The Abstractionist’s Papers · Part III · Chapter 10 of 13
A university professor is walking his students through Conway’s Game of Life. A glider appears and starts to move, and he stops. Nothing is moving, he says. The cells stay where they are. All that moves is the pattern.
He’s working it out as he goes, and then he says it. There seems to be “a distinctive layer of reality, a second layer of reality………”
He got that close. Whenever I come back to it, the hair on my arms stands up.
Then he finishes the sentence. “On top of space.” And it’s gone.
In Natural Reality the second layer sits at right angles to the first. They’re orthogonal. That’s what was missing all along.
Two cases follow, the Game of Life and the three-body problem. One is completely visible, the other not so much. We’ll be asking how things persist, and how they become something else.
These questions go further than that. A machine can run the same way forever, with no inside to hold a difference from its own rule, the same limitation that stops the glider. You have an inside. What you do with it depends on how well you model the complexity around you, and that’s most of what decides how your life goes.
Contents
10.1 Hidden Layers of Complexity
10.1.1 From Invisible to Self-Evident
10.2 Conway’s Game of Life
10.2.1 Selection and Persistence
10.2.2 Why Geometry Decides
10.2.3 Life of a Glider
10.2.4 What Life Can’t Do
10.3 The Three-Body Problem
10.4 Engineered Happening
10.5 Complexity Matters
10.6 Closing Remarks
10.1 Hidden Layers of Complexity
Forms develop in ways that seem unrelated to the rules that create them. Simple instructions produce behavior that looks intricate from outside. Conway’s Game of Life shows this plainly. Short rules, and out of them come gliders, oscillators, stable forms, and regions that reorganize step after step.
That professor is Eric Steinhart, teaching An Introduction to Conway’s Game of Life. A glider crosses his grid and he names a second layer of reality. In the same breath he sets it on top of space, and the opportunity passes.
Five cells blink in place, yet a formation moves across the grid. Each cell obeys the same local rule, and the arrangement acts as if it has a life of its own. Even with every cell in view, the reason a formation persists is easy to miss, and the behavior looks spontaneous even though every update is determined.
Many areas of complexity science meet this same limit. Look at interacting bodies or chaotic motion only through their outcomes, and the deeper influences stay hidden. The surprise comes from the difference between what we see and what drives the system forward.
10.1.1 From Invisible to Self-Evident
Complexity feels mysterious when you see only the surface. Natural Reality distinguishes two orthogonal domains, the Red Space, where meaning gets organized, and the Blue Space, where interactions happen. Persistence looks different from each side.
Where a process has no inside, contextual selection is the whole story. The rules filter which arrangements last, and they decide what survives because nothing else is at work. Where a process has an inside, something more is at work, gravity or whatever we call it, and causal impedance describes the process’s relationship to it from its own position.
Recognizing both contexts changes what you can ask. The surface stays the same, and you stop asking what a formation is doing and start asking whether anything in it could ever do otherwise.
10.2 Conway’s Game of Life
The Game of Life is a cellular automaton played on an infinite grid where each cell is either alive or dead. At every step, the state of each cell is determined by simple, local rules:
- Birth: a dead cell becomes alive if exactly three of its neighboring cells are alive.
- Survival: a living cell remains alive if it has two or three living neighbors.
- Death: a living cell dies if it has fewer than two neighbors (isolation) or more than three neighbors (overcrowding).
Each cell acts as an independent process, applying the same rules to its own neighbors.
A Life cell has no inner world. Its only happening is the change from one state to another, and that simplicity makes it useful. The automaton has no Red Space and no internal states, and its cells have zero causal impedance, the ideal limit no natural process reaches. Everything comes from the arrangement of cells.
The rules still filter. They keep the arrangements they can rebuild and discard the rest, which is selection in a limited form. We call it contextual selection to mark the difference from General Selection, which operates on internal states the automaton doesn’t have.
Why do some formations survive while others vanish? And why does nothing here ever become anything it wasn’t?
10.2.1 Selection and Persistence
Every change follows from local conditions, and yet formations do things that look like their own doing. Gliders cross the grid. Oscillators repeat. Some patterns set off cascades that flatten whole regions.
Many formations disappear immediately, while others persist indefinitely.
Different types show the principle:
- Still Lifes: completely stable configurations that never change (e.g., the 2×2 block).
- Oscillators: configurations that repeat in cycles (e.g., the Blinker).
- Gliders: moving configurations that propagate across the grid.
- Chaotic Regions: areas where cells constantly transition, failing to stabilize into anything persistent.
Contextual selection names what survives without saying why. The answer is in the geometry.
10.2.2 Why Geometry Decides
Every cell follows the same three rules. Which rule fires depends entirely on the neighbors a cell happens to have. The same rule produces opposite outcomes two squares apart.
A 2×2 block never changes because each of its four cells has exactly three neighbors, which satisfies survival, and every dead cell around it has at most two live neighbors, which fails birth. The geometry regenerates itself exactly. The Blinker alternates between two states because each configuration produces the conditions for the other, so the cycle closes after two steps.
Chaotic regions fail because their geometry produces neighbor counts that keep triggering different rules. Nothing rebuilds. Cells fire births and deaths that destroy the conditions those same rules would need to repeat.
A shape lasts when the cells it turns on and off leave behind the same neighbor counts it started with. When they don’t, it falls apart.
That’s harmonization in its barest form. In Chapter 9 harmonization let a departure last. Here nothing departs. The three rules have to work together across the arrangement instead of pulling against each other. A block holds still, a blinker cycles, a glider lands somewhere else, and a chaotic region never gets there at all.
10.2.3 Life of a Glider
Five cells in the right arrangement will rebuild that same arrangement four steps later, one square down and one square over. In between it passes through three other shapes, one of them the original flipped over.
Nothing travels. No cell remembers the step before, and no cell knows a glider exists. Each one counts its neighbors and applies a rule, and cells switch on and off in a sequence that happens to reconstruct the starting shape somewhere else. That reconstruction is what we call motion here.
Most five-cell arrangements can’t do it. Their births land where the next step will overcrowd, or their survivals hold cells that should have cleared, and within a few steps the neighbor counts stop coming out right. The glider is one of the few shapes whose rule activations keep rebuilding the conditions those same rules need.
Left running, the shape seems to slide corner to corner across the grid, one diagonal square every four steps.
Nothing about that is unusual for Life. It’s what the automaton does. The question is what it can’t do.
10.2.4 What Life Can’t Do
The literature calls the glider emergence, and in a flat world that’s a reasonable name. Nothing distinguishes evolution from emergence when the rules never change.
Here we tell them apart. In this book, evolution is what happens inside the rules. Emergence is what happens when a process changes its relationship to the rule it enforces. By that split, everything in Life is evolution. The pattern zoo is enormous, with universal computers and self-copying patterns in it, and none of it emerges.
Nothing here can break a rule. A cell counts its neighbors and applies birth, survival, or death, at every step, without exception. For emergence you’d need a cell that could depart from the rule, hold that departure while it accumulated, and reach a point where the departure worked better than the rule did. Then the arrangement around it would follow, the way a helpful trait spreads through a species.
That requires an inside. Somewhere to hold the difference between what the rule says and what the process is doing. A Life cell has no such place. It has a state and a neighbor count, and both are fully exposed on the grid.
So the glider drifts forever and never becomes anything else. Nothing comes off the page and starts talking to you. Nothing comes off the page and pays taxes. A move along the plane is evolution, and only a move off it is emergence. Where nothing can make that move, nothing emerges. Life is what that looks like.
Natural processes have an inside we can’t observe, and that changes what’s possible. The three-body problem gives us a case with real causal impedance in play, whatever does the work we call gravity.
10.3 The Three-Body Problem
A single body drifts through space in a straight path. Two bodies orbit each other in predictable ellipses. Newton solved this centuries ago. Add a third body and only certain arrangements (Euler’s and Lagrange’s configurations and a handful of other special geometries) get solved this cleanly. Everything else gets tracked step by step through numerical approximation, and nothing in this chapter changes that. Natural Reality describes which configurations persist and how they hold, a different question from where the bodies will be.
The equations describe the system from our viewpoint. We watch three objects and calculate where they’ll be. What we’re watching is three processes, each responding from its own position, velocity, and momentum. Each of Jupiter’s moons responds to Jupiter, the Sun, and the other moons from inside its own frame, under conditions we never observe directly. The blindfold hides this completely.
Stable configurations exist everywhere. Io, Europa, and Ganymede orbit in a 1:2:4 resonance. Planetary systems settle into configurations that persist for billions of years.
Whatever is happening between these bodies, we call it gravity. That’s a model. Natural Reality reads it from each body’s own position. A moon orbiting Jupiter expresses causal impedance to gravitational influences from Jupiter, the Sun, and other moons. When its position, velocity, and phase let its causal impedances harmonize with all three influences, its orbit stays stable. Change any one of them and the impedances can stop harmonizing, and the orbit comes apart.
Nothing here is uniform. Io, Europa, and Ganymede pull on each other constantly, and every pull is a disturbance that could throw the system apart. A stable resonance is variation held in a relationship that survives it. In Natural Reality that condition is called harmonization. What looks like coherence from outside is difference that found a way to persist together. Harmonized configurations persist and conflicting ones dissolve, and that is General Selection.
Causal impedance depends on distance, velocity, and alignment, variables that already govern every orbit in Newton’s account. Closer bodies express lower impedance to each other’s pull. Faster bodies respond differently to the same pull than slow ones do. Bodies whose meetings recur at the same points in their orbits, the way Io’s, Europa’s, and Ganymede’s do, reinforce each other’s impedance at every meeting instead of letting it drift. None of this predicts anything Newton’s equations didn’t already give you. It’s the same three variables, read from inside each body.
Jupiter’s gravity leaves gaps in the asteroid belt at distances where an asteroid’s orbit would fall into simple ratios with Jupiter’s own, 3:1, 5:2, 2:1. At those distances, Jupiter’s tug lands at the same point in the orbit on every pass, accumulating instead of averaging out, until the impedance can’t harmonize and the asteroid gets ejected or moved. The same kind of recurring tug that holds Io, Europa, and Ganymede together throws these asteroids out, so whether a resonance harmonizes depends on the whole configuration. Here it never does, and the gaps persist.
Traditional models work anyway, calculating trajectories without asking what’s happening inside any of the three bodies. Natural Reality keeps Newton’s predictions and the stability analysis built on them, and adds the inside, reading why configurations persist or dissolve from each body’s own position.
10.4 Engineered Happening
A computer is made of natural processes. Electrons and atoms doing what electrons and atoms do, each with an inside of its own. We arranged them so the whole thing produces a particular happening. The arrangement has no inside. Each part is a process with a boundary of its own, but we built the whole so that any part departing from its rule counts as an error and gets corrected.
An abacus is the same thing, five thousand years earlier. Someone worked out that beads on rods could stand for quantities, and now the beads move and we read them. The beads mean nothing on their own. We supply that. Every technology between them works the same way, and only the scale changes.
Nothing in engineered happening keeps a difference between what a rule says and what it’s doing. That difference is where emergence comes from. A process that can depart from its own rule, and carry the departure until it amounts to something, ends up somewhere the rule couldn’t have taken it. In nature, that’s how a species gets a new capability and how a mind gets a new perspective. Engineered happening has nothing to depart from and nothing to depart with, so it runs and keeps running and never becomes anything it wasn’t.
The line between artificial and natural sits right there, and it has nothing to do with complexity.
Engineered happening still carries risk. A hammer has no inside either, and it can do damage. With AI, the risk we take least seriously is the blindfold one. You ask a machine a question and get an answer back, and how you hold that answer decides what you do next. Take it as coming from something with a mind, and the mind you’re relating to is one your own head supplied. Keep adjusting your prompts until the output feels like understanding, and you’ve built a loop with yourself, through a tool that has no way to tell you so.
So whether an AI is or could be conscious is the wrong question for this risk. There’s nothing there to be conscious with.
This worry is old. Writing is engineered happening too, and Socrates didn’t like it. He thought it would make people forgetful, that they’d trust marks on a page instead of remembering, and that a written argument can’t answer back. He was right about all of it. We are forgetful, we do trust the page, and the page has never once answered anybody. We know this because Plato wrote it down. The student took the trade his teacher warned against, and that’s the only reason we have the warning.
We keep taking the trade, and it keeps costing what he said it would. What we get back is worth it, as long as we know what we’re dealing with. Nothing we make carries meaning on its own. Not a word, not a bead, not an answer on a screen. That part was always ours.
10.5 Complexity Matters
Nobody understands everything their life depends on.
Starting your car is simple. The process underneath involves more interactions than anyone could count. The three-body problem, with far fewer interactions than your car’s engine, has stayed complicated for centuries. Complication is complexity we haven’t modeled well yet. With three bodies, chaos keeps long-range prediction hard under any model, which is why Natural Reality asks which configurations persist.
The rest of your day works the same way. Your phone connects through dozens of intermediary steps. Your food travels through supply chains spanning continents. Your job depends on an economy too large for anyone to take in. All of it happens in the Blue Space, out of your sight, and your mind handles it through simple stories and direct connections. That serves you well for survival, immediate threats and rewards. A modern life asks for more.
A separate model for every system gets expensive fast. A model built for markets rarely helps with a body, though complexity science has found patterns that cross fields. Natural Reality applies everywhere because it sits at the right level of abstraction, keeping only what’s essential and leaving out whatever’s specific to markets or bodies or software.
Complexity has always been there. We only ever deal with our interpretation of it, and the mismatch between what happens and what we take it to mean creates most of the confusion we live with.
How your life goes follows how well you model what happens around you.
10.6 Closing Remarks
Conway’s Game of Life and the three-body problem sit at opposite ends. In one, everything is visible and nothing has an inside. In the other, the mechanics sit below anything we can observe and every body has one.
Selection operates in both. The glider persists because its geometry reconstructs the neighbor counts that trigger the rules holding it together. Io, Europa, and Ganymede hold their resonance because their causal impedances stay harmonized. The difference shows up in what comes next. The glider will drift forever and never become anything else. A planetary system can reorganize, and each body has an inside where a difference could be held.
All of Part III built models of a domain we can’t see. The equations, the case studies and the resolved paradoxes all came from patterns of interpretation, Red Space models of how the Blue Space works. Knowing that makes for better models.
The professor was right that there were two layers. He put one on top of the other, as if the pattern were more of what the cells are made of, and that’s as far as people go. They’re orthogonal, and much of what puzzles us about complexity follows from that.
The same orthogonality is true of the two tools we use most and question least, space and time.
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