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12:19 AM
@bdegnan Maybe the digital ones were not enough exact? What if the digital circuits use signal levels of 10 digit precision? What if they use 20 digits?
 
 
3 hours later…
3:01 AM
@bdegnan hey, I had to drop off and go home, but it was very interesting reading the chat here! :)
I've only just been exposed to these techniques/methods so I'm interested in learning more
 
vzn
3:54 AM
@bdegnan checks out! :) (reserving judgement on your other wild story) :P Temperature robust programmable subthreshold circuits through a balanced force approach smartech.gatech.edu/handle/1853/47548
 
 
3 hours later…
7:11 AM
It's hot in the UK.
2
 
we will all die
 
And forecast to get hotter
 
yeah hot in Germany too. Tomorrow shall be the hottest day
 
Indeed. Tomorrow sounds like a good day to hide from the sun and do ... well ... as little as possible :-)
 
but I'm in the north of Germany. So it wont get as hot as in the south-west. There its said they gonna break the 40 C (104F)
I filled vacation request form today for tomorrow and the day after tomorrow. It will get too hot in the office (no AC or such)
anyway, I was thinking about Can a photon loose "energy" or decay or something like that? I was thinking about if its wave-like, will the wave be "flattened" over time and space until its undetectable? Because I was thinking about what would happen to a photon if it's placed into a tiny sealed box which is reflective on the inside? Would it just bounce forever in the box?
 
7:33 AM
@undefined if the mirrors in the box were perfectly reflecting then the photon would bounce forever. In real life mirrors are more like 95% reflective so it doesn't take many microseconds for the intensity to fall to zero.
 
7:45 AM
@JohnRennie how does it fall to zero and what exactly does fall?
 
@undefined suppose we have a metal mirror. The light has an oscillating electric field and that makes the conduction electrons in the mirror oscillate. Those oscillating conduction electrons reradiate light and the incident and reradiated light interfere. The result is a wave going back away from the surface i.e. we get reflection.
But this reradiation is never 100% efficient because the oscillating conduction electrons can scatter off the metal lattice and transfer energy to it i.e. some of the light energy is converted to heart and lost.
 
is it the same photon or is the original photon lost the electrons emit/reradiate a new one?
 
It's very tempting to regard light as an array of photons. Kind of like little balls moving in a group. But the photon is a great deal more complicated than this.
 
yes
 
Light is a quantum field and photons and waves are just different ways the quantum field can appear to interact.
 
7:52 AM
All photons are the same photon
One photon universe
 
Good morning
 
@undefined So asking if it's the same photon isn't that useful a question because for phenomena like reflection the particle approach to light, i.e. photons, is not an approprate approximation to use. We would use a wave approximation instead.
@Slereah Fock that
@undefined you might be interested to have a read through:
45
Q: Do photons truly exist in a physical sense or are they just a useful concept like $i = \sqrt{-1}$?

JensReading about photons I hear different explanations like "elementary particle", "probability cloud", "energy quanta" and so forth. Since probably no one has ever seen a photon (if "seen" it supposedly - and rather conveniently - ceases to exist) but many experiments seem to verify its properties ...

 
yes but as far as I know and understand we are able to create single photons. And if this photon bounce off a mirror, is it still the same we created? Maybe its a stupid or not useful question but for me somewhat still interesting. But if I think longer about it, I'm not sure if its even answerable
I read that question yesterday already many times :)
 
@undefined what we call a photon is actually something called a coherent state that I have to admit I don't really understand.
A coherent state is more like a wavepacket than a particle.
 
if the word photon is bad in that question then one could also ask if its the same wave
 
7:57 AM
@undefined well the reflected wave has a different momentum. If you insist that a wave is a specific momentum state then incident and reflected waves have to be different waves because they have different momenta.
Whether this is really a useful statement is debatable.
 
@JohnRennie you are one of the most smart people I know. If even you don't understand it, I don't think I'll ever understand it :/
 
Coherent states falls into the area of quantum optics, and though I've never studied this we have lots of people who have. Emilio Pisante for example is something of an expert in this area.
 
@JohnRennie so it could be the same wave but with different momentum? Or could it also be possible that the electrons of the reflective surface create/emit a new wave?
 
This is largely just terminology. Whether it's the same wave or a different wave depends on how you define the wave and it isn't a useful distinction anyway.
 
my thoughts behind all those questions was, how/if it the answer would change if we have entangled photons
 
8:08 AM
It's outside my area of expertise, but I believe that reflection does not change any entanglement of the original light i.e. you can generate pairs of entangled photons and after reflectin you still have a pair of entangled photons.
Whether it's the original photons forming an entangled pair or new photons forming an entangled pair doesn't make any difference.
 
ow for me it does make a difference. I'm not sure why but I feel like its interesting
 
If you ever find yourself working in experimental quantum optics you'll get over it :-)
 
but only after I know the answer :)
because I don't like it if I don't know something. And if I have the opportunity I'm always putting all my effort in finding an answer
my boss often calls me a "stickler for details"
he dont like it much, tho
 
Apparently the Bohm people like to call standard QM "Orthodox Quantum Mechanics"
to make it sound more sinister, I presume
 
8:24 AM
is there some kind of formula to calculate the deference in momentum from reflected waves?
 
@undefined yes, the total momentum is $p = h\lambda$ and if the incident wave has momentum $(p_x, p_y, p_z)$ and we take the mirror to be in the $xy$ plane then the reflected wave has momentum $(p_x, p_y, -p_z)$.
It's no different to the elastic collision of a ball with a surface.
 
When I went home for the summer I didn't expect it'd actually be hotter
 
@JohnRennie thank you. Does this formula have a name, so that I can read more about it?
 
@undefined I'm not sure if it has a name. It's just the result of a collision with an infinitely heavy object. When you conserve momentum and energy you get this result.
(we assume the mirror is infinitely heavy so it doesn't move in the collision)
 
@JohnRennie I see. I would just like to read about what exactly the h and mean λ
 
8:39 AM
don't buy an infinitely heavy mirror
it's hard to move up the stairs
 
lol
 
@undefined $h$ is Planck's constant and $\lambda$ is the wavelength of the light.
The equation $p = h/\lambda$ works for all particles, where for massive particles $\lambda$ is the de Broglie wavelength.
 
thank you
 
8:54 AM
This seems copy pasted from quoraPandya 41 secs ago
 
9:30 AM
You know, I know a bunch of linguists and such
and how glad am I that it is always possible to find a physics paper online
it is much harder in the field of humanities
you may have to ask libraries
order books and such
 
9:47 AM
"Seeliger's papers, especially his (1895a), contain the most detailed and general development of the problem. The price is that his exposition is the most cumbersome of an expositions; he alone resorts to infinite series expansions in Legendre polynomials and includes tidal forces in the analysis. all later commentators managed to reduce the exposition of the core to one or two lines of formulae."
Bloody Seeliger
 
9:59 AM
reading historical physics is always a bit weird
like you realize how many problems of the days are never really commonly discussed anymore
 
10:44 AM
Hallo hbärs!
Anyone familiar with Bayesian optimization? I have a few questions :p
 
11:26 AM
"Kelvin addressed the question of whether was imponderable, that is, has no weight."
 
11:54 AM
... or, as has been said previously, "Your brain is continuously and egregiously lying to you about what your eyeballs have actually detected". — Emilio Pisanty 11 secs ago
cc @dmckee
 
12:20 PM
@JohnRennie hola @EmilioPisanty Do you maybe have an answer to this?
ow wrong @ I'm sorry
 
12:35 PM
@JohnRennie “nobody has ever seen a photon” tickled me
@EmilioPisanty do you know a guy called Tijmen Euser?
 
I have seen a photon
I keep it in my pocket
 
you lucky :)
 
@undefined what is "this"?
@undefined it it's this, then John has already answered it
@undefined if it's this, I'm utterly uninterested in that type of metaphysics
 
"Herr Seeliger sees in the fact that, according to Newton's law, an infinitely long matter-filled cone would also exert an infinitely great attraction on a point on its axis, an objection against the general validity of the law itself;
the author of a cosmogonic hypothesis can only draw the converse conclusion, that that mass distribution, purely imagined by him and inaccessible to observation, could have been possible at no time, for it cannot be explained by the forces abstracted from the world of experience accessible to us." (Wilsing 1895a: 388)
Snap!
 
12:54 PM
@EmilioPisanty no, more like the question if a reflection affects the entanglement in anyway
and I dont want to discuss but I would be glad if you could elaborate why you call that metaphysics? Because it's not important/meaningless?
 
@Slereah historical math is strange too. I've been trying to trace the origin of a certain stats concept and it's been surprisingly tricky despite the fact that I only care about the story from roughly 1890 onwards
 
@undefined What's the physical definition of "same proton"?
 
(namely, the notion of a "hilbert space of random variables". it's simple enough to verify that that makes sense, but figuring out who first had that insight is not so easy)
 
@Semiclassical Kolmogorov?
 
That seems the most likely, yeah.
For instance, there's a 1941 paper of his on stationary sequences in Hilbert space which addresses stochastic processes
 
1:08 PM
@JMac Photon, not Proton. I would like to know/understand/learn that too
 
the 1941 paper is found here on google books
 
@undefined I meant photons
 
just before Pearl Harbor
 
actually, the clearest page in that book is from another 1941 Kolmogorov paper (same topic area): books.google.com/…
 
"Is Octonionic Quantum Gravity in the Pre-Planckian Regime of Space Time Violated? Input from a Worm Hole Bridge from Another Universe Considered as a Model for Examining This Issue."
Oh Vixra
 
1:18 PM
Interesting that Kolmogorov references his book in that section. I've looked in it and haven't seen any sign of Hilbert space geometry in there
(might be implicit somewhere of course)
 
Apparently Newtonian gravity is totally unfit to deal with homogeneous mass
quite unfortunate
 
riiiiight
 
It's troo
Has been known since the 19th century
you just get divergent potential all over the place
 
and you can't do any regularization that works in a consistent way
 
1:23 PM
ew
 
basically Newtonian mechanics was a shambling corpse by the end of the 19th century
it was full of holes and it's quite fortunate that QM and GR appeared
 
@Semiclassical Kolmogorov is credited with introducing measures in probability theory
 
@RyanUnger yeah, or at least for making clear how to properly axiomatize using measure theory
(Borel had tried to introduce measure theory to probability I think but he didn't succeed?)
@Slereah I imagine that's related to the issues with classical electrodynamics e.g. self-energy
 
@Semiclassical Well not really, although that was certainly part of the picture
although of course
Me saying that it was done is only with hindsight
I'm sure most people thought those issues had solutions within the framework
 
@RyanUnger The interesting thing is that there's a 1936 paper of de Finetti where he also gives a geometrical interpretation of random variables as vectors, along with distance/inner product/angle between them
(He actually gives two such interpretations, the second being the familiar one and the first being a quotient of such. but I don't think that's so essential)
 
1:30 PM
Hm
Apparently Newtonian gravity's issue comes from the lack of unique solution to the Laplace equation if you drop boundary conditions
 
see pages 8-11 here (brunodefinetti.it/Opere/AboutCorrelations.pdf) for the de Finetti paper
@Slereah i mean, classical electrodynamics and newtonian gravity both involve inverse square laws so I imagine there's some necessary similarity between their issues. big difference I guess is that gravity is purely attractive
that and, y'know, only one scalar potential for newtonian gravity
 
@Semiclassical Oh yes
The same problem arise if you consider homogeneous charge (that isn't zero)
but of course that's less of a problem in EM
 
I'm having to write the graduate school about my transcript
If I have to send it again I'll be pissed
 
1:45 PM
@peterh The issue with "bits" is actually that noise has value in the biological systems as it makes hysteresis. Analog is basically infinite bits. The C. elegans models match the analog behavior very well, and the VLSI implementation that is digital does not. This is basically due to the "hum" of the analog circuits.
 
@bdegnan Yes, but doubling the worthy bits of the signals roughly doubles the computing effort, while it squares the signal-to-noise ratio.
 
@RyanUnger is that quartic scalar stuff
 
@peterh I just wanted to mention that I had no idea in the "bit equivalent" side of these systems. :)
 
2:20 PM
@bdegnan n-bit signal means a signal, where the values can have $2^n$ different, value-quantized, discrete values.
@bdegnan For example, if we have a 3-bit signal, between 0V potential and 1V potential, then the allowed values are 0V, 0.125V, 0.25V, 0.375V, ... 0.875V
@bdegnan Most calculations in digital circuits depends roughly linearly with the bit size. This is a very raw estimation but roughly so is it.
 
@peterh I'm aware of that, but in the context of how it changes the neural network behavior. I made the ADC/DACs for programming the floating-gates on the neural networks. I have just never looked into the digital neural network models nuances. I only know that the FPGAs 1) didn't follow our models, and 2) used a lot of power.
 
@undefined It doesn't.
@undefined I find the question "but is it the same photon?" to be about as interesting as "but have you ever really looked at your hand?" coming from someone that's been staring at their hand for the past two hours while smoking weed.
I don't think it's interesting as a question and I'm uninterested in discussing it.
 
2:42 PM
@bdegnan That I agree! Also I've always tought that neural networks should work with analog circuits. They exist, there are EPAC (eletronically programmable analog circuit). Essentially, you can "upload" the analog circuit diagram into the chip, and then you will have the analog chip.
@bdegnan FPGA is good for massively parallel tasks, but it is very bad for general computing. Probably your FPGAs were not enough well-developed.
@bdegnan I suspect, human brain could be already simulated even with the todays technology, with a network of EPACs. We need around 10billion neurons with around 20Hz. Next step will be to analyze the circuit of a human brain with image recognition algorithms, and then create the equivalent network with EPACs. If it would work, the result would be... maybe the heaven, maybe the hell. Somewhere deeply I really hope, there is some inherent, unknown thing in the universe what avoids it.
 
Ha, you don't need better imagery, you need epistemology.
 
Imagine that you get a dead man. Extract his brain and freeze it in liquid oxygen. Then grind it in 0.1$\mu$m slices, and you take a photograph, also with 0.1$\mu$m precision, from all the slices.
You save the whole thing into a big database. Then, you eat it with image recognition algorithms. So you will have the circuitry of the whole, once lived human. You create the equivalent analog circuity, and upload it into a network of EPACs.
 
You won't have enough information.
 
At this point I say, heaven would be better
 
Besides, someone's figured it all out with pure research (no biology).
 
2:50 PM
@theDoctor What information would be missing?
@theDoctor With what research? I think, todays technology could already do it, but even 20 years old tech wasn't yet enough well-developed for that.
 
As I said it didn't require more biology or neural imaging, but more epistemology.
 
@theDoctor Can you upload a human soul into a computer with epistemology?
 
3:19 PM
@peterh we have neuron ICs. I have ganged up 10s of these: hasler.ece.gatech.edu/Published_papers/Neuron_papers/…
I don' t know the max the lab did. I went off to make cool stuff on 14nm.
 
4:19 PM
0
Q: Cases in which edits are an unethical mean to generate attention

TheoreticalMinimumI made 6 minor edits to my latest answers. The last edit (addition of a link to a lecture on the topic) I did 2 days after I gave the answer. I noticed that the question received a lot of new attention after the edit. It seems with each edit the question is bumped up on the main site again. Don'...

 
@undefined I have the inverse problem - I'm on vacation but the office with its AC would be by far the most tolerable place to be!
@EmilioPisanty I think you undersell how interesting hands can be ;)
@Slereah Unlike reading modern physics, which is never weird!
 
4:38 PM
@ACuriousMind give the guy a break. He's still at school and already knows more vector calculus than I did at school. And it had never occurred to me that there could be other than the trivial solutions for a Newtonian gravitational field in a vacuum.
 
@JohnRennie I mean what I say - I don't understand the question! That's not supposed to be a judgement of the abilities of the asker at all - maybe they know what they mean and can explain it - but as it stands I can't tell what one would answer to this question except "No, that's not a wave".
 
@ACuriousMind modern physics is weird but it's like
We're aware of what's wrong
 
@ACuriousMind fair enough, it just struck me as a little harsh at first reading. Rereading your comment I guess it isn't but I still think it could have been friendlier.
 
@JohnRennie I've added a second sentence - is that better?
 
@JohnRennie @ACuriousMind what question is this?
 
4:49 PM
 
I mean this thing isn’t even periodic in space
So how could it be a wave
 
@RyanUnger it can't, but the guy is a high school student and that isn't necessarily obvious to him at this point in his education. That's why he is asking.
 
Lmao that comment
“Laplace’s equation is a wave equation with infinite speed”
Is that some deep physicist nonsense
 
That...actually sounds like a standard physicist move
2
I.e. it's not more or less non-sensical than most other manipulations of infinity in physics :P
 
@ACuriousMind otoh this might be some kind of deep singular perturbation theory
 
4:58 PM
Sadly, it doesn't really seem to lend itself to a good answer. "Yeah, you could say that, but it doesn't get you anything" is all that I can think of
 
@JohnRennie I added a constructive comment.
 
@RyanUnger thanks :-)
 
vzn
@undefined in contrast to another harshly expressed expert view, and in the spirit of being friendly/ nice even to n00bs, feel you have asked a very deep Zen question with full shoshin mind and the real answer is both "the sound of one hand clapping" and the future of physics :) will elaborate on the answer but also likely you cant handle the truth :P ... (ps maybe with great benefit of hindsight even 20th century physics will also someday be seen as a "shambling corpse" lol!)
 
5:14 PM
@bdegnan Uhh that is extreme! How many artificial neurons could you create on a single chip?
 
@RyanUnger Group contraction baby
 
@vzn this comment is unreadable
@Slereah what is that?
 
In theoretical physics, Eugene Wigner and Erdal İnönü have discussed the possibility to obtain from a given Lie group a different (non-isomorphic) Lie group by a group contraction with respect to a continuous subgroup of it. That amounts to a limiting operation on a parameter of the Lie algebra, altering the structure constants of this Lie algebra in a nontrivial singular manner, under suitable circumstances.For example, the Lie algebra of the 3D rotation group SO(3), [X1, X2] = X3, etc., may be rewritten by a change of variables Y1 = εX1, Y2 = εX2, Y3 = X3, as [Y1, Y2] = ε2 Y3, [Y2, Y3]...
 
I pray that this has been made rigorous
@ACuriousMind ?
 
@RyanUnger What looks non-rigorous to you about it?
 
5:20 PM
"That amounts to a limiting operation on a parameter of the Lie algebra"
what does that mean
 
You start with a Lie group, take its Lie algebra, take some limit on its commutation relations to obtain different commutation relations, then go looking for another group with that algebra and call that group its "contraction"
It's not obvious why this process is useful, but I don't see any problems with its rigor
 
Oh I see
You find a new group
 
Yes, it is very much not a limit of a sequence of groups
 
It doesn't seem like you're doing any mathematics, you're doing a formal computation to motivate which group you're looking for
 
I agree, there is no real theorems you need here beyond the correspondence between groups and algebras
The curious thing is that it yields physically meaningful results, like having the Galilean group be the contraction of the Lorentz group
 
5:24 PM
"The curious thing is that it yields physically meaningful results"
Wigner wrote a paper about that...
 
vzn
> When average persons learn of the Dao, they are indifferent.
 
6:10 PM
@peterh 30k on that IC. We generally focused more on connectivity than neuron count. Neurons are high fan-in, and regarding the models, it was better to have 100s of dentritic connections over doubling the number of neurons.
I think that the most we had was 100k.
They just take too long to program otherwise. I can program 100 neurons a second back from fab, so it's a long process. I hear that they had it down to 1000+ neuron a second to program initial state.
 
vzn
@bdegnan hi again... some strange stuff to digest... were you joking about the book?
 
6:52 PM
physics problem : it's too hot
How do I solve this
 
dry ice
 
Now my body has frozen solid and shattered
T-1000 style
 
Well, at least the heat isn't your biggest problem anymore!
happy to help
 
@RyanUnger @ACuriousMind dunno about the wave equation. But you can do the same with the heat equation and you basically get relaxation methods for solving Laplace.
 
@EmilioPisanty what? There's no speed in the heat equation
Do you mean just let $t\to\infty$?
 
7:05 PM
@RyanUnger trade speed for heat diffusivity or whatever is the name of the constant in front of the time derivative
 
LOL that's 1 in my book
do you have a reference
 
Then just take $1\to\infty$
6
 
The point is, wherever you find these ugly manipulations, there's a better than even chance that there's a deep physical connection that can indeed be suitably formalised
 
I'm currently very interested in obtaining solutions of elliptic equations as limits of parabolic equations
But in a more sensible fashion, I think...
@EmilioPisanty ok a reference would be appreciated
I haven't heard of this being used in geometric analysis
 
Or at least, it can be formalised if you have a superhuman superphysicist patience
@RyanUnger I don't know any
 
7:07 PM
so is this just a rumor?
 
I have seen relaxation methods in use
Probably in Purcell's EM book
 
ok can you be a bit more precise then
 
I'd also check in numerical recipes
 
do you solve the heat equation up to time 1, say, and then let the parameter go to zero?
 
Or just t to infinity
Same thing
 
7:09 PM
Ya I guess so
So it's what I'm doing right now
see, for instance
Theorem 11.1 here is a very high brow version ams.org/journals/jams/2000-13-03/S0894-0347-00-00338-6/…
This is not really a physical principle
 
7:59 PM
That's interesting, sending $c \to \infty$ in $(\frac{1}{c^2} \frac{\partial^2}{\partial t^2} - \nabla^2 ) \psi = 0$
 
8:35 PM
Why is it so hard to make color epaper display?
 
@NovaliumCompany Have you seen the type of novel setup it takes just to get 3 colour epaper?
 
no?
Just use the lcd method but with the capsules?
black/red, black/green, black/blue
 
It would be hard to do a lcd method I imagine, there's no way to change the intensity of each colour AFAIK, so i don't think it would work like a normal screen does
 
8:51 PM
What if you put very small current? So only part of the balls get attracted?
 
@NovaliumCompany The way I've seen them do 3 colour (I can't find the video anymore) seemed really convoluted. They had 3 different inks in each pixel, and they could manipulate the currents in specific ways to make only one of the inks float to the surface of the display
 
Well, that doesn't seem so complicated
 
@NovaliumCompany what they had to do to get the inks to respond was the weird part, thats why i wish i could find it again
 
Are the balls ionized to different levels or?
 
@NovaliumCompany youtube.com/watch?v=MsbiO8EAsGw It's in this video somewhere
about 4 minutes in he starts to draw how it supposedly works with the 3 colours, and that was only red white and black (although this might actually be a very novel approach, and not the best method)
around 8 minutes he gets into the multi-colour specifics instead of general epaper stuff
 
9:08 PM
Why not make it red blue green
I mean, I believe it can be made an rgb epaper using neighbouring capsules and the method in the video
 
@NovaliumCompany It doesn't seem like you get much mixing from it. Odds are attempts at red blue green just look awful
 
If you have 3 of those red, white, black capsules next to each other but one of them has green instead of red and the other one blue?
The 3D cube example looks damn good to me
A question:
How do startups make their prototypes. For example, If I was the creator of the epaper displays and I wanted to build a prototype, how would I go about doing this?
I mean, epaper displays currently are manufactured by special machines which do the microscopic work and so on...
 
9:25 PM
@NovaliumCompany Uh, you pay money to acquire the machines and resources you need? I don't really understand the question.
 
So it's pretty expensive?
How do you know what machines and resources you need? You ask your engineers?
 
Well, whether it's "expensive" depends on your definition, but sure, you certainly need money to make money.
 
@ACuriousMind Or at least time.
 
@NovaliumCompany I don't quite understand how one would arrive at the stage of wanting to make a prototype for X without knowing how one manufactures X.
 
@ACuriousMind What's so hard to understand about it? I may know how the technology works, but not how to manufacture it (the steps, techniques...)
 
9:32 PM
Well, then you first need to pay someone to figure that out for you :P
 
Got it. Simply put, you need money.
 
@NovaliumCompany You could also invest the time to figure out how to manufacture it; but with access to money it's probably easier, because you can go to someone with experience in manufacturing already and it's one less thing you personally have to do well
 
Alright, thanks guys
Goodnight
 
9:51 PM
Btw can the epaper capsules be made bigger?
Like, "lower resolution"
Just physically bigger epaper capsules?
 
 
1 hour later…
11:21 PM
@vzn No, the book. My secretary bought a laptop, jewelry, and a car, on the P-card. I took her filming porn in her office to get her dismissed because she was a state employee. (boards.atlantafalcons.com/topic/…) You cannot make this stuff up. This is also why I do independent research with an affiliation: I don't have to deal with the dynamics of a university.
So, yes, there's a book in the works. It's already in editing.
 
11:42 PM
0
Q: Why did my ancient question suddenly got attention?

NeinsteinAlmost exactly 4 years ago (07.18.15) I asked this average-awful question: Naked singularity: how would it behave?. At that time I got a mediocore answer the same day that I accepted a bit later, got some views, then the question was forgotten - common boring story of most SE questions. Fast for...

 

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