Zeno, Fractals, and the Zero Field

How Pattern Field Theory Reinstates Zeno — No Paradox, Just Fractal Reality

Zeno’s Argument Revisited

Zeno famously argued that to move any distance, you must first cover half, then half again — infinitely. Classical physics dismissed this using finite summation. Pattern Field Theory (PFT) reinstates Zeno’s logic: motion occurs over an infinitely divisible structure.

In PFT, each division always returns to “one-half traversal logic”: 1/2 divides to 1/4, but immediately reframes itself as a new half. You never run out of halves, only gain new recursive boundary points.

Fractal Resolution Explains Motion

Motion is not smooth passage through emptiness, but coherent traversal across fractal recursion layers. Movement skips unresolved subdivisions via curvature coherence — making finite motion across infinite recursion possible.

Zero Field and Meta Continuum

The Zero Field holds dormant structural potential — infinite unresolved subdivisions. Traversal moves along coherent rendering layers, never fully resolving every division.

Fractal Traversal Formula

The classical “distance halving” equation aligns with PFT fractal recursion:

$$ D = \\sum_{n=0}^{\\infty} \\frac{L}{2^n} $$

But: Every division creates a new half from remaining structure, maintaining coherent traversal without limit collapse. Traversal is recursive rendering, not crossing fixed emptiness.

Conclusion

Zeno’s Paradox is not a contradiction — it is a demonstration of the infinite fractal structure of motion. PFT reframes Zeno’s logic as foundational physics: motion is recursive traversal, always halving but never terminating, skipping unresolved recursion.

“Zeno proved recursion; we mistook it for paradox.”
— James Johan Sebastian Allen, Pattern Field Theory