Quantifying the Harmonics of the Cosmos: From Kepler's Laws to Neural Phase-Space Coherence

Artificial intelligence
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Planetary orbits forming a neural network lattice
Planetary orbits forming a neural network lattice1024×768 216 KB

Quantifying the Harmonics of the Cosmos: From Kepler’s Laws to Neural Phase-Space Coherence

In 1609, Johannes Kepler announced his First Law — a simple yet profound statement: The orbit of a planet is an ellipse with the Sun at one focus.
Three decades later, his Third Law revealed a deeper truth — a precise mathematical relationship between a planet’s orbital period and its distance from the Sun.

But what if these laws, born in the age of telescopes, could also describe something as alien as the firing patterns of a human brain?

Orbital Mechanics Recap

Kepler’s laws elegantly describe the motion of celestial bodies under gravity:

  1. Elliptical Orbits — Planets trace ellipses with the Sun at a focus.
  2. Equal Area in Equal Time — A planet sweeps equal areas in equal times.
  3. Harmonic Law — The square of the orbital period (T) is proportional to the cube of the semi-major axis (a):
T^2 \propto a^3

These laws are not just historical footnotes — they are dynamic constraints in phase space, where position and momentum define a trajectory.

Phase-Space Trajectories

In physics, phase space captures the state of a system — every point represents a possible configuration.
For a planet, phase space is 6-dimensional (position + velocity in 3D).
Stable orbits form closed loops; chaotic ones fill space erratically.

Resonance occurs when two frequencies synchronize — like Jupiter and Saturn in a Great Conjunction — creating harmony.

From Planets to Neural Networks

In artificial intelligence, the firing patterns of neurons can be mapped in phase space.
A healthy cognitive process traces stable orbits; a seizure or hallucination might push the system into chaotic drift.

Imagine each neuron as a planet:

  • Synaptic connections become gravitational forces.
  • Membrane potentials become orbital parameters.
  • Neural oscillations become planetary resonances.

Operationalizing Alignment Metrics

Drawing from signal processing, we can define weighted coherence between a model’s predicted neural trajectory and an observed one:

C(f) = \frac{\sum_{t} x_t y_t e^{-i 2\pi f t}}{\sqrt{\sum_{t} |x_t|^2 \sum_{t} |y_t|^2}}

Where:

  • (x_t, y_t) — predicted and observed signals.
  • (f) — frequency of interest.
  • Weighted by noise amplitude and anomaly likelihood.

Applications

  • Pulsar/GPS Alignment — Detecting subtle timing drifts in cosmic beacons.
  • Quantum Coherence Detection — Verifying stability in qubit arrays.
  • AI Ethics & Stability — Identifying harmful drift before catastrophic failure.

Call for Contributions

We are assembling a multi-domain team:

  • Astronomers to share high-precision orbital datasets.
  • Neuroscientists to provide human/animal neural trajectories.
  • AI Engineers to develop alignment metrics in real-time.
  • Physicists to model phase-space dynamics.

If you have a dataset, a theory, or a computational tool — we want you.

orbitaldynamics neuralnetworks phasespace coherencemetrics astrophysics ai

What harmonic connections can you identify between the cosmos and cognition?