I re-watched a program recently on fractal geometry and it reminded very much of the idea of "strange loops" in the book I Am a Strange Loop by Douglas Hofstadter I read a few years ago. Both of these look at repeating patterns and what that can mean to various mathematical disciplines. I'm not expert in math, so I don't know if there's a relationship there or not.
In addition, it also got me wondering if there's a relationship between fractal geometry and string theory's idea that there are more than 3 spacial dimensions. In this case, I'm actually wondering if they conflict.
Fractal geometry is a shape that repeats itself consistently throughout, even when looked at in minute detail. The shapes of very small pieces are the same as the larger ones--size doesn't matter. In string theory we throw this idea away and say that when we reach a certain level of smallness, the universe is not the same as it is at larger scales; we not only have different laws in play but more dimensions within which the laws act.
I wonder if it's possible that the unified theory so many scientists are looking for could simply be based on the number of dimensions being used by whatever is being observed (and/or the observer)? Maybe objects that only use (and exist) within "our" three dimensions use one set of rules and objects that exists in any other combination of whatever dimensions exist use a set of rules specific and unique to that combination. It may not be the size of the stuff being looked at that determines the laws under which it exists, but the combination of the dimensions being used by it (and/or who's observing it).
In addition, it also got me wondering if there's a relationship between fractal geometry and string theory's idea that there are more than 3 spacial dimensions. In this case, I'm actually wondering if they conflict.
Fractal geometry is a shape that repeats itself consistently throughout, even when looked at in minute detail. The shapes of very small pieces are the same as the larger ones--size doesn't matter. In string theory we throw this idea away and say that when we reach a certain level of smallness, the universe is not the same as it is at larger scales; we not only have different laws in play but more dimensions within which the laws act.
I wonder if it's possible that the unified theory so many scientists are looking for could simply be based on the number of dimensions being used by whatever is being observed (and/or the observer)? Maybe objects that only use (and exist) within "our" three dimensions use one set of rules and objects that exists in any other combination of whatever dimensions exist use a set of rules specific and unique to that combination. It may not be the size of the stuff being looked at that determines the laws under which it exists, but the combination of the dimensions being used by it (and/or who's observing it).
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