lol, today's xkcd is pretty good:

dark matter? only the universes biggest hidden variable theory o_O

wow those are some heavy space lines

Isn't there some sort of theory that takes field lines to be more fundamental than the fields? I'm pretty sure I heard that in a pop science book, so I'm not sure how valid it is

I think that's roughly the view that Faraday had

@danielunderwood "fundamental" is a very annoying word. It doesn't actually mean anything most of the time :P Sure, instead of thinking about a vector field as a collection of arrows you can think about it as its collection of integral curves (=field lines). What does it mean to say one of these things is more "fundamental" than the other?

@ACuriousMind Is your picture from the game 'age of wonders I'?

@AlexClark No, it's from Pillars of Eternity 2

AoW was an excellent game too, though ;)

:D

The case of fringes in the maths world

@Secret I don't think there's anything surprising there. Think about what these "fringes" would be if the two numbers were integers/rationals: Then they would be exactly periodic and the multiples of the two numbers would coincide there. But of course irrationals are very close to rationals, so what you're seeing is simply a slightly distorted version of what you'd get if you did that for two rationals close to $e$ and $\pi$.

@Secret For instance, fractional approximations accurate to two decimal places are 22/7 and 19/7, so given the inherent approximation of drawing such a graph, it's very likely all you're seeing is the pattern for 22/7 and 19/7.

@Semiclassical what's this?

@Akash.B It's the current xkcd

@ACuriousMind What do you meant by xkcd?

@Akash.B xkcd.com

It's a webcomic

@ACuriousMind what does it says?

@ACuriousMind Ah I see, though I would kinda expect that as the integers gets bigger and bigger, eventually, say the contribution of the 100th decimal place will make an impact to decimal places near the unit place due to the carryovers piling up in the multiplication process, but the fringes showing this quasiperiodic like phenomenon suggests somehow, if the decimal places of an irrational gets too tiny, they never can contribute to corrections that shift e.g. the 22/7 behaviour. But then again I

have not tried plotting 1000001 to 10000020 yet, so perhaps the quasiperiodicity does breaks down higher up

@Akash.B I don't understand the question - can't you read it yourself? (if it doesn't make much sense to you: it's meant as a joke)

@Secret Sure, the higher you look, the less it will look like the pattern of the crude approximations. I still don't see what's interesting about that, though.

Well, blame the human tendency to see patterns when there is nothing interesting. I thought I saw an exact periodic structure in the two multiples and thought I can use that periodic structure to predict when the coalescence will happen, but more detailed investigation showed it is only quasiperiodic, thus it is not very useful, but it is still interesting for me to understand how it arises

btw, confirmed what you said, as the integer passes 100, the difference started to become visible (red and blue are the approximations) and it gets larger, thus result in the drifting phenomenon

At higher 1000-1020 for $\pi$ and 1150-1190 for $e$ the fringes have drifted so much that they are anti-quasiphase to each other, though the width of the fringes is relatively unchanged. I am guessing that's the moire pattern that is described in the answer

so the fringes, regardless of how big the integer is, is dominated by the 22/7, 19/7 fringes beaviour and larger contributions of lower decimal places only serves to shift the pattern

Actually... there's another moire pattern, a very broad fringe whose centre where $\pi,e$ is anti-quasiphase with $22/7,19/7$, situated near 1150 is separated from the next one by 1000 something units

@ACuriousMind ahh that is true. Just different ways of defining a vector. And I kind of dislike the word fundamental too, but I'm not sure what would be a better word.

I've just read the wiki page on tensors. I must say that it is very interesting. Where can I learn more about them?

any good books that you have read?

Do you want to study tensors for math or for physics?

physics

Then I guess a decent GR book would suffice. Carroll is one.

Chapters 1 and 2, if I remember correctly.

There was a Blue here too. Now a Yellow. Color invasion on PSE?

The best explanations I've seen for tensors have been video lectures that present mechanics from a geometric perspective

Though those were after reading over some explanations in GR books, so they may have only made sense after that material

@Blue Now that's a printer.

Oh yeah I thought I read RGB

there is no red

I have an inkling there will be one soon.

They keep asking me to change my password...eventually I'm gonna run out of passwords -.-

Why?

lol

"security" reasons I suppose

@Avantgarde Actually, most printers have a CMYK color scheme, not RGB :P

@ACuriousMind Well, I learned something new. I've probably read about using cyan and magenta long ago..

password1...password2...password3

SO machine learning answers seems wanting...

just saw some iffy answers get upvoted

Gotta get their answers in to make people think they're good at ML

user asked about Keras non-trainable params...both answers mention hyperparameters which is not what Keras non-trainable params mean...-.-

both answers get upvoted

Speaking of which, have you happened to mess with exponential activations? I tried them out while playing around and they seem to have worked better than relu for my case, but I'm not sure if there was actually something better about them or if they were just converging faster.

Maybe they upvoted each other lol

I've seen SELU units being used

I don't know if there's any real advantage to them over a RELU or a PRELU

or a leaky relu

it's really just...try them out and see I suppose lol

I asked a stupid keras question over a year ago on SO and I still get answers and comments on it from time to time. I think it has a comment by me realizing what I did and I may have even self-answered it

I dunno how much I trust SO answers on stuff like that now -.-

probably stick with strict coding questions

Yeah I trained about 500 networks yesterday with different activations and layer numbers and hopefully I'll get a chance to comb through the results sometime this week. I was going to do it as they were training, but tensorboard got pretty unhappy

heh

And yeah I don't really trust SO answers that aren't purely conceptual now. I loved them when I started programming and could just copy/paste the answers, but I think some people kept doing that rather than trying to learn what they were copying/pasting

I also think there's an effect on SE where the better questions don't really get asked because the people with those questions have an idea how to find answers on their own

I've seen a lot of android stuff on SO that's just plain wrong lately too. And a lot of blogs that are the same. It's kind of sad

I just notice the ML ones...

maybe it's just sampling error on my part tho :P

Yeah I do wonder how much is wrong but I don't notice since I don't know enough

I'm sure I'm looking at stuff like that if I look up nutrition or some area that I don't really have any knowledge in

sometimes I find wrong physics answers...but not too often

I haven't really seen any that I recognized on this site. But I see news stories and blog posts that are wrong (or at least sensationalized)

I actually thought there was some project working to determine how reliable various articles on the internet were, but I don't remember what it was

o.o

@Blue Probably, yeah. But the last time I looked at a printer cartridge was many years ago.

I think facebook had something like that, but I was also thinking that there was a similar public project

Maybe it's not a whole project, but just something people are doing for fun? towardsdatascience.com/…

facebook is doing something about finding "fake news"

and removing it I think

"removing"

Censorship is always a fine line tho...

cus eventually you can certainly have politicians just ban vast swaths of media based on "fake news"

Yeah I definitely don't like government censorship. I think it also gets kind of bad for a private company to censor things if they've grown to be a large source of news. I don't really know what could be done about it though

Evening everybuddy. :3

@danielunderwood How are you? :-)

well I'm working on android code, so not the best lol

you?

Pretty good, thanks. I can code Android too, Java right?

Android Studio I suppose?

I'm doing this one in Kotlin

It's a lot like Java, but with some of the annoying parts taken out

But with more mysterious error messages

Hmm, cool. Are you working as an android dev, or just for fun?

It's an app prototype for work. I think it would take me a lot to work on android for fun

Well, I hope it works out well :) I see you code C++, that's amazing. I know quite a lot of programming languages but I never had the guts to learn C++, it seems complicated.

I have been unable to contact my dev in like a month...got ghosted...-.-

I tried to learn it once, but It didn't work out. It takes so much work to do simple things, but you get more control. Also the memory management system is also great. Like, if you are making a big open-world game, memory management comes in handy.

I really love C++, but it can be a bit of work. Especially managing the build system and dependencies. I use python for most stuff these days since it's so easy to do about anything

C is an interesting language to learn too and you can learn it in a weekend since it doesn't really have much to it. It's up to you to build data structures and everything though

O.O

Got a problem with C++? The bearded men will come and get you

Or maybe the bearded men go with C

@danielunderwood If I never have to manually allocate memory for arrays again it's too soon :P

it'll be*

How "manual" we talkin here?

Or some monstrosity like that...I haven't messed with C in a couple months

but that's going to lose your pointer anyway

just fix it with an a -= 2*2*2*2*2*2

Or I guess you could do assembly where you manage what's in the registers vs RAM yourself...I think. I haven't been fortunate enough to mess around with assembly

fun beans...

...I just took an hour to debug a problem that happened because android studio thought I didn't need some of the imports and automatically removed them

I added them back and it's like "Oh you're right, you did need those"

lol

Hi, is there a method to calculate the total curvature created by the mass of luminous matter in the Milky Way Galaxy? My goal is to find the extra space created by that curvature.

welp, I'm kinda out of ideas on what I should be doing now...

@mertyildiran not sure that's a well defined concept...perhaps if you embed space-time in a higher dimensional manifold you could make such a comparison...but then I don't know what that comparison would actually mean.

@enumaris what do you mean by "embed space-time in a higher dimensional manifold "?

well you can mathematically embed 4-D spacetime in some higher dimensional Euclidean space

that might make it possible to compare "straight line" lengths with "curved lengths"

@enumaris do you know a research done in this topic? I mean I can't be the first person in the world who wants to know the total curvature of the Milky Way Galaxy, right? I scanned the literature for a while but couldn't find any result.

It depends, maybe, on what you mean by "total curvature". As you've stated the question, it seems to be ill defined.

You could maybe integrate the Ricci Scalar over some space-time volume? In that case your definition of "total curvature" is basically (a constant multiple of) the Einstein-Hilbert action.

@mertyildiran the "total curvature of the milky way" is not a well-defined concept

And there is no "extra space created".

:(

I would enjoy the extra space...maybe lowers housing prices...

@enumaris by "total curvature" I mean the total difference in the curvature of space caused by the mass. If there is no mass it's flat space right? Then think that suddenly a single blob of a spherical object with 9 x 10^{10} solar masses worth of luminous matter appeared in the vacuum. So how much it bends the space and creates extra area/volume when it compares to vacuum state of that space.

@ACuriousMind by "extra space" I mean the increased area/space in this kind of an analogy en.wikipedia.org/wiki/Einstein_field_equations#/media/…

hmmm

@mertyildiran Yeah, that analogy doesn't stretch that far

@mertyildiran thing is, curvature in GR is not a single number, it is s a 4-tensor, I. E. a 4d array of numbers varying at each point in spacetime

Certainly one can compute the curvature around a blob of matter with a certain mass, but that just looks the same as the curvature around any smaller spherical body and is determined by the Schwarzschild metric

dang, I forgot to charge my phone

now it's running low on batteries

@ACuriousMind OK, let me simplify my question. The Schwarzschild metric is a special case of Einstein field equations for a spherical mass, with no angular momentum, no charge etc. right?

Aye

aye aye cap'n

Well, a special case of solutions

slaps ACM for bringing up technicalities again

aye aye cap'n

@ACuriousMind so you say, we get "4d array of numbers varying at each point in spacetime" as the output from the Schwarzschild metric?

He means the Riemann tensor when he says that. You can calculate the Riemann tensor at each point in space-time given the Schwarzschild metric.

@mertyildiran Yes, it's called the Riemann curvature tensor

You can compute it for any metric

big pain tho

tbf

OK with calculating the Riemann tensor at each point we get a curved spacetime right?

A flat spacetime will have R=0 everywhere, you can still calculate R even for a flat spacetime tho.

@enumaris so can we calculate the Riemann tensor just for 3D space? I mean excluding time dimension?

You can, but then such a tensor would depend on how you foliate spacetime

assuming the spacetime is globally hyperbolic anyways

in before ACM brings up more technicalities

@mertyildiran You can compute its restriction to a 3d subspace,but be careful: The essence of relativity is that there is no unique choice for "the time dimension"

Fun beans

@ACuriousMind OK, what would be the comparison of applying the 3D Riemann tensor to each point in a spherical volume with no mass and applying the 3D Riemann tensor to each point in a spherical volume with some mass in it. Wouldn't it shift the points outwards when there is a mass? So that the spherical volume extends?

@mertyildiran No, that's not how it works

*expands

When you go from one scenario to the other, it's not easy to define how you foliate the manifold in a consistent way.

But you will go from R=0 to R=some values

"expansion of space" really only happens in cosmological scales and not just because of curvature

Is it just me, or is the following unfair? Timothy downvoted the Ron MAimon answer at physics.stackexchange.com/questions/5888/… and claimed there was no need to explain why, because it should be obvious by juding the comments. Fair enough.

But then he writes up an answer that adds nothing compared to the accepted answer (a full long paragraph to come up with the exact same conclusion than the simpler accepted answer), and he doesn't even answer the OP question about the sinking of a black hole...

I feel like OP's "expansion of space" is related to the Shapiro delay. But it's not apparently how the Shapiro delay (which is path dependent) could somehow be integrated into some single number representing "extra space"

You also can't "apply a Riemann tensor". I'm sorry, but there's no intuitive way to explain the nature of curvature. Either you live with the rubber sheet analogy and don't ask in too much detail or you learn the formalism. At a certain level of detail, there's no way around the math

@ACuriousMind I'm not talking about the "expansion of space" actually. Please just think of the drawing of the Riemann tensor on a 3D graph. Wouldn't that drawing expands with a mass?

please don't ask us to imagine drawing a 4-D tensor on graph paper.

It leads to crying.

cries

^that

@enumaris but you guys said it's possible to calculate in 3D?

It is still a 4-tensor even in 3d!

You can calculate the values. Calculating a bunch of values is very different than visualizing them...T_T

Maybe you don't know what an n-tensor is: A 1-tensor is a vector, a list of numbers. A 2-tensor is a matrix, a 2d array of numbers. A 4-tensor is a bunch of numbers indexed by four indices. You can't really visualise it

OK, one last question: Do you know a software or any implementation of Einstein field equations in a programming language so that I can tweak with the values and see what happens in my computer? Not necessarily a visualizer.

Solving the EFE in any but the simplest cases numerically is rather difficult. I'm not sure implementations of EFE solvers exist outside of research code

I don't know specifically for the Einstein field equations...but something like Mathematica probably would handle stuff like that o.O

solving them is a whole different can of beans

but given a metric, calculating the curvature tensors and stuff is not too bad using something like mathematica (as far as I know)

@enumaris could you share the link to the related Mathematica page? I couldn't find anything except a page with some information mathworld.wolfram.com/EinsteinFieldEquations.html

uhhh...I have not had to deal with them...a quick google search yields these: library.wolfram.com/infocenter/MathSource/8847 web.physics.ucsb.edu/~gravitybook/mathematica.html

@enumaris OK, thank you so much!

np

hmmm you say that you can calculate the curvature for any metric. Is it possible to have a non-differentiable metric?

If so, does it still have a well-defined curvature?

I guess you wouldn't have a (pseudo?)-Riemannian manifold in that case though

@danielunderwood The metric has to be well-behaved in some sense, but it can get pretty weak

I'm sure @Slereah has examples with some very irregular metrics where you still get some sort of curvature

You can have a non-differentiable metric, yes

Although it needs to obey some rather specific properties

Depending on how regular you want everything to be

the curvature is then a tensor distribution

usually they're not very irregular, just

they're mostly used for boundary problems

response time faster than batman

ie the metric is $g^+$ inside some area and $g^-$ outside

If the metric is continuous and the derivatives aren't too badly behaved

the curvature is well defined as a distribution

If the metric is $C^0$ btw you lose a lot of theorems

Since you can't assume the existence of a normal neighbourhood

Which requires a $C^2$ metric

hmmm interesting. The metric itself is still required to be continuous, right?

yes

I mean I guess technically you could have non-continuous metrics, but then what are you even doing

What does $\delta'(x)$ mean as a matter source

Is that different than considering a point charge?

Point charge is $\delta(x)$

Ahh right. For some reason my brain didn't process the prime

Is there a standard term for these non-differentiable metrics or do they just pop up where needed?

there's a few terms, depending on the type

Geroch-Traschen class metrics

cut and paste metrics

thin shell metrics

distributional metrics

Or just $C^0$ metrics for the most general case

I'd say the most common term is thin shell metric but that is a specific type of spacetime

But there is a theorem

If your metric is of Geroch-Traschen type (that is, the curvature is a distribution), the matter distribution will only be singular on a 2D surface

So in effect they are kind of all thin shell metrics

[[[except for Colombeau algebra sort of metrics]]]

Also that is assuming you care about curvature

I've seen a few papers who just studied $C^0$ metrics for the sake of it

(mostly the causal structure)

In this solved example, we can see that isospin is considered to be conserved. At the same time we see that on the lhs we have 1 and 1/2, on the rhs we have 1/2 and 0. So why is it considered to be conserved?

@Slereah thanks!

pain

hunger

trying to wrap my head around rationalizability

mmm

you might say that you're trying to rationalize it

this ain't no joke bro

very serious

super cereal

@mertyildiran GR has recently been related to solid mechanics in this groundbreaking paper by Tenev-Horstemeyer and that opens up many possibilities; there are many simulation tools from engineering field that are nearly applicable, although they dont discuss this angle. arxiv.org/abs/1603.07655

You've been harping on that paper for almost exactly two years now, isn't it time to find some new material? It's not really related to what mertyildiran wanted to know either way.

Maybe he's Tenev or Horstemeyer's PR guy, can't blame him for that :D

@vzn 2 years PR'ing an article based on a basic misunderstanding at that, in all that time one could have learned GR, basic qft and basic renormalization and found out what the problem with merging them actually is, and why papers like this say nothing about it

D:

I feel like an elasticity link like this to Einstein's equations is in basic books in the sections I skipped

I guess people throw away decades based on basic misunderstandings vixra.org and no amount of friendly advice will help will only encourage further :(

That is a very counter-intuitive psychology result I don't appreciate very much yet

Relativity has the most papers on there, (3022) haha

@bolbteppa paradigm shifts move at the speed of human comprehension :P

@vzn Maybe the recent vixra.org/abs/1808.0205 is the "major paradigm shift" we need?

(I had that ready before you posted haha)

Both the author, and the contrarian in the comments section of that, reference stuff they wrote in 2003 or 2000 on this stuff, wow

'Climate Research (71)' the smallest

welp, 2 chapters of Game Theory down

some moderately interesting stuff in here

not as interesting as the RL book I had before tho

What's interesting about it

e.g. why would someone give up a susy book for it :p

Got W&B again today

hmmm, I think as a rigorous mathematical framework for figuring out player strategies, it's pretty interesting

If you were playing poker, could you figure out what they're doing

But I mean, it's strictly mathematical...doesn't really have to reflect real world decisions since in the real world the assumptions in Game Theory rarely prove true lol

so far in 2 chapters I've only gone over static games of perfect knowledge

so poker isn't in here lol

dynamic games of incomplete information doesn't start until chapter 8

Making chess is the pinnacle for a comp sci student, gaming poker for a game theory student :p

it's like 2 chapters per "type of game" roughly

Ah

next up is dynamic games of complete information

Oh man there's a 'Set Theory and Logic' section on there

on where?

vixra.org

"An alternative archive of 25013 e-prints in Science and Mathematics serving the whole scientific community"

they italicized "whole"

feels like they a re taking a shot at arxiv lol

It's arxiv backwards :p

ah

can I just submit whatever i want to there

(In every possible sense?)

Basically

It's where you go with your 'Shortest Refutations of the Zermelo-Fraenkel (ZF) Axioms' etc

hmmm

how to refute axioms?

I'd like to learn this skill.

1+1=2 <--- refute that?

I didn't know about arxiv's endorsement policy before...

It's amazing how uniform the relativity articles are in style, perspective, amount of equations, types of equations, versions of equations etc etc

even tho I've submitted multiple times to it lol

who has time to write this stuff and submit to vixra...

25,000 articles...

how is there so much time...

I try to be sure to write 5 papers a day

The real stuff is so hard, takes so much time, requires a hard honesty, that I get the sense it's all about feeling like you're writing by candlelight a note on electricity to (or as!) Benjamin Franklin for most of this

maybe if someone like Perelman chose to publish exclusively on vixra...

hmmm

hmmm vixra.org/author/george_rajna

(He may be :p)

Woah, 2895

look at the dates

his "papers" seems to be just summaries of various articles cobbled together?

more like a blog maybe...

4 a day...but how can he even type that much lol

This is a vice article in waiting

copy pasted?

"the Planck Distribution Law" shows up a lot in his early work :p

More blog than I could make lol

I wonder if I submit a physics paper

on GR

I did have a classmate that would write like that though. I saw one of his senior lab papers and it was like 20 pages. Most of ours were 1-2

and it's entire body is "I'm BATMAN"

if it would work...

And it was just full of stuff pulled out of tectbooks

I swear I've seen something like that uploaded somewhere

like format it to look like a PRD paper

2 columns and everything

but the entire text just repeats "I'm BATMAN"

can even add some equations like

I+M=BATMAN

$I^M\subset B_{ATMAN}$

$_\mathcal{I}\mathbb{M} \in \mathcal{B}\int_{-\infty}^\infty A^T \otimes _M A dN$

someone do it

Format it really well

$I \cdot \mathbb{M}(B,A,T,M,A,N)$

So he's a tensor multiplied by the identity in the ring the tensor maps to

sounds legit

fqxi.org/community/forum/topic/1445

I guess a world w/ feedback etc builds up around all this

O.O

haha

What is going on here

Could you imagine the emails that the more well-known physicists get?

I once mailed a well known physicist without realizing he was well known.