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A comment on Gaussian Distributions Are Soap Bubbles.

Re:Gaussian Distributions Are Soap Bubbles by woopwoop on Saturday November 11, 2017 @09:08AM (#15676403)
I was going to comment that what's going on here doesn't have much to do with the Gaussian distribution. In high dimensions, almost all of the volume of the unit ball is concentrated near the unit sphere. In the first comment, Frank Morgan makes the same remark, pointing out that you get the same effect with the uniform distribution on the unit cube in high dimensions.

High dimensions are weird.

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Re:Gaussian Distributions Are Soap Bubbles by paulgb on Saturday November 11, 2017 @10:00AM (#15676590)
It's true! I just made a colab notebook to visualize the effect: https://colab.research.google.com/notebook#fileId=1znFHwemxa...

(seems to require a Google account, sorry in advance)

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Re:Gaussian Distributions Are Soap Bubbles by semi-extrinsic on Saturday November 11, 2017 @01:51PM (#15677532)
Instead of plotting the cumulative mass distribution, why not just plot the mass distribution itself? I.e. the derivatives of the curves you've plotted?
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Re:Gaussian Distributions Are Soap Bubbles by tomas_fiers on Saturday November 11, 2017 @02:01PM (#15677582)
Great, thanks!
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Re:Gaussian Distributions Are Soap Bubbles by Sharlin on Saturday November 11, 2017 @10:47AM (#15676770)
In retrospect it's pretty trivial to see why it is so: it directly results from the basic fact that the hypervolume of an n-body grows as the nth power of linear size.
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Re:Gaussian Distributions Are Soap Bubbles by dwaltrip on Saturday November 11, 2017 @03:02PM (#15677865)
How much of this stuff has fundamental implications for the hardest problems that scientists, researchers, and policy makers are facing today?

My intuition says many of those problems have high dimensionality, but I'm not really confident about my intuition here.

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Re:Gaussian Distributions Are Soap Bubbles by trhway on Tuesday November 14, 2017 @07:04PM (#15700441)
this is probably why such things like "average" person (or any other object with multiple characteristics) practically don't really exist. Everybody is [close to] exceptional in at least some of their characteristics or their combination :)
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