The Mathematics of Summa Metaphysica:
Fractals & David Birnbaum’s Philosophical Paradigm
By Mark Davis
Potentialism is a cosmological theory asserting that the universe moves, with a coordinated effort, towards a distinct goal. Unlike previous cosmological models of the last century which dealt with such models as Randomness – a theory that the universe is chaotic and without purpose, Potentialism draws the opposite conclusion, citing as its proof the universe and its perceivable order itself.
Potentialism draws on a teleological model of cosmology – that is, that something intentionally drives the universe and its evolution. Specifically, Potentialists assert that the universe is driven by the Quest for Infinite Potential. Broken down simply, the universe can be viewed as a biological individual. A person, in their totality is both what they are and Potentially what they may become. By logical extension, that same person is also all the Potential lives they may create through reproduction. Obviously, not every Potential will be realized, but it is self-evident that the Potential exists. And that Potential is infinite.
One of the most important concepts of Potentialism is the infinitely nested nature of Potentiality. For instance, the person we mentioned has the Potential to create children, but those children also have the Potential for offspring themselves, hence the original person holds not only their own Potential, but the Potential for all generations to come – an Infinite Potential within an Infinite Potential iterating on infinitely. Potentialists call this concept Q4P for short.
What is important though, is that this rule applies not only to humanity, but the universe as a whole. Indeed, nested systems occur in nature pervasively both in parallel and from the micro to macro scales. It can be seen in the similarities between atomic makeup up to the galactic and every stage in between – the repetitive nature of nucleus and orbiting satellites, whether it be electrons, planets or stars orbiting a nucleus, star, or galactic core.
This pervasive nested infinite nature is also present in the fundamentals of mathematics. Integral calculus is designed to quantify such irrationalities as infinitely complex surfaces. Likewise, fractal mathematics is a pure expression of nested infinities. Fractal mathematics would just seem an interesting side-note, a coincidental similarity between Potentialism found in mathematics if fractals were a purely mathematical expression. But that couldn't be further from the case.
Fractals are as pervasive, as they necessarily have to be by the definition of Potentialism, as every other proof of Potentialism. Fractals can be used to study the iterative designs of nature, from leaves to wing patterns. It is far beyond coincidence - the observable similarities that occur mimicking this unusual mathematical phenomena.
In less tangible spheres, fractals have shown to be natural extensions of concepts. In fact, wherever a seeming bidirectional choice or demarcation presents itself, fractals naturally appear conceptually. Take for instance, a jury determining a verdict for a complicated case. The variables possible in any given case are so infinite to make a straight demarcation of guilt or innocence impossible. Instead, the infinite factors create an irregular, fractal pattern along the line of legal and the illegal.
Even the human sub-conscious has been shown to display elements of fractal mathematics. Computer analysis of famous Pollock paintings have proven to contain fractal patterns and the human preference for fractal patterns can be seen worldwide in primitive arts such as textiles. These patterns likewise show up in architecture and art on a global scale. Somehow, it seems, even humanity is wired to express itself in this odd mathematical area.
But this is wholly predicted by Potentialism. Q4P not only expects this to be the case, it considers it a necessity. The harmony of fractal mathematics with the Quest for Infinite Potential is just as it necessarily has to be for our universe to work properly. To Potentialists, it's just a reassurance that everything is still working exactly as it was designed to. Fractals are just another expression of the nested, infinite nature of the cosmic order as it strives to realize its infinite Potentiality.