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== Abstract ==

== Abstract ==

I will discuss some interesting properties of simple geometric objects (such as unit spheres and unit cubes) in high dimensions.

I will discuss some interesting properties of simple geometric objects (such as unit spheres and unit cubes) in high dimensions.

Our intuition about space is formed in two and three dimensions and this can often be misleading in higher dimensions.  

Our intuition about space is formed in two and three dimensions and this can often be misleading in higher dimensions.