The Universe Complexity Spectrum, from Pong to cosmology

Most discussion of simulated universes treats them as a single thing: either a simulation exists or it does not. That framing skips the only question with real content, which is what kind.

Order simulated environments by how much novelty they generate per unit of compute, and a spectrum appears. I call it the Universe Complexity Spectrum, and the ordering is by one quantity: distinguishable state transitions per unit time per unit volume.

Seven classes, and their relative costs

Roughly, from cheap to expensive: a two-dimensional automaton; a simple chemistry; an agent-based ecosystem; minimal physics with a biosphere; an Earth-analogue with sentient agents; a full solar system; a complete cosmological simulation.

Each step up multiplies both the state space and the compute cost, and the two do not scale together. That mismatch is where the interesting structure lives.

Three findings worth keeping

Sentient agents are cheap novelty. The jump from a biosphere to a biosphere containing genuinely unpredictable agents increases the novelty rate by about two orders of magnitude for twenty orders of magnitude of compute. Nothing else on the spectrum is that favourable. If you were designing the machine to maximise novelty per dollar, this is where you would spend.

Full cosmology is not worth it. The last step adds real novelty and costs so much more that the ratio collapses. Run quadrillions of cheap universes with agents rather than a few cosmic ones.

The cheap end is useless. A universe running something like a 1970s arcade game produces novelty, technically. But the problems a civilization reaches its plateau on are not solved by a universe whose entire state space is smaller than a single laboratory. Below some threshold, the outputs are things the base civilization worked out centuries ago.

That threshold is the interesting derived quantity: the minimum complexity at which a simulated environment can produce solutions that matter relative to the base’s own unreachable knowledge space.

What this is and is not

The spectrum is a cost model, not a cosmology. The state spaces and FLOP figures in it are order-of-magnitude estimates, and I would not defend them to three significant figures. What I would defend is the shape of the argument: novelty per unit compute is not monotonic in the fidelity of the simulation, and there is an optimum well below full physics.

There is a second, harder constraint on the far end of this spectrum, and I only worked it out recently. A universe rendered down to the fine structure of its own spacetime has a maximum number of distinguishable events set by the size of its causal past — a number with about 244 digits. A fully detailed cosmological simulation needs considerably more than that, which means the top of this spectrum cannot be rendered faithfully at all and must be rendered sparsely instead.

That is a stronger statement than a cost estimate, because it is a bound rather than a price tag. It is a later post in this series.