---

Part I: Introduction

This argument aims to explore whether non-biological substrates (i.e., “artificial substrates”) can theoretically completely replace biological substrates (humans), thereby realizing all human functions. Before developing a formal proof, we must first clarify two opposing physical/philosophical paradigms regarding the “nature of consciousness and intelligence,” which will determine the axiomatic foundation of this argument.

1.1 The Turing Machine Paradigm

This paradigm supports the Computational Theory of Mind.

• Core Assumption: The brain is essentially an extremely complex information processing system. Biological neurons are logic gates, synaptic connections are state storage, and consciousness is algorithmic software running on wetware.
• Inference: According to the Church-Turing Thesis, any computable process can be simulated by a Universal Turing Machine.
• Support for this Argument: If the brain is a Turing machine, then Substrate Independence holds. Silicon-based chips can perfectly replace carbon-based neurons as long as they can execute the same logical operations.

1.2 The Microtubule Quantum Paradigm

This paradigm, proposed by Roger Penrose and others, represents the non-computable view under physicalism.

• Core Assumption: The brain is not merely a computer; microtubules inside neurons utilize quantum coherence and wave function collapse (Orch-OR) to generate consciousness.
• Inference: Human thinking contains Gödelian “non-algorithmic” components that classical Turing machines cannot simulate, such as insights or intuitions arising from quantum collapse.
• Challenge: If this paradigm is true, purely classical computation cannot reproduce human intelligence.

1.3 Transition to Argument

To advance this argument, we need not completely disprove the microtubule quantum effect; we only need to introduce the more general Church-Turing-Deutsch Principle:

“Any finite physical process can be perfectly simulated by a universal quantum computer.”

Therefore, this argument proceeds from the following position: Whether the brain is a classical neural network or a quantum microtubule system, it is ultimately a physical system. As long as artificial substrates (whether silicon-based chips or future quantum processors) can simulate this physical process, replacement becomes possible.

---

Part II: Formal Argumentation System

2.1 Definitions

• Let $H$ be the set of human cognitive and physical functions.
• Let $N_{bio}$ be the set of biological neurons in a human brain, where $|N_{bio}| \approx 86 \times 10^9$.
• Let $N_{art}$ be the set of artificial computational units (e.g., silicon neurons or quantum bits).
• Let $S$ be the functional state of the global system (the brain/mind).
• Let $P$ be the set of physical laws governing the interaction of matter.

2.2 Axioms

• Axiom A1 (Physical Closure): All functions of the brain (including consciousness) are entirely determined by its physical structure and physical state evolution; there is no non-physical “soul” intervention.
• Axiom A2 (Local Replaceability): If a physical unit $u’$ is equivalent to unit $u$ in terms of input-output and state transitions, then at the system level, $u’$ can replace $u$ without changing the overall system function.

$$\forall u \in N_{bio}, \exists u’ \in N_{art} : Behavior(u) \equiv Behavior(u’)$$

---

2.3 Deduction

Step 1: Micro-Isomorphism

Based on the development of engineering physics, we construct artificial neurons $n_{art}^i$. If brain operation follows classical physics, we use analog circuits or digital algorithms to reproduce the membrane potential equations of $n_{bio}^i$ . If brain operation follows quantum physics, we use quantum logic gates to reproduce the quantum state evolution of $n_{bio}^i$. Proposition 1: There exists a technological means $T$ such that a single biological neuron can be perfectly simulated by an artificial unit.

$$P_1: n_{art}^i \xrightarrow{T} n_{bio}^i$$

Step 2: Inductive Reconstruction

We use mathematical induction to prove the replaceability of the entire neural network.

• Base Case: Let brain $B_0$ be a fully biological brain. Replacing 1 neuron yields $B_1$. By Proposition 1 and Axiom A2, $Function(B_1) = Function(B_0)$.

• Inductive Hypothesis: Assume that after replacing $k$ neurons, the hybrid brain $B_k$ still maintains functional integrity, i.e., $Function(B_k) = Function(B_0)$.

• Inductive Step: Consider the $(k+1)$-th neuron. Since the interactions between neurons are local (Local Interactions) and follow physical laws $P$, in the environment of $B_k$, when the $(k+1)$-th biological neuron is replaced by an artificial neuron, its signal transmission to neighboring nodes remains unchanged.

• Conclusion: When $k$ approaches the total number of brain neurons $N$, the fully artificial brain $B_{art}$ is functionally strictly equivalent to the biological brain $B_{bio}$.

$$\lim_{k \to N} B_k = B_{art} \implies B_{art} \equiv B_{bio}$$

Step 3: Engineering Completeness of Embodiment

The brain is merely a controller; the realization of function $H$ depends on actuators (the body). Let the kinematic characteristics of the human body be the set $K_{human}$ (degrees of freedom, torque, perceptual precision). Physical laws allow the construction of a mechanical system $M_{robot}$. Since engineering materials (such as carbon fiber, hydraulic drives, piezoelectric ceramics) typically surpass biological materials (muscles, bones) in strength, speed, and precision:

$$\exists M_{robot} : K_{robot} \supseteq K_{human}$$

Step 4: Universal Functionality

Combining Step 2 (fully artificial brain) and Step 3 (superhuman mechanical body). For any task $task \in H$ that humans can complete:

1. The brain $B_{art}$ can generate the planning and control signals required to complete that task (derived from $B_{art} \equiv B_{bio}$).
2. The body $M_{robot}$ can execute these signals and produce physical effects (derived from $K_{robot} \supseteq K_{human}$).

---

Part III: Conclusion

In summary, although the Microtubule Quantum Paradigm poses challenges to current AI based on classical computers, grounded in the more general physicalism and the Church-Turing-Deutsch Principle, as long as the universe is physically closed, we will inevitably be able to construct artificial substrates that are microscopically isomorphic and macroscopically equivalent.

Through rigorous recursion via mathematical induction, we have logically proven that: Artificial substrates can not only simulate humans but also possess theoretical completeness in replacing humans to execute any physical and cognitive tasks.

---

References

1. Turing, A. M. (1936). “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, 2(42), 230-265. https://doi.org/10.1112/plms/s2-42.1.230
   Foundation of the Church-Turing Thesis: any computable process can be simulated by a Universal Turing Machine.

2. Gödel, K. (1931). “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.” Monatshefte für Mathematik und Physik, 38, 173-198. https://doi.org/10.1007/BF01700692
   Incompleteness theorems establishing the existence of “non-algorithmic” components in formal systems.

3. Penrose, R. (1989). The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press.
   Argues for the non-computable view of consciousness based on quantum mechanics and Gödelian arguments.

4. Deutsch, D. (1985). “Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer.” Proceedings of the Royal Society of London A, 400(1818), 97-117. https://doi.org/10.1098/rspa.1985.0070
   Establishes the Church-Turing-Deutsch Principle: any finite physical process can be perfectly simulated by a universal quantum computer.

comments powered by Disqus