Incognito Ergo Sum
Charms and quarks and inferential matter; at a ‘fundamental’ level our reality is told to be comprised of mathematical entities, inferred by blips on the Y-axes of charts generated by 50-mile long underground machines which, we are told, shoot invisible ‘things’ at each other at near light speeds in order to occasionally ‘smash’ them into each other, at which time said blips on said charts are generated. This, we are told, is the substratum, the Absolute Ground of Being.
All things, then, are ‘built up’ out of these invisible mathematical entities, in a series of nested loops (“Nature’s Nest of Boxes”) out of which, at some arbitrary and as-of-yet undefined point, the invisible/inferential world gives way to the world of the visible, in which case we can ‘see’ these tiny building blocks, either with the naked eye, or, more likely, with a series of increasingly magnified lenses, which function similarly to the eye except they can zoom in exponentially further, with astonishing clarity.
But when, then, does nothing ‘give way’ to something? Suppose that we continue creating increasingly magnified lenses; then, will we keep seeing “smaller” and “smaller” entities, ad infinitum? Or at some seemingly arbitrary but fundamental level, does the threshold of ‘size’ melt away and, immediately, the apparent ‘object’ just dissipates into nothingness, heretofore to be mathematically inferred only? This is what we are told via the “Planck Constant,” the mathematically-inferred ‘rule’ that provides us with the absolute minimum size at which an ‘object’ can be said to have ‘size.’ Beyond that, apparently, we move immediately and inexorably into the realm of pure math.
Think of the volume bar on your phone. It is comprised of a series of ‘steps’ corresponding to a particular volume level; these settings are built in to the operating system and cannot be manually overridden. Say there are 11 volume levels, from 0–10; you can set the level to 1–10 and hear something, even if the sound is very faint, but the moment you skip to the level below 1, to 0, the sound immediately and entirely dissipates. There is literally no more sound being produced. This process, this series of predetermined ‘levels,’ is the fundamental property of digital systems.
In contrast — supposedly — is the mechanical knob on an old record player. You can turn the knob with your own hand, but there are no predetermined ‘grooves’ for the knob to click into. Other than the binary realities of minimum value (let’s call it 0) and maximum value (let’s call it 100), the knob will simply stop turning whenever you let go of it. And, theoretically, there are an infinite number of ‘stopping places’ between 0 and 100.
If that’s confusing, it’s because it’s not entirely accurate. The notion of analogue-ness is predicated on a belief that physical systems (such as knobs, space-time, etc.) are not comprised of pre-existing ‘notches’ or ‘levels’; as Zeno teaches us, there are an infinite number of possible steps between where I currently sit and the other side of the room.
But is this true? Or are we conflating two different concepts, making what philosophers call a “category error,” where we use a certain framework to define another, unrelated reality? Physical reality appears analog because we have as of yet determined a mathematical way to ‘chunk’ space-time into entirely discreet, pre-determined ‘levels.’ This is because of the way we mathematically treat 0, and infinity, and the notion of limits.
However, we now have a disconnect between the reality-describing tool of mathematics, which purports to define reality as analog (in accordance with our perception of it), and the inevitable logical reality of a universe that is, apparently, built out of mathematical entities. The “Planck Constant” is an entirely digital concept, a mathematical constraint that allows us to make up (and then ‘observe’) certain rules about the universe. If there is a fundamental level of being, no matter how tiny, then it stands to reason that there is a second-smallest level, and a third-smallest level, and a fourth-smallest level, etc. In this way, then, physical reality is a digital construct, comprised of pre-determined building blocks of various sizes (“Energy can neither be created nor destroyed”). We have returned to an atomistic conception of reality.
But how is this digital nature of physical reality reconcilable with the notion of reality being analog, as in the record player dial? It is not. So, then, is the record player dial really analog? Turn the knob a million times, then a billion, and so on. It is likely, if not inevitable, that you will continue to ‘stop’ on new ‘places,’ ad infinitum. In other words, as long as we can continue zooming into the knob’s dial to ‘measure’ new, discrete levels, you will be capable of landing there. This means that the only constraint on a so-called analog system’s spectrum of possible levels is our ability to measure them.
But we now run into a problem. The Planck Constant is the smallest measurable ‘thing,’ after which physical reality magically ‘melts away’ into the mathematical-only realm of quantum physics. So, it must be accepted that there is a fundamental limit to the number of levels on the record player knob — because the smallest possible interval between two notches is represented by the Planck Constant. This means that, between 0 and 100, there actually is a finite number of levels — so the so-called analog knob is really digital.
What does this mean? It means that physical reality, as we currently conceive and measure it, is a digital phenomenon; whereas, paradoxically, quantum reality is an analog medium. How does this follow? Only in the realm of pure mathematics, in the equation itself, do we find fluidity and the possibility of unconstrained motion. Note that the so-called “quantum level” is literally described as ‘size-less’ — it is a mathematical or probabilistic reality only, and cannot, by definition, be ‘seen,’ only mathematically inferred. There are infinite possible numbers between 0 and 1. But in physical reality, which is described by but not, in fact, built out of mathematics — due to our positing of a fundamental size minimum for an ‘object’ in space-time (the Planck Constant) — objects, space, size, and so on must be digitally constructed.
We can, then, think of the universe as a sort of inverted computer. The quantum level is the code, running somewhere unseen. The code is actually analog, in the sense that its numbers and logical entities are relational, unconstrained, size-less, and entirely relative. The instantiation of the code, the appearance of the world it creates, is pixelized, constrained by the tiny, albeit fundamentally limited, building blocks it is made of. There is no fundamental size limit to number; there is a fundamental size limit to ‘matter’.
In this way, then, the category error we are making is our continued search for a unified theory to ‘unite’ quantum physics (math) and standard physics (matter) once and for all. They cannot be united; they are already united. Analog systems underlie and describe digital ones, not the other way around. Reality is limited, comprised of unseen but inevitably finite building blocks; only the code, forever unseen, is limitless.