Moving from binary to ternary is harder than from ternary to binary

Taking the Shortcut by W. H. Norton

Moving from binary logic to ternary logic is harder than from ternary to binary. Today I suddenly realized this, and was delighted because it solves one of the deeper "why" questions on the prevalence of binary logic, which is everywhere, in everything you see, think, feel, know, and do. In the Western culture, we are deeply embedded in it, which I have written about many times, so I won't go into that much now.

Today's insight is more in the direction of moving out of the binary world, than figuring it out and seeing it for what it is. The insight came as I was thinking about "shortcuts" and specifically about an observation I made to my young daughters over the past few days.

Shortcuts vs the right way

As a family, we have long talked about the virtue of doing things "the right way" as opposed to taking shortcuts. One daughter is a little older and she gets it; she has crossed that threshold of understanding, and is more self-managed in this area. The other daughter still tends to find shortcut ways of doing things, which leads to complications.

So when I pointed out one of the deeper reasons why we don't do shortcuts, it happened in the context of strengthening the foundation beneath this imperative to do things the long way, not the easy way. There's a delicate balance here because "the right way" can be an impossibly high standard, and trying to meet that impossible standard creates another kind of problem (letting the perfect get in the way of the good). So there's an equilibrium in coaching children; too little and they do not gain an important skill, too much and they gain it in exaggerated form that also doesn't work.

I began the conversation by prompting: "Why is it not a good idea to do shortcuts a lot?"

She thought about it, and answered "Because it's being lazy," which we have discussed previously, so it was an easy answer. I grimaced internally at my own teaching, which is a form of negative reinforcement, but knew I had something better to offer which was indicated by the last two words of my question, so I continued:

"Yes," I said, "but deeper than that." She was stumped, and had no better answer. At this point she doesn't think about it independently and accurately repeats back what we've discussed previously. It's a topic I drive until one day she has enough information to figure it out for herself, as her older sister did at about her age.

"For starters, it's addictive," I said (continuing with the negative reinforcement approach).

We've talked about addiction before, using child-friendly topics like addiction to sugar, video games, and so forth, these being behaviors they understand well. They're also culturally aware enough to know about addiction to drugs, but thankfully only vaguely so far. I continued:

"When you do a shortcut, you want to do it again the next time you have the opportunity, and you have to train yourself not to, or else you get addicted."

She thought about that. I wish I were better at the Socratic method, but I learned in the pedantic style so deeply (we all did) that it's hard for me to re-train myself to be more Socratic in moments like this. I'm working on it, and at least I started with a question. I should have asked her another question, letting her come to the realization, but instead, I continued my narrative pedantically:

"But even deeper than that is a problem that comes up after you get addicted to shortcuts. You develop a whole lifestyle that is oriented around shortcuts. Everything you do is a shortcut, because it's easier that way. I would say it takes about five years, a little here and a little there, but soon enough everything you do is a shortcut."

I paused, forming my words for the insight I had discovered earlier that morning when I was intentionally using shortcuts in meal preparation in order to get everyone out the door to school on time... and thus realized the positive value of shortcuts: Sometimes you need them.

"...and then, when you get into an emergency," I continued, "you need to do a shortcut because there's an emergency and a lot has to happen quickly. But... you can't, because everything you do is already a shortcut. There are no shortcuts. You've used them all up."

This was too abstract for them. I needed a concrete example but couldn't think of one. It was only later I realized I should have been more Socratic. Both girls were silent, listening, but it didn't feel like I was connecting. I knew I would talk about this again, so I soon left the topic and we went on to other things.

It was while thinking about that conversation again this morning, that I realized an even deeper insight, the one that draws me to the page to write about. It is this: "Ternary is harder than binary."

The ternary path is the harder path in the short term

To take the ternary path is to take the harder path. For an example of what I mean here, the difference between "love" and "duty" comes to mind. Both are hard, both get easier with practice, both end up driving similar actions. On the surface, it can sometimes be a challenge to tell them apart. Love is hard but emotionally rewarding. Duty is nearly as hard but will burn you out eventually, unless you find ways to manage the built-up stress.

Binary logic will lead you down the easier path every time. I have long known that the binary way of organizing information -- which we all do, it's so deeply embedded in our culture -- is a categorically "lazy" approach, but I never took that thought further and realized that the extra layer of context (embedded in ternary information) makes the ternary approach harder to do, in the same way that "the right way" is harder to do than "the easy way."

I've written elsewhere about how logic does not have power -- it is merely a way of organizing information. It must be connected to some other force in order to actually have the power to change things. So I well know that logic is a legal system without an executive branch. Logic can clearly define the change that needs to happen, can plainly describe the delta between what is happening and what needs to happen, but it cannot of itself drive that change. Brute force, rhetorical persuasion, emotional triggers, or any of a host of motivations can be coupled with logic to drive the change, but in the end, logic itself is analytically powerful but not executively powerful. A good way to understand the difference: logic is of the mind, and power is of the heart.

Logic defines an abstract path through a map over a real territory

Ternary logic will define a path forward out of some situation or another differently than binary logic -- in most cases, what each form of logic prescribes for action is quite different from the other. Binary logic creates a wholly separate abstraction of the reality it perceives, a map. Actually, ternary logic also creates a map, but its map is much closer to the reality than the binary map, and there are technical reasons for this. That one extra pole of logic is not quantitive, but qualitative, and thus more intimately connecting the "map" and the "territory," to borrow Alfred Korzybski's terminology.

The binary map has the advantage that it is quantitively more compressed, but it loses qualitative information which is retained in the ternary map. That qualitative information makes the ternary map closer to the truth. In other words, if you organize them by order of integrity, the order is NOT numerical. I write about this elsewhere, so I will only show a brief ASCII illustration of this point:

---------------------Binary map---------------------

---------------------Ternary map--------------------

--------------Territory (i.e. "reality")------------

Within the context of "the right way" and "the easy way," ternary logic is the former, more integrated-with-reality, and binary logic defines the latter, easy path. (For those who are seeing this ordering for the first time: in that same map, quaternary is above binary since it is simply a derivation from the binary map.)

Binary logic enables an addiction to shortcuts

When ancient Greeks introduced binary logic, it was the first time in Western Civilization that logic was being written about and discussed at that philosophical level, so when Aristotle first started writing about logic, his ideas came with "first-mover" advantage. By the time the Stoics wrote about it, they came up with a different flavor of logic, but it was still binary as initiated by Aristotle, not ternary.

For many centuries -- nearly two thousand years -- few people thought about how there might be different forms of logic than the insightful Aristotelian "true" and "false" dichotomy[1]. Eventually, only a couple hundred years ago, as non-Euclidean geometries were arising, non-Aristotelian logic was also, and we began slowly breaking out of the Greek model of thinking.

Today, we have a great understanding of polyvalent logics, with multiple forms of ternary logic and other variations, but for about fifteen centuries, our entire culture was embedded wholly within binary logic. Thus it is still deeply embedded in all we think, say, feel, know, and do. For example, it's in our grammar, so as we learn to speak, we learn to divide everything in two.

Thus we are in the condition I was describing to my daughter -- as a culture, we're addicted to shortcuts, and since everything is a shortcut, we have no ability to do shortcuts to hasten things in the event of an emergency. This leaves us in a condition where we're continually stressed; we go from emergency to emergency without a break. We have no relief, no place to rest, we're always stumbling forward within a logical domain that is poorly organized because it emphasizes the short-term outcomes over the long-term.

As I hinted earlier, I've long wondered why it was so easy to go into the realm of binary logic, what was its attractive force? And this is it. It's "easier" to do the binary path, and so it does not take much effort to evangelize it, whenever the choice between two paths comes up.

Catastrophic failure becomes inevitable

Blue screen of death from WindowsWhat's fascinating to me is something I discovered long ago: the binary end of any path long enough is inevitable catastrophic failure. Binary is a logic optimized for taking shortcuts, and cannot sustain longer paths. It's missing the "excluded middle" where longer-term coherence exists.

There is much to say here, but I'll summarize: we can see what I mean very clearly with the example of a computer -- the best operating example of something using pure binary logic -- blue screen. Even after 30 years of sophisticated desktop PC development, we still get blue screens. The computer completely fails, and whatever was happening in dozens of dimensions all collapse, requiring a manual reboot and lots of sophisticated self-reflective code to repair or minimize the damage. On a cultural level, this happens too. And interpersonal relationships. It's everywhere.

Binary logic is a shortcut, and as with all shortcuts, it is simply not sustainable. Its focus on short-term solutions penetrates so deeply into the dysfunction woven thoughout our whole culture, that pretty much everyone is aware of short-term solutions as a systemic failure on some level or another.

Great thinkers for centuries have written masterpieces of analysis into this dysfunction and pointed toward solutions, and some have made great progress toward these solutions... but all of this is happening within the binary scope. We haven't even begun to escape the problem. One of those great thinkers, Rene Girard, even explicitly talked about the inevitable collapse of our culture, and thankfully, he went further. He talked about the rise of something wonderful that can only happen after such collapse. Although he never said so, I'm convinced the post-collapse lifestyle is one embedded in ternary logic, but now I'm getting far afield of my original point, that ternary is harder than binary... but worth the extra effort.

The way out of our condition of being addicted to the easy path is hard work, as hard as it is for a meth, crack, or heroin addict to get free. It is fraught with peril, and with plenty of temptation to go back to the easy way.

But it can be done, and I believe the more people understand the ternary path, the easier it is for our culture to shift out of the shortcut mode and into doing things "the right way."



  1. ^ Since this weblog post was originally written, I have since learned more about the history of Aristotle and binary logic, and would write this sentence differently. The history of binary logic is a little more nuanced than I portray it here. I have since learned Aristotle was more interested in the structure of the syllogism than the truth values, but this sentence is close enough to the truth that it'll do for the purposes of this discussion.

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