Nassim Nicholas Taleb is triggered, then calms down a bit toward the end.
The math that explains why bell curves are everywhere
91–100 of 133 posts
Re: The math that explains why bell curves are everywhere
#92> the “steadfast order of the universe” that eventually overcame any and all deviations from the bell. I can’t believe the author wrote that without explaining why it’s called the bell curve. I find the article spends a lot of time talking about repeating games without really getting to the meat of it. If you throw a dice a million times the result is still following a uniform distribution. It isn’t until you start s…
A huge amount of nonfiction writing, especially nonfiction books, feels padded to length.
It’s something I’ve gotten out of AI. Summarize, please, and it’s pretty good at extracting the key ideas.
If I want a story I read fiction, which is writing with a much wider set of objectives than just conveying information and ideas (though it can do that).
Re: The math that explains why bell curves are everywhere
#93A result of broader applicability is that of convergence to infinitely divisible distributions, more generally the stable distributions https://en.wikipedia.org/wiki/Infinite_divisibility_(probabi... https://en.wikipedia.org/wiki/Stable_distribution This applies even when the variance is not finite. Note independence and identical nature of distribution is not necessary for Central Limit Theorem to hold. It is a suff…
I think part of why we're much more likely to learn about the iid, finite-variance CLT is that it's a lot easier to prove than the more general ones.
Re: The math that explains why bell curves are everywhere
#94A result of broader applicability is that of convergence to infinitely divisible distributions, more generally the stable distributions https://en.wikipedia.org/wiki/Infinite_divisibility_(probabi... https://en.wikipedia.org/wiki/Stable_distribution This applies even when the variance is not finite. Note independence and identical nature of distribution is not necessary for Central Limit Theorem to hold. It is a suff…
I think part of why we're much more likely to learn about the iid, finite-variance CLT is that it's a lot easier to prove than the more general ones.
Yes that's a big part. The proofs get hairier otherwise.
But I think there is more to it, the convergence to Gaussian also gets slower.
In practice, we deal with finite averaging, so speed of convergence matters. For some non-iid case, the convergence may be so slow that the distribution cannot be approximated well by a Gaussian.
Re: The math that explains why bell curves are everywhere
#95Okay at my core I'm an inductionist. However this article is a mere tautology at best.
The article doesn't explain why. It explains a bunch of cases and works backwards to show that the original premise was true. This sounds fine but the end of the article specifically mentioned that this is dangerous because the world doesn't always work like this.
This is the problem with induction, it might work in 99% of cases, I've never seen a Black Swan so there must not be any black swans?
Deduction has more value when it comes to math specifically... I'll admit that as an inductionist.
Re: The math that explains why bell curves are everywhere
#96A requirement is multiple independent influences. An example of what shouldn't target a normal distribution are a single course's grade outcomes, having a teacher and a defined curriculum goes against that. Yes, there is a variability of student effort and aptitude. But a top teir university selects a group of students based on some merit their student body isn't random. There are airheads who were dragged over the finish line with connections and family money and some students fall prey to substance abuse and mental illness. I argue a different distribution recognizing that a skilled teacher can get a class grade distribution centered around at least a B of not B+, A-. I feel grading on the curve and limiting A's to a fixed percent target can encourage bad test design or worse bad grading.
Re: The math that explains why bell curves are everywhere
#97Earlier quoted context omitted.
> Anyone familiar with linear algebra will know that repeated matrix multiplication by non degenerate matrices reveals it's eigenvectors. TIL that I'm not "familiar" with linear algebra ;) But seriously, thanks for sharing that knowledge.
If you are not speaking in jest (I strongly suspect you are), knowledge of linear algebra is one of the biggest bang for buck one can get as an investment in mathematical knowledge. So humble and basic a field. So wide it's consequences and scope.
You're doing this multiple times, but it's can only mean "It Is" or "It Has".
Re: The math that explains why bell curves are everywhere
#98Earlier quoted context omitted.
If you are not speaking in jest (I strongly suspect you are), knowledge of linear algebra is one of the biggest bang for buck one can get as an investment in mathematical knowledge. So humble and basic a field. So wide it's consequences and scope.
You're doing this multiple times, but it's can only mean "It Is" or "It Has".
Thanks for the heads up. I meant 'its'.
Phone autocorrect always interferes and I get tired and lazy about correcting it back. It does get it right most of the time.
Re: The math that explains why bell curves are everywhere
#99> the “steadfast order of the universe” that eventually overcame any and all deviations from the bell. I can’t believe the author wrote that without explaining why it’s called the bell curve. I find the article spends a lot of time talking about repeating games without really getting to the meat of it. If you throw a dice a million times the result is still following a uniform distribution. It isn’t until you start s…
True and false. You don't need anywhere near a million samples to get a good approximation for your normal distribution. Far fewer than 100 is sufficient (and 14 is a fine place to start if you are really constrained on data and need to get to 90-10).
Re: The math that explains why bell curves are everywhere
#100[dead]