And yes, base 4 does have distinct names in this system — and they're all in Unicode (though HN may not render them):
Two digits give you the Four Symbols: Old Yang (U+268C ), Young Yang (U+268F ), Young Yin (U+268D ), and Old Yin (U+268E ). Add a third digit and you get the Eight Trigrams (U+2630–2637 ), a core symbol of Daoism. Double that to six digits and you arrive at the 64 hexagrams — the I Ching, the Book of Changes, which many Chinese have believed could be used to divine the future.
Actually, Taiji, Yin-Yang, and Daoism are deeply related. Dividing Taiji gives you Yin and Yang — humanity recognizing something out of nothing, order emerging from chaos, duality arising from the void. You learn what "good" is, then you know "not good"; we coined "LLM," and we also invented "not LLM." They always come in pairs — that's the fundamental rule. We're essentially dividing iteratively, building our culture and recognition by inventing new names, mappings, and combinations to carve distinctions from some "embedding space." And we humans, including LLMs, learn from those names.
So the progression is: Void/Chaos/Taiji → 2 (Yin / Yang ) → 4 (Four Symbols) → 8 (Trigrams) → 64 (Hexagrams). At its core, it's philosophical thinking — and personally, I believe there's great wisdom in it. For example, we should never be trapped by names and should always think beyond it.
(Shameless plug: I came to know about this about a year ago and still find it fascinating. I even built a site about all this — https://ichingdao.love)
Quaternary