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Science excels at periodic phenomena — orbits, waves, cycles. We build technology on them because we can predict them. But there are phenomena in the universe that aren’t periodic yet aren’t random either. They follow rules, and the rules don’t compress. The only way to know where they lead is to follow them, step by step, all the way.
Stephen Wolfram calls this computational irreducibility. Some processes cannot be shortcut. To know the billionth digit of π, you must compute it. To know where a fractal goes, you must iterate: z = z² + c, again and again. No formula leaps you to the answer.
This matters because the two most significant phenomena we know — life and mind — belong to this category. Biological evolution doesn’t unfold according to a formula you can solve in advance. Neither does the growth of human knowledge. Both are learning processes: they generate possibilities, test them, and retain what works. Both move through combinatorial spaces so vast that the universe cannot contain all their possibilities at once.
This is why reasoning about your own life is hard. You can predict the periodic parts — seasons, schedules, recurring patterns. But the part that matters most, the part that is you, is computationally irreducible. You cannot skip ahead. You can only experience it.
Further reading:
Wolfram, Stephen. A New Kind of Science. Champaign, IL: Wolfram Media, 2002. Chapter 12: Computational Irreducibility
Science excels at periodic phenomena — orbits, waves, cycles. We build technology on them because we can predict them. When we design a bridge or launch a satellite, we rely on behaviour that repeats, behaviour we can model with equations and solve in advance.
But there are phenomena in the universe that aren’t periodic yet aren’t random either. They follow rules, and the rules don’t compress. The only way to know where they lead is to follow them, step by step, all the way.
Stephen Wolfram calls this computational irreducibility. Some processes cannot be shortcut. To know the billionth digit of π, you must compute it. To know where a fractal goes, you must iterate: z = z² + c, again and again. No formula leaps you to the answer. The process is the answer.
This matters because the two most significant phenomena we know — life and mind — belong to this category.
Two languages of infinity
David Deutsch observes that human brains and DNA molecules are both general-purpose information-storage media. More remarkably, the information they store shares a property of cosmic significance: once physically embodied in a suitable environment, it tends to cause itself to remain so. Deutsch calls this self-perpetuating information knowledge, and notes it is unlikely to arise except through error-correcting processes — biological evolution or human thought.
Both are learning processes. Evolution generates variation through mutation, tests it through selection, and retains what survives. Human knowledge grows through conjecture and criticism — we propose ideas, test them against reality, and keep what works. The parallel is not metaphor. It is structural.
Both processes move through combinatorial spaces so vast that the universe cannot contain all their possibilities at once. The space of possible molecules dwarfs the number of atoms in existence. The space of possible thoughts is no smaller. These are not spaces you can map in advance. You can only explore them by traversing them.
Biological evolution doesn’t unfold according to a formula you can solve in advance. Neither does the growth of human knowledge. You cannot shortcut four billion years of selection. You cannot leap to what humanity will know in five hundred years. The only path is through.
Why your life is hard to reason about
This is why reasoning about your own life is difficult. You can predict the periodic parts — seasons, schedules, recurring patterns. But the part that matters most, the part that is you, is computationally irreducible.
Your knowledge grows through the same error-correcting process: you conjecture, you test, you revise. Each step opens new possibilities that didn’t exist before. The space you move through expands as you move. No formula captures this. No shortcut exists.
You cannot skip ahead. You can only experience it.
Further reading:
Wolfram, Stephen. A New Kind of Science. Champaign, IL: Wolfram Media, 2002. Chapter 12: Computational Irreducibility
Deutsch, David. The Beginning of Infinity: Explanations That Transform the World. New York: Viking, 2011.
Science excels at periodic phenomena — orbits, waves, cycles. We build technology on them because we can predict them. When we design a bridge or launch a satellite, we rely on behaviour that repeats, behaviour we can model with equations and solve in advance. For centuries, this approach has been so successful that we sometimes forget it has boundaries.
There are phenomena in the universe that aren’t periodic yet aren’t random either. They follow rules, and the rules don’t compress. The only way to know where they lead is to follow them, step by step, all the way. Science often filters these out as noise, because they resist the tools that made physics so powerful.
Stephen Wolfram calls this computational irreducibility. Some processes cannot be shortcut. To know the billionth digit of π, you must compute it. To know where a fractal goes, you must iterate: z = z² + c, again and again. No formula leaps you to the answer. The process is the answer.
This is not a minor footnote. It suggests a category of phenomena that are fully deterministic — governed by rules — yet fundamentally unpredictable without traversing the full computation. Traditional science, optimised for compression and prediction, systematically overlooks them.
This matters because the two most significant phenomena we know — life and mind — belong to this category.
Two languages of infinity
David Deutsch observes that human brains and DNA molecules are both general-purpose information-storage media. More remarkably, the information they store shares a property of cosmic significance: once physically embodied in a suitable environment, it tends to cause itself to remain so. Deutsch calls this self-perpetuating information knowledge, and notes it is unlikely to arise except through error-correcting processes — biological evolution or human thought.
Both are learning processes. Evolution generates variation through mutation, tests it through selection, and retains what survives. Human knowledge grows through conjecture and criticism — we propose ideas, test them against reality, and keep what works. The parallel is not metaphor. It is structural.
Both processes move through combinatorial spaces so vast that the universe cannot contain all their possibilities at once. Sara Walker, a physicist working on the origin of life, illustrates this with the molecule taxol. With a molecular weight of 853, taxol can take so many unique three-dimensional shapes that creating one of each would fill more than one universe in volume. And taxol is a single molecule. The space of all possible molecules — let alone all possible organisms — is incomprehensibly larger.
This is why natural selection exists at all. The universe cannot explore every possibility simultaneously. Something must choose. Selection is not an accident of biology; it is a consequence of combinatorial vastness. Any structure that can reproduce itself gains a statistical advantage over structures that cannot. Life is what happens when information learns to persist.
The same logic applies to mind. The space of possible thoughts is no smaller than the space of possible molecules. Human knowledge grows not by surveying this space from above, but by moving through it — one conjecture, one criticism, one revision at a time.
Biological evolution doesn’t unfold according to a formula you can solve in advance. Neither does the growth of human knowledge. You cannot shortcut four billion years of selection. You cannot leap to what humanity will know in five hundred years. The only path is through.
The vegetation top
Erwin Schrödinger, the physicist who gave us the quantum wave equation, spent his later years thinking about life and consciousness. In Mind and Matter, he offers a striking image: the nervous system is the place where our species is still engaged in phylogenetic transformation. It is, he writes, the Vegetationsspitze — the vegetation top — of our evolutionary stem.
Think of a tree in spring. At the edge of each leaf, there is a thin bright line where growth happens. This is where the leaf is still becoming. The rest of the leaf — the part already formed — is fixed. But at the tip, the structure is still open, still responding to sunlight and environment.
Schrödinger suggests that consciousness is like this. It is the edge where learning still happens. The vast majority of what we are — our reflexes, our instincts, our automated behaviours — was laid down long ago, either in our evolutionary past or in our early development. But at the margin, at the vegetation top, we are still being shaped. That margin is what we experience as awareness.
This framing shifts perspective. We are not isolated minds piloting bodies. We are leaves on a tree — a tree of knowledge that has been growing for billions of years. Most of what we are comes from the tree: the language we speak, the concepts we think with, the culture that shaped us. Our individual contribution is a thin green line at the edge.
It is hard to see the tree. Our individual perspective is so vivid, so immediate, that we naturally ask “how is this good for me?” Autonomy feels fundamental. But the tree is what gives us our capabilities. The knowledge we inherit — from DNA, from culture, from all the minds that came before — is what makes thought possible at all.
Why your life is hard to reason about
This is why reasoning about your own life is difficult. You can predict the periodic parts — seasons, schedules, recurring patterns. But the part that matters most, the part that is you, is computationally irreducible.
Your knowledge grows through the same error-correcting process: you conjecture, you test, you revise. Each step opens new possibilities that didn’t exist before. The space you move through expands as you move. No formula captures this. No shortcut exists.
You are at your own vegetation top — the bright edge where your becoming is still open. What lies beyond cannot be computed in advance. It can only be reached by the process itself.
You cannot skip ahead. You can only experience it.
Further reading:
Wolfram, Stephen. A New Kind of Science. Champaign, IL: Wolfram Media, 2002. Chapter 12: Computational Irreducibility
Deutsch, David. The Beginning of Infinity: Explanations That Transform the World. New York: Viking, 2011.
Schrödinger, Erwin. Mind and Matter. Cambridge: Cambridge University Press, 1958.
Walker, Sara Imari. Life as No One Knows It: The Physics of Life’s Emergence. New York: Riverhead Books, 2024.