Calling the universe a computer can mean that physical processes can implement computations, that physical models can be simulated, or that computation supplies the world's underlying ontology. These are different claims, and evidence for one does not automatically establish the others.
Three claims to separate
A physical computer uses controlled states and transitions to implement operations on encoded information. Its inputs, outputs and allowed interventions give those operations an identifiable role. This is a claim about a particular physical device and its use.
A simulation represents another system through a mathematical correspondence. It may reproduce selected observables with controlled accuracy while using a very different physical mechanism. Simulating the flow of water in a processor does not require the processor to contain that water flow.
An ontological proposal goes further: it identifies some computational structure with the fundamental constitution of the world. Such a proposal needs a physical dictionary, a law selecting the computation and a reason for its observable consequences. The availability of numerical models alone leaves those questions open.
The same cycle can have different encodings
Consider a four-state device that repeatedly visits A, B, C and D. Encode those states as 00, 01, 10 and 11. In this representation, the device performs addition of one modulo four.
Now encode the same physical states as 00, 01, 11 and 10. Its displayed sequence becomes 00 → 01 → 11 → 10 → 00. This is a Gray-code cycle: neighbouring labels differ in one bit. The device's physical transitions have not changed, but the rule expressed in the new labels has.
The correspondence between encodings is a relabelling. Predictions agree when preparations, transitions and readouts are all translated consistently. If the readout is left untranslated, the two descriptions can appear to disagree merely because different meanings have been assigned to the same symbols.
This small example shows why seeing bits in a model is not yet a unique physical explanation. A bit assignment must be connected to controllable states and measurements. The complexity of a written rule can depend on the representation.
A trace is less than a machine
One observed sequence does not establish all the counterfactual behaviour of a computer. A recording that plays 00, 01, 10, 11 repeatedly can reproduce the counter's ordinary display. It might fail immediately if asked to accept a new input, reverse its direction or start from an independently prepared state.
To identify an implemented computation, test the transitions relevant to the proposed inputs and operations. State preparation, control and readout matter alongside a passive time series. This prevents a convenient retrospective labelling of one trajectory from carrying more explanatory weight than it deserves.
The same lesson applies to a cosmological proposal. A claim about universal computation must specify which operations are physically admissible and what resources they require. It cannot be established solely by finding a suggestive sequence in an observed process.
Simulation has resources and units
The simulated time variable and the computer's elapsed running time are generally different. Doubling the processor speed can shorten a calculation without changing the simulated interval. A numerical time step also need not correspond to a fundamental tick of nature.
Questions of representability, approximation and efficiency should be kept separate. A finite calculation can approximate a selected observable without storing every microscopic detail. Conversely, a formally specified simulation can require resources far beyond practical reach.
Deutsch's work on universal quantum computation connects computational possibilities to physical law. It is relevant because a physical theory constrains what a machine can implement. It does not by itself establish that every physical process is executing a uniquely privileged digital programme.
The generative question
SMM/DTT proposes a generative account of observable succession. A computational realization could help make that proposal precise by specifying histories, updates, completion and detectors. Its value would be the predictions forced by those choices, not merely its ability to display an animation.
The book's auditable-model programme suggests a manageable route: calculate several outputs from one finite construction, retain a common calibration and compare explicit alternatives. The companion essay on simulation and explanation separates accurate computation from physical validation.
Until a proposed computational ontology supplies such constraints, the careful conclusion is conditional. A model may express physical relationships computationally and still leave open what the world fundamentally is. That openness is a research question to sharpen, rather than a gap to conceal with a familiar metaphor.
Sources and further reading
- David Deutsch, Quantum theory, the Church–Turing principle and the universal quantum computer, Proceedings of the Royal Society A 400 (1985), 97–117. Author-hosted published-paper copy.
- The two encodings and counter-versus-recording comparison are teaching examples developed here.
- Mohamed Haj Yousef, What a reconstruction must contain and A model that can be audited.