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On the Mystical Explorations of Arithmetic

What is mysticism? Why do we perceive numbers? What do the relationships of numbers to each other reveal about the manifested universe?

5 min read

Mysticism is an orientation towards the interior as well as the exterior that acknowledges the inherent mysteries of what one perceives. Often, mystics are driven by a desire to make sense of these mysteries but the moment one lands into the (fallacious) belief that the mysteries have been solved (Eureka!), one is no longer a mystic.

Throughout the human history of thought, mystics and scientists were one and the same – Pythagoras, Plato, Newton, da Vinci, Ramanujan, Jung.

In the reactionary separation of western wisdom disciplines (colloquially referred to as "science") from the Catholic Church due to the horrible excesses of the supposed "men of God" (see Pope Benedict IX ~1000 AD, Leo X ~1500 AD, Alexander VI ~1500 AD) – mysticism and any references to the divine/God went underground as the period of Scientific Enlightenment dawned upon us. This split is most clearly visible in the split of Astronomy from Astrology – Copernicus (1473-1543) was an astronomer as well as an astrologer, Galileo (1564-1642) was only an astronomer.

The West left the era of exploration of cosmos for meaning making and slowly entered the era of exploration for the sake of utility. Utility over meaning – the aftershocks of this detour still visible in modern day McMindful life coaches presenting meditation as a "bio-hack" to "improve productivity".

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A framing of the work to elevate consciousness could be presented as "attempts to perceive the underlying current of oneness in the separate entities that one encounters in the manifested universe".

The ability to perceive Separateness allows us to bear witness to the rich diversity of the manifested universe. All movement emerges from the attempts of the Separate to Merge. If our perceptions became "perfect" and we only saw Oneness – then our universe would come to a standstill. Perfect, in quotes, because it's perfection from a narrow lens – the kind of narrow lens that causes one to confuse psychedelic "ego death" with "Enlightenment".

In addition to seeing Separateness, our perception also has the ability to categorize. We look at two oranges and categorize them as the same fruit because momentarily we are blind to the Uniqueness of each.

It is this aspect of our perception (crucial to perceiving the richly manifested universe) – the ability to simultaneously see objects as separate yet similar but not One or Unique – that gives birth to the concept of Numbers.

So the intricacies of how Numbers relate to each other has the potential to reveal insights about the mysteries of existence.

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I believe most devout Mathematicians understood this, at some level. This is what drove the pursuit of Mathematics. An attempt to make meaning of the world by observing the oddities of the relationships between numbers. Arithmetic is the most basic of Mathematical disciplines – dealing with adding, subtracting, multiplying and dividing numbers.

In the early 1900s, there was an attempt to rid Mathematical work of the biases of mathematicians bring their own conscious/subconscious meaning making tendencies and muddying the rigor of a mathematical proof. The German mathematician David Hilbert was at the forefront of this movement. As much as I detest the notion that Mathematics and meaning–making should stay separate, I liked Hilbert's insistence to develop rigor in the proof techniques – I see it as a desire to delay meaning–making. The true meaning emerges on its own and makes itself abundantly clear when the human being can relax their anxious mental meaning–making faculties and allow their breath awareness to softly and slowly expand in all directions.

Hilbert began the 19th century with a grand address at the International Congress of Mathematicians in Paris, listing out 23 open problems in Mathematics.

One of these problems was to prove the consistency of the axioms of arithmetic.

An axiom is a self-evident truth inside a system of Logic. A system of Logic is a symbolic framework exploring the journey and interdependencies of truths. Logic is Philosophy but expressed in symbols. Hilbert wanted to ensconce Mathematics in a system of Logic where the underlying assumptions ("axioms") could be clearly stated – far too many Mathematicians before were prone to wrapping their subconscious biases under references to God. A noble endeavor for a German from the early 1900s when so many of his fellow countryfolk were soon to fall prey to the Aryan supremacy bias. If such an axiomatic system of Arithmetic could consistently prove all truths, it'd be a system that completely captures manipulation of Numbers – and why wouldn't that be the case? Seems fairly reasonable, no?

Enter Gödel who proved that, that was precisely *not* the case. That there were truths in an Arithmetic system that were beyond the grasp of proofs from an axiomatic deductive system.

He even constructed such a sentence in Arithmetic – an oddly fascinating construction that relies on self-referentiality. What is it about this sentence that it escapes the logical deductive proof-making apparatus?

Even more fascinatingly, there are "weaker" Arithmetic systems (with fewer operations), where all truths are indeed provable. But then if you introduce an operation here or there, suddenly there emerge truths that cannot be proved. Suddenly, there seems to emerge the ability to make self-referential statements.

What is it about these operations that allow for self-referentiality to emerge? A sense of Self to emerge? Within the realm of Arithmetic, what is the boundary of awareness of the Self? Within this boundary, all truths can be proved and no sentences can be constructed that reference to themselves. Beyond this boundary, there are unprovable truths and a statement can reference itself.

The rift that was created in Mysticism and Mathematics stands repaired since Gödel's work came into light.

If this is of interest to you and you'd like to dive deeper into understanding this work (high school Math experience sufficient), please comment below or reply to this email so I can keep you posted on a potential "seminar" offering that I'm contemplating hosting.

Albert Einstein portrayed as a new age guru. He is dressed in flowing, colorful robes with intricate patterns, and he wears various mystical accessories like beads, crystals, and amulets. Einstein has his characteristic wild hair and mustache, and he has a serene and wise expression. The background features a peaceful, natural setting with elements like lush greenery, flowers, and a clear blue sky, adding to the tranquil and spiritual vibe. Einstein is seated in a meditative pose, surrounded by symbols of knowledge and enlightenment.
Prompt: Albert Einstein as a new-age Guru
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