Digital Philosophy
G J Chaitin's AIT(Algorithmic Information Theory) (in a mini-dialect of Lisp)
and
Stephen Wolfram's NKS(a New Kind of Science) (in his Mathematica)
are both available online. They are the two most important theories about digital philosophy. MrMathematica is the language!
My understanding of the two theories:
Intelligence is the ability to compress data.
There are two kinds of compression: lossless and lossy.
Q: If real numbers are unreal, why modern math use it heavily?
A: It provides a method to do lossy compression.
According to NKS, most computaions is uncompressable (modular lossless compress). But we can still find ways to compress them losslessly.
Q: What's the distinction between real-random and psudo-random (with a huge inner state)?
A: If there is no way to access the inner state of a psudo-random generator, and only finite output can be observed (compare to it's inner state), no difference. (Occam's razor)
For more discussion, contact me at mrmathematica at yahoo dot com.