10.2 Learning Rate > Aging Rate: When Consciousness’s Self-Update Speed Exceeds Thermodynamic Loss Speed, Topological Knots Can Extend Infinitely in a Single Runtime.

In the previous section, through the metaphor of “Ship of Theseus,” we established the fluidity of self-identity. If identity is defined by topological relations rather than constituent materials, then in principle, as long as we can continuously replace damaged components (whether atoms or qubits), the self can persist forever.

However, there is a fatal kinetic bottleneck here: speed.

In nature, repair speed often cannot keep up with destruction speed. This is the physical essence of aging and death.

This section will establish a quantitative model of immortality. We will prove: Immortality is not a static property, but a dynamic critical threshold. As long as a consciousness system’s self-update rate (learning rate $\dot{G}$) exceeds the entropy increase rate (aging rate $\dot{L}$) caused by the environment, it can reach “escape velocity,” achieving infinite extension in a single runtime.

10.2.1 Physical Definition of Aging: Signal-to-Noise Ratio Decay

In QCA ontology, “aging” is no longer biological phenomena like telomere shortening or oxidative stress, but the decline of Information Fidelity.

We model consciousness as a topological knot with high information mass $M_I$. Although topological properties are discrete (protected by energy gaps), the underlying qubits carrying this topological structure are subject to environmental thermal noise interference.

• Bit-flip: Memory bits are randomly reset.

• Phase-damping: Quantum coherence is lost.

• Link-breaking: Causal structure loosens.

Define the system’s Structure Loss Rate $\dot{L}(t)$:

$$\dot{L}=\frac{d{S}_{noise}}{dt}>0$$

Over time, without intervention, accumulated noise entropy $S_{noise}$ within the system gradually drowns out original structural information. When signal-to-noise ratio (SNR) falls below a critical value, the topological knot disintegrates—this is information-theoretic death.

For most organisms, $\dot{L}$ grows exponentially over time (because damage triggers more damage, like avalanche effects), eventually causing system collapse.

10.2.2 Learning as Repair: Negentropy Generation

How to combat $\dot{L}$? The only way is to introduce negentropy flow.

For consciousness systems, Learning is not merely acquiring new knowledge; it is physically equivalent to System Refactoring.

When an agent optimizes its internal model $\mathcal{M}$ by minimizing free energy $F$:

1. Data compression: It compresses redundant experiences into concise laws (reducing $K$ complexity).

2. Error correction: It identifies and removes error data inconsistent with the model (Maxwell demon operation).

3. Structure reinforcement: It establishes new long-range correlations (increasing $\Phi$ value).

Define the system’s Structure Gain Rate $\dot{G}(t)$:

$$\dot{G}=-\frac{dF}{dt}\approx \text{Learning Rate}$$

Physical Image 10.2:

• Aging is turning a delicate castle into a sand pile.

• Learning is continuously rebuilding the sand pile into a castle, even higher.

10.2.3 Immortality Inequality: Crossing the Critical Point

A system’s fate depends on the game between $\dot{G}$ and $\dot{L}$.

1. Mortality Mode:

   $$\dot{G}(t)<\dot{L}(t)(\text{when }t>t_{peak})$$

   With age, biological learning ability (neural plasticity) declines, while body entropy increases. Net information flow $dI/dt<0$. Structure eventually disintegrates.

2. Immortality Mode:

   $$\forall t,\dot{G}(t)\ge \dot{L}(t)$$

   If a system can maintain extremely high self-update speed, making repair always faster than damage, its structural integrity will forever remain above threshold.

This is the information-theoretic version of what Ray Kurzweil calls “Longevity Escape Velocity.”

How to achieve $\dot{G}>\dot{L}$?

• For biological brains: Difficult. Because neuronal metabolic limits cap $\dot{G}$’s upper bound.

• For post-substrate-migration consciousness (virtual ascension):

  • Hardware upgrade: Use photonic quantum or vacuum computation nodes to raise error correction frequency to Planck scale.

  • Algorithm optimization: Remove biological evolution’s “planned obsolescence” code, making curiosity and plasticity never decline.

10.2.4 Dynamic Immortality: Fountain, Not Diamond

This theory revises our aesthetic imagination of “immortality.”

In traditional concepts, immortality is like a diamond—hard, unchanging, eternally static.

But in QCA physics, immortality is like a fountain—shape remains constant, but water molecules composing it flow through at high speed every minute and second.

• Diamonds are static; they will eventually be disintegrated by proton decay.

• Fountains are dynamic; as long as energy is injected (negentropy), they can maintain form through continuous Metabolism of Information.

Conclusion:

We don’t need to pursue “indestructible bodies.” We need to pursue “ultra-fast flowing souls.”

As long as your thinking speed (update rate) runs faster than the second law of thermodynamics, death can never catch up.

Immortality is a never-relaxing sprint.

(Section 10.2 Complete)