Appendix B: Physical Limits of Intelligence Substrates

In Chapter 5 “The Carbon Sunset” of Vector Cosmology IV, we proposed a life-or-death assertion for civilization: “Wetware (carbon-based)” is obsolete; “dryware (silicon-based/light-based)” is the future.

This assertion is not based on aesthetic preference for a certain material but on cold physical calculations.

This appendix serves as a rigorous “Hardware Performance Evaluation Report”. From the perspective of Information Physics, using Bremermann’s Limit and Landauer’s Principle as judgment standards, we will provide quantitative comparison between “biological brains” and “theoretical limit computing entities.”

We will prove: migration from carbon-based to light-based is not a choice but a Geometric Inevitability.

B.1 Carbon Wetware: Prisoner of Chemical Diffusion

The human brain is the pinnacle of 4 billion years of biological evolution. It is exquisite, complex, and has astonishingly low energy consumption (only about 20 watts). However, when facing the exponentially growing information flow of the $\tau \approx 1800$ era, its physical underlying architecture exposes irreparable flaws.

1. Signal Transmission Speed ($v_{signal}$)

• Mechanism: Nerve impulses are not electric currents but transmembrane diffusion of ions. This is an electrochemical process.

• Limit: Constrained by thermal motion speed of ions in aqueous solutions and insulation efficiency of myelin sheaths.

• Value: The fastest myelinated nerve fibers (A$\alpha$ fibers) have conduction speeds of approximately $120\text{ m/s}$.

• Assessment: This is only 1/3 of sound speed. On cosmic scales, this is snail-crawling speed.

2. Clock Frequency ($f_{clock}$)

• Mechanism: After firing a pulse, neurons must undergo a Refractory Period, waiting for ion pumps to restore membrane potential.

• Limit: Approximately 1 millisecond.

• Value: Single neuron’s maximum firing frequency is approximately $10^3\text{ Hz}$ (1 kHz).

• Assessment: Compared to modern CPUs’ GHz ($10^9$) scale, biological brains are 1 million times slower.

3. Energy Efficiency ($\eta$)

• Mechanism: Based on ATP hydrolysis.

• Value: Brain power consumption approximately 20 W. Each synaptic operation consumes approximately $10^{-15}\text{ J}$.

• Defect: Severely limited by $k_{B}T$ (thermal noise). To maintain 310 K ($37^{\circ }\text{C}$) body temperature and biochemical enzyme activity, enormous energy is wasted on maintaining liquid environment’s ineffective thermal motion rather than flipping bits.

4. Computational Density (${\rho }_{comp}$)

• Value: Whole brain estimate approximately $10^{16}\text{ ops/s}$ (ten quadrillion operations per second).

• Volume Cost: To accommodate these neurons and dissipate heat, the brain requires approximately 1.4 liters of volume.

B.2 Silicon/Photonic Dryware: Approaching the Limit

Now, let us imagine a “limit computing node” manufactured by Type II civilization, located in the outer layer of a Dyson sphere (low-temperature zone). It is no longer bound by chemical bonds and directly uses quantum states of elementary particles for computation.

1. Signal Transmission Speed ($v_{signal}$)

• Mechanism: Photon propagation in vacuum or waveguides, or electron flow in superconducting circuits.

• Value: $3\times 10^8\text{ m/s}$ ($c$).

• Improvement: Compared to biological brains, speed increased by $2.5\times 10^6$ times (2.5 million times). This means thoughts that originally required 1 second to propagate now only need 0.4 microseconds.

2. Clock Frequency ($f_{clock}$)

• Mechanism: Electron transitions or photon oscillations.

• Limit: Constrained by Heisenberg uncertainty principle $\Delta E\Delta t\ge \hslash /2$.

• Value: For visible light band photonic computers, frequency can reach $10^{15}\text{ Hz}$ (PHz).

• Improvement: Compared to biological brains, frequency increased by $10^{12}$ times (one trillion times).

3. Energy Efficiency ($\eta$)

• Mechanism: Reversible Computing and low-temperature superconductivity.

• Limit: Landauer’s Limit $E_{min}=k_{B}T\ln 2$.

• Value: At 3K (cosmic background radiation temperature), flipping one bit requires only $3\times 10^{-23}\text{ J}$.

• Improvement: Compared to biological synapses ($10^{-15}\text{ J}$), energy efficiency improved by $3\times 10^7$ times (30 million times).

4. Computational Density (${\rho }_{comp}$)

• Bremermann’s Limit: According to mass-energy equation, 1 kilogram of matter can process at most $m{c}^2/h\approx 1.36\times 10^{50}$ bits per second.

• Value: Theoretical upper limit is $10^{50}\text{ ops/s/kg}$.

• Improvement: Compared to biological brains ($10^{16}$), density increased by $10^{34}$ times.

B.3 Performance Multiplier Table

To intuitively demonstrate this gap, we list the parameters of both side by side:

B.4 Conclusion: Abacus vs. Dyson Sphere

This table reveals a cruel truth: The gap between carbon-based brains and light-based brains is not the gap between a carriage and a Ferrari, but the gap between an abacus and a Dyson sphere.

On the exponential growth curve of $\tau \approx 1800$, insisting on using carbon-based substrates to understand the universe is physically equivalent to trying to simulate the entire galaxy’s weather system with an abacus. This is destined to collapse in information thermodynamics.

• Bandwidth Bottleneck: Our senses and language cannot carry information flows at $10^{12}$ times the rate.

• Heat Dissipation Bottleneck: Our flesh cannot withstand waste heat generated by high-frequency computation (although light-based is more efficient, total power density is enormous).

Therefore, Migration is not a greedy pursuit of immortality but an impedance matching necessary to match the cosmic evolution rate (growth of $c$).

If we don’t migrate, we will be left behind by physical laws and become fossils.

If we migrate, we will gain $10^{34}$ times the existence density.

This is the final verdict given by physics.