Non-Integer Dimensions

[ICN5D]

I remember reading somewhere how fractals can be expressed as fractional dimensions, like 2.5, or 4.2. Kind of makes me wonder about the fractal nature of our universe. We're right in between the sizes of solar systems and atoms, yet in some general way the resemble each other. In both scales we have a central core of high energy surrounded by several locations/fields of lower energy. This sort of reflected physical form can be expressed in a fractal context. I think the article said we're in 2.7 dimensions or something on the surface of earth. It was interesting.

[anderscolingustafson]

I have also heard that fractals can be thought of as fractional dimensions and I can see why the surface of the Earth could be considered a none integer dimension as it has hills and valleys allowing you to go up and down along it but you also have to change your location in terms of longitude and latitude in order to change your elevation so the Earths Surface isn't fully 3 dimensional.

What about could a piece of paper be considered to have a none integer dimension considering that it has 3 dimensions but the 3rd dimension is very thin? And could the Universe be considered to have a none integer dimension because it might have 11 dimensions but seven of those eleven dimensions are so small we don't notice them?

[wendy]

Fractals are supposed to have non-integer dimensions, but i usually have a different way of seeing the measure, since fractals in euclidean space and the cascade infinities in hyperbolic are identical, and the cascade infinities are essentially a class-two infinity.

[ICN5D]

Well, just speculation, but I believe the universe has 26 dimensions. Ten or eleven was the initial experiment in string theory, but they later found that it wasn't enough. There were too many different equations making the same things, because there were deeper underlying patterns. They had to add even more dimensions to unify those into one. I'm not caught up on the recent stuff.

As for the piece of paper, I guess it could be really close to 2, but just a little bit more because of the thickness. Even if the sheet was one atom thick, it would still be 3D. I guess the limit for a 3D sheet is 2.0...1, where there would be infinite 0's in ...