Reading the February edition of the New Scientist (about space-time being possiblly quantized in its own right) I read that the event horizon of a black hole is a 2-dimensional entity that may possibly encode all the information to describe the 3- 0r ->3 dimensional universe inside. That is interesting of course but am I right to wonder how the surface of the black hole can be described as 2-dimensional in the first place? In my poor little mind it would only qualify as 2 dimensional (and then only in theory) if it was purely idealised as a surface with zero width. This would be impossible unless the black hole was to exist in isolation to the rest of the universe. To my mind 1- ,2- 3- dimensional obnjects are all idealisations from the established 4- or higher dimensional setup we work in at the moment. That seems to be my main point: I can cope with gazillions of hypothetical extra dimensions but not with any subtraction of those we already seem to be dealing with. Have I got things by the wrong handle somehow or am I just naturally obtuse (or both obviously) ?
When it comes to dimensions, you have to think a little differently. When you hear of a two dimensional object you're probably thinking of a infinitely thin flat sheet of paper. It has no depth, just length and width. However, in modern math and physics the following objects are all classified as two dimensional: an infinite cylinder, the shell of a sphere, the shell of a torus, and the mobius strip. Thats because if you zoomed in on each object, the surface would look like R^2, or the flat plane. If something lived on these spaces they would only know of 2 dimensions, since the tangent space to each of these objects is 2 dimensional. FYI, a referred to the shell of a sphere and torus to emphasize that they are hollow. Normally a shell of a 3 dimensional ball is referred to as a 2d dimensional sphere and the shell of a doughnut is just called a torus. So the surface of a black hole is a 2d sphere according to these definitions. How is it possible to encode information on a smaller dimensional object? Well that's because gravity is weird :).