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.
Two different recurring patterns
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, the Hero, the Trickster, the Wounded Healer. The stories differ, but the relationships stay the same: someone cares, someone carries responsibility, someone disrupts, someone heals while also hurting. These are not cosmic blueprints. They are situations people repeatedly create and inhabit—and only later do we name them as archetypes.
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 may 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 may work because it resonates with how complex systems reorganize under strain—something we encounter, not something we invent.
A second possible invariant is polarity—paired interdependence that appears whenever systems co-stabilize: parent and infant, predator and prey, charge and counter-charge, call and response. The stories come later. The form already exists.
So I do not claim that all archetypes are psychological or relational. I am saying we should not treat them all as metaphysical simply because they repeat. Some emerge from human social conditions; a smaller subset seems to reflect deeper constraints on how experience and life can take shape. The work is to tell those apart.
When a pattern feels deep, but the situation is structuring the outcome
Many Jungians treat archetypes as if they exist outside the psyche—as if meaning waits in metaphysical space. The main argument is repetition: If a pattern appears across cultures, it must be embedded outside of us.
Repetition matters—but it does not, by itself, prove metaphysical truth. When I trace these experiences back to where they form, I keep finding relationship, dependence, exclusion, conflict, vulnerability, loss, and efforts to hold things together. The same kinds of situations recur because social and psychological pressures keep pulling people into them. Meaning can then feel like destiny when it is really arising from how we keep ending up in familiar situations.
So I’ve come to ask:
Are we encountering a timeless structure of reality—or the ways life keeps pushing us into the same kinds of relationships?
Where Jung—and Roderick Main—go further than I do
In Synchronicity: An Acausal Connecting Principle, Jung wrote that “number is an archetype of order… not invented by man but found or discovered. Numbers are pre-existent to consciousness” (Jung, 1952/1973). For Jung, numbers—and by implication some archetypal forms—are built into reality itself, not shaped through human life.
This is where I part ways with him.
Jungian philosopher Roderick Main extends that view, arguing that synchronicity and archetypal symbolism reveal a meaningful order already present in the world, in which psyche and cosmos share a structural kinship (Main, 2004). In that view, the psyche does not merely create meaning; it participates in meaning that the world already contains.
I understand synchronicity as meaning that emerges through curiosity, relationship, and context—especially in moments of transition or uncertainty. An event may feel larger than us because its force grows from how people are living inside particular relationships and systems, not from a metaphysical order waiting outside them.
Main is speaking about correspondences built into the world—relationships that may resemble the Planck-like invariants described earlier. I am speaking about recurring relationships in human life. They may look similar—but they are not the same. Mandalas and polarity, in this framing, may belong to that world of invariants—but the meanings we give them come through human experience.
Comment
When recurring relationship patterns are mistaken for cosmic law, hierarchy, sacrifice, domination, and “chosen-one” narratives can start to feel inevitable—as if they belong to the nature of reality rather than to history, power, and human design. Meaning becomes something we submit to instead of something we examine.
But when we return meaning to relationship, culture, memory, and shared life, archetypes stop looking mysterious. They become situations whose origins we can understand—and sometimes change.
The “rule of 9” moves wonder away from metaphysics. Some patterns feel timeless not because they are written into the cosmos, but because they grow out of the mental and social worlds we keep living inside. Some archetypes are simply how we have learned—so far—to make sense of our lives. And if that is true, we are not trapped inside them. We can notice them, question them, and—slowly—begin to build different ones.
