Information and sphere’s interior versus surface… not.

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SUMMARY

The discussion centers on the concept of information storage within a sphere versus its surface, highlighting a perceived contradiction. Participants argue that the claim that a sphere can hold an infinite amount of information is flawed, as it suggests that one can infinitely nest smaller spheres within a larger one. The conversation also touches on the mathematical implications of normalized versus non-normalized vectors on the sphere's surface, emphasizing that physically, more objects can fit inside a sphere than on its surface.

PREREQUISITES
  • Understanding of basic geometric concepts, particularly spheres.
  • Familiarity with information theory and data storage principles.
  • Knowledge of vector mathematics, specifically normalized and non-normalized vectors.
  • Basic grasp of mathematical concepts related to infinity and limits.
NEXT STEPS
  • Research the principles of information theory and how it applies to physical objects.
  • Explore the mathematical properties of spheres and their implications in geometry.
  • Study the differences between normalized and non-normalized vectors in vector mathematics.
  • Investigate the concept of infinity in mathematics and its practical implications.
USEFUL FOR

Mathematicians, physicists, computer scientists, and anyone interested in the intersection of geometry and information theory.

rrw4rusty
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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
 
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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)
 

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