Update pending!!!! Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's MUH).
A Mathematical Universe
Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. Platonism is a theory that numbers or other abstract objects are objective, timeless entities, independent of the physical world and of the symbols used to represent them. read more ...
The Physical Constants
The physical constants form the scaffolding around which the theories of physics are erected, and they define the fabric of our universe. And yet, no one has ever successfully predicted or explained any of the constants. Physicists have no idea why they take the special numerical values that they do. if many of them were even slightly different, living beings would not be possible. The desire to explain the constants is behind efforts to develop a complete unified description of nature, or "theory of everything". Physicists have hoped that such a theory would show that each of the constants of nature could have only one logically possible value. It would reveal an underlying order to the seeming arbitrariness of nature.' read more ...
Programming a Virtual (Mathematical) Universe
Using the computer game as analogy, the 2 principal problems in designing any programmable universe that is essentially a series of mathematical routines (the computer simulation approach) is for the programmer;
1. to create self-aware substructures (see Max Tegmark's mathematical universe hypothesis definition) who both perceive themselves as having a free-will which equates to self-awareness (as opposed to being controlled externally by game players) and also;
2. to create a physical space (the appearance of a physical reality) within the confines of a mathematical 'software' framework that these self-aware substructures would then perceive as being a physical reality.
Discussed here is a novel approach to this problem that proposes;
1. there is a mathematical model behind swarm intelligence and that this swarm mathematics can be used to create self awareness in complex systems and that;
2. the physical (dimensional) reality of the virtual (programmed) universe is a localised function of virtual particles. As the virtual universe expands (FOR n = big_bang TO the_end; DO ... LOOP), within this incremental 'n' loop we may simulate motion and momentum as a function of this expansion, as well as dark energy, time and the arrow of time. As time is a function of this expansion and as we can define the dimensions of mass, space and charge in terms of time, we have measurable (dimensioned) parameters whilst remaining mathematically dimensionless.
This theory is divided into 5 parts (in brief);
1. The sqrt of Planck momentum is used to derive the structure and formula for a black hole electron and define a ratio of mass, space and time that sums to unity. From this ratio we can reduce the number of basic SI units from 5 (kg, m, s, A, K) to 2 (i.e.: kg, s) and using the model behind these formulas we find that we can re-write and solve the physical constants in terms of the 3 most precise natural dimensioned constants. Solutions are consistent with CODATA 2014.
2. Dimensionless mathematical (geometrical) forms for the physical Planck units; mass, space, time, charge are proposed. These forms permit us to further reduce the number of required units to 1 (i.e.: s). These Planck units are constructs of 2 (fixed) mathematical constants, 1 dimensioned unit and 2 variable scalars via which this model can be applied to any system of units whether local or terrestrial (see Max Planck quote - Prussian Academy of Sciences 1899). These formulas can then be used to duplicate the formulas above for in terms of and thus can be used as a cross reference. The mathematical constants are the fine structure constant alpha and a proposed constant Omega. The dimensioned unit can be any 1 of the Planck units.
3. Our physical (observable) universe is treated as a black-hole universe fed in Planck-size increments by a contracting white-hole universe. Results for a 14.6 billion year old black hole are consistent with NASA WMAP CMB (cosmic microwave background) parameters. These increments replace dark energy.
4. Atomic and gravitational orbits are treated as the sum of physical orbits, particles and objects are thus linked directly and not via an abstract force.
5. The universe is seen as an expanding virtual (dimensionless) 4-axis hypersphere. It is this expansion which gives the universe clock rate and thus ultimately our unit of time and arrow of time and an analogous 'velocity' of expansion from which we derive the speed of light c. The Lorentz equations can be used to translate between the 3-D space of modern physics and this virtual 4-axis co-ordinate system. In this system both time (the clock-rate) and velocity (the speed of expansion = c) are fixed, all particles and objects thus travel at, and only at, the speed of light. All measured velocities are thus measures of relative motion (relative space and time) and not actual motion. Our 4-D space time is thus a measure of contrast (a relativistic Mach's principle hyper-sphere surface area) superimposed upon a Newtonian absolute virtual background.
The following was written as an essay, however it gives a basic introduction to the model.