I don't understand Radix Economg, but Balanced Terinary looks very close to what I described in my experiment with 3-D Di-Polar chains, how they acted like molecules.
You can use any shape, but imagine a cube. It has six sides.
You give side S the Cube's Identity, such as in Hawthrone's case, God.... just the concept. You are left with 5 sides, four opposing into two polarities. You can add a value like Love to a side joining God, and put the opposing value opposite. Then, repeat another two terms. You end up with a cross, one you can build up again from any direction.
Issue is, space asserts the inability to sort out the direction these cubes can build out into, and I was expecting a shape (and 3-D regular shape like pyramids or cubes or higher) when they class to contradict logically.... and they usually don't. It is a random mix.
You also have to worry about a problem inherent in logic, but next to never observed because we rarely use large systems..... numbers play by their own damn rules. We designed our number theory to have a pattern, and it has unexpected random chaotic characteristic Wolfram explored in his "A New Kind Of Science"
https://www.wolframscience.com
It is purely coincidental I went with a 3-D approach using cubes, I could of written it out, but the rules for patterned Chaos would of played out eventually in any logical system I produced from it. He explored these patterns, a lot match up with certain patterns we observe in nature, like waves moving in the ocean, or how renessiance siege works were designed to safely advance infantry through trenches under artillery barrages, and how to slope the land to counter that.
It would exist written flat as relations, or expressed in 3-D.
A bigger issue would be if you used a data set so large that the values accidentally did something completely unexpected, like take on a characteristic of self replication. One case exists for this, that I know of, but was done intentionally:
https://m.youtube.com/watch?v=A8B5MbHPlH0
That uses the basic idea of Cellular Automata, and what we are discussing in this thread is very closely related.... might not look like a basic kind of logic you learn with binary rules, remember, it took 33 million operations for it to self replicate.... but it can in theory happen, and perhaps on a much smaller scale. A potential for some sort of ghost hidden in the chaos of our date sets we work with, asserting itself in bizarre manners over time.
They run off very, very, very simple logic. If I can convert a Di-Polar set up into 3-D squares, and they can construct complex ideas seeking syllogusm and contradiction (I'm not too pleased with the results, can be done much better I think, mapping it out, but not so well how I was doing it, can work sometimes), but can also do the work flat, in a more traditional format, it means the rules of cellular autonoma and the chaos, and even the mimicking of life and intelligence is capable of appearing in our logic as well, unintentionally.
I can't begin to say how much this annoys me. St Augustine would laugh saying of course, but I don't hold to the idea that mathematics, laws of nature, and other such systems are the thoughts of god.
I suspect the higher you increase it, once pass 4+, the more likely you are to trip up some bizarre autonomous actions on the part of logic itself, where the data seems to have a perverse mind of it's own.
Highest I myself can use is the system given by Dignaga, in his Hetucakra.
https://en.m.wikipedia.org/wiki/Hetucakra
https://www.amazon.com/Buddhist-Formal- ... ds=dignaga
It seems to be a evolution upon Aristotle's Square of Opposites (could very well have a independent evolution), examining the reality of what is apparent, using 9, with three variables per the nine to assert if some assertion can be true.
I've tried combining Dignaga and Aristotle a few times already, into a cube, but keep getting messed up.... some angles work, but others.... well, unexpected oddities assert themselves that forces me to rethink it. Been a long lasting headache for me, thought I nearly solved it at times at combining the two systems together. Rule Number 9 is particularly tasking given how Aristotle approaches his square, which is more or less how Viveka expresses Nargajuna. I don't like the implication, as I see it pop up in philosophy all over the place, but can't wedge all that extra stuff into a cube. Might have to try a different shape all together. I get tantalizingly close only to see it fall apart, with the parts making sense but the whole not really looking beautiful and simple.