I experience a recurring dream: In the dream I am aware of an object (house, flower, doesn't matter). That object is vanishly "small." I consider the object. Then as I understand the object a new version of the same appears behind it. It is ridiculously "large." Going back and forth between this small and large version of the object makes my head hurt. The only way I can describe it is to say that my mind "glitches." It is a very peculiar feeling. I've had this glitch in waking times, but not very often. If it lasted more than a second it would be debilitating...
These dreams started for me very early on. Like in kindergarten times, as best I can fix them. That's way before I ever knew what a "fractal" is. That freaks me out a little bit.
I wonder: is nature recursive? We know recursion lends itself toward explanations of objects we see around us. Nature seems at its core a "feed-back" system. But the math we use to model these objects is not something which scales naturally.
What does the computational system of the universe look like? How does it work? I'm thinking that our mathematics needs to incorporate recursion as a basic given. Not as something we afix later on (in advanced computational science, at best). Consider the amount of precision required to perform an "integration." Can the universe really compute with infinite precision? Or is it limited to quantized interactions? My bet is on a fixed amount of computational power and hence precision to the world at large.
I wish I knew more math... :)