When I was learning multiplication, my father showed me the “rule of 9.” Multiply any number by 9, he said, and then add together the digits of the product, and you will always land on 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 stimulated my curiosity.

The pattern works only because we use a base-10 number system. Change the system, and the pattern changes with it. In base-2, used in computing, there is no repeating-9 rule. In base-60, still embedded in hours and minutes, no similar pattern appears. Once you change the base, the inevitability disappears. The pattern was not universal. It came from the number system itself—the mental world I had grown up inside.

But some relationships do stay the same no matter how we write numbers. The ratios behind physical constants—such as Planck’s constant—do not change with the numbering system. Nor does the striking 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 our counting system.

That contrast became the deeper lesson. Some patterns emerge from the tools we use to describe reality—like the rule of 9. Others come from relationships beyond the human mind. The challenge is learning to tell the difference. That question led me into thinking about archetypes and Jungian metaphysics.

What we call “archetypal” is not a single category. I see two.

The first grows out of recurring human situations that cultures express through familiar archetypal figures—the Mother,........

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