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3:43 AM
Q: Seeking a more natural proof and intuitions for $\left<T\right>=\frac12\left<\textbf x\cdot\nabla V\right>$

SzetoI am currently self-learning quantum mechanics with A Textbook of Quantum Mechanics Second Edition by P. M. Matthews and K. Venkatesan. In Example 3.15 on p. 105, the author proved $\left<T\right>=\frac12\left<\textbf x\cdot\nabla V\right>$ in any stationary state, where $T$ is the kinetic energy...

I like these interpretation questions
even though this one is like homework
1 hour later…
5:10 AM
Hi everyone !
Is it possible to have desktop notification with a pop-up on any reply to stack exchange chat ? If yes than how ?
2 hours later…
6:43 AM
Someone's robo-reviewing really hard: physics.stackexchange.com/review/suggested-edits/310048
This is really bad :(
@ACuriousMind I know I should be using flags for this, but please consider taking some action for this particular user, and in general, please consider introducing review audits on PSE. I don't think that adding review audits on our site has any disadvantages, whatsoever. It only has advantages.
Moreover, the fact that the user in question is one of the most prolific reviewer lately, makes this scenario even more problematic. Who knows how many other robo-reviews they did...
7:04 AM
@Slereah I want to know exactly what went wrong...all the details,what abstract entities popped in...and all...Can you give a reference to all this?
This review also shows that the user in question barely takes the time to even see what was edited: physics.stackexchange.com/review/suggested-edits/307688
Here's a SEDE query which looks out for suggested edit which a user approved, but the edit was, at last, rejected.
7:22 AM
@PM2Ring Actually, it's impossible to divide a line into 7 equal parts. All you can do is an approximation. I mean, since 1/7 is infinite, that means that each of those parts will (in theory, not in practice) not have a precise value.
I'm not sure though
@JingleBells BTW, that's true for any fraction.
I don't think it's possible for something of a size 1/7 to exist. Whatever it is, it would be an approximation and the number will terminate at some point. In theory, the length will never be defined (won't have a precise value).
@FakeMod 1/2 = 0.5
@JingleBells You could also never half something "exactly". What you'd get is just an approximation of 0.5.
@JingleBells Just because you can write it, doesn't mean you can do it.
Why not? You have a 20 atoms line, divide it 50/50 and you end up with two 10 atom lines
7:28 AM
FWIW, if I was using base 7, then I could easily write 1/7 as 0.1, but that does not allow me to divide something exactly in 7 parts.
@JingleBells If you had 14 atoms, divide it in 1/7, you end up with seven 2 atom lines.
Why not?
But the only thing is, we can never be so precise.
welp, i guess i'm confuse dnow
The notion of something infinite existing is a bit weird to me
7:30 AM
@JingleBells Infinite does not exist. In fact, infinity is not even a real number (I am talking about $\mathbb R$).
Hmm, interesting.
That's why we always use an open intervals when talking about infinities, implying that they are not to be included. For example, the solution set of $x>2$ in $\mathbb R$ is $x\in(2,\infty)$ implying neither 2, nor $\infty$ is to be included.
To just avoid infinities, we have even started (years ago) assigning finite values to divergent series.
Potting the diameter of a circle along its circumference pi times is a bit confusing to me. How can you plot something infinitely many times and still arrive at a point where it "fits" along the circumference?
(I'm talking about in theory, in practice, it's obviously very complicated (and probably impossible))
Just an example: $1+2+3+\dots=-\frac{1}{12}$
7:36 AM
The question which baffles me is, why does pi take the value it takes( ignoring all the number base convention stuff)?. In other words, can we derive the value of pi from something more fundamental?
I heard there's a global database of universal constants somewhere around Jupiter
Starbucks around the world
poor russia lol
I see a correlation with my previous graph of UFO sightings. USA and UK have the most Starbucks and the most ufo sightings, therefore I can conclude that Starbucks makes you go nuts and see aliens
so starbucks is dangerous and it can induce delusional aliens visions
or maybe the aliens have created Starbucks :O
15 hours ago, by Faded Giant
@JingleBells nice observer bias
wat do you meeean?
Just google it man.
Draw a line 7 cm long. Now what's so hard about marking the points at 1 cm, 2 cm, etc?
Of course, matter isn't perfectly smooth, it's made of atoms, so any geometric diagram we draw is only an approximate representation of the idealised geometric object.
7:50 AM
@PM2Ring yeah, figured that. But the notion of plotting the diameter of a circle undefined amounts of times (pi) along the circumference and yet still arriving at a point where the diameter "fits" the circumference is a bit confusing.
Is the universe scale invariant?
@FakeMod googled it, I need more details about what you're tryinna say with this.
@JingleBells It's the other way around. You first plot the circle and then xee that the ratio comes out to be pi.
@JingleBells I won't be the best person to explain it, sorry.
@FakeMod then why do u use it lol (i'm making the assumption that you're inability to explain it comes from you not completely understand it)
7:52 AM
BTW, people were doing arithmetic with fractions
long before the modern way of writing numbers like 3.14159 was developed, which reached pretty much its present form about 500 years ago. See https://en.wikipedia.org/wiki/Decimal#History_of_decimal_fractions
@JingleBells I know what it means, but I don't think I will be able to explain it to you in a satisfactory way.
@FakeMod oh ok
The way I understand observer bias is when someone gathers data but is biased towards something, for example, exposing USA as idiots who imagine aliens. So the data ends up being gathered incorrectly due to human behaviour and is therefore biased towards proving or disproving some point and not really showing how things are
So either you'll go home confused, or you'll end up misunderstanding the thing, if I try and explain you.
@PM2Ring hmm, how plotting the diameter of a circle undefined amounts of times (pi) along the circumference leads to arriving at a point where the diameter "fits" the circumference?
Coincidence, probably.
7:57 AM
Yes, but you're plotting it undefined amounts of time, and arrive at a defined point of it "fitting"
@JingleBells Sure. It's hard enough just figuring out how to compare the curved circumference of a circle with its straight diameter. Philosophers & mathematicians have spent countless hours pondering that, and related matters. So you're in good company. ;) But a couple of thousand years ago, Archimedes came up with an ingenious way to do it that seems pretty valid. At least, nobody has found a fatal logical flaw with it, and it can be used to do practical calculations that give useful results.
The techniques pioneered by Archimedes eventually became the foundations of calculus, but it took almost 2 millennia to get from Archimedes to Newton.
@FakeMod There are various infinite families of formulae which can be used to define pi. The simplest family relates to the arctan function, eg pi=4arctan(1). The Taylor series for arctan(1) has abysmally slow convergence, but you can speed things up using arctan relations. Define a(x)=arctan(1/x). Then a(1)=a(2)+a(3),
This question would make a really nice click-baity HNQ: physics.stackexchange.com/questions/572073/…
8:12 AM
Electrons and black holes having hair... this is getting out of hand
@PM2Ring Hmm... But isn't this a bit *circular". I mean, trigonometric functions are after all circular functions, which inherently have been defined using circles. So at some point, we have used $\pi$ while defining $\arctan$. Using $\arctan$ to redefine $\pi$ doesn't seem to accomplish anything, IMO. I might be very wrong, so please correct me.
@FakeMod Since you know a fair bit of calculus, you should find it easy to show that the Taylor / Maclaurin series for arctan(x) = x - x^3/3 + x^5/5 - ... Or you could use Archimedes construction, which is conceptually simpler, but the arithmetic gets a bit ugly to do by hand, due to nested square roots.
@PM2Ring Ah, yes. Taylor series do lead us to the Leibnitz formula. Indeed! That slipped off from my mind.
FWIW, about 20 years ago, I used the arctan series, and a 3 term Machin-like formula which I discovered myself, to compute pi to 10 decimal places, totally by hand (i.e., no computer, calculator, or slide rules were used). It took about 3 sheets of A4 paper, including the proofs for the arctan series & the other arctan formulae I used to derive the Machin-like formula. Unfortunately, I no longer have that paper.
Euler was rather pleased with himself when he proved that $\pi^2/6=\zeta(2)$. That's the 1st member of another infinite family, there's a simple relation between $\pi^{2n}$ and $\zeta(2n)$ and the Bernoulli numbers
@FakeMod Curiously, that same topic came up a few weeks ago. See the link in G. Smith's comment.
@FakeMod No. You can use things like the Bohr radius to define the scale.
9:03 AM
Is this a good/consistent example of a category: The position-space stationary states of a system are objects, the maps sending the state of the system before measurement into the state of it after measurement are morphisms, and together they form a category. The map sending the position space objects into e.g. momentum space objects, with the morphisms transforming in the obvious manner, is a functor (is it just the identity functor?).
9:30 AM
@FakeMod that "result" is based on an abuse of notation :P
not even based on the idea behind series convergence
@SirCumference People want additions, they don't want analytic continuation
@Slereah i wasn't aware there was such a demand for additions
that we'd go this far
Have you ever seen a crank paper
Crank papers are almost entirely powered, if they have math at all, by addition and multiplication
not a math one, to be fair i probably couldn't distinguish crank terminology from real ones i haven't learned
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined. == Summation == Ramanujan summation essentially is a property of the partial sums, rather than a property of the entire sum, as that doesn't exist. If we take the Euler–Maclaurin summation formula together with the correction...
9:34 AM
@PM2Ring what on earth is this
i stand corrected
assuming this stuff is legit
Would Ramanujan have invented that if he'd had proper mathematical training? Maybe not... :)
Analytic continuation is an old trick
welp it ostensibly has "properties which make it mathematically useful in the study of divergent infinite series"
Also pretending that infinite sums are finite is an old physicist trick too :p
For simpler examples, you can abuse the formula for the sum of a geometric progression, S=a/(1-r). Eg, 1+2+4+8+... = -1
9:37 AM
i feel like every math proof involving abused notation is labeled a "physicist trick"
unfortunately it's kind of true
the number of "differential"-based proofs (e.g. involving $dx$) i've seen in QM and EM is concerning
$$\frac{df}{dx} = f \to \frac{df}{f} = dx \to \int \frac{df}{f} = \int dx = \ln(f) + C = x$$
Therefore $f = e^{-C} e^x$
Worst math
@SirCumference It's ok, if you know what you're doing. ;) And if you're not quite sure what you're doing, then you can rationalise it by saying "my mathematical model is obviously an approximation, but the 'true' mathematical model has to give a finite physical result".
@PM2Ring You say that until you realize that everything was wrong the whole time!
@PM2Ring i never really felt like i knew what i was doing when i pretended infinitesimals existed in R
like a 5 y.o. can tell you that infinitesimals and infinities aren't in the reals, yet an undergrad has to slowly nod their heads when they seem em
There is an infinitesimal in $\mathbb{R}$
It is $0$
9:48 AM
but the textbooks aren't referring to zero :P
@Slereah :D Still, in physics, we can confidently assert (for example) that a proton has a small finite mass, even if we do use divergent series to compute it. Pure mathematics doesn't have that comfort when it gets into bizarre territory.
@PM2Ring We know it because we have measure it
We don't know if the proton has a small mass as derived from the standard model
@Slereah Exactly. The universe isn't obliged to conform to our models of it, and it doesn't care whether our models are simple or complicated, beautiful or ugly. OTOH, we have made good progress by searching for beauty, and trying to keep things as simple as possible.
Not sure about beauty :p
@SirCumference You don't "need" infinitesimals to do basic calculus. But it took a couple of centuries to get from Newton & Leibniz to the delta-epsilon stuff of Weierstrass.
9:59 AM
@PM2Ring yeah. i'm wondering why in the world physics textbooks insist on reverting back several centuries
@PM2Ring But won't Bohr radius also change when we change the scale?
looking at you Townsend QM
And then it took almost another century before infinitesimals were given a (relatively) rigorous foundation.
learning QM from townsend was a horrible experience for a multitude of reasons, but the wonky problem sets asking me to manipulate differentials was one of the worst
also just dropping QM out of the sky instead of motivating it
@PM2Ring afaik Newton's calculus was pretty unrigorous, which was much of the reason it wasn't taken seriously at the time
@PM2Ring i'm still not really aware of their rigorous foundation
@SirCumference Can QM be motivated? Except just saying that "experiments show that CM is wrong, so here comes QM" :P
10:04 AM
Spivak told me to ditch that notation
Can't all this stuff be made rigorous so that as written it all makes sense, there is a name for this stuff I can't remember now
@FakeMod QM is largely based on CM, you just change certain assumptions (which ends up having big results)
the same can be said for most physics
but the biggest issue i had was not knowing how to connect it with the CM i had long known
other textbooks thankfully existed to help
@SirCumference Oh, I see what you meant by motivation.
'non-standard calculus/analysis'
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis was originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or infinitesimal quantities seems to appeal naturally to our intuition...
@bolbteppa reminds me of this
Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. It defines "q-calculus" and "h-calculus", where h ostensibly stands for Planck's constant while q stands for quantum. The two parameters are related by the formula q = e i h = e 2 π i ℏ {\displaystyle q=e^{ih}=e^{2\pi i\hbar...
:55203139 oh, i thought you were referring to uses of infinitesimals in standard analysis
10:08 AM
non-standard quantum calculus would probably be a new thing
tbh leibniz's notation of derivatives ought to go
make way for euler's notation
so much cleaner and less confusing to newcomers
10:22 AM
@FakeMod I don't understand why you said that you know you should raise a flag for this and then...didn't.
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below. == Introduction == The evaluation of nonstandard analysis in the literature has varied greatly. Paul Halmos described it as a technical special development in mathematical logic. Terence Tao summed up the advantage of the hyperreal framework by noting that it allows one to rigorously manipulate things such as "the set of all small numbers", or to rigorously say things like “η1 is smaller than anything that...
Am I wrong or is the whole bundle philosophy of constructing something that locally looks like a direct product just a way of enabling one to treat things like vectors (one part of the product) as functions of variables e.g. scalar or vector variables (other part of the product) locally
@ACuriousMind I thought raising a flag after posting it here would be redundant.
Also, I wanted to (again) request you to add review audits, so I thought it would be better if I said it all here, instead of flagging for that bad review and coming to the chatroom and urging for audits without any contect.
@FakeMod It's not, flags are visible to all mods, while your ping here pinged only me and not all mods read the chat transcript.
@ACuriousMind Oops! Flagging now!
10:35 AM
@FakeMod Turning on audits is not something the mods can do on their own (SE has to turn them on) and I'm not sure a single questionable reviewer is worth annoying everyone else with audits, especially since the low volume (compared to SO) of PSE means there isn't a large pool of audit resources. If you think we need review audits, please start a meta discussion about it, this is something the community needs to discuss.
@ACuriousMind Hmm... I am afraid that the audits might be any disturbances given their sparse occurence, however, I don't see myself starting a Meta thread any soon. Though, I will definitely start one, once I get some time.
@FakeMod I don't know if review audits would stop that person's bad practices. He was bad when he was just suggesting edits, and the reviewers approved his rubbish. :( As I've said before, I've tried to communicate with him in comments, but he just ignores me.
I could say more, but I don't want to get banned... OTOH, if HCR doesn't change his ways, I will seriously consider deleting my account on Physics.SE.
10:58 AM
@FakeMod From en.wikipedia.org/wiki/Scale_invariance "Scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor". But the size of atoms sets a natural length scale. So if we sent a message to some alien scientists, saying that the lattice constant of sodium chloride is 564.02 picometres, they'd be able to work out how long a metre is.
Ok, we'd also need to specify the temperature, and use isotopically pure salt, but they're just minor technical details. We'd probably use a different crystal, like diamond or silicon.
11:44 AM
"One of the most important developments in the last half-century has been the interplay between field theory and the theory on the mass shell. I always thought that they were 2 different ways of saying the same things. Geoff Chew and Landau tried to say that field theory was rubbish. It turned out that what they were objecting to was not field theory, but non-Yang-Mills field theory.
As soon as you have Y-M with limitations on the particles you are introducing you have an asymptotically free field theory and all the things that they were worried about go away. This was also what leads to superstring theory. The way I view the transition for a unified theory." arxiv.org/abs/2007.12615
Pretty cool
12:17 PM
Q: Is asking how to derive an expression in a paper on topic here?

mattiav27Is asking how to derive an expression in a paper on topic here? If not where should I ask?

1 hour later…
1:28 PM
Hi everyone !
Can someone tell me what will be net work done on s system if tje system performs a negative work on me and I do a positive work on the system. And in equal amount
1:52 PM
"For gauge theories and higher gauge theories the configuration spaces of the physical system are in general not plain manifolds or similar, but are orbifolds or more generally smooth groupoids, smooth ∞-groupoids. (An exposition of and introduction to much of the following is at geometry of physics.)" ncatlab.org/nlab/show/action+functional ...
"Moreover, smooth groupoids are at the very heart of the geometry of physics: modern fundamental physics is all based on the “gauge principle” and in Model Layer – Gauge transformations in electromagnetism we explain how, mathematically, this is essentially nothing but the theory of smooth groupoids." ncatlab.org/nlab/show/geometry+of+physics
@Slereah a masters thesis supposedly explaining stacks and their relevance to physics ncatlab.org/schreiber/show/bachelor+thesis+Eggertsson
I'll give it a looksy
"Notice here that what we know as gauge transformations in physics are the morphisms of this groupoid"
"Hence when you open books on "Quantization of Gauge Theories", such as that by Henneaux-Teitelboim, which tell you that such quantization proceeds by the BRST complex, they are secretly saying that it proceeds by Lie algebroids, hence by Lie groupoids. Only that they don't say these words, but that's exactly what it is." physicsoverflow.org/40292/…
2:09 PM
So instead of working with vector fields in the set of sections of a vector bundle on a manifolds, or equivalently a sheaf of vector spaces on the manifold, one needs to set up the analogue of a sheaf of vector spaces on a manifold for a groupoid instead of a manifold, and I think a gerbe is basically a sheaf of groupoids or something (wrong, but some nonsense like this)
This is supposed to motivate going from sections of bundles to groupoids. Basically working with $A_{\mu}$ in a theory invariant under $A_{\mu}' = A_{\mu} + \partial_{\mu} \lambda(x)$ but not going to the quotient space means you should be working with a groupoid rather than a group, and as a category the fields $A_{\mu}$ are the objects while the transformations from $A_{\mu}$ to $A_{\mu}'$ are morphisms
It's also not a bad paper as to whatever nlab is talking about regarding manifolds
It's still a bit too category-y, as in you can't go in from scratch, but I think I can probably follow it with some effort
2:50 PM
From slide 2 here it looks like a stack really is supposed to be the analogue of a sheaf of vector spaces on a manifold, but for a groupoid, where you want to go to groupoids instead of manifolds because of that $A \to A'$ stuff
3:01 PM
I think the gerbe thing is some special instanton thing one can ignore in general
They call an action a morphism of groupoids here not really calling it a gerbe, and they completely separate off gauge theory from action functionals on configuration space all in ideological servitude to groupoids, this really looks ridiculous
3:33 PM
For some strange reason, none of this groupoid stuff is mentioned in the DBI entry ncatlab.org/nlab/show/Dirac-Born-Infeld+action it's all configuration space actions again
3:46 PM
4:26 PM
@PM2Ring However, review suspensions would (hopefully) stop that person's bad practices, and review audits are necessary for automatic review suspension.
@PM2Ring Meh, a bad reviewer isn't a good enough reason for leaving a site. Such things will pass.
@PM2Ring Oh, I see.
@FakeMod Mods can impose review suspensions without needing audits.
The audits, as I said, are more for sites on the scale of SO where manual suspensions don't scale anymore
4:52 PM
what are the rules which are used while solving calculus questions in physics like I know that they are into dr×dt could be approximated to 0 sin dtheta could be written as dtheta and Cos dtheta could be written as one know what are all other rules which are needed?
@FakeMod Maybe not. But it isn't just his bad reviews, it's also his bad edits. He makes pointless edits, like converting all numbers to MathJax. And his MathJax conversions of values with units sometimes introduce errors. He rarely corrects grammar or spelling errors, but I guess that's because his own grasp of English grammar isn't very good.
Don't get me wrong, I like to encourage people to make edits that improve the site. But HCR's edits are likely to make things worse, and require someone to follow him up to fix the damage he causes. :(
Guys I ran into a small problem..would appreciate some help
So if I have a solid sphere and a hollow sphere, both of same material and radius
Which one will have more mass?
Considering that the hollow Sphere has inner radius $\approx$ outer radius
Intuitively, I can tell that the solid should have more mass, but I can't prove this mathematically...
Cus both spheres have the same volume, I'm getting the masses to be equal
5:14 PM
Thermal equilibrium and statistical equilibrium are different - the former refers to a system with constant macroscopic quantities while the latter refers to an ensemble consisting of constant microscopic states.
Sorry cap, I don't think I get you, could you please elaborate?
@sai-kartik There would be no volume density in the second case, it would be surface density. Unless you have a tiny amount of thickness, wherein volume would be $4\pi r^2 \cdot dr$ which is infinite less compared to that of the solid sphere.
@Safdar you mean like just less than the solid sphere?
@sai-kartik nope infiitely less. dr << R
Ohh right got it
So if a solid sphere and a hollow sphere have the same mass, the hollow sphere must be made out of a much more dense material right?
5:30 PM
@sai-kartik If the hollow sphere is essentially infinitely thin, then it would also be approaching 0 mass. Since they are the same material they should have the same density. To calculate the hollow sphere you could find the mass of a full sphere, minus the mass of the missing interior sphere where it is hollowed out. V would be $4 \pi r_o^2 - 4 \pi r_i^2$ and since $r_o \approx r_i$, $V \approx 0$
@JMac gotcha! Thanks!
1 hour later…
6:47 PM
I think in my statement above I should replace thermal equilibrium by thermodynamical equilibrium.
7:32 PM
@ACuriousMind I concur :-)
@PM2Ring True...
@PM2Ring I brought this up in his (now closed) chatroom, and we both agreed on making worthwhile edits, however his actions haven't changed a tiny bit even after that conversation.
@FakeMod Please refrain from discussing other users specifically here when they're not aware of it - it's kind of like talking behind someone's back.
@ACuriousMind Yeah, I feel that I am now lengthening it without any reason. I am dropping the issue from my side. Thanks for reminding me.
If you're concerned about other users' behaviour, raise a flag (as you already did). Keep in mind that many moderator actions will not be visible to you, so do not infer from no visible change that nothing happened. I get that this can be frustrating at times, but we generally prefer that frustration on the part of the flaggers over public accusations.
7:43 PM
@ACuriousMind I think SE should go back to the system of public flogging; that way we know users are being punished, and the anguish on their faces serves as a good deterrent to keep the rest of us in line!
@ACuriousMind No, I am pretty cool with you guys taking action, you almost always do. It's just that I was momentarily flabbergasted, so ran to the chat here, and then a series of comments regarding a particular user started off. This might not repeat again (though, no guarantees ;-) jk).
@JMac Was there a time like that?!?
@FakeMod Not on SE, but public punishment was definitely a thing in... less enlightened times I guess you could say.
@JMac Less enlightened, definitely! But probably more effective, I guess...
@JMac I know you're mostly joking but I largely don't believe in the deterrent power of punishment, especially not in the context of an online site where it's free to create a new account :P
7:48 PM
@FakeMod Depends on the effect you want to achieve. Probably pretty good as a short term deterrent; but in the long term I feel like it could promote revolting and stuff.
@JMac Public punishment? SE tried that last year; it didn't go so well.
@JMac That happens anyways ;-)
I don't have hard stats but I feel that there are very few users with just one suspension - most stay repeat offenders, and the suspension is not a deterrent but simply the means by which we stop them from continuing
but that might just be because we mods have to repeatedly deal with the repeat offenders, while we usually don't see those that behave well afterwards again :P
@ACuriousMind Yeah definitely kidding. It seems hard to come up with effective deterrents online. In my experience you need to be a lot more creative than just "look what happens when you break the rules, you don't want this".
@JMac To me, it seems scary enough to be banned for a year or so (as long as I am addicted to the site), so I wouldn't mess up. But, that's me, and the average Joe on the internet has probably a tougher skin (and less addiction) than I have ;-)
7:54 PM
What's the physical meaning of the $t$ coordinate for the Schwarzschild metric in Kerr-Schild form (see e.g. Equation 42 of arxiv.org/pdf/0706.0622.pdf#page=11)?
@FakeMod You've also seemed to always want to help improve the site too, so I don't think you're someone who really needs much of a deterrent to keep from causing trouble. I can't imagine you would spend so much time looking at user moderation if you weren't concerned about the site. You don't really need creative deterrents for people you can directly reason with, and typically that's not where the problem is.
@JMac Hmmm...
8:09 PM
@JMac Sure, but then I don't think we need "effective deterrents" at all. Suspensions are less about depriving the suspended users of anything and more about stopping them from doing any more harm. In the real world that's a lot more difficult because things like imprisonment are definite harms in themselves and you have to establish a right to inflict that harm,
but in the context of an online community there is no evident right to participate in it at all, so taking it away is much easier to justify.
Should I refrain from starting a bounty which is, in the end, to be awarded to an answer by a deleted account? I guess that the answer is yes.
Also, should I refrain from using bounties as a reward for exemplary answers? How often is acceptable?
This isn't real-world law and justice, it's a voluntary community built on altruism (and not even reciprocal altruism - we don't require askers to provide commensurable answers or something like that)
@FakeMod It's acceptable as long as you have the rep to do so - it's a standard bounty reason so why would it not be acceptable to use it?
I am an ALTRUIST. Are you?
(the above msg was a joke)
8:12 PM
@ACuriousMind No, I remember you saying this:
May 1 at 13:57, by ACuriousMind
@FakeMod You're technically free to offer bounties on whatever questions you like. But I personally think this is against their spirit.
@ACuriousMind The rep reason holds regardless of any other reason, definitely :P
@FakeMod That was in a context where you weren't awarding the bounty for the answers themselves, but for the collective work of the author
In this case you haven't said anything of the sort, so I don't see a problem
@ACuriousMind Oh, yeah. I am focusing only on the specific answer, so it does seem appropriate.
Kthxbye I wish you and your loved ones a very warm farewell, and bid you goodbye. May we meet again, intermittenly, in our impending life. And on that sweet note, I wish you an exemplary night. May your dreams be as serene as our interaction was.
8:19 PM
Alright now, I didn't want it to sound romantic, but I am sorry, I ain't that skilled.
what if I want my dreams to be action-packed and exciting?
@ACuriousMind It's up to you, man. Drink tequila and then go to sleep.
Ugh. nothing good ever happens after tequila
@ACuriousMind Well, I said tequila just because I remember playing an online game where a guy goes mad/crazy after drinking tequila and starts shooting zombies which are attacking him. Really action-packed.
I've only drank tequila a couple times, and I remember very little about either
8:22 PM
@JMac Yeah, that's about the best you can hope for with that drink of the devil :P
It's like liquid blackout for me. Not a big drinker anyways, so tequila is a pretty big no go for me now.
The top 3 hangovers of my life are easily traced back to poor decisions concerning tequila
Does hangover feel calm, or does it feel strange?
If you're feeling "calm" you're not hungover :P
I mean, how does it feel?
8:25 PM
@FakeMod Imagine not being able to stop sweating, and this making you very cold, so obviously you need blankets and stuff to warm up; making you sweat more. Combine with this and awful feeling in your head and a terrible sickness in your stomach.
@JMac Ah, so getting a fever, in a nutshell.
@FakeMod It depends on the person and how much you actually drank. For instance, some people easily get extreme headaches, others have more problems with feeling nauseous.
@ACuriousMind I haven't been hungover yet. I just want to decide whether I should ever be or not.
Regardless of how it specifically feels for you, it's never something you want to actively aim for :P
My bad hangovers are like the worst part of a flu. Sick to the stomach, head hurts, sweaty. It's amplified knowing that you directly caused it.
8:27 PM
@ACuriousMind Ugly stuff. Me no likey hangovers :(
@ACuriousMind true!
It's not always that bad mind you. Some hangovers for me are just a bit queasy or my head hurts. It's the really bad hangovers that feel like torture to me.
Sure, there's a spectrum depending on how close to ethanol poisoning you got :P
For me a big problem is I'll drink like 1-2 times a year, so if I mess up and drink too many drinks and don't hydrate/pace myself it usually gets me pretty bad.
What makes you calm, except drugs? Isn't there some kind of something which makes you go hazy, sleepy and calm and serene?
8:30 PM
When I was younger I like never had a hangover for the first couple years.
@FakeMod Everything that will change your mental state is technically a drug :P
@JMac What dod you mean by "first couple of years"? Isn't the legal age 18?
you're probably looking for weed or sleep medication :P
@ACuriousMind I mean, not the terribly addicting ones...
@FakeMod Well 19 here, but I mean the first few years I started drinking, so around like 18.
8:32 PM
@ACuriousMind Not old enough for the first, not brave enough for the second :P
@JMac It definitely gets worse with age, but I'm still not sure it's because my body doesn't deal with it as well anymore or because I can drink more without having to stop
@ACuriousMind You're a man with determination, thus it must be the second reason :P
Anyways, I gotta go. I wish you and your loved ones a very warm farewell, and bid you goodbye. May we meet again, intermittenly, in our impending life. And on that sweet note, I wish you an exemplary night. May your dreams be as action-packed as our interaction was.
@ACuriousMind I assume it has something to do with age for me, but I also could drink more when I was younger. I kinda stopped drinking for the most part when I moved on to greener pastures for my intoxication.
But it's also weirdly situational - I can go to festivals and be drunk days in a row without feeling more than a little worse for wear and then I drink a bit too much at one "normal" party and the whole next day is just terrible
@JMac Ah, you're in Canada, right?
8:37 PM
@ACuriousMind Yeah
I guess if it were legal here I'd still do more of that, too
Yeah I got into it a bit before it was legal, because it was pretty normal at that point already.
I'm not so much bothered by the legality as such as by the difficulty of finding a trustworthy source :P
Anyway, how exactly did we get here?
Ah, right, tequila
Yeah that got pretty off track
Well, there are times in this chat's history when this would have passed as one of the more coherent conversations :P
Dec 31 '17 at 15:36, by ACuriousMind
Nobody does weird quite like this chat :P
Wait, '17 is already far in the past?
Dammit I'm getting old
9:02 PM
Pff how do I come up with a business idea
I know all the stuff about filling a gap and starting from the customer, solving problem but... am I supposed to sit around and wait for it to pop up?
I want to do something in AI and ML but I gotta think
I always wonder how in the world people like Elon Musk come up with such ideas that somehow work... he founded his 3 most successful companies in a 5 year span
Where do I look for gaps, where do I find the customer need...
@JingleBells For every successful idea, there are plenty of unsuccessful ones. The idea that there is a special quality that makes you a successful "idea-haver" is a pernicious myth. People like Musk come from money, they have very different starting conditions than you have
You constantly complain about where to get money - someone born to a wealthy family, knowing a lot of business people, simply does not have that kind of problem. You can hire people to execute an idea well, you don't need to be brilliant in everything yourself.
When I constantly harp on economics not being fair, this is what I mean - the world is not filled with people rising to the top by their own impeccable virtues, it's filled with people getting a head start by the sheer luck of where, when and to whom they were born, doing plenty of scammy behaviour along the way, and then telling everyone it was their own virtue that got them where they are.
(Yes, this is my personal opinion and you may call me a hippie socialist for it)
@ACuriousMind I have NEVER complained about where to get money.
I'm not talking about execution or funding. I'm talking about the idea itself. Successful ideas seem so obvious and they fill a gap, such as electric cars or online payment tool
9:18 PM
@JingleBells Okay, I phrased that poorly, sorry - you have asked a lot of questions about how to get some specific service done cheap/for free, that usually costs plenty of money.
@JingleBells They seem obvious in retrospect, after they have been successful
And "electric car" is not really an idea - science fiction has talked about that for decades. Likewise cashless payments have been imagined since people started toying with the idea of networks
Once again, it's not the "idea" that makes the business
Okay. Suppose I have money. What do I do? Where do I look for ideas on which to execute? How do I stumble upon something that has any chance of it succeeding?
It's not as if there's plenty of engineers standing by idling and they just produce an electric car from nothing once some genius tells them that that might be a thing they could make. You need to fund their research, hire people who can actually build the thing, then figure out a way to do so profitably
(and the people who figure that out are usually not the CEO)
Yes, totally agree, there are high barriers to entry for this specific business.
@JingleBells There's no recipe for that. Either you have the idea yourself, or you meet someone with an idea convincing you that it's worth to put your money into. If there was a foolproof recipe to generate new businesses just from money, don't you think everyone would do it?
Economists like to pretend that the economy is rational, but trends are anything but that. Maybe your idea isn't even good, but you're good at marketing it. Maybe it's brilliant, but you don't find funding. Maybe you invest in other people's ideas only to find out they scammed you and ran off with the initial funding. The world economy is not a fair place that you can game by learning a set of rules
Yup, true
It's obvious that there is no formula to great ideas
And it still makes you wonder how serial entrepreneurs do it (how they know which ideas to attack)
9:28 PM
you don't hear about the ones that fail
if you throw a million people at a task at which they will succeed with 1% probability, one of them statistically will succeed 3 times in a row, but there's nothing special about them
so luck? Lucky entrepreneurs stumble upon good ideas, and if you're really lucky, you'll stumble on a few?
Luck, compounded by not being punished severely for your failures if you're already wealthy and not a complete fool
I'm sensing a bit of socialistic bias in your sentences :P
18 mins ago, by ACuriousMind
(Yes, this is my personal opinion and you may call me a hippie socialist for it)
Nevertheless, thanks for the help. I'll get to thinking and hopefully I do something some day
10:31 PM
Am I right in saying that a single element of the tangent bundle $i\in TM$ defines an entire vector field on a manifold?
I only ask because I can imagine there being some ambiguity there, since the tangent bundle is all tangent vectors to all points. There's no reason $i$ couldn't define two tangent vectors at the same point
@Charlie No, your $i$ is a single tangent vector at a single point
Locally, you have that the part of the tangent bundle $i$ lies in is isomorphic to $U\times \mathbb{R}^n$, where $U$ is a part of the base manifold, so you have $i = (x,t)$ in these local coordinates, so it's the vector $t$ tangent to the point $x$.
Ahh I see thank you

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