Wow. I was simply thinking about a coastline that continued to be “complex” as one zoomed in. It would, in fact, be infinite, yet somehow less than two dimensional.
I’m not that familiar with string theory so I don’t see the similarity in patterns you describe. Will you point me to a good starting point?
The way this problem is related to non-integer dimensions (maybe only in my mind) is that crazy math and crazy physics somehow support each other.
I believe that the concept of non-integer dimensions is crazy math, and if physicists claim that there was a time when there were non-integer dimensions then that is crazy physics.
Crazy math is OK because it is all hypothetical. However, crazy physics seems counterproductive. It no longer gives us insight into how things are, it just makes it easy to solve physics problems.