Arithmoí - A Study of Mathematical Cohesiveness in Physics and Metaphysics
Arithmoí - Mathematical Foundations and the Singularity is the first book in a series studying existence as a mathematical construct. Essential to the undertaking is that mathematics be the means of conveying the topic. The synthesis presented in the book starts by first bringing to light the historical human biases pervasive in mathematics, physics, and metaphysics subject matter. Anthropomorphism, meaning attributing human emotions, traits, and intents to non-human forms, is a deeply rooted inclination in the human psyche. Evidence for this abounds when we consider religion and mythos, where divine entities took human forms, traits, and qualities. How the human sensorium interprets phenomena lends itself to the tendency to overemphasize what is physically perceived while abandoning the concern of understanding the holos. Anthropocentrism, also known as homocentrism, is another closely related belief system that places humans at the center of the Universe. A prime example of this in the past was the geocentric model, which put the Earth at the center of the solar system during a time that preceded any understanding of what galaxies and the Universe were. Some still believe that the observer plays a fundamental role in the observed quantum mechanical system, and this should be considered a form of anthropocentrism.
The model we emphasize in the Arithmoí series is the Arithmocentric model, which places mathematics as the universal center. This does not represent a new model, considering the ancient Pythagoreans held the like-minded philosophy that all is based upon numbers. Today, the difference is that mathematics is much more refined than it was for the ancients. In particular, the last two hundred years have heralded an exponential increase in our knowledge of the subject matter. In this period, we have been able to move beyond the confinements of Euclidean geometry, which started in the early 19th century when hyperbolic geometry was first defined. This book uses this and many other advances from the recent period, including real, complex, and harmonic analysis, group/Lie theory, topology, and non-Euclidean geometry. The most impressive advances in physics and science have been due to this better understanding of mathematics and the improved capacity to reason it has enabled.
To advance the Arithmocentric model requires that we do away with empiricist thinking and not be obliged to our physical senses. Unlike the tools of the experimentalist, the mind is not limited to the physical domain, given its transcendent capacity. The logical conclusion is that the mind is not physically tethered and resides outside space and time. For any grand unifying theory to be complete, consciousness must be fundamental to that theory. Anything short of this indicates, at best, that the theory is incomplete.
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