The Rule of 9 and archetypes

When I was learning multiplication, my father showed me the “rule of 9.” He said to multiply any number by 9, then add together the digits of the product, and you’ll always get 9.

9 × 2 = 18 → 1 + 8 = 9
9 × 3 = 27 → 2 + 7 = 9
9 × 12 = 108 → 1 + 0 + 8 = 9

Every time, the addition came back to 9. It really sparked my curiosity.

The pattern works as we use a base-10 number system. Change the system, and the pattern changes to. In base-2, which computers use, there isn’t a repeating-9 rule.and in base-60, still used for hours and minutes, you won’t find a similar pattern. Once you change the base, the inevitability disappears. The pattern wasn’t universal; it came from the number system itself-the world I’d grown up understanding numbers in.

But some relationships stay the same no matter how we write numbers. The ratios behind physical constants-like Planck’s constant-don’t change with the numbering system. Neither does the amazing proportion that allows the Sun and Moon to appear nearly the same size,making total solar eclipses possible. These are relational invariants-patterns rooted in the world, not in how we count.

That contrast became the deeper lesson. Some patterns come from the tools we use to describe reality-like the rule of 9. Others come from relationships that exist beyond the human mind. The challenge is learning to tell the difference. That question led me to think about archetypes and jungian metaphysics.

Two Different Recurring Patterns

What we call “archetypal” isn’t just one thing. I see two distinct types.

The first grows out of recurring human situations that cultures express through familiar archetypal figures-the Mother, the Hero, the Trickster, the Wounded Healer. The stories differ, but the relationships remain consistent: someone cares, someone takes obligation, someone disrupts, someone heals while also hurting. These aren’t cosmic blueprints. They’re situations people repeatedly create and inhabit-and we only name them as archetypes later.

But not every recurring form fits that category. Some patterns may operate more like invariants-closer to the “Planck side” of the analogy. The mandala might be one of these. Circular, centered symmetry appears across cultures, and it also shows up in biological and physical systems that stabilize around a center. The symbol likely works becuase it resonates with how complex systems reorganize under strain-something we can observe in nature.