We present two thought experiments to establish that the universe we observe must be ultimately substrate independent and timeless.
Consider a digitized human DNA, and a simulation of it running on a computer. If consciousness is produced by human DNA, it must also be produced by an identical digital simulation. Both entities share the same axiomatic structure; just as the equation 2 + 2 = 4 holds true regardless of whether it is applied to apples or bananas, mathematical equivalence remains invariant across biological and digital mediums.
The simulation consists of code (the laws of physics as implemented) and data (the state of the simulated universe at each timestep). Denote the running simulation Talg. The simulation generates a simulated human, say Alice.
Now optimise the simulation code progressively by introducing lookup tables: replace computed transitions with precomputed results. At each step, the external runtime decreases while the internal state sequence — the ordered record of Alice’s experiences, perceptions, and actions — remains identical. Carry this optimisation to completion, replacing all computation with a static, precomputed dataset Tdata: the full execution trace, stored as a bitstring.
Let Eint denote Alice’s internal experience (her felt sequence of states) and Eext denote the external runtime of the computer (the number of CPU cycles executed). Code optimisation affects Eext but preserves Eint by construction:
In the limit Tdata, the external runtime Eext is zero: no state transitions are executed; the complete execution trace exists as static data. Does Alice’s consciousness persist in Tdata?
Suppose it does not. Then there exists a minimum code-to-data ratio below which consciousness ceases. This minimum ratio is a new physical constant: a threshold property of information processing not derivable from A1 through A4. Its existence would constitute an addition to the physical laws of A2, contradicting the completeness of that axiom.
Conclusion 1. Consciousness is a property of the information structure of the execution trace, not of the process that generates it. A static bitstring encoding a conscious observer’s state sequence contains that observer’s conscious experience. Time and subjective experience emerge solely from the internal structure of information.
Conclusion 2. The optimisation argument yields a family of distinct execution traces {T1,T2,…}, each encoding the same observer state sequence. The observer Alice Eint is not any particular trace but the equivalence class [A] = {Ti : Ti ∼ Tj ⟺ Eint(Ti) = Eint(Tj)}. Real-world Alice is one member of this class, not a privileged representative.
Consider a multi-threaded computer running two DNA simulations concurrently: τA (Alice) and τB (Bob), with a minimal time slice of one CPU cycle per thread. The execution trace of the computer is an interleaved sequence of segments from both τA and τB. As the number of concurrent threads increases without bound, the bits originating from τA are separated by increasingly large intervals of unrelated data. In the limit, the execution trace in which Alice’s bits are embedded approaches white noise.
Does Alice’s consciousness depend on the contiguity of her bits in this external trace? Suppose it does. Then there exists a minimum bit-contiguity or thread-density threshold required for consciousness. This threshold is again a new physical constant not derivable from A1 through A4, contradicting the completeness of A2.
Conclusion 3. Conscious experience cannot depend on the contiguity or density of its encoding in any external execution trace. What matters is the internal structure of the information — the relational order of Alice’s state sequence — not its arrangement in any external substrate.
Conclusions 1 and 3 together establish the central result of this paper.
Substrate Independence. Consciousness is a property described by certain finite information structures. The physical substrate in which such a structure is instantiated — silicon, neurons, magnetic domains, or static bitstring — does not determine whether the structure describes consciousness. A computer running a simulation of a conscious observer and the simulation itself are two arrangements of the same information. Neither is causally prior to the other. Neither is more fundamental.
This is not a claim that all information structures describe consciousness. It is a claim that consciousness is determined by information structure rather than by substrate. The specific structures that describe consciousness are those satisfying A1 through A4: structures that encode the state sequence of a DNA-based observer with causally efficacious subjective experience.