
An Adventure in the Nth Dimension (2011) [pdf] - DyslexicAtheist
https://www.americanscientist.org/sites/americanscientist.org/files/201110101628308738-2011-11CompSciHayes.pdf
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theoh
Previous, related:

[https://news.ycombinator.com/item?id=1846682](https://news.ycombinator.com/item?id=1846682)

[https://news.ycombinator.com/item?id=3995615](https://news.ycombinator.com/item?id=3995615)

Neal Gershenfeld's book on mathematical modelling (from 15 years ago) mentions
that points in distributions/objects in higher dimensions are always close to
the surface -- as dimensionality increases, the degree of bulk and interior
space goes away.

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gtani
there was discussion also on threads about the book "Foundations of Data
Science" by Hopcroft /Kannan/Blum but i can't find those threads

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ssivark
An intuitive answer has to do with the fact that a unit volume is defined by a
"box" of unit side length. While a sphere with unit diameter would touch the
walls of the box, the box has an exponentially large number of corners
(2^dimensions) where the sphere has no presence. That is why the volume of a
unit diameter sphere is much smaller than that of a unit box in high
dimensions.

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welcome_dragon
An extremely accessible article on higher dimensional geometry!

