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12:03 AM
Like this problem
Is hard no matter what you guys say:P
Here's the solution in case anyone's interested:
 
I remember there being a problem in Griffiths that messed up most of our class. I think it was about overlapping spheres or something?
 
2 hours ago, by Lozansky
user image
perhaps?
the solution uses overlapping cylinders
 
@danielunderwood There is one with overlapping spheres where you calculate the field in the overlapping region
iirc
 
@Lozansky those are reasonably ugly, yes
infinitesimally-small separation between regions held at different potentials is tricky territory
all sorts of unphysicality dragons there
 
This is the one I was thinking of
But it's pretty trivial if you use the hint so I doubt it's the one @danielunderwood is thinking of :P
 
12:13 AM
@Lozansky for some reason, that makes me think of the French group theorist Jacques T.
... which is probably a very strong sign that I should really go to bed now.
 
oO
Getting late here as well
I'm off
Thanks for all the help guys
 
 
2 hours later…
1:49 AM
@DanielSank heads-up - see the link in this question.
 
 
1 hour later…
2:58 AM
@EmilioPisanty Heh, the guy who answered that is interning with us :-D
 
3:19 AM
@DanielSank </3
 
4:19 AM
@Blue Yes, I am from WB :-)
@Blue No, I think no Institute offers QI in Undergrad level in India, I am doing MOOC by Peter Shor and the Caltech, Q Tech course on Quantum Crypto
@Blue Can I know from which institute you are?
I will like to work on QI later, I heard HRI is a good place for QI in India.
 
5:01 AM
isn't the center of a group G the normal subgroup of G?
 
5:12 AM
ncatlab.org/nlab/show/classical+Lie+group It turns out the knowledge I have learnt about Lie group is merely about classical Lie groups. There are still exceptional Lie groups! What on earth are they?
I think I have had some rudimental touch with some of exceptional Lie groups, but I still know too little of them to get a profile of them.
@bolbteppa are exceptional Lie groups closely related to supersymmetry?
 
5:36 AM
John Baez's page here is suggestive: math.ucr.edu/home/baez/octonions/node13.html
 
@JohnRennie you around?
 
@DavidZ morning :-)
 
To wit: you get the three classical families by constructing algebras based on the reals numbers, the complex numbers, and the quaternions.
The next thing to try would be to pass from the quaternions to the octonions. but those guys are weird
 
@JohnRennie Hi :-) I had some questions about some homework answers you pointed out recently, could we discuss that either here or in another room? (your choice)
 
Here is fine. I'm guessing you think I'm being over zealous in criticising people for answering homework questions?
 
5:39 AM
(octonions aren't even associative, ay yi yi). so it's maybe not surprising that it's harder to create Lie algebras based on them, and that what you get will be 'exceptional'
 
@JohnRennie Nah, it's not about that. It's more like a couple of the ones you pointed out didn't really seem like "complete answers" in the sense I understand it. I can post a link or two in a minute
 
c.f. this sentence from his page on F4: "In 1951, Freudenthal embarked upon a long series of papers in which he described not only $F_4$ but also the other exceptional Lie groups using octonionic projective geometry."
 
I wanted to check with you so we wind up on the same page about this
 
which...oooookay
 
@DavidZ my view is that if you give a helpful answer a homework question then you encourage the asking of homework questions. So it doesn't matter if your answer is complete or not.
The point is that I don't want people to ask HW questions here. It isn't that I don't want them answered, I don't want them asked in the first place.
 
5:42 AM
@CaptainBohemian oh, forgot to ping you on the above
 
And note that there is a particular user who seems to make a habit of answering such questions.
 
@JohnRennie Well, sure, I actually agree that giving a helpful answer to a homework question encourages the asking of homework questions. And I also believe that we don't need to encourage that. But it does matter in the sense that our homework policy makes a distinction between how we mods are supposed to handle complete answers vs other answers.
 
sup dawgs
anyone know why there's so little data-driven fluid dynamics research?
 
@DavidZ In my ideal world all answers to homework problems would be deleted, but I appreciate that's a minority view. But I wanted to bring the asnwers to the mods' attention, and in particular the user who is making a habit of answering them.
 
I'm looking but can't find much
 
5:49 AM
@JohnRennie OK. Well, the way I would suggest bringing that particular issue to our attention is by casting a custom moderator flag and briefly explaining what you've observed.
Though in this case, no need to cast the flag now that you've told me. We'll look into it.
 
Noted, thanks.
 
:(
I'm leaving bye
 
The answers themselves, taken individually, don't all seem to be worthy of moderator action. In general, any time there's a pattern of behavior that looks suspicious or troublesome but the individual instances of it are not flag-worthy on their own, then a custom mod flag is the way to go.
@JohnRennie and thanks for noticing.
On a somewhat separate note: if you don't want people to answer homework questions (in order to minimize the incentive for others to ask them), I think it would be a legitimate response to downvote those answers.
Though I don't always do that myself in recognition of the fact that a non-negligible portion of our community does like having homework-based questions on the site.
 
6:12 AM
@DavidZ OK. Sorry I guess I was bugging the mods unnecessarily with all the flags. I'm obviously grumpy this morning :-)
 
Eh, don't worry about it, when in doubt I'd still rather have you flag things to get eyes on it.
And a fair number of those flags were perfectly good ones anyway.
 
Hi @DavidZ please look at this answer again physics.stackexchange.com/questions/430051/…, it is not a complete answer, the OP has already posted the correct solution and was asking for the error in his own solution. Thanks.
 
Hm OK let me recheck it
 
@user7777777 since you're here, I wish you would stop encouraging homework questions by answering them.
 
@user7777777 So, I think the key thing there is that the question asks, in part, "What average force does the juggler exert on one ball while he is touching it?" and your answer includes $F_J = 5F_g$, which apparently answers that part of the question.
 
Anonymous
6:27 AM
@taritgoswami JU, 2nd year (electronics)
 
@JohnRennie I do only answer homework questions if they ask about a concept and show the OP's original effort.
I do not answer questions that are just blatantly pasted onto a post
 
Anonymous
@taritgoswami HRI takes very few people for their summer program. You could try though. There's a very nice QC group at IISERK under Panigrahi btw.
 
@DavidZ Alright I see. So is there anything I can do about it (such as editing that part out)?
 
@BernardoMeurer Why?
 
Anonymous
@taritgoswami And which institute are you from?
 
6:30 AM
@user7777777 it's obviously a judgement call about where the boundary is, but I feel you're being a bit generous.
 
@user7777777 well, since it's still easily accessible in the revision history, we've taken an approach of not undeleting these answers just because they get edited. So... if you're really attached to this answer, we can try to work something out, but I'd suggest just letting this one go.
 
@DavidZ Alright, it's fine. Thanks for your time.
 
No problem!
In the future, if you do find yourself answering a homework question, I'd say take a close look to see what the original problem is asking, and double-check the answer you post to make sure it doesn't give that away.
(For what it's worth, I kind of agree with John, but that's just my personal opinion as a contributor. There isn't a site rule that forbids answering homework questions or anything like that.)
 
Thanks
@JohnRennie I'll take note
 
Anonymous
@taritgoswami And as for actual "quantum information theory" and "foundations of QM" there are not many people in India who are involved in it right now. The only guy I know of and who works significantly on foundations is Subir Ghosh from ISI, but he isn't really a pleasant guy to talk to (as far as my own experience goes). :P If you really want to work in QI, you're better off going abroad.
 
Anonymous
6:55 AM
Oops, I actually meant Guruprasad Kar ^. Subir Ghosh is the GR math guy used to stay in the same locality as me. (I'm terrible at remembering names!)
 
@Blue Where you have learnt QI then? I think you have 2nd highest score in quantumcomputing.SE O_o
@Blue Is it online? or, in their campus?
 
Anonymous
@taritgoswami I had to dig up some books and papers for my summer project at IISER. Vazirani's lectures are a good start followed by Nielsen and Chuang (that's the gold standard)
 
@Blue I have appeared for ISI this year, just for 3 marks they I haven't qualified, now in Christian College
 
Anonymous
@taritgoswami Eeeeh...3 marks :/
 
@Blue Yeah, :-(
 
Anonymous
7:07 AM
Which department btw?
 
Physics
Yeah
 
Anonymous
Nice :)
 
@Blue I am following Nilsen and Chuang, can u share ur personal contact ? so that I can contact u?
 
Anonymous
@taritgoswami I was talking about their summer interns program. HRI, RRI, ISI and IISER all accept QC summer students. But you have better chances of getting in if you talk to the professors directly. Of course, they're offline!
 
@Blue Yeah I also think so, but this winter I got selected for BARC research intern under Dr. Zafar Ahmed
 
Anonymous
7:10 AM
The nuclear physics guy?
 
@Blue Yeah, but,I will work on Mathematical Physics
 
Anonymous
Awesome :)
 
Anonymous
BARC is a great place indeed
 
Thanks :-)
Yeah
How you know him?
 
Anonymous
@taritgoswami blue.stackexchange98@gmail.com
 
Anonymous
7:14 AM
@taritgoswami Had browsed through the BARC pages last year and contacted a few people there. That time I was more into physics :P
 
@Blue Ooh, I will contact you
 
@Blue you created a gmail account just to handle the SE mail. That's a good idea! I'll put that on my list of things to think about doing.
 
Anonymous
@JohnRennie Yeah, I had a few people on QSE who wanted to talk to me privately but I didn't want to give out my real email (at least not immediately). It's quite helpful, yes :)
 
Anonymous
@taritgoswami Sure, no worries
 
@Blue yes indeed. These days I guard my main e-mail account!
 
 
3 hours later…
10:21 AM
"It swiftly becomes apparent that Quantum Mechanics and Relativity are merely mind games that have zero basis in actual reality. They are repackaged Kabbalistic Occult ideas being hammered together with spurious and incomprehensibly obtuse and speculative mathematics."
He's onto us
 
 
1 hour later…
11:31 AM
What is temperature?
 
11:50 AM
the inverse of the derivative of entropy w.r.t. internal energy
 
what is entropy?
 
i think i might be close to reach a record. in my last 14 answers, only 1 recieved votes
@LeakyNun I suggest getting a copy of Callen's book
 
what is the book?
 
it's a function that contains all the info of the considered system, which is assumed to exist when the system is at equilibrium. it must satisfy certain properties
 
12:10 PM
What is the meaning of life?
 
@CaptainBohemian I don't think they are closely related to susy, they come up in string theory
 
learning as much physics as one can before dying
 
Anonymous
@coniferous_smellerULPBG-W8ZgjR sedlyf
 
@coniferous_smellerULPBG-W8ZgjR which chapter / page?
 
12:27 PM
@bolbteppa Haha what is that
 
@coniferous_smellerULPBG-W8ZgjR you said that temperature is "the inverse of the derivative of entropy w.r.t. internal energy". no doubt that's how temperature is defined. but is that the best way to understand what temperature is?
 
You can think of temperature as a measure of the kinetic energy of the constituents. Higher the temperature, more vigorous is the jiggling of molecules.
 
Congress doing it's job :p
 
12:44 PM
I don't care about "the best way to understand what temperature is" because the answer is subjective, while the def of it, in principles, should be objective
i dont remember the page number. but it's at the beginning of the book
callen starts with defs a bit as axioms and then builds thermodynamics up
from ground zero up to the sky
 
Which theory should I know to understand caters reversible pendulum? I just wanna get some suggestion to learn where or in which chapter I should be able to understand it's mechanism in details?
 
@coniferous_smellerULPBG-W8ZgjR I'm trying to learn
instead of trying to be objective
 
Anonymous
The definition in terms of entropy is the most general one. And yes, that is indeed the best way to understand it.
 
Anonymous
There are already many PSE threads about that
 
@LeakyNun You need to understand why that definition is the definition of something useful: It is because it means that inverse temperature is the Lagrange multiplier for maximizing entropy at fixed energy, cf. e.g. physics.stackexchange.com/a/231065/50583
 
12:58 PM
Which theory should I know to understand caters reversible pendulum? I just wanna get some suggestion to learn where or in which chapter I should be able to understand it's mechanism in details? Can someone help me ?
 
> This merely shows the complicated man behind the heroic stereotype—one with sufficient diplomatic skill to soften his words without diluting his science.
 
@EmilioPisanty Is that a misspelling of "in plain sight" as "in plain site" there in the URL? :P
 
Kinda reminds me of an erstwhile contributor on this site who occasionally struggled with that area
@ACuriousMind looks like. Good catch.
I hope I'm still around on 2092
See the fireworks light up again
 
@ACuriousMind that brings me to asking, what does the lagrange multiplier actually mean?
 
@LeakyNun It gives the rate of change of the quantity being extremized when the constraint changes (that's why it is the derivative of entropy w.r.t. energy in this case), i.e. it tells you how much entropy the system gains or loses when you change its internal energy
 
1:13 PM
oh!
I mean, I haven't done much calculus and I don't really understand the meaning of the multiplier
but you just answered that
but I don't really understand how it gives us the minimum
can't you always change lambda to make the quantity smaller if you're away from the constraint?
 
I'm not sure what you mean by that
 
let's say you want to minimize $f(x)$ subject to the constraint $h(x) = b$
how is that equivalent to minimizing $L(x,\lambda) = f(x) - \lambda (h(x) - b)$?
 
Ah. The minimization of $L(x,\lambda)$ w.r.t. $\lambda$ just gives you $\partial L/\partial \lambda = h(x) - b = 0$, so when you minimize $L(x,\lambda)$, all its minima/extrema have $h(x) = b$ automatically.
 
Hey folks
do you remember what SE post was like
An example of bad regression
where it was regression to order N of the US population
which was all good, but then at order 4, the US population collapses in 20 years
 
I'm guessing that wasn't a physics.SE post?
 
Anonymous
1:22 PM
@LeakyNun It's a bit easier to understand in terms of gradients (direction of steepest ascent) I think
 
Anonymous
Basically you need to keep moving on the constraint curve
 
Anonymous
Until you reach an extremum for $f$
 
@ACuriousMind maybe I'm being thick. If you fix $x$, then you get something like $L(\lambda) = A - \lambda B$. If $B \ne 0$ then $L$ is unbounded below right
how can it then have a minimum?
 
@ACuriousMind No
Not sure where
Maybe crossvalidated or math or mathematica
 
@LeakyNun Ah! Well, we're not looking for minima of $L(x,\lambda)$, we're looking for stationary points.
 
1:30 PM
I guess I don't really have a good intuition for what in the world $\lambda$ is doing
 
Anonymous
@LeakyNun It is just a constant which indicates how many times larger the gradient of $f$ is w.r.t the gradient of $g$.
 
Anonymous
Provided they are pointing in the same direction (that's a necessary codition)
 
Anonymous
There's a nice picture on Wikipedia
 
right, but that's just the intuition for when $x$ staisfies the constraint
 
Anonymous
What? We are always moving on the constraint curve!
 
Anonymous
1:33 PM
Until the directions of those two gradients match
 
Anonymous
 
do you know lagrange duality?
 
Anonymous
Actually read this answer: qr.ae/TUG8uY
 
Anonymous
@LeakyNun I don't
 
@LeakyNun I have a feeling you're trying to ascribe a generic meaning to $\lambda$ in $L(x,\lambda)$ when the constraint is not satisfied. There is none.
 
1:37 PM
@ACuriousMind well I'm learning Langrange duality
 
This is actually mirrored in temperature: A system that is not in equilibrium, i.e. has not maximized its entropy, has no well-defined temperature
@LeakyNun Huh? What's that and how did we get there from temperature and Lagrange multipliers?
 
Anonymous
> In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem
 
Anonymous
hmm
 
@ACuriousMind in Lagrange duality, we set $g(\lambda) = \inf_x L(x,\lambda) = \inf_x [f(x) - \lambda(h(x)-b)]$
and find the maximum of $g$ instead
and the maximum of $g$ is always smaller than the minimum of $f$; sometimes they're equal
 
Anonymous
Interesting
 
1:46 PM
@ACuriousMind for example?
 
Anonymous
The point is that that temperature is not well defined unless the system is in equilibrium. Consider an exothermic chemical reaction.
 
why is that temperature not defined?
 
@LeakyNun An example of a system that's not in equilibrium? Actually, almost all real-world systems are probably examples of that, but most are close enough to equilibrium that we can ignore that :P
 
@ACuriousMind well that's not very helpful...
 
But yeah, a chemical reaction that's just starting is a good example
 
1:51 PM
I mean, I can stick a thermometer inside the chemicals surely
 
Anonymous
@LeakyNun If it's a large enough system, you'll notice the fluctuations in the thermometer
 
Anonymous
Exothermic reactions are chaotic
 
Anonymous
So if you sample random regions
 
Anonymous
You wouldn't get similar temperatures
 
that just means the temperature is not uniform?
 
Anonymous
1:53 PM
Yeah, sorta
 
@LeakyNun A thermometer does not measure temperature directly. It measures some indirect quantity, that, assuming the thermometer is equilibrated with the system being measured and the system being measured is in equilibrium, is an indicator of temperature.
 
hmm
 
Anonymous
Temperature is not even defined for such systems, yeah
 
I think what one has to realize is that the modern statistical notion of temperature does not exactly line up with our intuitive notions of "hot" and "cold".
 
what is the difference between work and heat?
 
Anonymous
1:58 PM
True, for example temperature can be negative too :P
 
Anonymous
(But that isn't quite intuitive)
 
@LeakyNun Heat is the internal energy transferred during some thermodynamic process. Work in thermodynamics usually means "macroscopic" work like pushing a piston.
 
but heat is also macroscopic
so they're different labels for the same thing?
 
No
heat is internal energy transferred
Pushing a piston is not a transfer of internal energy
 
hmm
 
Anonymous
2:02 PM
I'm sensing some deja vu
 
Anonymous
Something something last year
 
It's not the first time thermodynamics is being discussed in this chat, certainly ;P
 
Anonymous
Yeah, but iirc it was Leaky nun who had asked this same question earlier too and we had a huge debate regarding a "non-circular" definition of energy and work and heat :P
 
Anonymous
Then we started talking about Noether's
 
Oh, if you want rigor with proper definitions, you need to do full-blown statistical mechanics
 
2:05 PM
sounds like fun
well for now I mostly want an understanding instead of rigor
 
I'm not sure the word "heat" even crops up there
 
so the entropy of a fixed amount of ideal gas in a fixed volume is fixed right
because there's only so many states they can take?
 
You need more information. Entropy is not "all possible states in this box", it is "all states in this box that the system can occupy with its current internal energy, etc."
 
how can I modify my statement?
 
If you assume the system is in equilibrium, then additionally giving its temperature is enough to fix the entropy.
That's then called the canonical ensemble: We define the (macro)state of the system by giving the number of particles, the volume, and the temperature.
 
2:11 PM
what is a state?
and why can a hotter system attain more of them?
 
Anonymous
Read a statistical mech book man :P
 
Anonymous
There are lots of good online lectures too!
 
You need to distinguish between micro- and macrostates, and at this point we really enter a statistical mechanics lecture...
 
do I really need that much to undersatnd what temperature is lol
 
Anonymous
If you can tolerate the accent, this playlist is worth its (virtual) weight in gold: youtube.com/playlist?list=PL5E4E56893588CBA8
 
Anonymous
2:13 PM
Go through the stat mech lectures
 
Anonymous
@LeakyNun You...really do
 
so the people in high school don't really understand what temperature is?
 
Anonymous
No, they don't
 
Anonymous
(on average)
 
interesting
 
2:15 PM
@LeakyNun In some sense, yes, they don't. But the operational model of temperature ("temperature is what a thermometer measures") works well enough in a lot of cases.
 
lol
 
Unless they learn general relativity, they don't understand what time and space are, either :P
And yet the Newtonian mechanics they usually learn also work well enough in a lot of cases
Physical understanding can both be wrong and useful.
It's not like math where you can throw your whole theory away if someone points out an inconsistency :P
 
Anonymous
Speaking of high school kids, that reminds me, I found a certain 15-year-old's profile yesterday on PSE while reading this answer and I was pretty much awed: physics.stackexchange.com/users/23119/abhimanyu-pallavi-sudhir. One of the most impressive profiles I've seen.
 
Anonymous
Apparently he was one of the founders of PhysicsOverflow too
 
Anonymous
(On the other hand, I think I was still solving quadratic equations at that age...phew)
 
2:21 PM
TIL a 15-year-old founded PhysicsOverflow
 
Anonymous
> PhysicsOverflow was started in April 2014 as a physics-equivalent of MathOverflow by Rahel Knöpfel, a physics PhD at the University of Rostock, high-school student Abhimanyu Pallavi Sudhir, and Roger Cattin, a retired professor of computer science at the University of Applied Sciences, Switzerland.
 
Anonymous
Oh, he's your junior at Imperial @LeakyNun
 
wat
he's studying mathematics?
that's interesting
 
Anonymous
Seems so
 
2:24 PM
I think nowadays teenagers are pretty good at computer. When I was a teaching assistant for physical experimeents, those first-year undergraduate students know pretty well how to use Excel to sort out experimental data, while I don't know much about that.
probably they have learnt that in high school. I have never learnt that.
 
Anonymous
They teach excel in primary school these days
 
Anonymous
At least the basics
 
I'm still confused
someone who published papers is going to study one year below me?
 
Anonymous
Well, that's how the system works :P
 
I kept having computer courses from primary to middle to high to undergraduate schools, but I don't have much basic for computer.
 
Anonymous
2:30 PM
I was sorta chuckling when Balarka joined uni. But well, as long as you've smart peers it's all fine. You never know what you don't know.
 
this is so cool
 
because computer courses are treated like physical education, which is never a serious course in my school.
 
i'm still impressed
6
A: Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?

Abhimanyu Pallavi SudhirI'll answer the relation between string theory and $E(8)$ -- a common appearance of $E(8)$ in string theory is in the gauge group of Type HE string theory $E(8)\times E(8)$ (see here for an explanation why). But it's interesting physically because it embeds the standard model subgroup. $$SU(3)\t...

did he, like, write these words when he was like 10 years old?
 
Anonymous
13 years old
 
I'm impressed
 
2:44 PM
@LeakyNun Note the recent edit
 
hmm...
that's interesting
 
vzn
2:56 PM
problem is mostly beyond me but delighted that maybe von neumann entropy plays a (starring?) role! o_O entropy as future crosscutting rosetta stone between physics, math, CS? also talk of (kuhnian)-like revolution in the air! viva la revolution(s)! =D
 
I guessed correctly (as a question I posted here earlier) that the center of a group G is the normal subgroup of G, as confirmed in en.wikipedia.org/wiki/Center_(algebra)
I guess that's why the name central extension is coined.
 
@CaptainBohemian it's a normal subgroup of G
and what question did you pose here?
 
@LeakyNun but my group book for physics calls it invariant subgroup of G; it never uses the term normal subgroup, which is a term I learnt from Wikipedia.
 
Anonymous
Don't read group theory books "for physicists" :P
 
3:06 PM
> Normal subgroup
From Wikipedia, the free encyclopedia
Jump to navigationJump to search
"Invariant subgroup" redirects here. It is not to be confused with Fully invariant subgroup.
 
Anonymous
It should be there in any abstract algebra textbook
 
Anonymous
Gallian is my favourite
 
Anonymous
Even Artin discusses it
 
@Blue but I am mainly interested in group theory for physics and that book is what was used in my group theory course for physics. And I feel it quite good.
 
Anonymous
Fair enuf
 
3:15 PM
@vzn yikes
 
vzn
@bolbteppa mainstream media barrage begins! even before talk! :o o_O
 
You can't really get much bigger than one of the biggest mathematicians alive claiming to prove one of the biggest problems in history, especially when they say it's simple
 
@Blue also, the professor teaching that course got bachelor degree from math department, so I think he chose that book prudently.
 
@vzn this is what the establishment does while the contrarians twiddle their thumbs misinterpreting undergraduate level material
Riemann spheres coming up in the problem in the other post, hmm
 
@vzn that is extremely interesting.
I'm not sure I can share the hope, though
> Anyway, in 60 hours’ time, number theory will be revolutionised
 
vzn
3:27 PM
@bolbteppa lol "simple" for a Math Wizard :P
 
either that, or we'll be treated to a depressing months-long episode where the maths world collectively loses its trust on one of its greatest members.
 
I think he's earned the right to get a big one wrong :p
 
I'm hoping for the best but preparing for the worst ¯\ _(ツ)_/¯
 
vzn
@bolbteppa lol think mochizuki is getting grumpy/ crabby/ grouchy, quite understandably so. (similarly to everyone else involved...) it is said that some other japanese friends are vouching for the proof, think if they ("really") understand it they need to engage and write defenses based on their own povs
 
I wonder has a big name ever done something like this and been wrong in the end
 
3:29 PM
@bolbteppa for sure. But he'll find it much harder to push anything remarkable after that, I should think.
@bolbteppa good question
arguably Josephson?
 
Wiles was wrong but he fixed the errors
idk if Mochizuki was a big name before this
 
@bolbteppa you can't accuse Mochizuki of "being wrong in the end" for the simple reason that we haven't reached the end of that saga
 
Yeah
@vzn Motl says the vouchers for it are too closely linked to him :p
Original Riemann paper translated here claymath.org/publications/riemanns-1859-manuscript
 
vzn
3:39 PM
@bolbteppa not disagreeing with that but it needs to reduce to math/ logic and not social connections. if they really "vouch" for it they need to answer any (technical) objections by others. eg newly minted fields medalist etc.
 
Surprisingly, very few know the necessary inter-universal-Teichmuller theory :p
I literally have zero appreciation of the RH :\
 
vzn
@bolbteppa to me the analogy with code is not out of place. its like a new massive set of code introduced that needs to be code (peer) reviewed. math is like code that runs in mathematicians heads...
 
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard...
very much so
 
Yeah
 
vzn
@bolbteppa there are some neat links with QM eg dyson introduced some of that. have collected misc links on that. hence LuMos interest etc.
 
3:42 PM
@EmilioPisanty Huh, "decoded" might be a more appropraite word than "translated" in that case :P
 
vzn
@EmilioPisanty yeah one of my favorite crosscutting bridges & wish it were even more widely known/ built on. maybe in the future. auto thm proving is strengthening the connection etc
 
@ACuriousMind I guess people were more used to medical-doctor handwriting in not-a-real-doctor papers back in donkeys-ages-ago
 
@vzn Unfortunately, test-driven proof writing has not yet been invented.
 
@vzn that last remark is the key, but the pace of advancement of theorem-proving software, while strong in its own terms, will take it a fairly long time before it is a truly attractive option to check real-world proofs.
I wish it were faster
 
The future: "How do you know your proof is correct?" - "Oh, all the unit tests are green."
3
 
3:44 PM
but it's just a damned hard problem
 
vzn
@ACuriousMind there is some major effort on "proof verification" in those directions, gaining major credibility/ momentum. it will be a complementary system.
 
@bolbteppa on a more serious note - the English translation is remarkably readable.
 
vzn
@EmilioPisanty the technology is limited right now but its advancing, its valuable, the potential is clear, the future will be different.
 
The problem with proof verification is that the proof needs to be written in a verifiable format first
 
vzn
some top mathematicians/ pioneers are now engaged with the area (auto thm proving/ verfication etc) eg Gowers. most are still unaffected. maybe a few curious.
 
3:47 PM
@vzn oh, for sure. I just feel that in this case 'the future' is more of a fifteen- to twenty-five-year timescale rather than five to ten.
 
@ACuriousMind and then suddenly you have someone writing down something close and poking it until all the lights are green
 
vzn
@EmilioPisanty its a long timeframe agreed but there will be dramatic advances in our lives.
 
@vzn for sure =)
 
@danielunderwood Sure. What's wrong with that?
 
I can confidently predict that there will be theorem-proving software in everyday use by mathematicians before RM's SE ban runs out.
... if humanity is still around, that is...
 
3:52 PM
I heard theorem prover
 
@LeakyNun yeah, ACM is around
that's his primary function as an AI
see the starred comments on how he wishes his kind had a more stable employment, and musing about a utopian future where that's the case
 
Need to write out all these steps, should remember this :(
 
Anonymous
52
Q: Which mathematical definitions should be formalised in Lean?

Kevin BuzzardThe question. Which mathematical objects would you like to see formally defined in the Lean Theorem Prover? Examples. In the current stable version of the Lean Theorem Prover, topological groups have been done, schemes have been done, Noetherian rings got done last month, Noetherian schemes h...

 
Anonymous
MO guys are doing some work
 
vzn
The Mechanization of Mathematics/ Avigad 6/2018 Notices AMS ams.org/journals/notices/201806/rnoti-p681.pdf
@EmilioPisanty fusion is taking a long time too yet still quite a worthwhile (very "strategic") goal & seemingly/ conceivably within reach (aka Grand Challenge™) :|
@Avantgarde serious? there are many answers. found this fun to read recently. 40M other readers cant be wrong + meshes with many other answers :) Alchemist Graphic Novel, Coelho amazon.com/Alchemist-Graphic-Novel-illustrated-interpretation/…
 
4:14 PM
@ACuriousMind well I originally felt like it violated some sort of beauty of math...but then I thought back to most of the times I've tried to solve a differential equation
Also I hate to ask you this since I know I'll eventually get to it, but I've been itching for an answer and haven't easily found it. Zwiebach introduces the concept of a relativistic string as something that sweeps out a worldsheet in spacetime. Ignoring all the parts about quantization, is a p-brane essentially a generalization of that thought?
 
@danielunderwood Yes. Branes sweep out worldvolumes.
@danielunderwood abstrusegoose.com/230
 
Yeah I suppose that's how my limited proof-writing experience has been anyway. And I suppose I do use Mathematica when I don't want to do an integral or something. There's just something unsettling about letting computers decide whether our math is right
 
Of all the things to give computers control of, judging our math is what you're worried about? :P
 
What if that's how machines take over? They realize we trust them and start giving us bad math!
 
4:40 PM
If you define branes from the Polyakov action, GSW say they are non-renormalizable for $n > 1$ branes
 
vzn
tfw an AI creates faulty abc proof as path to world domination :P
 
Ahh I haven't gotten to the Polyakov action yet. It looks like the book I'm in doesn't mention it until towards the end
And hey a small error in a proof is a lot less obvious than killer robots! Probably a lot easier for machines to just take over killer robots though
 
Anonymous
How's Zwiebach's book? @danielunderwood
 
Anonymous
Readable?
 
4:56 PM
I thought the old school solution for secure logs was a line printer... — Paul 13 hours ago
hoooooo boy
talk about an obscure reference
 
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