Nothing is Smooth

Many years ago, I came upon a facinating book, Three Scientists and Their Gods by Robert Wright. The section I found most compelling described the theories of Edward Fredkin. This book also told the interesting tale of Fredkin's life and the path to his theories.
The foundation of Fredkin's theories describes a universe where all quantities in nature are finite and discrete. That means that nothing is smooth or continuous, that everything is grainy and particulate and that any quantity can be represented exactly by an integer. Also, in nature there can be no infinities or infinitesimals. There is a whole lot more, but everything depends on this principle.
I've recently found some interesting papers published by Fredkin and others. Check them out.
From the horse's mouth: http://www.digitalphilosophy.org/
A great resouce for papers on this and related subjects: http://digitalphysics.org/Publications/
A terrific site with some good explanations and examples: http://www.bottomlayer.com/bottom/finite-all.html
This stuff even wanders around between the worlds of physics, metaphysics, and philosophy, which is another reason I find it interesting. It attempts to address some questions that traditional physics has tended to avoid. I can't say that I've bought into all of it (yet), but it sure gives one lots to think about.