Dear Dean & Jessica,
I have a theory that EXACTLY matches your idea and DR. Tegmark. my theory "quantum statistical automata" .
Reality exists hence we say it is true. But what is really true besides that more than anything else which we can really trust, it is mathematical facts. So, to my mind I connect both since both seem to be a statement of truth. So I took a guess that reality is something akin to a circle (truth). The relations between the points give you a mathematical structure whereby you get PI which defines the structure of the circle.
the structure that leads to our reality is random numbers and certain unavoidable RELATIONS(and only possible ones) between them. that is all.It is the most generalized dynamic structure possible. The mass of the electron pops from the system among many other standard physics results.
The system (I will not use the word model although you could with some caution) seems to mimic reality by exposing some of the very important essential features of Schrodinger equation, Dirac equation, QFT and Gravity! But only certain essential features of these theories, probably some heavy work and more elaborate simulations needed to map to the of standard physics.
On the other hand the system exposes features of reality that standard physics is simply in no position to do so. Particularly, the Lagrangian of the system falls out from the simulation and you get the values of charge, mass, c, h_bar and other values, even the Fine Structure Constant. Not to mention the beautiful unified picture of space (its points are the crossing of the lines-dynamic-), time(change of state-does not actually exist-), mass, charge, and energy.
The other really big result which I obtain is the essence of Dirac equation included the notorious non-locality. When I try to simulate the 2D situation, I am forced to restrict my line throwing activity to only lines that can go between particles directly so as to keep the invariance of quantities calculated in case the frame is rotated. And Wala, I get two particles to interact through their width in the second axis and it does not matter if each is on the other side of the universe, they are both linked!!!! When I calculate spin (what I believe to be) one is up the other down.
There are many other things in the system which I have not tried to do too much yet mainly due to lack of time including gravity which I have done in limited way and I do get the small attractive force but probably much more work is needed.
I should mention that the theory is at heart a generalization of Buffon's needle which ties to many other concepts which are used in high end physics like twisters, categories, network theory, Ising and many others.
http://en.wikipedia.org/wiki/Integral_geometry
http://en.wikipedia.org/wiki/Buffon's_needle
Once you understand it, it will become clear to you that it could not have been otherwise.Attachment #1: 1_newqsa.pdf