It required several years of studying ternary logic -- which at that time I still called trinary -- before I began to glimpse a realization that the way we understand ternary is with a profoundly binary lens. In those early glimpses, I began to understand that even the people who discovered ternary logic were relating to it using binary logic's hidden "excluded middle" which is embedded in language itself. Kind of like looking at the color blue with red lenses, you're not going to see what you're looking at even though it is right in front of you until you remove the red lenses. Discovering a fascinating website dedicated to the ternary logic of the Aymara language awoke me from my dogmatic slumber, so to speak. I fell in love immediately, and finally had a model that allowed me to begin developing a way of seeing ternary logic in a complex enough manner to start escaping from the binary trap.
This began a long journey, which I had no idea at the time would occupy me for the rest of my life, for it is clear to me now that there is enough depth in this area to keep me and many others occupied for a long time yet to come. Fascinated with ternary logic and amazed that so few considered it interesting, I continued to study and contemplate on it, now for over two decades. At least once a year, I spend a few days searching far and wide across the Internet to see what others are doing with ternary logic. All along this journey there have been deeper and deeper glimpses into the ability to see ternary logic as ternary logic sees. I've been peeling back layers -- thousands of tiny layers -- of binary perception, removing the "binary-colored glasses" which are embedded in our language and culture so deeply that we are actually learning binary logic before we even leave the womb. As we learn language, in almost all cultures on earth, we're learning binary logic. Everybody takes it for granted that this is the best and likely only way to parse information, who even knows enough about it to question this assumption?
Native Logic of Heaven?
Speaking of leaving the womb, the challenge of raising children has provided me some of the better insights in how ternary logic works. I'm now convinced it is the native logic of heaven -- in which I strongly believe children to be operating during the first few years of their lives, until they have fully learned binary logic and the other "dirty devices of this world" as Thomas Traherne describes near the end of this beautiful passage:
The corn was orient and immortal wheat, which never should be reaped, nor was ever sown. I thought it had stood from everlasting to everlasting. The dust and stones of the street were as precious as gold: the gates were at first the end of the world. The green trees when I saw them first through one of the gates transported and ravished me, their sweetness and unusual beauty made my heart to leap, and almost mad with ecstasy, they were such strange and wonderful things: The Men! O what venerable and reverend creatures did the aged seem! Immortal Cherubims! And young men glittering and sparkling Angels, and maids strange seraphic pieces of life and beauty! Boys and girls tumbling in the street, and playing, were moving jewels. I knew not that they were born or should die; But all things abided eternally as they were in their proper places. Eternity was manifest in the Light of the Day, and something infinite behind everything appeared which talked with my expectation and moved my desire. The city seemed to stand in Eden, or to be built in Heaven. The streets were mine, the temple was mine, the people were mine, their clothes and gold and silver were mine, as much as their sparkling eyes, fair skins and ruddy faces. The skies were mine, and so were the sun and moon and stars, and all the World was mine; and I the only spectator and enjoyer of it. I knew no churlish proprieties, nor bounds, nor divisions: but all properties and divisions were mine: all treasures and the possessors of them. So that with much ado I was corrupted, and made to learn the dirty devices of this world. Which now I unlearn, and become, as it were, a little child again that I may enter into the Kingdom of God. — Thomas Traherne, Centuries of Meditations
These days, it is clear to me that every thought, word, and action in our culture is embedded with binary logic, with its zero-sum, winner-take-all, positivist, categorical, imperialism marching across the world, through the ages, harvesting everything that glitters and ignoring (or spraying pesticide on) everything whose value is out of binary scope. Hence, language carries the knife we use to divide children from their heaven-borne ternary logic and replaces it with an idea that everyone and everything is separate from everyone else, as if being made of dust were not only our origin but our eternal destination too! Oh dear, I'm waxing poetic, so let me return to the point I want to make, and for which I prepared this illustration some time ago. Please understand it is a rough sketch that will likely be improved in the future as I understand these different perspectives better:
More continuous than discrete
I can state this with assuredness: Ternary logic is not "three poles" of Yes, No, and Maybe which is the closest binary logic can come to seeing it, because binary divides everything into discrete parts. Nearly everyone makes this same mistake, across all dimensions of studying ternary logic. Even a genius like Donald Knuth, when he talked about the "flip-flap-flop" to extend the "flip-flop" model of binary gates, was seeing the third pole as another implementation of the first two poles. There are glimpses, throughout the history of research into ternary, of the much more nuanced, continuous nature of "true" ternary, but almost always such glimpses are laid aside as curious but irrelevant. One quick example is buried in this obscure EDIT to an answer to a Quora question about ternary vs binary.
I have thought further on the matter, and I have thoughts that possibly ternary may be superior to binary in AI. Maybe we need yes-no-defer gates. It occurred to me that human decision processes are not yes-no issues. They tend to be yes-no-wait and see. With additional new information, we change our minds a thousand times a second. It is possible that a fully formed treatment at a hardware level is necessary to make effective AI hardware.
I love this answer because it captures a certain epiphany that -- once you experience it -- will draw you deep into the curious role of infinity within ternary logic. There are many other equally obscure glimpses into the empryean byss. A collection of them ought to be started, because when you encounter them one by one, you can easily miss the forest for the tree, but when you see a handful of them together, you start to see that there is something immense, subtle, and beautiful hiding just beneath the surface in the "included middle" pole of ternary logic. (My personal favorite of these historical glimpses is hidden behind my use of the word "byss" above. It is from a peculiarly deep mathematical observation made by -- of all people -- Winston Churchill, but before I digress further let's continue with the current narrative and compile that list some other day.)
In fact, ternary logic -- on its own terms -- does not see three poles; it does so only when communicating with someone embedded so deeply in the binary mode they cannot conceive of the singularity underlying everything. The singularity behaves in a manner which -- when described analytically -- is closer to ternary than binary, even though you might think it would be otherwise. With their innate tendency to divide (and conquer) everything they encounter, the closest that binary-trained minds can come to the holographic unity is to break it into three pieces (and out of habit, rapidly try to discard one of the three, but again I digress). Only from this fragile promontory of "three pieces" can a binary mind begin to wonder how ternary logic's third pole contains an infinite range of values which are equal in value to the two extreme poles. It doesn't make sense. It's a paradox. Surely there is a better way to say this, but here is what we have for now. Like Gödel's theorems broke the completeness illusion of math, it literally breaks the binary brain to think about how infinity is buried in the ignored middle area. In my experience it must be approached many times in small doses over a long period of time before the insight can be seen for what it is: a completely different way of seeing everything, as different as quantum mechanics is from classical.
Speaking of quantum mechanics, that's why we're here. I'm writing today specifically because yesterday's periodic review of the state of the Internet on the subject of ternary logic turned up the actual nature of the qubit. After reading through the fascinating "Ternary Computing Testbed: A 3-Trit Computer Architecture," I was saddened to see that the infinite nature of the 3rd pole was nowhere being explored. Again. I'm used to this by now, but I still hold out hope someone else will see it independently. The adventure of making the 3-trit computer is delightful, but it follows the Knuth flip-flap-flop model, with no reference to the whole range of infinity I know somehow exists within the "flap."
Qubits are poorly formed
During my research, some article mentioned qubits, so I finally took the extra 60 seconds required to understand how a qubit works. It didn't take long. I quickly realized a qubit is equally poorly formed. I can see are looking at something which is by nature ternary (continuous), and forcing it into our binary perceptions because we have no other way of seeing, not because that's what it actually is. As I see it, the "qubit" is what we invented by forcing binary logic onto an underlying physical structure which is fundamentally ternary, with the continuous third pole smoothly touching the two extremes, uniting them into a spectrum instead of dividing them into particles. I recognize that this insight, if true, represents a fundamental change to the way we understand quantum mechanics (but that is another conversation, so let's finish this one before we get to that).
The qutrit is a step closer to this underlying truth, but also makes the same mistake, not allowing for infinity because doing so breaks the brain (even though infinity itself has been chopped up into many pieces which do not share middles). So I dug in some more and, lo and behold, found another glimpse of the infinite nature of the third pole which is embedded in all transistors . . . There it is, right in front of us (see pic related below), and what do we do but saturate the transistor so it can only handle 0 and 1 with nothing in the middle. I have long desired the ability to build a ternary computer (not a 3-trit, but something more continuous and subtle which dances in the periphery of imagination) so I immediately recognized what was before me. I was startled to realize we've been building ternary computers all along and **intentionally suppressing the third pole** in order to fit our binary model. What I thought was a problem with quantum computing turns out to be a problem with classical computing also. Take a look:
Eureka!
AT LAST! With the transistor example, I finally have a metaphor *everyone* can understand in order to come closer to the underlying nature of smooth ternary curves being confined into digital 0s and 1s. It was finally time to write this essay. Now having written it, I feel like I am very poorly writing what I intend, but writing at this stage is better than bouncing around in my head, where nobody can access the insights, and start to make sense of them. I have thought about this so many thousands of times, it deserves the proper treatment.
I really want to sit down and write the whole book that is required to transition a reader incrementally from binary seeing into ternary seeing. But for now, I'm simply writing about the key illustration above, giving it some context so others can begin to think about this insight and come up with their own angle. This image tumbled around in my mind for years before I finally took a minute with Paint.NET to draw it up.
I'm not yet happy with it because even a sine wave isn't exactly a way to convey a continuous field which underlies everything, but it's smooth, and close enough to convey the general idea. That small discontent is why it lay quietly on my computer desktop for a couple months before I finally just now published it here with this essay. It summarizes the essence of much meditation, but is still only the tip of an iceberg, and I hope to be able to come up with a better way of illustrating the point eventually.