesting/nontrivial way
Whereas garden-variety crackpottery is wrong in boring ways
 
bolbteppa
bolbteppa
9:28 PM
That's how this could pan out
If wrong it's probably interesting enough to hint at something deep
Wonder what the Hirzebruch paper is about
 
Kyle Kanos
Kyle Kanos
@coniferous_smellerULPBG-W8ZgjR dunno who it was...I have a guess, but that doesn't do me any good
 
enumaris
enumaris
is the world building SE super laggy for anyone else?
it's always super laggy when I go there
I wonder if it's the background or something
not familiar with Mochizuki
 
Anonymous
@enumaris You haven't seen the IUT memes?
 
enumaris
enumaris
nope
 
bolbteppa
bolbteppa
Abc conjecture
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985). It is stated in terms of three positive integers, a, b and c (hence the name) that are relatively prime and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d is usually not much smaller than c. In other words: if a and b are composed from large powers of primes, then c is usually not divisible by large powers of primes. The precise statement is given below. The...
 
Anonymous
9:34 PM
 
enumaris
enumaris
oh, the dude who wrote all those papers that nobody understands
they're all wrong or just his ABC conjecture proof is wrong?
 
Anonymous
@enumaris Afaik I don't think he's been proven wrong
 
bolbteppa
bolbteppa
 
enumaris
enumaris
People stopped scrutinizing it?
it's been 6 years or w/e
should have been long enough for someone to figure it out lawl
 
Anonymous
> While there were no experts on IUT in 2012, their number increased to a two-digital one in 2017
 
Anonymous
9:39 PM
> Mochizuki refuses to travel outside Japan to help explain his work, and his written explanations can seem impenetrable.
 
bolbteppa
bolbteppa
From Motls blog comments:

'By the way, I guess that Atiyah's supposed proof is probably based in Hirzebruch' thesis

http://hirzebruch.mpim-bonn...Über%20vierdimensionale%20Riemannsche%20Flächen.pdf

rather than in the celebrated Hirzebruch-Riemann-Roch theorem of that same year (1954) that Atiyah likes so much. We shall not know until Atiyah's talk is published elsewhere.'
 
Anonymous
Chat doesn't accept non-ASCII URLs :/
 
enumaris
enumaris
This is the thing where Japanese mathematicians say "ABC Theorem" and everyone else still says "ABC Conjecture"?
 
bolbteppa
bolbteppa
Can anybody tell me what the Riemann-Roch theorem is
 
enumaris
enumaris
no clue
 
bolbteppa
bolbteppa
9:43 PM
What kind of memes are these
 
enumaris
enumaris
11% .... existential crisis intensifies
 
bolbteppa
bolbteppa
Need to read the Dirac paper the Hirze one and what's the von Neumann one :(
 
Semiclassical
Semiclassical
@bolbteppa I was supposed to understand that at one point
I failed
 
bolbteppa
bolbteppa
I think I meant to try :\
I mean vaguely I tried and failed if that counts
I would say it's to do with Dirac operators
 
Semiclassical
Semiclassical
The context in which I knew of it was the one sketched in the Wiki article, ie Riemann surface business
The Hirzebruch-RR stuff, by contrast, was well beyond me
 
bolbteppa
bolbteppa
9:57 PM
Hirzebruch–Riemann–Roch theorem
In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result contributing to the Riemann–Roch problem for complex algebraic varieties of all dimensions. It was the first successful generalisation of the classical Riemann–Roch theorem on Riemann surfaces to all higher dimensions, and paved the way to the Grothendieck–Hirzebruch–Riemann–Roch theorem proved about three years later. == Statement of Hirzebruch–Riemann–Roch theorem == The Hirzebruch–Riemann–Roch theorem applies to any holomorphic vector bundle E...
'It was the first successful generalisation of the classical Riemann–Roch theorem on Riemann surfaces to all higher dimensions'
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings. Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch ...
 
Semiclassical
Semiclassical
They do relate in the HRR entry to Atiyah-Singer
And the Atiyah-Singer page in turn indicates that HRR can be straightforwardly derived from A-S
The closest thing I come to understanding classical R-R is this bit: “the theorem may be roughly paraphrased by saying ‘dimension − correction = degree − genus + 1’.”
 
bolbteppa
bolbteppa
'Essentially, the theorem determines the number of linearly independent meromorphic functions on the surface that have at most a specified finite set of poles'
Why would Riemann or Roch even care about this, they obviously cared about something more basic
3
A: On the original Riemann-Roch theorem

danielA partial answer. According to the Wiki entry, it was originally proved by Riemann and generalized by his student Roch. The following contains the original statements. It does not address the question of how they were originally proved, which is given in the references. Roch's generalization fir...

 
Semiclassical
Semiclassical
Presumably that’s the more modern formulation
 
bolbteppa
bolbteppa
'A translation of Riemann's quote is: A function of the form $x+yi$, which is given on a part of the $(x,y)$-plane, can be extended continously in only one way.'
So something about analytic continuation of functions
 
Semiclassical
Semiclassical
The problem is that this all falls well short of the Dirac operator context
Classical R-R is presumably not the important idea
 
bolbteppa
bolbteppa
10:11 PM
If you're analytically continuing a function from a bounded region to the whole plane then in general you're working with meromorphic functions otherwise by Liouville's theorem you'd only be working with constant functions?
 
Semiclassical
Semiclassical
Sounds right?
 
bolbteppa
bolbteppa
'for an abstract Riemann surface, it is not immediately obvious that there are any non-constant meromorphic functions at all! As the poles are isolated and the surface is compact, a meromorphic function can only have finitely many poles'
 
Semiclassical
Semiclassical
this somehow gets to elliptic function and theta function madness
 
bolbteppa
bolbteppa
Hmm, if you took a holomorphic function on a given region of the plane and analytically continued it to the whole plane, you might think they'd all end up as constants or something, so maybe one has to prove the extension is unique at all points along the extension?
 
Semiclassical
Semiclassical
(The weirdness with elliptic functions I guess being that they’ve got infinitely many complex poles, but only finitely many in the fundamental domain.)
 
bolbteppa
bolbteppa
10:19 PM
My guess is the whole Atiyah stuff is about treating differential operators as like holomorphic functions and doing this with them
 
Semiclassical
Semiclassical
No idea
In particular, no idea how this is supposed to relate to the Riemann hypothesis
 
Lozansky
Lozansky
@Semiclassical I have a little E&M problem from Griffiths that bothers me :(
 
Semiclassical
Semiclassical
I’m on mobile right now so I probably can’t help much. But set it up
 
Lozansky
Lozansky
Can you view pictures? Might be easier if I just send a printscreen of the problem text
 
bolbteppa
bolbteppa
Maybe he analytically continued the Zeta function or some differential operator related to it in such a way that the zeros did X
 
Semiclassical
Semiclassical
10:24 PM
@Lozansky I can, yeah
 
Lozansky
Lozansky
 
Semiclassical
Semiclassical
Okay
 
Emilio Pisanty
Emilio Pisanty
@Blue damn.
> All the numerical data shows π(x) < Li(x), and Gauss thought this was always true, but in 1914 Littlewood used the Riemann hypothesis to show the inequality reverses infinitely often. In 1933, Skewes used RH to show the inequality reverses for some x below 10^10^10^34
 
Lozansky
Lozansky
@Semiclassical I have the solution, I just don't understand why it works :P Lemme send it as well
 
Emilio Pisanty
Emilio Pisanty
that's one large number
 
Lozansky
Lozansky
10:28 PM
 
Semiclassical
Semiclassical
I think I wrote up the solution to that problem myself as a TA, heh
 
Lozansky
Lozansky
Yaay :D
 
Semiclassical
Semiclassical
But, what don’t you understand?
 
Lozansky
Lozansky
So what does he mean "two cylinders of opposite[...]", like are they superimposed?
I guess I don't understand how to go from polarization to charge densities
 
Semiclassical
Semiclassical
That’s not obvious to me either. The way I remember doing the problem was to compute the surface bound charge
 
Lozansky
Lozansky
10:34 PM
I know polarization is defined as dipole moment per unit volume, so what we would want is to create "infinitesimal" dipoles (uniformly) in the cylinder by somehow bringing together a positive and a negative charge density? :/
 
Semiclassical
Semiclassical
maybe the idea is like this: suppose you take his setup but allow the two cylinders to be slightly off-center
That’d give you a few regions. outside and in the overlap, there will be no net charge
That’ll give two regions, one with positive charge and the other with negative charge
 
Emilio Pisanty
Emilio Pisanty
@Lozansky basically, yes
 
Lozansky
Lozansky
@Semiclassical But the polarization is not uniform then?
 
Emilio Pisanty
Emilio Pisanty
@Lozansky it is, but only in the limit of infinitesimal displacement
 
Semiclassical
Semiclassical
If I now move the cylinders close enough so that they almost entirely overlap, then the remainder looks a lot like a surface charge
 
Lozansky
Lozansky
10:39 PM
Fair
 
Semiclassical
Semiclassical
Not sure how to validate that, but it sounds very similar to what he does earlier in the chapter
 
Lozansky
Lozansky
Yeah with the sphere
 
Emilio Pisanty
Emilio Pisanty
@Semiclassical you can indeed formalize it, but you probably need to pull in some heavier guns from distribution theory.
The core of that is that the charge distribution of a point dipole is the directional derivative of a Dirac delta
with the upshot that any problem that says "calculate the field with uniform polarization $\mathbf P$" can be reduced to "calculate the field with uniform charge density in those same regions, and then take the directional derivative"
which is basically what the superposition of charged cylinders is doing
 
Emilio Pisanty
Emilio Pisanty
In more physical terms,
when you say "a region with uniform polarization $\mathbf P$", what you're really saying is that each (meso/)microscopic cell of your material, at some suitable level of magnification, is really two blobs of equal-but-opposite charge, and that those are displaced by some amount
the two-displaced-charged-regions is an extension of that mental model
take all your microscopic cells, take the negative charge, discard the positive charge, and then join up the charge from all the cells. That will yield one large cloud of negative charge.
do the same with the positive charges from all the cells, and you'll get one large cloud of positive charge
 
enumaris
enumaris
crap, something wrong with my query :(
 
Emilio Pisanty
Emilio Pisanty
10:47 PM
that will be displaced from the negative cloud by some amount
... and you get the method!
 
Lozansky
Lozansky
So essentially a capacitor? :P
 
enumaris
enumaris
I think I know where the problem is...
 
Emilio Pisanty
Emilio Pisanty
@Lozansky the dielectric inside one.
 
danielunderwood
danielunderwood
@enumaris is it in the query?
I bet it's in the query
 
enumaris
enumaris
I think I neglected to account for one issue in my WHERE statement
not entirely sure how to best fix it, but adding an absolute value helps a lot
I think I got it
I have to do date_diff<= 6 and date_diff>0 rather than just the first one
 
danielunderwood
danielunderwood
10:55 PM
Are you comparing some dates with the older one first and some with the newer one first?
 
enumaris
enumaris
gotta put the dates in there in the same order
 
bolbteppa
bolbteppa
Cruz-O'Rourke and Hirzebruch why not
 
enumaris
enumaris
pretty sure I got the order right
 
Semiclassical
Semiclassical
I really do want to see them get walloped
 
Lozansky
Lozansky
@EmilioPisanty @Semiclassical OK, well I think I can follow the rest of the solution. Thanksss
 
Emilio Pisanty
Emilio Pisanty
10:59 PM
@enumaris do date_diff(date1, date2) <= 6 and date_diff(date2, date1) <0 just to confuse the hell out of whoever tries to mess with your code
 
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