# Thread: Information and sphere’s interior versus surface… not.

1. 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

2.

3. I think you saw this when either reading an article on the entropy of black holes and the information loss problem, or talking about the Holographic Principle which from what I know, is purely speculative.

The Entropy of black holes is calculated using the area of the event horizons surface, where you would of thought it would be volume of the sphere. Im not going to pretend i know why this is, ill leave that to someone else.

The holographic principal leads on from this, and from what i can tell is mostly speculation and forms part of string theory. Basically it means information about any volume can be obtained from its boundry. I assume this must involve more than 3 spatial dimensions, but im not sure.

You are looking at it from the more speculative angle. So far I have only seen it used for objects like blackholes, which is necessary to try to explain the loss of entropy when it absorbs matter. The Area is used in the maths for hawking radiation.

I can only point you in the right direction, sorry for all the links to wikipedia, but they are generally a good place to start, and the references point to good sources to read. I myself dont know an awful lot about it, but i might take this opportunity to read up on it.

4. Originally Posted by harvestein
I think you saw this when either reading an article on the entropy of black holes and the information loss problem, or talking about the Holographic Principle which from what I know, is purely speculative.

The Entropy of black holes is calculated using the area of the event horizons surface, where you would of thought it would be volume of the sphere. Im not going to pretend i know why this is, ill leave that to someone else.

The holographic principal leads on from this, and from what i can tell is mostly speculation and forms part of string theory. Basically it means information about any volume can be obtained from its boundry. I assume this must involve more than 3 spatial dimensions, but im not sure.

You are looking at it from the more speculative angle. So far I have only seen it used for objects like blackholes, which is necessary to try to explain the loss of entropy when it absorbs matter. The Area is used in the maths for hawking radiation.

I can only point you in the right direction, sorry for all the links to wikipedia, but they are generally a good place to start, and the references point to good sources to read. I myself dont know an awful lot about it, but i might take this opportunity to read up on it.
harvestein,

Actually I assumed most people would have heard this. You are right in that this claim stemmed from Bekenstein and Hawking's conjecture regarding the total amount of information held by a black hole was equal to the total area of the event horizon (loosely stated). The statements concerning a sphere I heard in an audio lecture and also read in a book but I am at a loss as to which lecture and which book. I will try to locate these or other sources.

Rusty

5. I can't comment on the validity of the idea as a whole, but I can point out why your counterexample doesn't work.

If you assume the holographic principle then all of the information in the sphere is already on the surface. If you put a smaller sphere inside the first one, you are changing the inside, and therefore changing the surface, but you can't simply add information. Remember, in this context information means something very specific and somewhat non-intuitive.

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