Every Canvas a Mirror (Overview)

On Understanding the Understanding

I’ve posted the essay Every Canvas a Mirror to my website. It’s easily the single most important thing I’ve ever written, the longest among all my writings (by a factor of four), and — taking full advantage of being hand-written in HTML — the most arborescent. Building a new website from scratch was necessary for me to implement the detailed hypertextual structure I wanted: not just endnotes, but sidenotes, context-providing hovertips, expandable sections of superfluous material such as proofs, and additional hidden-but-revealable endnote sections

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. Because of that, I can’t simply copy-and-paste it here; again, here is the link — or click the button below. This will just provide an overview.

The core tautology underlying the essay is that the world is for us as it is for us. I cannot understand anything about the world that I cannot understand. The world for me has a thoroughgoing conceptual nature, a set of maps detached from any actual territory, because this is the only way in which it can be for me, in which I can understand it. I ought therefore to understand the faculty of understanding itself, that I may seek to expand the space of things it can represent — perhaps getting me a bit closer (pragmatically speaking) to reality, which is not necessarily given in any nice, readily conceptualizable way. For the abstract forms of which we can form understandings are not themselves the core sensory-cognitive building blocks (‘conceptive figures’) of understanding, yet may nevertheless be be imported as building blocks

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; yet due to our lack of awareness of this process, we cannot improve upon it, doing it conscientiously or even consciously.

Therefore, while the conceptual nature of the world for me — the fact that everything is merely my map of it (yes, including the concept of “concept”, let alone “map”, “territory”… “me”) — is an existential nightmare, it is at the same time a source of limitless potential so long as we are capable of understanding the understanding.

In the essay, I formalistically discuss the structure of such a project.

• Technique-wise, I (subjectively, illusorily) it up into three parallel, interacting divisions. The phenomenological division concerns directly looking at the form of the understanding as it is given mentally, the metacognitive division concerns the structural examination of the formation and application of understandings to the world, and the transcendental division examines the ability of our understanding of the world to be veridical

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• Progression-wise, we must notice the recursion inherent to the notion of an understanding of the understanding; such a project, which I call an analytic, necessarily builds itself in a circular manner. Not that this consigns us to futility — our ability to turn the complex arrangements portrayed in cognitions into the atomic schemata from which cognitions are built allows the arc of the analytic to progressively ascend — not a loop, but a helix.

Of course, talking about such a project is no good if we don’t actually work through it; I haven’t attempted to do so in this essay, but will steadily introduce the progression over time. While I’ll probably keep Twitter as the first place for announcements and discussion, everything will be announced — when feasible, replicated — on Substack. So don’t forget to like and subscribe and so on; here are some buttons.

1. I’ll make the code public, probably via Github, once it’s actually clean enough to be understandable by anyone other than me.

2. This is roughly how we progress in our mastery of fields, and it is how the maturity of a mathematician or programmer is built. For instance, the other day I learned about the pumping lemma, and — as soon as I read the statement of it — saw within perhaps one or two seconds how to prove it. I knew beforehand that regular languages had finite-state automata that could recognize them, and the image presented itself in my head of a string running parallel with an automaton, each character next to a state, the string being long enough that the automaton eventually had to run into itself, looping - this loop being the repeatable section of the string that could be ‘pumped’. The intuition “it gets too big to not run into itself” becomes “use the pigeonhole principle on {what gets too big? the number of character-associated states}”. The automatic association of abstract mathematical concepts with sensorimotor images — the presentation of recognition of a string by an automaton as a literal string ‘running along’ the bead-necklace-like image of the automaton, for instance — was what allowed me to instantly conceive of the correct proof.

3. For instance, we can, despite the fact that nothing about it is given to our understanding a priori, end up understanding solid state physics, coming up with a vast network of abstract formalisms and corresponding sensorimotor associations which culminate in humans being able to build the very computer I’m writing this on. How exactly does this work?