Information and sphere’s interior versus surface… not.

[rrw4rusty]

Hello,

I have heard the following from several places:

The amount of information that can be stored within a sphere is equal to the amount of information that can be stored on its surface.

This seems like a contradiction or, a self-defeating statement. It seems to instead say that a sphere can hold an infinite amount of information. For example:

Since the amount of information you can put within the sphere is equal to the amount you can put on its surface… just put the information on its surface… then, with the interior of the sphere empty; put a slightly smaller sphere within and put more information on its surface then repeat this process until the space within the sphere offers diminishing returns. Then, jump back to the outer most sphere and place a slightly larger sphere around that… ad infinitum.

I’m I cheating, missing the point, or… missing something else?

Cheers,
Rusty

 

[LostConjugate]

I have not heard of this before. A normalized vector moves around on the surface of a sphere and since non-normalized vectors are linear it could be a mathematical concept and not a physical one.

It is obvious that you can fit more pebbles inside of the sphere than on the surface assuming (surface width << diameter)