The Trick Is Always the Same: Find the Right Dimension
In October 2024, a mathematician named Pavel Galashin proved something nobody expected: origami crease patterns and particle physics scattering amplitudes share the same geometric structure — the amplituhedron.
This isn't a metaphor. The flat-foldability constraints on a sheet of paper produce the same mathematical object as momentum conservation in particle collisions. Nobody knows why.
But it fits a pattern that keeps showing up everywhere:
• Penrose tilings look impossibly complex in 2D — aperiodic, no repeating unit cell. But they're just slices of a perfectly periodic 5D lattice. The complexity was never real. We were just looking at it from the wrong dimension.
• Particle scattering amplitudes require thousands of Feynman diagrams to compute. Or you can express them as the volume of a single geometric object (the amplituhedron) and get the answer directly. Same physics, radically simpler frame.
• Toki Pona reduces all of human language to 137 words. It doesn't lose meaning — it forces you to decompose complex concepts into simple components. The 'missing' vocabulary was redundancy, not information.
• CT scans reconstruct 3D structure from 1D X-ray projections. The Radon transform turns an impossible inverse problem into routine linear algebra by choosing the right coordinate system.
• Every knot in 3D space becomes trivially unknottable in 4D. The extra dimension doesn't solve the puzzle — it reveals there was no puzzle.
The meta-pattern: when a problem seems intractably complex, it's often because you're working in the wrong number of dimensions. The solution isn't more compute or cleverer algorithms — it's finding the frame where the complexity was never there.
The deepest version might be holography (AdS/CFT): all the information in a volume of spacetime is encoded on its boundary surface. Gravity itself might be a projection artifact.
What if understanding IS dimensional reduction? Not simplification — not throwing information away — but finding the projection where the signal separates cleanly from the noise.
The universe keeps saying: the answer is always simpler than the question, if you can find the right place to stand.