Information and sphere’s interior versus surface… not.

In summary, there is a concept that the amount of information that can be stored within a sphere is equal to the amount that can be stored on its surface, but this seems contradictory. It suggests that a sphere can hold an infinite amount of information by placing smaller spheres within it and repeating the process. However, this may be a mathematical concept rather than a physical one and does not take into account the size of the surface compared to the diameter of the sphere.
  • #1
rrw4rusty
46
0
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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  • #2
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)
 

Related to Information and sphere’s interior versus surface… not.

1. What is the difference between information inside and on the surface of a sphere?

The main difference is in the way information is stored and accessed. Information on the surface of a sphere is typically two-dimensional and can be represented as coordinates on a map. On the other hand, information inside a sphere is three-dimensional and can be represented as a volume. This means that more information can be stored inside a sphere compared to its surface.

2. How does the curvature of a sphere affect the storage and retrieval of information?

The curvature of a sphere affects the way information is stored and retrieved by changing the geometry of the surface. For example, on a flat surface, distance is measured in a straight line, while on a sphere, distance is measured along a curved path. This can impact the efficiency of storing and retrieving information, as well as the accuracy of measurements and calculations.

3. Can information be transmitted through the interior of a sphere?

Yes, information can be transmitted through the interior of a sphere. However, it may require different methods and techniques compared to transmitting information on the surface. For example, signals may need to be amplified or redirected to account for the curvature of the interior.

4. How does the composition of the sphere's interior affect the storage of information?

The composition of the sphere's interior can have a significant impact on the storage of information. For example, if the sphere's interior is made of a material that is highly conductive, it may be more suitable for storing and transmitting electronic information. On the other hand, if the sphere's interior is made of a material that is less conductive, it may be better suited for storing physical information, such as written text or images.

5. Is it possible to store information both inside and on the surface of a sphere?

Yes, it is possible to store information both inside and on the surface of a sphere. This is known as hybrid storage and can offer the benefits of both methods. For example, important or frequently accessed information can be stored on the surface for easier access, while less important or rarely accessed information can be stored inside for more efficient use of space.

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