New Scientific Method

As I wrote in this blog earlier, Wolfram's NKS , requires a New Scientific Method. In its simplest terms, it must incorporate digital calculators (below, find the NYT piece on Babbage) to fit data. The most abstract element is the use of axioms, to better code data. I am reading professor Fivel's article in the arXiv. He was able to code in five Axioms, the conventional rules of quantum mechanics. He is following a path set by Dirac and von Neumann; now using tools by Shannon.

Axiom I: For every w, z $$\in$$ S:

                          w(z) = 1 if and only if w = z;

                                          w(z) = z(w):

Axiom II: S is compact in the d-metric.

Axiom III: The function a(x) is a frame function on S for every a $$\in$$ S.


Axiom IV: Given any two distinct elements a, b $$\in$$ S there exists a pair of orthogonal elements

c, c' and a number 0 < $$\alpha$$ < 1 such that 


                                  a(c)c + a(c')c' = $$\alpha$$ a + (1 - $$\alpha$$ )b:



Axiom V: The purities of the mixed states resulting from random measurements of a pure qubit state are uniformly distributed.


At first, these axioms are as mysterious, as the conventional rules of quantum mechanics, which they are supposed to "explain".


Just bear with me, and obviously with professor Fivel.