4.2 Frequency Concerto: Society Does Not Need Everyone Vibrating at the Same Frequency (That Is Resonance Disaster). A Harmonious Society Is a Multi-Band Fourier Series, Where High Frequencies (Creation) and Low Frequencies (Transmission) Support Each Other.

In the previous section, we discussed the complementarity between “frontline” and “rear” within families. Now, we extend this logic to the scale of entire social civilization.

Modern society often has a dangerous tendency: Homogenization. The education system attempts to train everyone into high-IQ elites, and the economic system attempts to involve everyone in high-frequency competition. We subconsciously believe that a “perfect” society should consist of equally excellent, equally hardworking, equally high-frequency operating people.

Physics tells us this is a fatal error. In dynamical systems, if all units vibrate at the same frequency, the result is not perfect order, but destructive Resonance Disaster.

This section will re-examine social structure using the perspective of Fourier Analysis. We will prove: A healthy civilization must be a Broadband System. Only when high-frequency creativity and low-frequency stability orthogonally superpose can civilization’s waveform propagate far.

4.2.1 The Lesson of Tacoma Narrows Bridge: Resonance and Collapse

In 1940, the Tacoma Narrows Bridge in the United States twisted, fractured, and collapsed in a gentle breeze. The reason was simple: the wind’s frequency exactly matched the bridge’s natural frequency, and the bridge structure was too uniform, lacking damping.

In QCA social physics, each person has a characteristic frequency ${\omega }_i$ (corresponding to fluctuations in their internal information update rate $v_{int}$).

• If society forces everyone to operate at the same frequency ${\omega }_0$ (e.g., universal military service, universal research, or universal idleness), the system’s phase space trajectory will rapidly contract to an extremely low-dimensional submanifold.

• This hyper-coherence makes the system extremely sensitive to external perturbations at specific frequencies. Once environmental pressure hits this frequency, amplitude will diverge exponentially, causing social structure disintegration.

Conclusion: Homogenization is fragile. A robust system must have a flat spectrum, i.e., distribution across all frequency bands, with no obvious resonance peaks.

4.2.2 Fourier Decomposition of Civilization

Any complex periodic function $f(t)$ (civilization’s evolutionary waveform) can be decomposed into superposition of sinusoidal waves of different frequencies:

$$f(t)=a_0+\sum _{n=1}^{\infty }(a_n\cos n\omega t+b_n\sin n\omega t)$$

In a healthy society, different groups play different Harmonic roles:

1. High-Frequency Components (High Frequency, Short Wavelength):

   • Groups: Scientists, artists, entrepreneurs, revolutionaries.

   • Physical characteristics: Extremely fast change ($d\psi /dt$ large), rapid logical depth growth, but also extremely unstable, short lifespan, high energy dissipation.

   • Function: Depict details and edges. In signal processing, high-frequency components determine image sharpness and transitions. They are responsible for exploring the unknown, breaking deadlocks, providing Novelty.

2. Low-Frequency Components (Low Frequency, Long Wavelength):

   • Groups: Teachers, doctors, farmers, order-keepers, transmitters.

   • Physical characteristics: Slow change, large inertia, very stable, high energy efficiency.

   • Function: Construct outline and tone. Low-frequency components determine the waveform’s main energy and overall trend. They are responsible for maintaining social stability, preserving historical memory, providing Continuity.

3. DC Component ($a_0$):

   • Corresponds to: Underlying physical laws, universal values, biological instincts.

   • Function: This is the baseline for civilization’s existence.

4.2.3 Rejecting the Hierarchy of Contempt: The Aesthetics of Orthogonality

In Fourier series, wave functions of different frequencies are orthogonal:

$$\int \cos (n\omega t)\cdot \cos (m\omega t)dt=0(n\ne m)$$

This means: High frequency is not superior to low frequency, and low frequency does not hinder high frequency. They do not interfere with each other in Hilbert space, jointly supporting the total waveform $f(t)$.

• If only high frequency (all noise), the waveform is a piercing screech.

• If only low frequency (all fundamental wave), the waveform is a monotonous hum.

• Only when they mix in specific proportions (such as $1/f$ noise or pink noise) can they compose a complex Symphony.

The hierarchy of contempt in society (high frequency despising low frequency’s slowness, low frequency despising high frequency’s madness) is physical ignorance.

• Without “low frequency” support, “high frequency” is just garbled code with no background foundation.

• Without “high frequency” embellishment, “low frequency” is just a dead line with no information increment.

4.2.4 Conclusion: Be the Wave at Your Frequency

This gives everyone’s life positioning:

Don’t force yourself to change frequency; find your frequency band and maximize amplitude in that band.

• If you are high-frequency, burn, create, don’t blame yourself for lack of stability—you are civilization’s peak.

• If you are low-frequency, guard, transmit, don’t feel inferior for lack of novelty—you are civilization’s carrier wave.

The universe’s synthesizer needs oscillations at every frequency.

Just as when we listen to music, we don’t say “violin is better than cello,” we only say: “Listen, how beautiful this harmony is.”

(Section 4.2 Complete)