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The graph below is something every Bitcoiner should print and put it in their bedroom.
From the Physics of Bitcoin book:
Bitcoin is the only asset that passes the Scaling Test.
Here's a model-independent way to prove Bitcoin follows a power law — no curve fitting, no cherry-picked dates, no assumptions.
Pick two random days from Bitcoin's history. Compute the ratio of the prices. Compute the ratio of the times. Plot one against the other. Repeat thousands of times.
For a true power law, those points should collapse onto a perfectly straight line — because if P(t) ∝ tⁿ, then P(t₂)/P(t₁) = (t₂/t₁)ⁿ. The ratio of prices is entirely determined by the ratio of times. It doesn't matter which dates you pick. It doesn't matter where you are in the cycle. The exponent is always the same.
Bitcoin does exactly this. Slope = 5.67. R² = 0.96. A tight linear cloud across 15 years of data — bull markets, crashes, halvings, exchange collapses — all of it consistent with a single underlying mathematical structure.
The S&P 500 and NASDAQ, using their full 55-year histories? R² drops to ~0.70. A third of the variance is simply unexplained by elapsed time. Gold is worse. These assets grow, but they do not scale. Recessions, policy shifts, and macro shocks leave fingerprints that no single exponent can capture.
This is the mathematical signature of scale invariance — the same symmetry that appears in critical phenomena, phase transitions, and the renormalization group in physics. When a dataset has this symmetry, it means the microscopic noise is washing out at large scales, leaving behind a single universal exponent.
Bitcoin isn't just growing faster than other assets. It's growing according to a different mathematical logic entirely.