What We Want
or, what’s left of the universe after the clockwork breaks
What you would probably want from a site like this one is a key to the kingdom. A small box of theory that, once read, would let you sit on your porch with a glass of bourbon and predict the future. Not in detail — nobody is that greedy — but in shape. Whether the empire is rising or falling. Whether your kid is going to be okay. Whether the storm is coming or going. Whether the species makes it through. I can’t give you that. I can’t give it because no one can. There are three different reasons no one can, each one fatal on its own, and the three of them together close the door on prediction so firmly that the door does not, in any meaningful sense, exist anymore. So let us name the three of them. Then we will talk about what is left.
The first reason is that the universe is not deterministic at the bottom. Some events happen that are not caused, in the strict billiard-ball sense, by previous events. A radium atom in your wristwatch will, sooner or later, emit an alpha particle. When it does so is not a matter of hidden information that a sufficiently advanced physicist could one day uncover. There is no fact of the matter, before the emission, about exactly when it will happen. This is not philosophical hand-waving — this is the position the experiments have backed us into, painfully, against the better judgment of just about every physicist who looked at them in the first half of the twentieth century. Einstein hated it and spent thirty years trying to argue his way out. He was wrong. The world is, at its smallest scale, a place where some things just happen.
On its own that would not threaten the clockwork. The quantum fluctuations are tiny. They average out. The radium atom in your wristwatch decays with statistical precision; you cannot predict the next decay, but you can predict the next ten thousand, and the second hand sweeps reliably. The problem is that some systems do not average out. Some systems amplify. A storm system, a brain, a billiard table after enough collisions, the weather over the next month — these are chaotic, in the technical sense the Tomorrow’s Weather page is about, which means a microscopic difference in starting conditions blows up into a macroscopic difference in outcomes over a finite time. So the quantum noise that would have stayed at the scale of an atomic nucleus, in a non-chaotic system, instead rides the amplification up into the world we live in. The virtual particle that went left rather than right becomes the storm system that turned south rather than north a month later. The Geiger counter that ticked at 3:04 instead of 3:05 becomes the decision its operator made before lunch instead of after. The bottom of the universe leaks into the top through the cracks chaos opens, and there is no patching them.
So that is the first door, and on its own it would be enough. But here is the second. Even if the universe were deterministic top to bottom — and it isn’t, but humor me for a moment — no finite predictor inside the universe can predict it. Any predictor lives somewhere. Any predictor has, at the moment it makes its prediction, access to information from only some finite region of space. That region is bounded by the speed of light. A predictor on this planet right now has access to events that happened on Mars eleven minutes ago, on the Sun eight minutes ago, on Proxima Centauri four years ago, and on a star four thousand light-years away exactly four thousand years ago — not a millisecond more recent than that, no matter how good its telescope. Beyond the past light cone of the predictor there is no information available. Period. Not because we have failed to gather it. Because the laws of physics forbid it.
Which means any predictor on Earth, right now, can be surprised. A gamma-ray burst from a star four thousand light-years away may be in transit toward us at this moment, having been emitted in some now-distant past we will never have data about, and arrive without warning. We will see it the moment it gets here and not before. Pierre-Simon Laplace’s demon — the imaginary being, named in 1814, who knew the position and velocity of every particle in the universe and could therefore predict everything that would ever happen — never existed and could not exist. No physical being inside the universe can be that demon. Being inside the universe implies a finite past light cone, which implies missing information, which implies surprise. The dream was incoherent from the start.
And here is the third door, the one Stephen Wolfram gave us in A New Kind of Science — a book Kelly is on record describing as “a great door stop” for its sheer mass, but the joke about the weight should not obscure the fact that the door stop made a discovery worth keeping. Even if the universe were deterministic and a perfect predictor existed inside it, the predictor still could not predict faster than the universe itself can compute. There is no shortcut for some systems. The only way to know what state a chaotic system is in at step ten million is to run ten million steps. There is no closed form for the future. There is no faster simulation. The universe is, for systems of this kind, its own fastest model.
This is computational irreducibility, and the experiment below is the canonical demonstration. It is a tiny universe — a one-dimensional row of cells, each cell either black or white, advancing in time by a simple recipe that looks at three cells of the row and decides what the cell beneath the middle one should be. There are eight possible patterns three cells can show, so a rule is a choice of black or white for each of the eight patterns — eight bits, two hundred and fifty-six possible rules. Wolfram numbered them 0 through 255. Most of these rules are predictable in a boring sense: they die out within a few rows, or settle into stripes, or fill with a uniform color, and a few minutes of pencil work will tell you in advance that is what they are going to do. But a small fraction of them are not predictable that way. Their pictures are, in Wolfram’s phrase, computationally irreducible — the only way to know what one of these rules will look like a thousand rows down is to run a thousand rows. There is no closed form. There is no faster simulation. And which fraction is which cannot be told from the rule number alone; you discover it by running each one. Rule 30 produces what looks like random noise, but isn’t — rule 30 is actually good enough at faking randomness that Wolfram’s Mathematica used the middle column of it as a pseudo-random number generator for many years. Rule 90 produces a Sierpinski triangle — a perfect fractal, falling out of nothing. Rule 110 produces gliders, small structures that move across the row at fixed speed, and is provably as powerful a computer as your laptop — you could in principle compile a chess engine to run inside it. Rule 250 produces a dull featureless triangle — that one you could have predicted from its bits without running it. The first three you could not. For the irreducible rules, the only oracle is the program itself. The rule is the recipe; the picture is what the recipe makes; and for the rules that matter, the two are connected by no shortcut.
So the dream of perfect prediction is dead three times over. The bottom of the universe leaks randomness up through chaos. The horizons of the universe withhold information from any predictor inside it. The structure of computation itself forbids skipping ahead for the systems that matter most. Newton’s clockwork — the universe-as-orrery, every gear meshing, every position and velocity unfolding from the previous one with the exactness of a mechanism — was a beautiful eighteenth-century idea. It is dead. Laplace’s demon has been retired. The all-knowing being of the philosophers, the one some traditions called God and others called the equations, cannot live anywhere physical and cannot be approximated by anything physical. The future is not knowable. Not in part. Not in principle. Not by anyone.
What we live in instead — and this is the point of this site — is a universe with grain. Not predictability, but patternedness. The unpredictability is real and it is not going away. But that does not mean the universe is featureless. The same shapes keep recurring. Power laws. Basins of attraction. Edges of chaos. The patterns selection produces when it has a body to work on. The patterns synchronization produces when many oscillators are loosely coupled. The patterns waves produce when an excitable medium is large enough to support them. These patterns are doing something substrate-independent. Carbon doesn’t know it is playing the same game as ant colonies. Ant colonies don’t know they are playing the same game as economies. The patterns don’t care. They appear anyway.
This is the bet of the site you are reading. We are not going to tell you what tomorrow looks like — no one can. But there is something we can tell you, and it is the next-best thing. We can tell you the shapes tomorrow has to take to be tomorrow at all. The universe will not let you predict the storm. But the universe will let you know that whatever the storm does, it will distribute its energy along a power law, and have a fractal coastline, and turbulence at every scale that follows a Kolmogorov scaling, and convection cells that look like the cells of every other convection on every other water-bearing planet. The future is unknowable. The shapes the future will take are not.
Which brings us to the form this site has taken. Each page is a short essay paired with a working program. The prose tells you what to look for and why it matters; the program is the thing itself, with the controls in your hands. The patterns this site is about are mostly the kind you cannot really understand by reading about them. You have to sit at them. Push a slider. Type a rule number. Watch a configuration unfold under your eyes for a while. The prose names what you are watching. The program is the watching. They do different jobs, and on the pages where the form works, both are doing the work at once. So when the prose below tells you that some of these rules are computationally irreducible — that there is no shortcut from the recipe to the picture — you are not going to take my word for it. You are going to run a few of them, and see.
Below is the smallest universe I know of in which the point can be made plainly. Eight bits of rule. A row of cells. A simple recipe. No shortcuts, no closed forms, no predictions from the rule number alone — for some of the rules, at least, and a few minutes of pushing the slider will tell you which ones. Pick a rule. Watch it for a while. Try another. The shock is not that the rules produce complexity. The shock is that they produce so few kinds of complexity, none of which you could have predicted from the eight bits alone, and several of which you will start to recognize from rule to rule.
The Experiment
Things to try:
Start on the default, Rule 30, with the random row. Watch the noise produced. The picture looks like television static, but it is not random — the same rule, applied to the same starting row, will produce the same picture every time. The noise is deterministic. Wolfram’s Mathematica used the middle column of this exact rule as a source of pseudo-random numbers for years.
Switch the start to Single cell and hit Reset. Now the picture grows from one black cell in the middle of the top row. Click through Chaos, Fractal, Computation, Traffic, Class 4, Dull, Dead in order. Each one is a different universe, governed by the same kind of rule, started from the same single cell. The Fractal preset is Rule 90 — a perfect Sierpinski triangle, falling out of three cells looking at each other.
Click the slider and scrub slowly through the 256 rules with the random start. Most rules are dull — they settle into stripes, or a uniform field, or simple repeating patterns. A few produce noise. A few produce structure. The interesting ones are rare. The universe is a particular rule, and so is each of these — and most particular rules, it turns out, are uninteresting.
Type 110 into the rule box. Use the Single cell start. Watch for a few hundred rows. You will see small persistent structures — gliders — that propagate diagonally across the picture at fixed speeds, sometimes colliding with each other and exchanging information. Matthew Cook proved in 2004 that this rule can simulate a general-purpose computer. A chess engine, a web browser, this paragraph — all of them are, in principle, encodable inside the picture you are looking at.
Try Rule 184 with the random start. This is the Traffic rule — a black cell represents a car, a white cell empty road. Watch how the cars sort themselves into a traveling jam at high density and a smooth flow at low density. The same rule, depending on the density of black cells in the initial row, produces either a phase of jammed traffic or a phase of free flow. A traffic engineer could spend a career on this single rule.
Now try Rule 54, the Class 4 preset. This is the rare and hard-to-find category: rules whose pictures contain persistent structures that move, interact, and don’t settle. Wolfram conjectured there are only four broad kinds of rule — dies-quickly, settles-into-stripes, chaotic-noise, and the interesting one with structures. Run all 256 rules and you will not find a fifth.
Finally, pick an irreducible rule — Rule 30 or Rule 110 are the cleanest examples — and stare at its eight-bit binary representation in the legend below the canvas. The bits are the entire description of the universe you are looking at. There is nothing else. No physics. No tuning constants. No initial conditions beyond the row of starting cells. For most of the 256 rules, those eight bits would be enough to tell you what is going to happen without running it. For these two, they are not. The recipe and the picture are connected by a shortcut for most rules and by no shortcut for some, and you cannot tell which kind a rule is without running it.
So the rule was eight bits, and the picture was unpredictable except by running it. And yet — and yet — the pictures fall into a small number of kinds. Wolfram classified them into four. Some rules settle to a uniform field within a few rows. Some lock into simple repeating patterns. Some produce noise. And some — the rare and interesting ones — produce intricate persistent structures that move, collide, and compute. Two hundred and fifty-six rules; four kinds of universe. Run all 256 and you will not find a fifth kind. That is the bet of this site, expressed in a thimble.
The future of an irreducible rule is unknowable in detail. There is no shortcut for what Rule 30 looks like at step one million. But the kind of future a rule produces — the family of patterns it belongs to — is a thing you can recognize and reason about. Wolfram could not have written down the bit pattern Rule 30 produces at step one million. But he could have told you, before running it, that the pattern would look like noise, because he had run other rules of that kind and learned what those rules do. The rules that produce gliders feel different from the rules that produce stripes feel different from the rules that produce noise. Different, in ways your eye recognizes within ten rows. There are families. The families are real.
The actual universe we live in is one of these rules — a particular rule the universe is itself running, on a substrate vastly larger and more entangled than a row of cells, with three escape hatches operating in the background that the cellular automaton does not have. The future of our universe is hidden from us in ways even Wolfram’s program is not hidden from Wolfram. But the shapes are not hidden. Boundaries gather action. Selection sculpts function. Density manufactures cities. Waves propagate but cannot reverse. Coupled oscillators find a beat. The patterns recur because they are the patterns the algorithm of physics keeps finding, the same way our rule explorer keeps finding triangles and gliders no matter which eight bits you hand it.
So here is what we want, the authors of this site. We are not going to predict the future for you — no one can, and anyone who claims otherwise is selling something. But the universe has been busy for thirteen point eight billion years, on a substrate of quarks and stars and DNA and neurons, and a number of the shapes it found are worth pointing at by name. That is the project. The future is the universe’s business and unknowable. The shapes are visible to anyone who looks at them in good light. Let us look at them together.