This is the Realm of Simply Beautiful Art

2:11 AM

Narrowed it down it seems this is causing trouble

$z_{o} \in \mathbb{Z}$ and $\big\{z_{o}\big\}_{j=1}^{\infty} \subset \mathbb{Z} \backslash \big\{z_{o}}\big\$

No, I'm not the best with latex though

@user21820 3 days to Galapagos. I'm having my sister login to my account everyday to get the 100 day badge. I'm at 80 now seems like a waste to let it go, especially given I don't have any gold badges, although admittedly it doesn't really have the same meaning as the others

Feb 12 is coming up as well.

@DavidReed Hahaha!

Although I may actually wind up coming in less as in addition to the single class I am taking I have to (on my own) go through a semester's worth of psychology, sociology, more biology, and 2 semesters worth of chemistry, in preparation for the MCAT this summer

I see.

@user21820 Would you mind if I anonymously posted your comment on a distinguished frame on Physics SE to see what is said?

2:28 AM

@DavidReed It's up to you. Note that I said it's a philosophical argument, not a physics one, that can justify a preference for having a distinguished frame of reference. Also that logically the current theory of relativity can trivially be extended conservatively by adding a single constant-symbol, so it's wrong for anyone to claim that relativity forbids a distinguished reference frame.

@DavidReed GAMIFICATION IS EVIL!

What is gamification?

Making games out of everyday shit

like awarding badges on MSE for certain actions

in an effort to get obsessive compulsive nerds to spend more time on the site

AND IT HAS (KIND OF) WORKED ON YOU!

DON'T GIVE IN! RESIST!

It only worked once I realized I was close to it, and all it succeeds in doing really is making sure one types in "math.stackexchange.com" every 24 hrs.

I will say they have kind of made this into an MMORPG with the reputation

@XanderHenderson It worked on me too. The first time I tried to get that badge, I failed because one day I just didn't feel like using my computer. The second time I succeeded.

2:36 AM

heh

grinding away with new "powers" as you level up

I MUST MAKE MY ePENIS THE BIGGERIST!

And then you realize that bot-like accounts like DSG can grind the ePeen better than anyone, and you cry :'(

Generally I don't notice it until I'm close to one. A week ago I could care less about rep than now that I'm at 1930 I feel a strong urge to hit 2000, after which point i will stop caring again.

heh

that being said, when I have more XP than this guy, I might retire :D

@user21820 I will have to chew on this. Your approach to physics is different than mine. Not to say its wrong, just different. I have never though of theories in physics in terms of being expressed as a language over FOL.I would have to think more on it from a perspective of translating the model into having some practically possible real-world implications.

2:43 AM

@DavidReed I see. Well by definition, conservativeness of the extension implies that the extension proves exactly the same theorems over the original language that the original does. So the only extra information 'gained' is in the theorems involving the extra symbols. Now in the case of constant-symbols, some people think that almost nothing is gained. I think it varies. For example you could axiomatize groups using just one binary function-symbol. But that does not elucidate the structure well.

It hence is quite philosophical whether a conservative extension is 'superior' to the original even for constant-symbols. (We are not even talking about non-conservative extensions, as in my claim that there is some philosophical reason to believe there is a distinguished reference frame.)

I guess the point I'm trying to make is that mathematical theories do not always perfectly translate over to reality, which is of central concern in physics. For instance, I do not think of the Banach-Tarski paradox as literally meaning one can cut up a tennis ball and build two out of it because the mathematical model of a sphere is not subject to the same rules

as a physical sphere made of matter (a tennis ball is not infinitely dense for instance, and is subject (under the constraints that would be of interest) to conservation of matter.

I find your approach fascinating though

I don't think I've ever met someone that has your genuine passion for logic

3:02 AM

@DavidReed That's correct. As you see from Terence Tao's answer to my question about Lebesgue integration, he too believes that physics need only very weak foundations and hardly anything near the Lebesgue measure.

hrm

Well you need the notion of measure for the probability theorems to work out. I'm trying to think of the degree to which they are used in things like statistical thermodynamics

Can you link the post?

Q: Physical meaning of the Lebesgue measure

48

Question (informal) Is there an empirically verifiable scientific experiment that can empirically confirm that the Lebesgue measure has physical meaning beyond what can be obtained using just the Jordan measure? Specifically, is there a Jordan non-measurable but Lebesgue-measurable subset of ...

@DavidReed Apparently, it seems Jordan measure is more than enough.

o/ there @user21820

@Zophikel Hi there! How are you?

@user21820 great ! nearly done with chap 2.) of my complex varibles book

3:10 AM

Nice. What's next?

@user21820 Calcuating Real Integrals over Contours

i'm going to be stuck on that for a while :>)

Ah okay.

@user21820 I'm thinking along the lines of whether you need the theorems in statistics that rely on dominated convergence for things along the following lines:

https://en.wikipedia.org/wiki/Statistical_physics

https://en.wikipedia.org/wiki/Ergodic_theory

@DavidReed I'd bet they don't need the full theory. In many applications of DCT one can get the results via hard bounds.

In fact, I loved to do that in the measure theory course I took last time; I would solve every problem that obviously wanted me to use DCT using hard bounds instead.

also anyone wanna hear some meme news :)

3:24 AM

@user21820 If you need it for the CLT (and I haven't seen a proof without it) then it is difficult to imagine studying things like entropy and energy distribution in thermodynamics without it. Ironically, the same author here gives several proofs of it, if you're curious to see if you can escape it. The first two proofs he gives make use of it. I haven't gone through all of them:

https://terrytao.wordpress.com/2010/01/05/254a-notes-2-the-central-limit-theorem/

@DavidReed A long time ago, I managed to prove CLT for coin flips by purely elementary means.

I suppose my proof could be adapted to prove it for all distributions, but I've never tried. I'm quite sure that CLT does not need Lebesgue integration, but I've never seen anyone mention the reverse mathematical strength of CLT.

If you're interested, I could give you a sketch of my elementary proof.

Bear in mind this doesn't necessarily mean that lebesgue measure is "physically" meaningful, rather that it proves things in the realm of human reasoning that are useful for studying and predicting physical nature

Let's ask SE!

I shall post it now

@DavidReed Ask about CLT?

Q: Do you need dominated convergence to proof CLT?

0

Does the proof of the Central Limit Theorem rely on the Dominated Convergence Theorem?

statistics probability-limit-theorems

@DavidReed There is a serious problem with just caring about whether a formal system efficiently proves things that are useful for predicting things. Note that given any sound formal system S, we have that S+¬Con(S) is consistent but unsound, and yet proves everything that S proves. So it is 'as useful' for predicting things, except that it also predicts some rubbish that we can never refute empirically, because ¬Con(S) effectively says that some program halts on some input but it never does.

That's why I'm so concerned with the whole system having real-world meaningfulness, otherwise we face such kind of issues.

3:39 AM

Let me give you an example of what I mean

@DavidReed You should have asked for the reverse mathematics point of view, otherwise nobody will give you the answer that is actually relevant to our conversation.

Arrhenius equation

The Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that Van 't Hoff's equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula...

Notice how much k resembles the normal distribution

Now granted this is actually not a good example as its described as an empirical law

what is reverse mathematics ?

but there are more formal instances where you need the fact that when dealing with a shitload of particles you can assume their energy/velocity etc is normally distributed

A: Are sets and symbols the building blocks of mathematics?

@Zophikel It's a branch of mathematical logic, roughly concerning the analysis of different formal systems and their 'strength', and what theorems can be proven in some but not weaker ones.

12

The things you actually write on the paper or some other medium are not definable as any kind of mathematical objects. Mathematical structures can at most be used to model (or approximate) the real world structures. For example we might say that we can have strings of symbols of arbitrary length,...

3:44 AM

Feel free to edit it if you would like

@DavidReed I've to go in a while.

Me too :(

If someone doesn't answer soon I'm just going to delete it and drop it in main chat

Kimchi's response does seem to imply that at least there are weaker versions of it that does not

@user21820 Here is a better example: en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution

"The distribution is seen to be the product of three independent normally distributed variables p x {\displaystyle p_{x}} p_{x}, p y {\displaystyle p_{y}} p_{y}, and p z {\displaystyle p_{z}} p_{z}"

Yokai The Monster

5:43 AM

This is the true legend :- stackoverflow.com/users/22656/jon-skeet salute him :- stackoverflow.blog/2018/01/15/thanks-million-jon-skeet/…

De Moivre–Laplace theorem

8:19 AM

@DavidReed: I did a Google search and it turns out that I have essentially gotten an early version of CLT:

In probability theory, the de Moivre–Laplace theorem, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions. In particular, the theorem shows that the probability mass function of the random number of "successes" observed in a series of n independent Bernoulli trials, each having probability p of success (a binomial distribution with n trials), converges to the probability density function of the normal distribution with mean np and standard deviation √np(1-p), as n grows large...

I'm 300 years too late, though.

8:31 AM

@DavidReed: I also found the following arXiv but I have not read it:

arxiv.org/abs/1207.6078

It claims what I claimed, namely that CLT can be proven elementarily.

2:00 PM

@amWhy: Hello!

@user21820 Hello! Good morning (ahem, good evening?)!

Hi! Well I have never seen so much trouble on Math SE directed towards me before.

@user21820 Given the Chen rant on Meta?

It's clearly not just one user that's at it, too. Who knows how many others are trying to talk behind my back. Sure, I can't see what they are saying but I already know it. They just cannot stand to have things done right.

@user21820 I feel precisely the same thing, and some of them get mad enough to turn around and serial delete my posts. People starving for more rep get desperate for it, and anyone standing in their way triggers the ire!

2:09 PM

I'm actually quite appalled at how many people on Math SE don't care about violence. So many try to ignore that aspect, as if it's unimportant, and yet it's the reason humans will be the most likely candidates for destroying the habitable earth.

There will just be nobody left to read the 'brilliant writings' that would just be dirt buried in the ashes of civilization.

@user21820 Indeed. And it's even more appalling that it happens here, where the topic is "mathematics".

Yes! I couldn't believe that apparently mathematics people would do this... I felt I had no choice but to put everything out in the public so everyone not just those with 10k rep can read everything he said.

I don't blame you. I think it's terribly sad when megalomaniacs and/or sociopaths become mathematicians or mathematicians become megalomaniacs/sociopaths. I think, given all the rants on meta about "my answer was deleted!!! " "My questions was closed, why?" It may, in some cases, as with gimusi, we need to stand up and state the facts; Perhaps I need to start listing comments left, in case of deletion, when I encounter problematic posts, and particularly when encountering frequent offenders

2:28 PM

@amWhy That's why I don't do anything until I have very solid evidence. =)

And then I dump the whole lot. =P

@user21820 =P

@user21820 I am downloading pdf now

My proof for the Bernoulli case looks very different from the one on Wikipedia, by the way.

Nice find!

Though they were only able to get the weak form of large numbers

I haven't gone through the proof but the abstract uses only the Riemann Integral for CLT

@DavidReed One day when I have nothing to do I will attempt to prove all that with bare hands.

2:51 PM

@amWhy: By the way, see the comments under my answer. Apparently some people are not satisfied with the size of the helping.

I think you and him may argue even more than you and I ;)

Its funny to watch sometimes actually

3:52 PM

@amWhy If you're here right now, I can tell you who is talking behind my back.

@user21820 Sure go ahead. We can always move it to trash, anyway.

Or if you'd rather, we can go to another, newly created chat to do so.

I think we're both room owners here in this chat; oops, perhaps you'll want to postpone now, @user21820

I think never mind; the less I say the better.

→ 2 messages moved to trash

4:14 PM

I see only two users... pretty pathetic chat, too.

Heh. There's so much junk underground that I don't feel like digging anymore.

5:10 PM

@amWhy @XanderHenderson: Now the question asker comes to upvote his friend's comments on my post. What beautiful cooperation!

5:21 PM

Sigh...

5:41 PM

@user21820 Ultimately, it is really a sad, sad state of affairs: two wanna-bes having each other's backs. Big sigh!

7:05 PM

@XanderHenderson Do you think Martin's answer here is acceptable?

https://physics.stackexchange.com/questions/380814/is-the-notion-of-lebesgue-measure-a-necessary-construct-for-statistical-physics/380816#380816

I'm trying to think of why you would NEED these functions to be lebesgue integrable.

Nvm, I think Daniel sank has just settled that

7:38 PM

@user170039 I see you have your Archive (auto site, which you should probably keep in a notebook anyway, because it aint a chat, it's you talking to yourself. Your "Archive"? Can't comment, don't want to, but I can see your preoccupations and fixations. Seeing what I see, and saw at your Random Discussion chat, you might want to affiliate at another SE site, because I see very little mathematical interest in the things you are fixated on.