Pardon the bald appeal to authority, but your assertion reminds me of a Richard Hamming quote:<p>&quot;&quot;&quot;
As we say, the volume is almost all on the surface. Even in 3 dimensions the unit sphere has 7&#x2F;8-ths of its volume within 1&#x2F;2 of the surface. In n-dimensions there is 1–(1&#x2F;2^n) within 1&#x2F;2 of the radius from the surface.<p>This has importance in design; it means almost surely the optimal design will be on the surface and will not be inside as you might think from taking the calculus and doing optimizations in that course. The calculus methods are usually inappropriate for finding the optimum in high dimensional spaces. This is not strange at all; generally speaking the best design is pushing one or more of the parameters to their extreme—obviously you are on the surface of the feasible region of design! 
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