... THE MATHEMATICAL ELECTRON ...
a Programmer-God Simulation-Hypothesis model
if we assign geometrical objects to mass, space and time at the Planck scale,
and then link them via this unit number relationship,
we can build a physical universe from pure mathematical structures.
Could a Programmer God have used this approach?
The Mathematical Electron Approach
The core insight is that a single dimensionless formula — $\psi = 4\pi^2 q^3$ — encodes geometrical objects $M$, $L$, $T$, $A$ that correspond to the Planck units for mass, length, time, and charge.
From these four geometrical objects, and using only the fine-structure constant $\alpha$ as the sole physical input, all known Planck units and dimensioned fundamental physical constants can be derived.
This means the physical constants ($G$, $h$, $c$, $e$ …) are not independent fundamental constants — they are emergent properties of the underlying geometry.
The model uses a geometrical base-15 structure — unlike any other framework in contemporary mathematics or physics — characterised by the rail $3M + 2T = -15$.
Malcolm Macleod has been developing this Simulation Hypothesis model since 2003. The foundational article was peer-reviewed and published in 2018 in the European Physical Journal Plus.
The model is developed as an independent research project. All simulation code is made freely available under the Creative Commons licence to encourage scientific engagement and reproduction.