Although nature seems most knowable when its wave-particle duality is intact, it hides that dual nature upon physical observation. Physical reality and the mathematics which describe it are further constrained by limitations of what may be logically proven, computed or predicted. However, these limitations of the observer effect and number theory would not apply if nature's duality could be fully described in purely geometric terms in probability space. This essay suggests a radical way to do just that. Starting from the prime numbers as the simplest elements of mathematics, the base-12 number system as arguably the most efficient number system for nature and the complex numbers as its natural language, a simple 3D double-helix waveform emerges in 4D quaternion space. When the 2D projection of this waveform is then interpreted as the fundamental probability waveform of physical reality, remarkable alignment is found with the way nature appears to work at all scales - including compelling explanations for open mysteries such as dark energy, dark matter, quantum gravity, time and the particle structure of the quantum world. Even if it's too simple to be true, it offers a back-to-basics approach to view nature at its conceptually simplest.
Michael Smith