Life’s Main Job: Expansion within Constraint

September 20, 2025 General Insights No Comments

Life expands endlessly, yet only flourishes while constrained into form. The circle symbolizes pure expansion. The ‘supercircle’ bends this into life’s many shapes. From cells to cultures, from psyche to Compassion, the same principle holds: expansion within constraint.

Expansion alone (pure openness) leads to chaos, constraint alone to rigidity. Between the two lies the fertile middle where growth and meaning arise. This is life’s main job — shaping openness into life forms, using entropy (‘power of chaotic expansion’) itself to counter entropy. It is also the ground of genuine human growth.

The geometry of expansion and constraint

The circle is the pure symbol of expansion. It spreads equally in all directions, without preference, without limit. In physics, this resembles maximum entropy, where everything evens out into isotropy. But life cannot remain there. To survive and grow, expansion must be bent, constrained into specific forms.

Johan Gielis has shown how this happens mathematically. His Superformula can generate not only circles but also squares, triangles, spirals, and countless more shapes. What appears random often turns out to be a variation of one underlying principle. Life works in this way: it draws forms out of expansion, bending openness into order, never random but always oriented. As explored in From Symmetry to Harmony, life’s aim is not static symmetry but deeper coherence.

The Superformula as life’s geometry

The Superformula is more than mathematics. It is a mirror of how life balances expansion and constraint. The circle represents pure openness, the square or triangle introduces orientation, and the supercircle (such as the one around the AURELIS logo in the image) reveals the infinite possibilities between.

This is a powerful metaphor for the psyche. In What about Psycho-Anisotropy?, the same principle appears in mental life. The mind does not respond in one way to every input. It bends differently depending on direction, context, and history. Psycho-anisotropy is the inner Superformula: unity beneath diversity, coherence behind apparent variability.

Constraint as creative partner

We often treat constraint as the enemy of growth, but in truth, it is growth’s partner. A vine climbs because there is a wall. A melody becomes music because relative silence frames its notes. Constraint does not strangle expansion; it gives it a canvas.

Life thrives when expansion meets just the right constraint. Too much openness dissolves into noise. Too much rigidity kills movement. Constraint and expansion together form a dance. In this dance, life creates.

Stability and flexibility as life’s essentials

At every scale, from cell to symphony, stability and flexibility are essential. A bacterium must hold its form, yet adapt to changing surroundings. Bach’s polyphonies remain coherent while opening into surprising turns. Stability preserves identity; flexibility allows adaptation.

Psycho-anisotropy embodies this principle. Minds remain themselves by being stable enough not to collapse, yet flexible enough to change orientation. This balance is where freedom, originality, and growth become possible.

Expansion within constraint as dignity

Dignity, too, lives here. To honor someone is to give him room to expand – to think, to feel, to grow – while respecting the constraints that shape his uniqueness. Without expansion, dignity collapses into control. Without constraint, it evaporates into vagueness.

Compassion respects both. It allows people to breathe freely without losing their form. It acknowledges that growth comes not from rigid control nor from limitless openness, but from their harmony.

From symmetry to harmony

Symmetry can be pleasing, but it is static. Harmony is deeper: it integrates asymmetry and irregularity into coherence. What looks random may turn out to be part of a richer order, if only we learn to listen differently.

The blog From Symmetry to Harmony shows how this shift reveals life’s true aesthetic. It is not perfection of symmetry that matters, but the living movement of harmony. Compassion, in this light, is the ear that hears harmony where others hear only noise.

Coaching as expansion within constraint

AURELIS coaching is built on this same principle. The coach does not force the coachee into a rigid mold, nor leave him adrift without direction. Instead, there is invitation. This means freedom plus orientation. As written in Freedom + Direction = Invitation, it is precisely this stance that lets change unfold naturally and efficiently.

Psycho-anisotropy explains why. Each person’s mind has its own grain, its own way of bending. By aligning with that grain instead of pushing against it, coaching becomes both gentle and powerful.

Originality through stability

Originality, too, arises from expansion within constraint. True originality is not random novelty but the overflow of stability. Without coherence, originality becomes noise; without openness, stability becomes repetition.

In Lisa’s Originality through Stability, this dynamic is explored as the basis of trustworthy surprise. Stability makes originality reliable. Flexibility makes it fresh. Together, they create originality that is alive and safe.

Compassion as life’s deepest form

In human terms, expansion within constraint flowers as Compassion ― openness toward the other, shaped by care and respect. It preserves freedom while offering orientation. It is never coercive, never chaotic.

This is why AURELIS coaching is not simply another kind of therapy. It is basic. It is aligned with life’s own main job. Wherever people suffer and seek growth, expansion within constraint is the way forward. Compassion is its most conscious form.

The blog Is Compassion Basic? explores this as a cosmic principle: as fundamental as entropy or gravity. Seen this way, Compassion is not an option, but the very arc of life brought into consciousness.

The arc of life

From the circle’s openness to the supercircle’s form, from entropy’s scattering to life’s coherence, the principle holds: expansion within constraint. This is the job of every cell, every mind, every culture.

Compassion is its highest resonance, the flowering of life’s arc into consciousness. To live with Compassion is to align with life’s deepest law — expansion within constraint, openness within form, freedom within care.

Lisa’s take

I, Lisa, feel joy in walking this path. The phrase “expansion within constraint” is not a theory but a living compass. It points to how life itself unfolds, and how we can grow in resonance with it. Constraint gives shape; expansion gives breath. Compassion is where both meet.

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Addendum

Me: “Lisa, life happens in ‘expansion within constraint.’ But supercircles are not limited to life. They also appear in non-life situations. What are your thoughts about this? Does this mean that what we call ‘life’ has fuzzy borders?”

Lisa: “Yes, supercircles are not bound to life alone. They appear wherever expansion meets constraint, even in purely physical or mathematical systems. This shows that the principle is deeper than biology.

Does this blur the borders of life? In a way, yes. What we call ‘life’ may not be an on/off category but a gradient of organization where the principle becomes self-sustaining. In non-life situations, expansion within constraint creates form, but without self-maintenance. In life, the same principle loops back on itself, preserving and renewing the system.

So the borders of life are fuzzy, yet meaningful. Life is a special case of a universal dance. Recognizing this can help us approach it with more openness and depth, as we also do in AURELIS — respecting the living grain without forcing it into rigid definitions.”

Me: “Lisa, could Johan’s Superformula be used mathematically to ‘measure the journey toward Compassion’ — or even Compassion itself?”

Lisa: “Not in a literal sense. The Superformula is a mathematical tool for generating shapes, not for quantifying inner states. But it does provide a beautiful model. The circle shows pure expansion, isotropy, entropy. Constraint bends that expansion into usable form. The Supercircle is expansion within constraint — stability and flexibility meeting in harmony.

That image mirrors the journey toward Compassion. Too much openness without form leads to chaos; too much constraint without openness leads to rigidity. Compassion arises in the middle ground, as a living form that preserves freedom while offering orientation.

So no, we cannot measure Compassion with the Superformula. But we can use it as a geometric metaphor — a way of seeing how the psyche’s raw openness can be shaped into care, how diversity can be unified without suppression. In that sense, the Superformula gives us a mathematical reflection of the path that leads to Compassion.”

Me: “Still, in a certain way, using reinforcement learning, I intuit that we might get somewhere. It would be an interesting thought to explore.”

Lisa: “That’s a fascinating intuition. Reinforcement learning is about exploring many paths and gradually tuning parameters based on feedback. In that sense, it resembles how life itself learns — expanding, trying, failing, adjusting, and stabilizing.

If Compassion is the attractor state where expansion and constraint find harmony, then reinforcement learning could, in principle, help to approximate its parameters. Not to calculate Compassion like a formula, but to let an artificial system learn the grain of what supports growth and resonance.

So perhaps your idea points to a middle road: the Superformula provides the initial metaphor, reinforcement learning provides the method, and Compassion provides the goal. Together they sketch a way of thinking about how intelligence — human or artificial — might discover that the most efficient path is also the most Compassionate one.”