"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."
Some patterns arise from the representational tools humans build, while others reflect external relational invariants. The base-10 "rule of 9" appears inevitable within that number system but vanishes in other bases, showing pattern dependence on notation. Physical ratios and proportions, such as Planck's constant or the Sun–Moon apparent-size coincidence that permits total eclipses, remain invariant across numbering schemes. Distinguishing tool-dependent patterns from world-rooted invariants clarifies which archetypes emerge from recurring human relationships and which stem from systemic constraints like polarity or mandala symmetry. Repetition alone does not prove metaphysical truth; meaning emerges through lived experience.
Read at Psychology Today
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