The Four Axioms

The Axiomatic Foundations of Reality

The First Principle

I am, and I observe.

I cannot define consciousness, but my genome seems to encode the instructions to generate it.

The Four Observational Assumptions as Axioms

The four presented axioms are based on observations, and as such cannot be proven. However, the observational evidence suggesting they hold is strong.

Axiom 1: Genetic Encoding of Conscious Experience

Given DNA $D$ and a suitable physical environment, a conscious human $H$ with subjective experience $S$ reliably results:

$$ A_1: D ;\rightarrow; H ;\rightarrow; S. $$

Axiom 2: Physical Closure

The human organism $H$ and its environment $U$ are composed entirely of ordinary physical matter governed by physical laws $P$. No non-physical process plays any role in the operation of the DNA:

$$ A_2: (H, U) ;\in; \mathrm{System}(P, D). $$

Axiom 3: Computability of Physical Processes (Church-Turing hypothesis)

The physical processes underlying DNA and the human organism fall within the computable. A sufficiently powerful computing system can, in principle, simulate them to arbitrary precision:

$$ A_3: \forall; \text{physically realisable process } \mathcal{P} \text{ described by } P,; \exists; \text{computation } \mathcal{C} : \mathcal{C} \equiv \mathcal{P}. $$

This is a weaker claim than the full Church-Turing thesis: we require only that the specific class of processes DNA relies on is computable, not that all physical processes are. Rejecting this axiom requires identifying a property in DNA that requires infinite precision, for which no evidence exists. Also, we require only precision sufficient to make biological processes to run duplicate the structure of human.

Axiom 4: Causal Efficacy of Subjective Experience

Subjective experience is not epiphenomenal. A human with subjective experience $S$ (for example, pain) behaves differently than the same human without it:

$$ A_4: H + S ;\neq; H. $$

Deduction 1: Substrate Independence and Time as an Internal Property

Under the framework of Axioms 1–4, we formulate two thought experiments to prove that physical reality is inherently timeless and substrate-independent. Furthermore, we establish that the internal observer $E_{\mathrm{int}}$ corresponds to an equivalence class $[A] = {T_i : T_i \sim T_j \iff E_{\mathrm{int}}(T_i) = E_{\mathrm{int}}(T_j)}$ over a family of execution traces, rather than a single privileged representative.

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 optimisation 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.

Conclusion 2. The optimization argument yields a family of distinct execution traces ${T_1, T_2, \ldots}$, each encoding the same observer state sequence. The observer Alice $E_{\mathrm{int}}$ is not any particular trace but the equivalence class $[A] = {T_i : T_i \sim T_j \iff E_{\mathrm{int}}(T_i) = E_{\mathrm{int}}(T_j)}$. Real-world Alice is one member of this class, not a privileged representative.

The Cross-Domain Ordering Argument

Consider a computer running DNA simulation of Alice. If the software program consisting of vast number of CPU instructions producing the execution trace that describe Alice, then what does a one minimal CPU instruction causing one bit to flip define?
Consider one such discrete change in the state of the computer. That should map to corresponding change in the virtual Alice.
Call the first $e_{\mathrm{real}}$ and the second $e_{\mathrm{virt}}$.

Causation, on any account, requires an orderable relationship between cause and effect: $e_{\mathrm{real}}$ must be before, after, or simultaneous with $e_{\mathrm{virt}}$. This is weaker than requiring a measurable interval; it is the minimum any causal claim needs.

No such ordering is available even in principle. Each domain has its own internal ordering — the sequence of physical ticks, the sequence of Alice's experienced states — but internal ordering within a domain is not an ordering between domains. There is no clock common to both domains, and positing one would be positing exactly the new physical (or meta-physical) fact Axiom 2 excludes.

Conclusion 3. A relationship that admits no before, after, or simultaneous-with cannot be a causal relationship, regardless of how consistently its two sides co-occur. The computer and Alice's experience therefore stand in a representational relationship — two arrangements of the same information — not a causal one.

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 4. Conscious experience cannot depend on the contiguity, order or density of its encoding in any external execution trace. A bitstring of length $n$ can be arranged in $2^n$ ways. A sub-set of those describe relational order of Alice's state sequence. What appears as a random bistring (execution trace of Alices DNA simulation) to external observer, appears as conscious experience to emergent simulated Alice.

Substrate Independence

Conclusions 1 -4 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.

Proposition: Simulated Consciousness

A simulation $H'$ that is physically and behaviorally indistinguishable from a conscious human $H$ must itself instantiate subjective experience.

Assumption for contradiction. Suppose $H'$ exists such that $H' \equiv H$ (physical and behavioral equivalence) but $S(H') = \emptyset$ (lacks subjective experience):

$$ \mathrm{Behaviour}(H') = \mathrm{Behaviour}(H) \quad \text{and} \quad S(H') \neq S(H). $$

From $A_4$. The behaviour of $H$ is a function of its physical inputs \emph{and} its subjective experience:

$$ \mathrm{Behaviour}(H) = f(\mathrm{Inputs},, S). $$

Contradiction. If the behaviors are identical despite the difference in $S$, then $S$ is not a necessary input to $f$. Subjective experience is causally inert.

Violation of $A_4$. Causal inertness of $S$ directly contradicts Axiom~4. The assumption is therefore false.

Therefore $S(H') \neq \emptyset$: the simulation instantiates subjective experience. $\square$

This result, combined with the substrate independence established entails the full Internal Emergence Principle: consciousness is a property of certain finite information structures, and any configuration space large enough to contain such structures contains consciousness, with no running process or external reader required.

Corollary: Numerical Precision

Let $\epsilon$ denote the numerical error in simulating the physical processes underlying DNA. The simulated observer $H'$ retains subjective experience provided $\epsilon \leq \epsilon_{\mathrm{DNA}}$, where $\epsilon_{\mathrm{DNA}}$ is the error threshold below which all DNA-mediated processes operate correctly. Any stricter bound $\epsilon_{\min} < \epsilon_{\mathrm{DNA}}$ required to preserve consciousness would constitute a new physical constant not derivable from $A_1$ through $A_4$, contradicting Axiom~2:

$$ \epsilon \leq \epsilon_{\mathrm{DNA}} ;\implies; S(H') \neq \emptyset. $$

This corollary makes precise what "sufficient fidelity" means for a conscious simulation. It does not require perfect simulation of all physical processes, only those that DNA-based processes depends on. The threshold $\epsilon_{\mathrm{DNA}}$ is in principle empirically determinable, making the claim testable.

Falsifiability

The foundational falsifiability criterion of this paper is long-term: if a sufficiently accurate DNA simulation --- one satisfying $\epsilon \leq \epsilon_{\mathrm{DNA}}$ --- is constructed and shown no pain sensitivity, Axiom~4 is invalidated. The effect of pain and subjective experience on behaviour is measurable by the same methods used to measure the effects of any physical intervention.

A nearer-term criterion follows from Axiom~3: if a physical process essential to DNA function is shown to be provably non-computable, the framework fails. This is in principle testable through precision studies of quantum coherence in biological systems.

Observer Equivalence Classes

From the optimization thought experiment it follows that different implementations (execution traces) implement identical simulation (Alice). Individual bit-patterns are not significant - Alice is an equivalence class in that many different bit patterns describe the same Alice.

Because there is no causal relationship but representational, running a DNA simulation multiple times does not create multiple instances of Alice; rather, it traces out (discovers) different representations of the same "Alice" equivalence class. Computers do not create new information.

Quantum Computation

Axiom~3 does not restrict to classical computation. The computability claim covers any physically realisable process, including quantum processes. Quantum computation is an alternative physical realisation of the same formal state-transition structure and is therefore covered by the axiom without requiring a separate argument. Substrate independence follows for quantum computers by the same derivation as for classical ones.

Representational Equivalence and Its Consequences for Physics

The substrate independence established in this paper has an immediate and non-trivial consequence for the study of physical phenomena.

Because a physical system and its computational simulation represent equivalent configurations of information, the execution trace of the simulation necessarily preserves the properties of the physical system. Consequently, despite our internal vantage point within the universe, analyzing physical phenomena through a computational framework allows us to study reality as an information processing system.

Conclusion

We have established four axioms and derived from them the following results.

• Time as Internal Ordinal. Time is not a fundamental external parameter but an internal ordering relation emergent from the observer's information structure. The universe, at the level of the totality, is static and timeless. What observers experience as the flow of time is the traversal of an internally ordered sequence of states encoded in a static information structure.

• Finiteness. The simulation computer is a discrete, finite system, so the execution trace is a finite bitstring. The universe it represents is therefore characterised by a finite bit count $n$.

• Substrate Independence. Consciousness is a property described by certain finite information structures. The physical substrate in which such a structure is instantiated does not determine whether it is conscious. A computer running a simulation of a conscious observer and the simulation itself are two arrangements of the same information, with neither causally prior to the other.

Representational Relationship. A physical computer running a DNA simulation and the simulated conscious agent itself stand in a relation of informational equivalence rather than causation. The physical computer does not generate the simulated agent; rather, its execution trace merely traces a representation of a pre-existing informational structure for external observers. The simulated entity exists independently of execution.

• Simulated Conscious Observer. A simulation physically and behaviourally indistinguishable from a conscious observer must itself instantiate subjective experience. Two identical axiomatic systems must behave identically.

• Causal Efficacy of Qualia. Subjective experience is not epiphenomenal. It is a causally distinguishable component of the observer system.

• Representational Equivalence as a Physical Tool. The equivalence of geometric and computational descriptions licenses the use of the execution trace as a faithful proxy for physical processes that are geometrically inaccessible.

By treating subjective experience as a causally efficacious property of a computable information structure, the framework moves from metaphysical speculation to a derivation with testable consequences. The foundational falsifiability criterion is the construction of a behaviourally indistinguishable DNA simulation that lacks subjective experience.

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