Clearhat

In the ongoing labor to develop an internally-coherent way of perceiving ternary logic -- and its most famous derivative, binary logic -- I have come to an understanding of how ternary logic is the proper logic of the continuum; not of particles, division, or separation. Particles, division, and separation are examples of what arises from the continuum, not the other way around.

By logic of the continuum I mean what is the internal logic of the quantum world, not of the classical physics, but of quantum physics where "mysteries" like superposition and entanglement and "wave vs particle" paradoxes live and play without being paradoxical because they are seen as they are, not as they are projected to be from within the classical realm. The classical perspective forces paradoxes into existence due to a founding, and proveably paradoxical, assumption known as the law of excluded middle.

Qualitum mechanics?

Coming at logic from another direction than what is common, I find the word "quantum" limiting because it clearly arises from within the classical paradigm, and propose a replacement: "qualitum." Alas, although that word sets a nice frame for what I'm writing about, it is not exactly right either. But it will do for now as a way of turning attention away from particles and toward continuities at a fundamental level.

Ever since the advent of binary logic with Aristotle, Euclid, and others in ancient Greece, our understanding of the world has grown increasingly more atomic. Or maybe I should say "atomized." The crown jewel of such an approach, scientific reductionism, has systematically conquered the previously irreducible problem of religious mythology and "faith: the evidence of things not seen" by eroding its over-centralized power from the edges until it collapsed into a more sensible form. This erosion happened in a manner which has settled religion in a condition of equality with science described well by Stephen Jay Gould's structure of non-overlapping magisteria.

The skeptical sword of science -- a light in the darkness -- has now flourished for centuries, driving great discoveries and extracting deep insights into the true nature of Nature. But its inherent reductionism has a limit, same as religion's unverifiable "faith" did. As scientism arises with a move to centralize power -- in a similar zero-sum fashion to what religion once did -- we've finally gotten to a point in our journey where more than a few people can see the weakness of over-reducing everything to tiny, disconnected, particles. Thanks to the baffling paradoxes of quantum physics, many people are aware that we've lost a sense of intrinsic wholeness which some are lately seeking to regain by stepping out of reductionism.

I'm part of that movement. One by one, the trees in my internal forest of inherited reductionist binary logic are felled before the march of a growing awareness of how ternary logic operates. One by one, new trees are planted in their place, creating a forest of holistic ternary logic. Like quantum physics compared to classical, and like quality compared to quantity, it operates in a manner that is very different from binary logic, which is increasingly revealed as a derivative subset of ternary logic.

Wait, what? Binary logic is an edge case of ternary logic?

I know it seems absurd to think of binary logic as an edge case within ternary logic. I used to have detailed conversations with people trying to convince me that "everything that can be done in ternary logic can be reproduced in binary logic" and "binary logic is more fundamental, because it requires fewer elements." In those days I was inexperienced and lost such reasoned debates. I have since learned enough to counter such arguments¹, but these early discussions led me to see how deeply binary logic is the lens through which anyone reading these words sees the world. So I'm learning to speak to that a little before I go into the merits of ternary logic.

The knife of binary logic is embedded so deeply in perception that it seems to be intrinsic to the nature of reality itself, but indeed, it is only a lens. Once the lens is replaced with a ternary lens, the elusive unicorn of the continuum, the true nature of infinity, the holistic view, becomes visible. When the continuum becomes visible on its own terms, we begin to see "things hidden since the foundation of the world" (as Rene Girard once famously put it as he revealed his own portion of this great project to make visible what has always been right before us).

For example: Even though we're two-brained, two-eyed, two-eared, and two-handed, meaning our perception appears to be intrinsically binary, the underlying reality we perceive is not divided into two. Nor is our internal model of the world which is fed by these binary perceptions. In other words, we have two eyes so we can see depth, not separation; our awareness of twoness exists in order to get at a third, integrated awareness.

Another example: The more we study artificial intelligence, the more we realize the importance of an underlying unified model of the universe. In a recent interview², Joscha Bach notes that this is the main thing lacking in Large Language Models today -- and the root cause of their hallucinations. GPT for all its wonderful abilities with language lacks a single universe model. We humans have that, and it's very important.

As it turns out, the binary perceptive lens is not for the purpose of dividing everything, but for the purpose of uniting everything³.

Twoness does not always imply division

Only the left brain operates in a divided manner, literally unaware of anything outside its local perceptions; the right brain sees the whole, encompassing any division. The right is not alternate to the left, but surrounds it. When we think of the two halves of our brain, we see it from the left perspective, and therefore tend to see half the picture: the left side sees the division between two, the right sees the unity of the two. The whole and the parts, not just the parts, as reductionist science sees everything.

In the West, our whole culture is embedded in this left-brain way of seeing everything, although the more unified way of perceiving is just as valid. At the rare balance point between the two is where ternary logic flourishes.

In the big picture, we are rediscovering the way people understood the world before ancient Greek concepts began to change everything. The best part of this restoration is: nothing is lost. We get to keep the extremely detailed "parts" knowledge that we gained during our lonely sojourn through reductionism. Reductionism is not wrong, it's just... part of the solution, not all of it.

We are already shifting from a zero-sum competition between left and right to a positive-sum cooperation between the left and the right, precisely as Iain McGilchrist captures in his "Master and Emissary" model of the two brain hemispheres. His book is an important part of this restoration because it is awakening people to an accurate model of how the left and right need each other. The fact that it is popular and influential is a good sign that people are taking his warning seriously: if we do not heed the right-brain's voice and relinquish some left-brain control, the Emissary is at risk of destroying the world because it lacks the greater context carried by the Master.

A trit is a ternary digit

With this in mind, I was in conversation this morning with some friends and mentioned the word "trit" in reference to a trinary digit. Musing aloud about the word "trit," because my listeners were unfamiliar with the word, I said: "A trit is a ternary digit." Their eyes continued to glaze, so I stumbled forward: "A bit is a binary digit. Did you know that 'bit' comes from combining the words 'binary' and 'digit?' That's the origin of the word 'bit.' The 'b' is from the first letter of binary, and 'it' from the last letters of digit. Binary digit. So a trit..." I suddenly stopped, seeing in mind's eye that the word trit is entirely the wrong nomenclature for the fundamental ternary logic element.

"Well, that won't work," I said, absentmindedly, losing my audience completely. I continued thinking aloud in hopes of regaining my thread: "Ternary logic is the logic which precedes binary logic, and therefore it doesn't have digits yet." Oops, rather than regaining, I went further away. Being autistic enough not to notice, I mused some more. "The word digit is talking about a binary structure..." I began pondering what would be a good word to replace "trit," something conveying the unique relationship with the continuum which is essential to properly understanding ternary logic.

I sadly lost my audience, but discovered something wonderful.

After a few minutes of thinking along these lines, I resolved a couple of things: 1. The idea of a wave in an ocean is closer to what a trit is supposed to represent than a particle -- a bit -- and 2. As soon as I get to a computer, I need to start looking at Latin stems around the word "wave." I knew even then that wave didn't fully capture the idea -- a wave is an isolated aspect of a greater whole, similar to a particle. But it was closer than "digit," which is even more particle-like. With this resolved, I recovered and rejoined the conversation with my friends.

Riffing on the ripples of rivus, Latin for river

Once I got to an English-Latin dictionary, I started with words like "fluctus" and "unda." Fluctus, wave, reminded me of Isaac Newton's fluxions, and I finally understood he was aiming at a similar idea when he invented calculus (which opens up a door to some future investigation into what exactly Newton meant by coining the term fluxion instead of using infinitesimal⁴). Unda, water, is a great word, because the flowingness of water and the boundlessness of water in an ocean come to mind, but no. Prefixing "tr" to "unda" makes a word that doesn't feel right. Tructus? Same thing; the word needs to ripple, to flow...

Truxion, as a play on Newton's idea with fluxions? That had a better feel to it, but "uxion" loses most of the "flow" or "wave" meaning, so I kept looking. I soon came upon "rivus," for river.

Aha! "Trivus" feels better, the idea of a flowing river comes through into English better.

A river is too large, though (I live near the Missouri River, whose size affects how I think of rivers). Not as large as an ocean, but larger than a stream. I noted that "bit" refers to something tiny, the smallest particle of binary logic. Pondering the importance of conveying a small size led me briefly to "trivet" which I liked for a moment because of its simplicity and similarity to "trit" which it would replace. I also liked it because Wikipedia describes it as: "A trivet /ˈtrɪvɪt/ is an object placed between a serving dish or bowl, and a dining table, usually to protect the table from heat damage." That placed between aspect immediately conveys an important ternary intuition, but... it also doesn't:

Placing the third "bit" between two binary "bits" is by far the most common way people begin thinking about ternary logic. However, after studying these things from a thousand angles for two decades, I have come to understand the third element is best seen as surrounding the two bits. Not merely injected between, but surrounding (which is a larger intuition that better includes the possibility of injection). This nature of logic encompassing rather than separating is a completely different way of seeing things. This is equally important to the intuition I want to capture in the new word. So the simplicity of trivet didn't work.

At this point I went back to the neologism "trivus." I liked the fact that a river is smaller than an ocean, yet they are connected in a continuous whole... and then I came upon "rivulus" and "rivulet."

Triple aha! There was the bit of gold I was seeking. Er, I mean trit of gold....

"Trivulet" embodies several conceptual layers at once. 1. Rivulet is a small stream, which eventually flows to a larger stream, which eventually meets a river, which eventually meets an ocean. Adjacency with "trivial" plays a role in the "small portion of a larger whole" intuition. 2. The word trivulet is full of wavy-like action, being unlike the static "bit" and much more active, energetic, with plenty of movingness, although perhaps too much. 3. It also has... three syllables, indicating the hidden recursive nature of a ternary logic element. Recursion is an important aspect that I wasn't even factoring in yet, but there it is. 4. The word nicely ends with the terminal "t" conveying a similar-ish feel as "bit" and "trit," thus reinforcing the smallness intuition essential to naming a fundamental element of ternary computing.

One could say as a detraction that "trivulet" is an inconvenietly longer word than the handy "trit," but think again: That is an observation forged in the perceptual system of binary logic, whose greatest weakness is that it truncates too much. Therefore: 5. Coining a word that overtly breaks the over-efficiency problem of binary logic is... exactly just right. We're still in the Goldilocks zone.

So trivulet it is. Trivulet of gold, not trit of gold. And with its appearance, we can now fully escape the law of excluded middle. I'm tempted to add a #6 to the list: tri-vu-let holds in its middle the syllable "vu," a pun on "view," reifying how the stumblingblock of excluded-middle (a kind of intentional blindness) is replaced with seeing. But that would be going too far.

Trivulet, the fundamental element of the ternary logic of the continuum, the true ternary logia, take a bow⁵. You've now been introduced to the world.

Footnotes:

1. The counterargument become self-explanatory once you understand something that took a long time for me to find: the "Law of Excluded Middle" is equal in strength to the assertion that there is "true" and "false." This means there are three elements required for binary logic to work: True, False, and LEM. The evidence for this is clear: In every discussion of binary logic fundamentals, this "law" is mentioned. It is assumed to be self-evident -- at least as strongly as Euclid's fifth postulate used to be. However, despite its name, the LEM is not a law, it's simply an assumption. Once it is replaced with another equally-reasonable assumption, the nature of "true" and "false" change. Although people initially have a hard time understanding true and false without polarity, it's quite possible, and plain-to-see within ternary logic. As you can imagine, ternary logic handles the trinity of True-LEM-False natively. From a ternary perspective, pure polarization is never true: no two things are ever exactly equal. Within this so-called "polarity," it can be shown that true is more fundamental than false. Here is how that works: False is a couplet of half-truths which appears as a singularity. Hence, anything we call false can be shown to have an intrinsic structural duality. Since the inner structure of false is composed of two half-truths, Occam's Razor tells us "false" cannot be fundamental in the way "true" is. Like a house built on sand, the trinity ("true"+("halftrue"+"halftrue")) falls apart, revealing a true singularity: truth.
2. The link above takes you to the YouTube video of Bach's conversation with Lex Fridman, with the timestamp set to the moment he is talking about how the GPT keeps track of identity within sentences and paragraphs but does not do so within a single universe yet. I strongly recommend watching the entire interview, and more besides. Joscha Bach's mind is stunningly beautiful and a delight to behold in a context with someone like Fridman or Curt Jaimungal, who ask really good questions and let Bach talk.
3. Wow, cool. I just discovered this pithy bit⁶ while writing it: "the binary perceptive lens is not for the purpose of dividing everything, but for the purpose of uniting everything." I'm stunned. This is a great insight, well worth writing this essay in order to discover it. I love it. We'll come back to this in the future post.
4. Speaking of things to come back to in a future post, here's a note-to-self: Newton's use of fluxion while Leibniz stayed with the ancient concept of infinitesimal, followed by the advent of Leibniz's way of doing calculus (where mathematicians today use Leibniz' nomenclature instead of Newton's)... these are clues that Newton may have discovered a more ternary way of doing calculus, which the world wasn't ready for. That is a hypothesis worth investigating.
5. Logia? It might be going too far to introduce two neologisms at once, but I sometimes wonder if the word "logic" itself might change with the advent of true ternary, for the following reason: The word logic, with that sudden stop at the end, "ic," conveys a kind of cutting, slicing, dividing feel to intuition. In comparison, the word logia has an open-ended flowing aspect to it which fits better into the continuum, coming and going more smoothly without sudden leaps. Hence, logia holds the original meaning of logic: "to gather words" a little better. Logia. Gathering and organizing ideas, not cutting and dividing them into smithereens. So if we're changing the names of things to better carry flowing concepts, logia might be a good replacement for logic. I recognize that would be going too far, and plus the word logia already has a referent. I'm not proposing this with the sincerity I am proposing trivulet. I'm just saying I play with words a lot in my mind, and the flowingness of trivulet goes better with logia than logic. But, logic will do.
6. Hm. I never saw a footnote that had a footnote before, but here we go: I wanted to use the phrase 'pithy trivulet' at this point instead of 'pithy bit' but realized that at this point of the essay I haven't yet justified its use, so anyone following the footnote might not appreciate me using 'trivulet' for 'bit'. However, here in a footnote to a footnote, I think I'm free to call the pithy bit a pithy trivulet.