/sci/ - Science & Math

explain the difference between the law of large numbers and central limit theorem. now.

>>11209594

law of large numbers is just something we all knew intuitively already

>>11209550
>tfw English, Spanish or Japanese are not my native tongues
>tfw I will never comprehend a single word

>>11209550
Isn't it completely obvious, or do I misunderstand something? When you e.g. throw five dice, you will much more likely have some central value, than all 1s, because there are several possible ways you can get 15, 16 etc.

>>11209709
well dice are usually assumed to be uniform distributons. but the CLT applies to almost any bounded probability distribution. so for example, if you had a bunch of very very loaded dice, or dice that were almost flat so only two sides would land, then even throwing a lot of those dice, you still get a gaussian distributed sum. and the gaussian shape gets more and more perfect the more dice you through. it's kinda intuitive but the fact that it works even for sums of very strange probability distributions is interesting.

so that means we see gaussians pop up in nature all over the place, like e.g. people's heights.

mysteriously, in QM a simple harmonic oscillator has a gaussian wavefunction for completely unrelated (?) reasons

>>11209550
did he really say that or is it just a meme?

>>11209868
>a simple harmonic oscillator has a gaussian wavefunction for completely unrelated (?) reasons
the Gaussian shows up in QM because it's the maximum entropy distribution for a given variance
it shows up in the CLT by replacing the distribution('s characteristic function) with its second-order Taylor approximation, i.e. neglecting all higher moments beyond the mean and variance
if you look at the derivation of the maximum entropy, it's not completely unrelated, but the link is indirect at best

https://en.m.wikipedia.org/wiki/Daniel_Everett

This guy got educated, dumped his wife and turned atheist just so he could BTFO Chomsky.

>>11209991
bro i wrote a paper on this once and saying that they don't have grammatical embedding is idiotic, its just that the grammatical devices marking it have null phonological realization. Also the stories about them having trouble with arithmetic are way overblown.

>>11209868
>or dice that were almost flat so only two sides would land,
It's called a coin.

>>11209550
Isn't this a more extreme version of the "if you don't learn a language before 8 years old you will never be able to speak it at a native level because of plasticity" statement?

>>11210139
no

>>11209594
>>11209597
>law of large numbers
are stembugs the biggest clowns in existence?

>>11209550
>Chumpsky quote
Imagine self-refuting yourself this badly.

>>11209594
>>11209550
Imbecile.

>>11209550
This is no different than arguing that arguing that "all things that can be learned are already known by your braincand jist need to be brought out." He's just redefining the word "learn" but to his credit so did Socrates.

>>11209594
Law of large numbers says that as the number of trials grows, the experimental probability approaches the theoretical probability.

Central limit states that as you add a bunch of random variables together their means create a normal distribution. Thought about in this context the central limit theorem is common sense. Of course the means of a distrivution when put into practice are going to dance around the theoretical mean.

The difference is the distribution vs soecifically referring to the mean.

How'd I do?

how does chumpsky explain dogs understanding commands

>>11210703
He can't.

>>11209603
Is that what he's saying? I thought he was saying that if you didn't have some innate, built-in language (be it English, Spanish, Japanese, or whatever), you'd never be able to comprehend a single word ... of anything, because the whole concept of language and communication via language would be a mystery to you.