Metaphysics

Meta-Metaphysics, or Elemental Construction

We still live in elemental metaphysics

Aidan Lytle
Intuition
Published in
7 min readJun 9, 2021

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Photo by Giammarco on Unsplash

Note: I will provide links for further reading at the end of the article. Please bear with me and trust that I am not rambling pointlessly

Recently, a friend of mine (Cameron Raissi, a real smart dude) was having a conversation with me about the elemental model of thinking. Specifically, he pointed out that we are in a “metaphysics of air”. When I prodded him to explain more, the conversation became really interesting.

“Well, for Heraclitus it was fire; people saw war and change. Now, it’s air; the stuff in your phone, information, energy”: these are all things described by mathematical equations, but are literally invisible. He is describing the interchangeability of existence into the ethereal. He is not the first to draw this conclusion, as it could easily be argued that Baudrillard, Deleuze, and others foresaw this shift. Air is less tangible and visual than fire. It is the next and natural step upward in the hierarchy.

What does this imply for us? Is it a nice metaphor, or does it hold significance for psychoanalytic approaches? To answer these, I think different tacks must be taken.

What it really boils down to is the distinction in our philosophy between the discretists and the continuists. This is the dichotomy that a metaphysics of air elucidates and proposes as the ground for debate. It is this ground that we must dredge to understand the roots of this thinking.

For hunter-gatherers and hunter-horticulturalists, as well as many mountain peoples, the obvious connection was Earth. The thing was solid, easily understood; literally, down-to-earth. It made plants and animals abundant, and stood the tests of time, unchanging in a human lifetime. We see animism and Heideggerian groundedness as modes of being.

The first civilizations note that fire, and air, are the domain of the magician. Thales and Lao Tzu said all was Water. Thales even re-routed rivers. It could easily be seen that water was the driving force for early agriculture; we had mastered the rain and the rivers, so we were able to grow crops. With this, the ideas of ebb and flow, of cyclical nature, take up thought and preoccupation.

Fire, fire was the next: from the industrial revolution on, we see the physics of combustion, steel, and machinery designed to contain and control fire. Even the firearm and the weaponry of its time is a metaphysical statement, albeit unintentional; when one deposes a Chinese emperor by mastering his own gunpowder and fire tools, one has shown that control of the fire is control over matter and man. Fire became the symbol of life. No more the golem, the men of stone (Hesiod), the men of water (the Atlanteans, the Hyperboreans), the new mode of control is control of fire. This peak came upon us with the atomic age. No one could claim to be master of the earth, or even their people, without threats of the atom and fire. Fire is uncontrollable but can be choked, contained, stifled, snuffed.

Finally, we have Air. What evidence do we have? Air is uncontainable, chaotic, complex, indescribably mathematical. It cannot be understood physically to be ended or begun. It is described by something seemingly unrelated, of continuous lines across surfaces, slipstreams, storms, it is almost (but not quite) a vacuum. Fluid dynamics (because that is how we see air, as fluid) are brutal and hard to understand. Many mathematicians and physicists spend their entire careers working on some sets of equations that arise in these studies (the equations go by the names of Navier-Stokes, the Laplace, the Diffusion, etc). What is notable, however, is that these equations also describe the flow of information, energy, and entropy. That is: he who can best master the network, the graph, the diffusion equation, the transport equation, the damped wave equation, or KDV equation, all of these symbols for the motion of chaotic and multi-body systems, these are symbols for the actual processes.

What any of these physicists and mathematicians will tell you is that these are uncontrollable systems to some degree, that they are difficult to understand and model and work within reality. The metaphysics of information is down to the level of the fundamental nature of reality. Bits flowing can replicate a diffusive process over a network. This is key: if we can pump information into a system, we can pump air into a system, we get back a higher saturation at the nodes.

When I say that it is down to the fundamental nature of reality, we see the conflict going back to that between Leibniz and Spinoza: is a reality composed of continuous, infinite fields? Or is it a bunch of discrete dynamical bubbles? That question could as easily be asked about air! How do we model it? Is it molecules, or a flow? Is the PV diagram for an engine process, etc, is it “fire” or is fire just another way to say air, because fire is plasma?

This is no small debate. Wolfram, Conway, and other mathematicians are “discretists”. They propose that the world is essentially monads, atoms, particles, at some basic infinitesimal level. Leibniz’s calculus of infinitesimals was based on a specific metaphysical claim like this, that when we say dx, we mean a really, really tiny thing, invisibly tiny. He was agnostic about whether this was really, truly an infinitely small object. Newton was a discretist as well, proposing early that light was like a particle.

Later, Fourier, Cauchy, and others all surmised (correctly) that an axiomatic formulation of the infinitesimal would require continuity to an arbitrary degree, meaning that the infinitesimal was a limit, or (to the non-mathematician) infinitely small. That would require it to be non-discrete.

The field or “continuist” camp, with thinkers like Feynman, Einstein, and the QFT founders, has a metaphysical forefather in Spinoza. In the introduction to his ethics, he outlines a beautiful metaphysics. Propositions 7 and 8 are clear about the building blocks of being:

7. Existence belongs to the nature of substances.

8. Every substance is necessarily infinite.

By claiming that substances are an existential requirement but that they are infinite, he describes a continuist statement about nature (and God, and existence, and others, but that is beyond this essay).

One important note here is that the discretists and the continuists are forced to recognize the existence of the chaotic and incomputable at the fore of their field. The paper which introduced chaos as a common term is about a continuous system of differential equations, “Period Three Implies Chaos”, along with the Lorentz attractor and others.

For the discretists, we get complex systems (both mathematically and literally) such as the Mandelbrot set, along with other discrete fractal-type systems. What this tells us is that chaos and complexity arise in both discrete and continuous systems, and must be recognized as distinct features of nature outside of a dichotomy presented.

The best (and most obvious) precedent for this kind of thinking is Anaximenes’ pneuma. Anaximenes’ arche was this “air”. His response was to Thales, in that they were both concerned with describing the process of the water cycle, but what Anaximenes saw was evaporation, condensation, and rarefaction, while Thales saw respiration, condensation, growth. The slight difference put emphasis on a “breath” and on the unseen vs. the seen.

This emphasis on the visible v.s the invisible is mathematically and physically presented as the very same debate between the continuist and the discretist.

We can also place the difference here on something mathematical: a network model and a partial differential equation describe radically different things. Topology, Real Analysis, and the foundations of mathematics have come down essentially on the side of the continuists. Even going back to Pythagoras, there was a fear of the fraction which led to an even greater fear of the irrational. Something which was no ratio of integers was an affront to the Pythagorean metaphysics of form.

A simple parallel today is the “mathematical reactionary”, like A.J. Wildeberger or (much longer ago) Kronecker. These men reject the continuous as a mode of thinking because it goes absolutely against the mathematical-geometric intuition.

It would seem in this debate, that clearly PDEs describe fluid and gas flow, so the continuists (and thus Anaximenes’ invisibilist view) are the ones which have and will win the day. God seems to be nearly anti-geometric.

What this tells us is this the next move will be the one toward the void: spacetime is a vacuum of matter. He who masters QG will master the future, in a century our science will see this as the major accomplishment of this century. QG seems to be majorly geometric in its construction. To the rest of us, the mathematics used to describe it will be tomorrow’s metaphysics. But for today, think: how do we function in a metaphysics of air?

Thanks to Cam

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Aidan Lytle
Intuition

Mathematician out of NC. Read and write philosophy and social theory.