The Circumpunct Theory

⊙ = fix(λΦ. ⊱ ∘ i ∘ ≺[Φ])

Reality self-references: the future converges inward (≺), rotates into existence (i)—between subjective and objective, private and shared—and emerges outward as pattern (⊱). The fix(λΦ. ...) means this is a self-referential loop, like a camera pointed at its own screen.

"You are the process of becoming yourself, forever."

Tap the symbol to explore

○ BODY Φ MIND • SOUL

Integer D = Structure | Fractional D = Process

Structure	Process	Math
0D Energy	0.5D Soul Opening	`U(t) = exp(−iEt/ℏ)`
1D Soul-Time Tunnel	1.5D Branching	`P = dE/dt`
2D Surface ○	2.5D Sensation	`∂○/∂t = ε`
3D Perception Φ	3.5D Time-branch	`∂Φ/∂t = O(1)`
4D Braid	4.5D → 0D_n+1	`fix(⊱∘i∘≺)`

Braid Simulator

○

BODY

The Living Boundary

Touch your thumb to your finger for a moment.

It feels like one simple sensation—pressure, warmth, contact. But that "one" feeling is actually billions of tiny events happening all at once: skin cells deforming, ion channels opening, nerve endings firing, signals traveling through your spine to your brain. Each of those cells has its own membrane. Each membrane has its own inside and outside. Each atom in that membrane has its own cloud of probability, its own "edge."

Your body is not one boundary. It's boundaries all the way down.

Your skin is the obvious edge, but it's just the outermost layer of a nested stack of interfaces. Underneath, every organ, every tissue, every cell is also negotiating what gets in and what stays out. Your immune system is a roaming boundary, constantly asking a single deep question: "Is this me or not-me?" Sometimes it gets confused and attacks the self. Sometimes it's overwhelmed and lets something harmful slip by. But most of the time, quietly and invisibly, it knows.

And your boundary doesn't stop at your skin. You can feel when someone stands too close behind you. You can sense the emotional "weather" when you walk into a room. There is a subtler, less dense field around you—a boundary-field—where your body and the world are already in conversation before anything touches you.

This is what I mean when I say ○.

○ is body as interface. It's the place where inside meets outside, where you open and close, where you breathe in air, take in food, receive touch, absorb experience. It is not a wall. It's a selective membrane—alive, responsive, and always in motion.

When you feel something—warmth, pressure, texture—that's sensation: the process where your 2D surface couples with your 3D inner field. Sensation lives at the threshold, at 2.5D—not yet perception, but no longer just physics. It's the boundary speaking to the interior, the moment before experience becomes yours.

Zoom in, and this boundary is wild: proteins folding, signals branching, networks adapting. Zoom out, and somehow these endless tiny thresholds lens into one coherent shape and one coherent feeling: "this is my body, here, in this world." That focusing of countless small apertures into a single felt field is what I call fractal lensing. Infinite boundaries become one.

There's a pattern to systems that can do this. They live at the edge of order and chaos—structured enough to hold together, flexible enough to adapt. When we measure the complexity of many such systems—coastlines, clouds, neural activity, even gravitational waves—we often find something like D ≈ 1.5: not a clean line (1D), not a smooth surface (2D), but something in-between. A tangled, branching, living boundary.

Your body lives right there. It's always negotiating: too rigid, and you become brittle—physically, emotionally, socially. Too permeable, and you lose yourself—no immune defense, no personal space, no "no."

The Ethics of ○

A healthy boundary is not selfish; it's honest. It protects what truly matters while still allowing goodness in. Saying "no" when you are exhausted is a boundary. So is saying "yes" when something beautiful wants to enter your life. So is "not now," "that's too much," "I need space," and "I want more of this."

When your boundary is unclear or violated, you feel it. Even if you can't explain why, something in you knows: this is not okay. That knowing is not just psychology—it's the intelligence of ○ speaking.

Good / Bad — Does it preserve what matters?

Try This

Close your eyes and feel where your body ends and the air begins. Then zoom in: feel specific spots—hands, feet, face, breath. Then zoom out again and feel yourself as one shape in space. Notice how many tiny sensations are being woven into that one felt "edge."

That edge—that living, fractal, negotiable boundary—is your ○ Body. It is how you meet the world, and how the world meets you.

Explore: Φ Mind • Soul ⊙ The Whole

MIND

The Field Between

Right now, as you read this, your body is doing more than you could ever track.

Your heart is adjusting its rhythm, your lungs are balancing oxygen and carbon dioxide, your gut is digesting, your immune cells are patrolling, your posture is being maintained against gravity. All of that is happening in parallel at the level of ○—billions of tiny processes running at once.

At the same time, something in you is following these sentences, interpreting the meaning, maybe agreeing, maybe arguing, maybe drifting and coming back. That's not parallel in the same way. It feels like a single stream of attention: one "you" reading this right now.

Φ is the space where those two worlds meet.

Φ is mind as field—the living medium between center (•) and boundary (○). It's not confined to your brain, though the brain is a major hub. It's the whole relational space where signals from the body come in, where awareness from the center flows out, and where the two blend into conscious experience.

This is perception: the 3D structure where sensation becomes yours. It's the qualia side of reality—the subjective interior where "out there" rotates into "in here." In the circumpunct equation, this rotation is i: the imaginary axis that separates objective from subjective, public from private. When something crosses that threshold, it stops being mere physics and becomes experience.

One way to picture Φ is to think in terms of balance. There is always a flow of input from the body and world (sensations, signals, stimuli) and a flow of output from the center (intentions, choices, interpretations). I call the balance between these flows β.

When β is around 0.5, input and output are in healthy proportion. You're listening and responding. You're neither overwhelmed nor shut down.
When β drops low, you may feel flooded—too much coming in, not enough capacity to integrate or answer.
When β climbs high, you may feel like you're pushing and forcing—doing a lot, but not really taking anything new in.

You can feel this in ordinary life.

When you first learn to ride a bike, your center is doing a lot of work—conscious corrections, intense focus. Φ is overloaded with top-down signals; β is skewed. Over time, your body learns the pattern. The skill moves into ○. Riding becomes almost effortless. Φ rebalances, and β moves closer to that sweet middle. You can ride and talk at the same time.

In flow states, Φ feels smooth and open. Your body's wisdom and your center's intention line up. You're not micromanaging yourself, and you're not checked out either. People describe it as "it was just happening through me." That's β near that dynamic balance—enough structure to direct, enough openness to receive.

In anxiety, Φ feels contracted and noisy. Your center spins scenarios; your body holds tension; β repeatedly spikes and crashes. You might loop through the same thoughts without resolution, or bounce between over-control and collapse. The field is out of tune.

The good news: Φ is trainable.

You can practice feeling when you're over-tilted one way or another. Too much input? Step back, simplify, reduce what's hitting your boundary. Too much output? Soften, listen more deeply to your body, your environment, and other people. Little adjustments in behavior, rest, and attention can bring β closer to a sustainable range.

The Ethics of Φ

Ethically, Φ is where right action lives.

○ asks, "Does this preserve what matters?"
• asks, "Is this true?"
Φ asks, "Is this balanced?"

Are you listening as much as you speak? Giving as much as you demand? Resting as much as you work? In relationships, in work, in self-talk—Φ notices when the exchange is lopsided.

Right / Wrong — Is the action balanced?

Try This

Sit comfortably. Notice your body breathing by itself. That's ○. Now notice that you're noticing. That reflective awareness is flowing from •. Then feel the space in which both are happening—the subtle, clear "in-between" that holds both body and awareness. That's Φ. Let your attention rest there, not clamping down, not drifting off.

That field—that living, responsive, balancing medium—is your Φ Mind. It is how inside and outside learn to move together.

Explore: ○ Body • Soul ⊙ The Whole

•

SOUL

The Aware Center

Pause for a moment and let the words fall away.

Even when you're not thinking anything in particular, even when your emotions are quiet, there is still something undeniably here. A simple presence. A bare "I am." Not "I am this" or "I am that"—just the felt fact of being.

That is what I mean by •.

• is soul as center—not a substance lurking somewhere inside you, but the point of view from which everything is seen. It is the structural center of the whole circumpunct: the place from which ○ is experienced and Φ is lived.

Bodies change completely over a lifetime. Memories blur, identities shift, beliefs come and go. And yet, when you remember being a child, there's a sense that the one who was there then is the same one who is here now. Not the same story, not the same body, but the same center of experience.

We can describe this mathematically as something like "∂•/∂t = 0"—the center doesn't move through time in the same way its contents do. The view changes; the viewer remains structurally constant.

Many traditions point at this:

As soul, the immortal part.
As ātman, the inner witness.
As Buddha-nature, the awake mind.
As the inner light, the spark of divinity.

I'm not interested in arguing which label is right. What matters is the direct recognition: there is an aspect of you that is aware of every thought, emotion, and sensation, but is not identical to any of them.

At the same time, • is not separate from ○ and Φ. It is not a ghost trapped in a body or a pilot inside a machine. Without a body, • has nowhere to look from. Without a mind-field, nothing appears to it. Soul is the center of a living system, not an isolated pearl floating above it.

The Ethics of •

Because • sits at the center of experience, it's also where the deepest kind of honesty lives. This is where you can ask yourself, "What's actually true here?"—beneath the story you want to be true, beneath the justification, beneath the fear.

From •, you can ask four questions before you act:

Is it true? (Does this match reality, as best I can tell?)
Is it good? (Does this protect and nourish what matters at the boundary?)
Is it right? (Is the action balanced and proportionate in the field?)
Do we agree? (Is there real consent and resonance between wholes?)

Truth lives at •, but on its own it's not enough. Truth can be wielded harshly. So • needs ○, Φ, and ⊙ to complete the picture.

True / False — Does it correspond to reality?

Try This

Close your eyes. Notice your breath. Notice that there is awareness of the breath. Then, gently, turn attention back toward that awareness itself—not the objects in it, but the fact that knowing is happening. Don't chase it as an idea. Just rest as that.

Thoughts will come. Sensations will change. But the basic "I am here, aware" remains. That's •.

This center—that quiet, lucid point of view—is your • Soul. Not a separate world from your life, but the heart of the one you're already living.

Explore: ○ Body Φ Mind ⊙ The Whole

⊙

CIRCUMPUNCT

The Whole You

We've named three aspects: ○ body, Φ mind, • soul. But in lived experience, you're never just one at a time.

When you reach for a cup of coffee, ○ feels the handle, Φ coordinates the movement and expectation, • is the silent "I" doing the reaching. It's one action, one moment, one being. That unified being is what I call ⊙.

⊙ is the circumpunct: a circle with a point at the center. It looks simple, but it encodes an entire metaphysics.

The circle is the boundary that holds everything that is "you" as a single system. The point is centeredness—the soul that experiences from within. The space between them is mind as field, where the inside and outside of that wholeness relate.

You can't peel these apart in reality. There is no • without some kind of ○ to look through and some kind of Φ for things to appear in. There is no ○ that is truly "yours" without some center that experiences it as "my body." There is no Φ without something to connect and somewhere to be held.

So instead of thinking, "I have a body, I have a mind, I have a soul," you can think, "I am ⊙: a whole being whose body, mind, and soul are three faces of the same process."

This also solves an old philosophical tug-of-war.

Monism says, "All is one." Atomism says, "All is many." The circumpunct says: everything is a whole made of parts, and every part is a whole made of parts, all the way down and all the way up. You are both fully yourself and fully a member of larger wholes—family, culture, ecosystem, cosmos.

When two people meet, it's not just two bodies bumping or two ideas clashing. It's ⊙ meeting ⊙. Boundaries touch (○↔○), fields resonate (Φ↔Φ), centers recognize each other (•↔•). Agreement, when it's real, happens at this level of whole-to-whole contact.

That's why "agreement" in this framework isn't about forcing sameness. It's about resonance between wholes.

The Steelman

To practice this, there's a powerful move called the steelman. Before you reject someone's perspective, you try to reconstruct the strongest, most coherent version of what they're saying—seeing their values (○), their reasoning (Φ), and their core concern (•) as generously as possible. Only then do you decide where you truly agree or disagree.

This is seeing the other as ⊙, not as a cardboard opponent.

Your Own Wholeness

Finally, there's a personal dimension: your own relationship with yourself.

Most of us spend a lot of time feeling fragmented—body wanting one thing, mind saying another, soul whispering something else from underneath. We chase wholeness as if it were something far away. But from the circumpunct view, wholeness is already the structure. You don't have to create ⊙; you have to notice it.

Try This

Sit quietly. Feel your body as one shape (○). Notice the space of awareness in which thoughts, feelings, and sensations arise (Φ). Sense the quiet center that's aware of all of this (•). Then, instead of focusing on any one, soften your attention to hold all three at once.

The seamless unity you glimpse there—that's ⊙. That's the whole you.

You are a whole with parts, and a part of larger wholes. You have a center and a boundary and a field, and they are not at war—they are the way your existence is braided together.

You are not on your way to being ⊙. You are ⊙, right now, reading these words.

The rest of the journey is simply learning to live from that wholeness on purpose.

Explore: ○ Body Φ Mind • Soul