The h Bar

12:06 AM

reddit.com/r/math/comments/9hl35w/… (Atiyah discussion)

'just plug it into the quadratic formula'

'There have been several occasions in the past hundred years when mathematicians have announced that they have proved the Riemann Hypothesis. But none can be stranger than the events that took place in New York in 1959 .... So when two-hundred and fifty or so mathematicians gathered to listen to Nash, there was an air of expectation in the lecture hall. Perhaps he really had done it? But as Nash got deeper and deeper into his 'proof', the audience of mathematicians became more and more aghast. It wasn't just wrong - it was nonsense.

Semiclassical

12:40 AM

Oof. Yeah, that’s the scenario I’m dreading @bolbteppa

bolbteppa

1:11 AM

Yeah

So it's happened with the RH of all theorems with huge names like Nash

Louis de Branges de Bourcia

Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis. Born to American parents who lived in Paris, de Branges moved to the U.S. in 1941 with his mother and sisters. His native language is French. He did his undergraduate...

Guy who proved Bieberbach claims to have done it also years ago

vzn

2:47 AM

@Avantgarde found it interesting how the novel pov on "meaning of life" correlates with some other major povs & the novels extraordinary popularity suggests it taps into something significant/ maybe near-universal. its interesting to study the question cross culturally and there are some commonalities. there is a lot of insight available in literature/ philosophy for anyone who has more than a casual/ idle interest. think it would help if you described your own motivation(s)...

user280247

3:13 AM

Is there any new interpretation of the wave function collapse which is generally accepted?

user280247

(after copenhagen)

user280247

Because this last one seems rather fictitious...

Avantgarde

@vzn Thanks for your reply. I agree that there are various avenues to gain insights from.

However, my initial question wasn't in serious vein .. :P

vzn

3:38 AM

Aug 26 at 22:15, by Avantgarde

@Blue hep-th/gr-qc

↑ meaning of life, (un?)seriously

Secret

3:57 AM

Last night dream a country passed a law which demands households to grow plants of certain height in their doorsteps or else be persecuted. The law also include cases where should you voice discontent of the law, or leave the country, you also violate the law and be persecuted later

vzn

@bolbteppa lunatic is a pre 20th century word for mental illness

Secret

The dream's situation is a "meta-non win situation" where even if you try to break the system, you lose

No-win situation

A no-win situation, also called a “lose-lose situation”, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of death by being hanged, shot, or poisoned, all choices lead to death; the condemned is in a no-win situation. This bleak situation gives the chooser no room: whichever choice is made the person making it will lose their life. Less drastic situations may also be considered no-win situations - if one has a choice for lunch between a ham sandwich and a roast beef sandwich, but is a vegetarian or has a wheat allergy...

The dream also have another no win scenario where there is some kind of expanding ball of heat which can penetrate rocks into the underground (and obviously roast and melt the surface of the earth also). I and some crew then tried to escape from it in a mining drill, but little did we knew that we will also be crushed and roasted by the underground heat, and there is no safe zone in between the two dooms

The lesson: Now that the dream have told me that these meta-no win scenario can exists, now to think about how to break them

Avnish Kabaj

4:13 AM

@Blue Who's that tho

Cows

6:06 AM

:)

Anonymous

7:15 AM

@AvnishKabaj A commentator on the $6000 Microsoft surface page on amazon.in

Anonymous

(more like commenter)

Leaky Nun

7:50 AM

hi @Blue

did you read my pic?

Anonymous

@LeakyNun I did see it, yes :) I have exams coming up so I couldn't go through the proof yet, though

Leaky Nun

sure

Anonymous

@LeakyNun Are you still into programming btw? Taking any algo classes?

Leaky Nun

quite, no

Anonymous

@LeakyNun Nice! What resources did you mainly use while learning?

Anonymous

7:56 AM

Recently I've been a bit interested in graph algorithms

Leaky Nun

i'm not the right person to ask

Anonymous

You do have an impressive code golf profile, but sure :P

Anonymous

1

A: Character Counting System

Retina, 30 28 bytes 2 bytes thanks to Martin Ender. +`((.).+)\2 $2$1 (.)\1* $.&¶ Try it online!

Anonymous

Phew, I haven't even heard the names of half the languages XD

Anonymous

Hmm, so Retina was specifically developed for code golf, I see

Anonymous

8:03 AM

(I don't have much idea about what CG involves other than writing minimal programs...so I might sound like a noob while making comments)

ACuriousMind

8:50 AM

@Blue That's because half of the languages have been designed for Codegolf :P

Anonymous

@ACuriousMind How can be people be..... that jobless :P

Anonymous

Kolmogorov complexity

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as descriptive complexity, Kolmogorov–Chaitin complexity, algorithmic complexity, algorithmic entropy, or program-size complexity. It is named after Andrey Kolmogorov, who first published on the subject in 1963.The notion of Kolmogorov...

Anonymous

This is something interesting tho ^

Anonymous

(Found just sometime ago)

ACuriousMind

@Blue Writing a small interpreted language isn't all that hard. If you have enough time to spare to answer dozens of code golf questions, you have enough time to spare to make that answering more efficient :P

Secret

9:16 AM

arxiv.org/abs/quant-ph/0405161

hmm... how do they derive this using only 0 and 1s of the conditional probability?

Secret

9:32 AM

Acuriousmind: Any ideas?

NormalsNotFar

9:51 AM

Hi all. I have been looking at a paper few papers by Witten et al. (see below for refs), and in both papers I have come across a process which I am unfamiliar with (and can't seem to find anything online about). The authors formulate gravity and conformal gravity in 2+1 dimensions via a gauge theoretic approach. To do this they require a non-degenerate bilinear form over the Lie algebra (I think it is closely related to the Killing form).

To construct the form, they first construct an invariant bilinear expression which is quadratic in the generators (I think this is closely related to the quadratic Casimir). But they do not explain how the arive at the form (aka the 'trace') via the invariant bilinear expression. Is anyone familiar with this process?

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.62.501
https://www.sciencedirect.com/science/article/pii/0550321388901435

ACuriousMind

@Secret I don't understand your question.

@NormalsNotFar Got a link that's not behind a paywall?

Secret

@ACuriousMind In that paper which describes how Born Rule is derived using the principle of envariance, the conditional probability highlighted above in the proof of the additivity of classical probabilities is said to be derived using only equations 28a, 28b, 29 and that for each $k \in \kappa$, the probability $p(k)=\frac{1}{|\kappa|}$ (call this X).

The author mentioned that they have proved additivity using only probability 0 and 1 events. Therefore I don't know how they recursively compute the highlighted conditional probability using only 28a, 28b, 29 and X?

The $1-\text{something}$ form seemed to suggest they are using 29 somehow, but I don't see what complementary event will give the required answer such that $\text{something}=\frac{1}{N-1}$

NormalsNotFar

@ACuriousMind I managed to find one for the second paper, unfortunately I can't find one for the first paper (which contains the less trivial application of this process).

It is on page 53-54 of
http://srv2.fis.puc.cl/~mbanados/Cursos/TopicosRelatividadAvanzada/Witten2.pdf

ACuriousMind

@Secret The complementary probability the l.h.s. of the highlighted equation is just $p(k_{N-1}\vert k_1\vee \dots \vee k_{N-1}) = \frac1{N-1}$.

Secret

10:07 AM

I see. That does not match the forms given by 28a and 28b though, (as it has the format $p(A|B)$ but $B \not\subset A$). Let me think how they build this thing up recursively using only 28a,28b,29 and X. I will check with you again shortly if I got stuck

ACuriousMind

@NormalsNotFar Alright. What exactly is your question about what Witten is doing on these two pages?

@Secret They're not using (28) for that line. You've misread the text.

NormalsNotFar

Witten states that from the invariant bilinear expression $W=\epsilon_{abc}P^{a}J^{bc}=2P_aJ^a$, there corresponds the bilinear form $\langle J_a, J_b\rangle=\langle P_a,P_b\rangle=0$ and $\langle J_a, P_b\rangle=\eta_{ab}$. I don't know how to connect the dots.

I can see how it follows if I write $2W=\langle J_a,J_b\rangle J^aJ^b+\langle P_a,J_b\rangle P^aJ^b+\langle P_a,P_b\rangle P^aP^b$. But I don't see why I should write it like that in the first place.

ACuriousMind

@NormalsNotFar The $W$ is supposed to be a bilinear form, i.e. a matrix, acting on the vector space spanned by the $P$ and $J$. When you write it like that you're just determining its matrix elements.

Secret

@ACuriousMind Ok now I am confused. Since throughout the text there is no derivation of conditional probabilities from consideration of the swapping operations of entangled states (only the derivation of Born rule and the principle of equiprobability), do the authors actually used the rules of conditional probability (in particular the formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$) as an already given rule?

ACuriousMind

10:23 AM

@Secret How am I supposed to know that? You read the text, you have to know what this text's definition of condition probability is.

Secret

That proof is the only line where conditional probabilities started to appear

hmm...

Well er... when I read your line "They're not using (28) for that line. You've misread the text.", I might have misread that as it gives me an impression you are familiar with the text

Hmm So... that means, they have derived some main rules of probabilities using only entangled states and envariance, but not all the main rules

ACuriousMind

@Secret No. But in the screenshot, they said they'd be using (28) and (29) in the proof that follows. There simply was no explicitly claim at all that the equation you highlighted was specifically derived using (28).

Secret

But using 29 we get $p(\{k_{N-1}\vert k_1\vee \dots \vee k_{N-2}\}|\{k_{N-1}\vert k_1\vee \dots \vee k_{N-1}\}) = 1-p(k_{N-1}\vert k_1\vee \dots \vee k_{N-1})$, but then there are no other equations nor the property X that will allow us to evaluate $p(k_{N-1}\vert k_1\vee \dots \vee k_{N-1})$ into $\frac{1}{N-1}$ unless they implicitly used $P(A|B)=\frac{P(A\cap B)}{P(B)}$

So if Equations 28,29 and property X is all that is given, the proof will get stuck at the highlighted step unless they actually allow using things beyond these given equations

user351417

Can somebody with 10k privileges check if these 2 questions are identical?

user351417

physics.stackexchange.com/questions/430189/…

user351417

10:35 AM

-2

Q: Finding tension in web of strings supporting hanging masses

Need help figuring this problem out: I have tried working this problem out. I have solved the forces that are acting on m1 → TA - W1 = 0 → TA = W1 on the other hand, I am trying to figure out what are the forces that are acting on m2 ,i have tried to find the two components "x" and "y". ca...

user351417

The first was deleted by the author

ACuriousMind

@Chair Not fully identical, but the picture is the same

user351417

Ah okee. Never mind then.

user351417

I thought I had seen that picture earlier; good thing I decided to check here instead of leaving a comment telling the OP not to ask the same thing twice.

Secret

...actually looking at the proof again, I think they did implicitly assumed $P(A|B)=\frac{P(A\cap B)}{P(B)}$ as with the given equations and properties throughout the text so far, they are unable to have a product of probabilities derived, as shown in the next step in the next page

ACuriousMind

10:40 AM

@Chair Next time you can also raise a mod flag if you see something suspicious like that.

user351417

@ACuriousMind Cool.

user351417

Just out of curiosity, what happened on the first one? Was it by the same person and was it closed as homework or something?

ACuriousMind

@Chair Not the same user, also closed as HW

Do note that I'm not allowed to disclose whether there's evidence that the accounts are socks, so please do not speculate about that

NormalsNotFar

@ACuriousMind Ah that makes sense. So I should be writing $W=\langle J_a,J_b\rangle J^aJ^b+2\langle P_a,J_b\rangle P^aJ^b+\langle P_a,P_b\rangle P^aP^b$ not $2W=\langle J_a,J_b\rangle J^aJ^b+\langle P_a,J_b\rangle P^aJ^b+\langle P_a,P_b\rangle P^aP^b$, right? (since the form is symmetric).

ACuriousMind

@NormalsNotFar Exactly :)

user351417

10:48 AM

@ACuriousMind Nah, there's an appreciable chance that somebody else saw that old question and decided that they had a doubt about the scenario too. That possibility fits well enough with the fact that the two questions are different.

NormalsNotFar

@ACuriousMind Thank you, have a nice day!

Secret

11:56 AM

ok so they really do use conditional probabilities as a given, and have not derived them like other probability rules

so if one is pedantic enough, they have not fully closed the circularity definition of probability (since additivity is needed to arrive the formula for conditional probability, and yet they use conditional probability to derive additivity)

But otherwise, everything flows in the paper (modulo any future results that debunk them)

Secret

12:35 PM

I still think Zurek does not really solve the measurement problem though (But I may be wrong, cause while I managed to finish reading the whole paper, I might not have sufficient enough quantum knowledge to ensure my deduction to be sufficiently correct):

In particular:

It does not really explain why the observer must get shunted into one of the branches after measurement with an observable which does not contain the state as its eigenfunction, although it managed to clarify fundamentally on why the procedure is probabilistic (because of the swap symmetries of the global wavefunction, thus the more states that are envariant, the more likely the state after measurement will end up there analogous to statistically sampling)

Experimentally it is also a challenge as how can you tell the rest of the universe to swap a given pair of states to restore the original state as the universe is much more likely to do a unitary transformation to the environment states in ways that are definitely not swaps

Checking Zurek's model with the 2018 paper of the extended Wigner experiment, since his is basically a no collapse model, it means only singular outcome of measurement (assumption S in the paper) is violated, thus most non collapse models are pretty safe

bolbteppa

1:16 PM

Yikes reddit.com/r/math/comments/9hl35w/… (Atiyah stuff)

Anonymous

@bolbteppa Ouch

bolbteppa

pbs.twimg.com/media/DnoKZ1RVsAAUdin.jpg (click :\ )

Captain Bohemian

1:37 PM

@bolbteppa are the Virasoro algebra and W algebra examples of the exceptional Lie algebra?

bolbteppa

@CaptainBohemian the Virasoro algebra is infinite-dimensional, the 5 exceptional Lie algebras are finite dimensional

Novalium Company

2:13 PM

Hehmgm, just doing some math problems and I was wondering (Warning! Stupid question ahead) if $x_1^2 + x_2^2 = (x_1 + x_2)^2$ is correct? I'm pretty sure it's not the same, because $3^2 + 5^2$ for example is not equal to $(3 + 5)^2 = 8^2$. I just wanna know if my understanding is correct?

Anonymous

@NovaliumCompany They're not equal :)

Novalium Company

Yey! :D

Anonymous

Also put an underscore in there x_1

Anonymous

$x_1$

Novalium Company

Yep, ahh... mathjax :D

Anonymous

2:16 PM

Why (a+b)2=a2+2ab+b2 ???? | Interesting Video | Mathemagic - Bawa Talks |

►

Novalium Company

@Blue Can I ask something?

I saw this pattern in math for example $\frac{1}{x_1} + \frac{1}{x_2}$ can be made into something like $\frac{x_1*x_2}{x_1 + x_2}$ or $\frac{x_1 + x_2}{x_1*x_2}$, I'm not sure. I see the same thing in the equation for 2 parallel resistors.

Anonymous

Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: 1 2 {\displaystyle {\tfrac {1}{2}}} and 17/3) consists of an integer numerator displayed above a line (or before a slash), and a non-zero integer denominator...

Secret

snipped

Novalium Company

@Blue Oh god, just now I recognize the pattern lol. I expected something complicated.

@Blue Thanks!!!

Anonymous

2:31 PM

Didn't you take an algebra class yet?

Anonymous

@NovaliumCompany No problem

Novalium Company

2:43 PM

@Blue Education in Bulgaria is messed up... teachers just show how to solve a problem, but doesn't explain anything else. I mean, the teachers usually tell you that for example $x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2x_1x_2$ but don't tell you how to get there. (Although in the example I gave it's obvious)

I mean, they assume all of the students have perfect pattern recognition skills.

Anonymous

@NovaliumCompany I see, and what about the textbooks? I think you should use the Schaum series books are references, as they usually are very comprehensive and contain all derivations

Novalium Company

Teachers tell you what textbook to buy...

Leaky Nun

I mean, that's a problem with high school math education in general

Novalium Company

Just 3 years and I'm free from the jail they keep me in xD

Anonymous

@NovaliumCompany You can get almost any book from libgen :P Use them as references apart from your primary school textbook

Novalium Company

2:47 PM

@Blue Yep, googling helps?

BEFORE YOU GO TO SCHOOL, WATCH THIS || WHAT IS SCHOOL FOR?

►

Anonymous

It does. Wikipedia is a great resource

Anonymous

But it takes a bit of maturity (mathematical)

Leaky Nun

@NovaliumCompany or ask us

Anonymous

True ^

Leaky Nun

35 mins ago, by Novalium Company

Hehmgm, just doing some math problems and I was wondering (Warning! Stupid question ahead) if $x_1^2 + x_2^2 = (x_1 + x_2)^2$ is correct? I'm pretty sure it's not the same, because $3^2 + 5^2$ for example is not equal to $(3 + 5)^2 = 8^2$. I just wanna know if my understanding is correct?

332

Q: Pedagogy: How to cure students of the "law of universal linearity"?

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: $$ \frac{1}{a+b} \mathrel{\text{“=”}} \frac{1}{a} + \frac{1}{b} $$ $$ 2^{-3} \mathrel{\text{“=”}} -2^3 $$ $$ \sin (5x + 3y...

algebra-precalculus education

@NovaliumCompany that's a common problem with math students

falsely assuming linearity even when it doesn't hold

Secret

2:53 PM

(missing comment from my long wall post a few hours ago): Zurek's derivation reminds of the derivation of the chemical potential in my 2nd year chemistry textbook, where it first equibrate between two gas systems, and then equibrate that with a mixsure of gas before finally the gas with a liquid.

Similarly, Zurek's derivation starts with equiprobability, and then working towards unequal probabilities, and then finally go from finite to discrete to rational and finally the continuum

So both proving approach have the commonality of first putting some known quantity with some target quantity, equalise it and use that symmetry to derive the unknown quantity, and then rinse and repeat

I wonder how many different kinds of deductive procedures can reach a new thing from some old things, similar to how supremum of a sequence does not necessary be an element of the sequence

Danu

3:13 PM

@ACuriousMind you gotta go to Atiyah's talk

Leaky Nun

is he invited?

bolbteppa

It'll be on youtube as well at least

ACuriousMind

@Danu I don't think the talk is open to people not participating in the Laureate Forum.

Danu

Aww

Yeah, there'll be a live stream

And now that I think about it, I think it's not really a "fun" occasion anyways

I makes me a little sad

ACuriousMind

Yeah, not sure I'd need to see it live even if I could

Danu

3:21 PM

:(

Still, I think I'll stream it

Leaky Nun

I don't really get the point of streaming it

2 days ago, by Blue

I'm voting to close this question as off-topic. It should be clear to everyone that Atiyah does not actually have a proof of RH. — Dan Petersen 7 hours ago

Secret

[Random]

Sep 23 The quantum inconsistency paper is tearing physicists apart

bolbteppa

I wont be able to understand it

No point in streaming except to watch for like signs he's waving his hands

haha

Secret

Sep 24 Atiyah RH is tearing the mathematicians apart

Anonymous

@LeakyNun I guess most people's (at least those care about it) feeling at the moment about it is similar to a student's on the evening before exam results are announced :P

Secret

3:33 PM

Sep 25? (will something tear chemistry and biology apart)?

bolbteppa

Where the exam question was 'solve the Riemann Hypothesis'

Secret

Also Sep 28 Hurricane Trami will arrive in Hong Kong (this may be more relevant to Leaky)

and what about Sep 26?, Sep 27?

---> wtf September???

Leaky Nun

@Secret what?

Secret

@LeakyNun hko.gov.hk/wxinfo/currwx/tc_gis_e.htm

Leaky Nun

well that's not very close to hong kong

compared to mangkhut

Secret

3:40 PM

Best to be prepared given the devastation that Mangkhut does

Hurricanes this year are much stronger on average than last year's

Leaky Nun

this trami is much weaker than mangkhut

Secret

I see
(unrelated)

arxiv.org/abs/1301.7696

This is more circular than Zurek's because of the additivity assumption of projectors and some of the density matrix language is used in the derivation

But I am soooo glad that the 4 papers that have been stuck open in my phone since the beginning of this year, are now finally read fully and thus can be closed away

Hopefully I can read much faster when I need to continue to read my chemistry papers...

Pandya

4:25 PM

Hi, can anyone help me with:

Very nice explanation. Btw, I have one query : according to the definition of force, force is rate of change of momentum i.e F = mass flow rate × velocity. Here mass flow rate is constant (conservation of mass) and velocity is increasing, so force should increase! — Pandya 2 mins ago

Pandya

4:38 PM

@ACuriousMind Namaskar!

ACuriousMind

@Pandya hey there

vzn

4:54 PM

@bolbteppa reddit.com/r/math/comments/9hl35w/…

@LeakyNun lol you dont get the point? do you work in math? why dont you go look up Atiyahs biography? or maybe you dont think math lectures should be in internet videos? en.wikipedia.org/wiki/Michael_Atiyah

Leaky Nun

@vzn my comment was followed by a quote. the quote is my reason.

vzn

@LeakyNun "it should be clear" Petersen is jumping to conclusions and doesnt have the ability to infallibly predict the future...

Leaky Nun

maybe the 54 people who upvoted that comment also jumped to conclusions

vzn

@LeakyNun lol (dis)proof by voting? (am amazed you have so much SE rep with these crude sentiments)

Leaky Nun

well maybe you should look up the incident regarding his complex structure paper

vzn

5:05 PM

@LeakyNun maybe you should post a citation

Leaky Nun

maybe you should post a citation of an expert saying that his paper on the complex structure is correct

Atiyah was a great mathematician. people wouldn't want to criticize him publicly.

vzn

@LeakyNun you seem to misunderstand some major part of the process of mathematics.

@LeakyNun an error in the paper nor his age do not invalidate his mathematical abilities. and what exactly is the error anyway? very advanced papers can only be understood by a few. what are they saying? did they write any of it down anywhere?

Ageism

Ageism (also spelled "agism") is stereotyping of and discrimination against individuals or groups on the basis of their age. This may be casual or systematic. The term was coined in 1969 by Robert Neil Butler to describe discrimination against seniors, and patterned on sexism and racism. Butler defined "ageism" as a combination of three connected elements. Among them were prejudicial attitudes towards older people, old age, and the aging process; discriminatory practices against older people; and institutional practices and policies that perpetuate stereotypes about elderly people.While the term...

vzn

5:20 PM

ok, concede his recent record does not inspire confidence, but theres a big difference between a faulty proof with an error vs a gap. the latter is sometimes fixable and has happened in other premiere cases eg Wiles/ FLT and arguably Perelman + others... was his last paper gobbledygook/ incoherent or is it full of solid math with some subpart that is questionable? etc btw have seen major gobbledygook paper(s) by younger phd theoreticians/ mathematicians, spent many weeks dissecting 1...

bolbteppa

@vzn Conway example is interesting in this regard

vzn

@bolbteppa ?

bolbteppa

Can't find where I read it, but someone compared it to Conway presenting his big proof in the 80's, was considered iffy and I think it said he'd presented wrong things around the time

vzn

5:37 PM

@bolbteppa now that you mention it maybe heard some eccentric story about him but cant remember what it was now. wikipedia says almost nothing about his personal life, almost wonder if its been sanitized en.wikipedia.org/wiki/John_Horton_Conway

ah yes. maybe forgot about this: bout with depression + suicide attempt. forgot about that. theres also another section about a "fallow period". but that reminds me of feymann who confessed to the same thing. theguardian.com/science/2015/jul/23/…

bolbteppa

It's from a comment on Motl's post

Leaky Nun

6:06 PM

@vzn sorry the building I live on has a fire incident

I’m on the highest floor now so I’m here

my sentiment is mainly based on my professor’s sentiment

whom I won’t really name

but I guess I'll consider it more

well we'll know in 12 hours anyways

Avnish Kabaj

7:13 PM

Um uh best of luck with the fire

Leaky Nun

7:41 PM

@AvnishKabaj it's ok now, thanks

vzn

@LeakyNun feel free to name your professor. the talk may be a waste of time. but watching it is a personal decision and think its not necessary/ in entirely good taste to try to persuade others. maybe a warning or caution label/ meme posted somewhere on the internet? agreed the whole scenario is nearly pulling rabbit out of hat™ do some miracles really come true™ etc

Physics Meta

0

Q: How to fix incorrect math in old accepted answers?

A couple of weeks ago this question was posted, and the question contained a simple typo in the equations for coordinate rotation. The first answer spent two lines politely correcting this. Then, as it happened, I noticed that the same typo was present in the accepted answer to this linked relate...

discussion editing suggested-edits

vzn

7:59 PM

vzn

8:56 PM

40

Q: Atiyah's May 2018 paper on the 6-sphere

A couple years ago Atiyah published a claimed proof that $S^6$ has no complex structure. I've heard murmurs and rumors that there are problems with the argument, but just a couple months ago he apparently published a follow-up which fleshes out the details. He writes: In [1] I gave a proof ...

dg.differential-geometry

bolbteppa

@vzn interesting, 'Atiyah notes that his original proof "failed to convince the many experts in the field," and adds, "Indeed there were many sound reasons to be sceptical." He notes two of these "sound reasons," and continues, "Having listened carefully to all these objections I have found a new and even shorter proof...."'

Semiclassical

the fact that the abstract claims the proof to be simple is worrying tbh

vzn

(reddit) rumors are atiyah is becoming more enamored with Physics. good or bad thing? (with friends like these who needs enemies?™) reddit.com/r/math/comments/9hl35w/… need to look more into von neumann entropy possibly used in proof! wonder how it shows up in physics + cs (+ math?)... got reddit downvotes on my comment mentioning entropy links across Computer Science + Physics + Mathematics :( need to blog on this soon...!

Semiclassical

9:11 PM

that he'd have a proof of the Riemann hypothesis is unexpected enough; that it's moreover a surprisingly simple proof, strains credibility

vzn

@Semiclassical it seems implausible but there are sometimes short proofs of very difficult problems that show up decades into research... rjlipton.wordpress.com/2018/09/21/the-specter-of-simpler-proofs

Semiclassical

eh. what jumps out to me is the title of that post: not "simple proofs" but "simpler proofs", i.e. proofs which are simpler by comparison with the original argument

bolbteppa

The most likely person to find a proof, especially a simple proof, is someone on that level in fairness

vzn

simpler proof: a semifamous example is Erdos proof of prime existence between n and 2n.

Semiclassical

@bolbteppa yeah, true

I mean, we'll find out tomorrow. (or, more precisely, the experts will have a chance to find out tomorrow; I'm dubious I'll be able to assess it fairly myself.)

vzn

9:15 PM

there will be some fast verdict(s) in cyberspace. social networks. twitter. blogs. even media... there will be some occurence of a world famous proof in the "social media" era, its just a question of when. perelman missed it by a short timeframe.

Semiclassical

well, yes.

but to the extent that those fast verdicts are trustworthy, it'll be because they either cite an expert or are experts themselves

vzn

the fast verdicts are part of the picture but not to be entirely relied on esp with very technical problems, again cf perelman/ wiles vs FLT etc

bolbteppa

'In the last chapter of the book "Paul Dirac: the man and his work" (1998, Cambridge University Press) authored by Michael Atiyah, we can find some of the main ideas coming from previous work that are most likely to appear in Atiyah's proof, regarding Dirac's operator and the work by Hirzebruch on a specific case of the Riemann-Roch theorem. How does von Neumann enter in this discussion... we will see it tomorrow.' (from the Motl comments section)

vzn

> Last year, however, he gave a talk at Cambridge presenting a proof of this geometrical inequality. I wasn’t at the talk, but apparently it involved expressing the logarithm of |δ| (possibly negated) as the von Neumann entropy of some system, and proving the strongest version of the conjecture as a corollary of entropy being non-decreasing. cp4space.wordpress.com/2018/09/21/atiyahs-problem

Semiclassical

what comes to mind is a scott aaronson blog post: scottaaronson.com/blog/?p=304

points 3,4, and 10 being what I'd have my eye out for

(and 7, to an extent---Atiyah's does reference Dirac/von Neumann/Hirzebruch, but these aren't recent sources)

I sorta wish Terry Tao had a blog post up about it, but I imagine he's refraining from such until Atiyah can actually make his case

bolbteppa

9:28 PM

5 could also be the big issue if using physics concepts

Yeah

I can't think of who else to check :p

vzn

@Semiclassical an old classic. aimed at papers. unmentioned, the simplest/ not bad crank detection system is usually looking at authors academic background and whether it is undergraduate or less. which yields a "(false?) negative" in this case. there is an entirely different "criteria" for established luminaries...

@Semiclassical "simple" engages rule 10 but note that the work already cited by Atiyah is not really "simple". maybe he means the argument is "brief" but that is not exactly the same as "simple". what is "simple" to a highly experienced mathematician can be very "remote/ formidable" to those with less experience. and yes, there are some "brief" proof formulations of some very complex problems...

Semiclassical

simple is contextual, yeah, which is one reason why I'd defer to experts on it

I look to 3,4 mostly because they don't rely on understanding where the argument fails so much as understanding what the argument would entail

If the argument would give you a conclusion which is known to be false, for instance, then the argument must be wrong no matter how persuasive it may seem

bolbteppa

Based on the recent issues, I'd say the most likely thing is he wont convince people but it will be debatable on both sides and the feeling will be he didn't do it :(

But you could rarely ask for a better situation of a gigantic name going after a gigantic theorem so for the record I am hopeful

vzn

11:25 PM

> By the way, in Rio I had a discussion with two of the fields medalists that I know well, and they told me he tried to discuss the Riemann hypothesis with them but nothing he was saying made any sens. reddit.com/r/math/comments/9hl35w/…

bolbteppa

That's the most significant comment of them all I think (insofar as you can trust random comments) :\

vzn

"coincidentally" it is a fields medalist trying to untangle Mochizukis proof also & saying he has come up emptyhanded after herculean effort (Scholze) :o quantamagazine.org/…

Secret

Sep 23: Physics got turned upside down
Sep 24: Mathematics got turned upside down
Sep 25: ?

It is still 1.5 years away from 2020 where everything will converge at the US election, but already reality is cracking here and there in 2018

Seems The Plan is working well, working a bit too well

But again, perhaps it is good that it works. She has no intention and is NOT going to resolve that feud in the past decade anyway, and thus the whole philosophical existence itself have to go down instead

What a good time to see politics effectively swamped academia

Secret

11:49 PM

(sarcasm)

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