Simulation Thought Experiments

Simulation Thought Experiments

Deduction 1: Time as an Internal Property of the Observer

Under the Axioms 1–4, we formulate two thought experiments to prove that physical reality is inherently timeless.

The Optimization Argument

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 $T_{\mathrm{alg}}$. 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 $T_{\mathrm{data}}$: the full execution trace, stored as a bitstring.

Let $E_{\mathrm{int}}$ denote Alice's internal experience (her felt sequence of states) and $E_{\mathrm{ext}}$ denote the external runtime of the computer (the number of CPU cycles executed). Code optimization affects $E_{\mathrm{ext}}$ but preserves $E_{\mathrm{int}}$ by construction:

$$ \mathrm{Optimise}(T_{\mathrm{alg}}) ;\rightarrow; T_{\mathrm{data}} ;\implies; E_{\mathrm{int}}(T_{\mathrm{alg}}) \equiv E_{\mathrm{int}}(T_{\mathrm{data}}). $$

In the limit $T_{\mathrm{data}}$, the external runtime $E_{\mathrm{ext}}$ is zero: no state transitions are executed; the complete execution trace exists as static data. Does Alice's consciousness persist in $T_{\mathrm{data}}$?

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 $A_1$ through $A_4$. Its existence would constitute an addition to the physical laws of $A_2$, contradicting the completeness of that axiom.

Conclusion 1. Consciousness is an emergent 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. Subjective experience and time emerge solely from the internal structure of information.

The Multi-threaded Argument

Consider a multi-threaded computer running two DNA simulations concurrently: $\tau_A$ (Alice) and $\tau_B$ (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 $\tau_A$ and $\tau_B$. As the number of concurrent threads increases without bound, the bits originating from $\tau_A$ 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 $A_1$ through $A_4$, contradicting the completeness of $A_2$.

Conclusion 2. Conscious experience cannot depend on the contiguity, order or density of its encoding in any external execution trace. What appears as a random bistring (execution trace of multi-threading computer running DNA simulations) to external observer, appears as conscious experience to emergent simulated observers.

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