100 year floods are not happening more often in most cases - it is just that the central limit therom teachs us the 10 year flood is almost as high water as the 100 or even 1000 year flood.
The math that explains why bell curves are everywhere
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Re: The math that explains why bell curves are everywhere
#22100 year floods are not happening more often in most cases - it is just that the central limit therom teachs us the 10 year flood is almost as high water as the 100 or even 1000 year flood.
Explain?
What are "most cases"?
Re: The math that explains why bell curves are everywhere
#23Earlier quoted context omitted.
As to ye philosophy of “why” the CLT gives you normals, my hunch is that it’s because there’s some connection between: a) the CLT requires samples drawn from a distribution with finite mean and variance and b) the Gaussian is the maximum entropy distribution for a particular mean and variance I’d be curious about what happens if you starting making assumptions about higher order moments in the distro
IIRC there's a video by 3b1b that talks about that, and it is important that gaussians are closed under convolution.
That makes it an equilibrium point in function space, but the other half is why it's an a global attractor.
Re: The math that explains why bell curves are everywhere
#24Hot take: bell curves are everywhere exactly because the math is simple. The causal chain is: the math is simple -> teachers teach simple things -> students learn what they're taught -> we see the world in terms of concepts we've learned. The central limit theorem generalizes beyond simple math to hard math: Levy alpha stable distributions when variance is not finite, the Fisher-Tippett-Gnedenko theorem and Gumbel/Fr…
Most things aren't infinite or extreme, though. Almost by definition, most phenomena aren't extreme phenomena.
Re: The math that explains why bell curves are everywhere
#25Bell curves are everywhere because all distributions of any properties clump in some way at some level. The basics of any probability shows this. The result is you “seeing” bell curves everywhere. Aka clumps.
This is a tautology to the extreme.
Re: The math that explains why bell curves are everywhere
#26Re: The math that explains why bell curves are everywhere
#27A little disappointing. All about the history of bell curves, but I don't think it does a very good job explaining why the bell curve appears or the CLT is as it is.
Re: The math that explains why bell curves are everywhere
#28Earlier quoted context omitted.
As to ye philosophy of “why” the CLT gives you normals, my hunch is that it’s because there’s some connection between: a) the CLT requires samples drawn from a distribution with finite mean and variance and b) the Gaussian is the maximum entropy distribution for a particular mean and variance I’d be curious about what happens if you starting making assumptions about higher order moments in the distro
It is the not knowing, the unknown unknowns and known unknowns which result in the max entropy distribution's appearance. When we know more, it is not Gaussian. That is known.
Exactly this. From this perspective, the CLT then can be restated as: "it's interesting that when you add up a sufficiently large number of independent random variables, then even if you have a lot of specific detailed knowledge about each of those variables, in the end all you know about their sum is its mean and variation. But at least you do reliably know that much."
Re: The math that explains why bell curves are everywhere
#29Hot take: bell curves are everywhere exactly because the math is simple. The causal chain is: the math is simple -> teachers teach simple things -> students learn what they're taught -> we see the world in terms of concepts we've learned. The central limit theorem generalizes beyond simple math to hard math: Levy alpha stable distributions when variance is not finite, the Fisher-Tippett-Gnedenko theorem and Gumbel/Fr…
I've often described this as a bias towards easily taught ("teachable") material over more realistic but difficult to teach material. Sometimes teachers teach certain subjects because they fit the classroom well as a medium. Some subjects are just hard to teach in hour-long lectures using whiteboards and slides. They might be better suited to other media, especially self study, but that does not mean that teachers should ignore them.
Re: The math that explains why bell curves are everywhere
#30Earlier quoted context omitted.
A lot of times on HN when a math topic comes up that isn't about 3b1b, someone will jump in to say "this isn't as good as 3b1b". Last time I saw that, I was moved to comment: https://news.ycombinator.com/item?id=45800657 3b1b doesn't have the same goal as Quanta, or as introductory guides. It's actually not that great a teaching tool (it's truly great at what it is for, which is (a) appreciation and motivation, and (…
there is no getting around that learning math requires actually having to buckle down and read and do math . A video will not suffice.
well for one who does buckle down and read and do math, the expected amount of new information brought to them by a 3B1B video as supplementary material upon a topic (with the normal distribution being one that admits a direct comparison from the article) is nonzero, by merit of it possibly having ideas to convey from outside their usual purview and formal background that may be applicable to the doing of math (as has been the case for me, someone who [does math](https://oeis.org/wiki/User:Natalia_L._Skirrow)), while for Quanta fluff pieces it's zero.
by the metric of "if this expository piece were to be taken to a time before its subject had been considered and presented to researchers, how useful would its outline be towards reproducing the theory in its totality," Quanta's writings (on both classical and research math) mostly score 0