These are examples of the 4/3 law so called by Hunt 1998. Lewis Fry Richardson’s 1926 measurements of wind eddies and Kolmogorov’s 1941 proof. John James Waterston’s 1845 on a gravitating plane. Clausius 1858 on 3/4 mean path lengths. Boltzmann’s 1884 derivation of Stefan’s law. Kleiber’s 3/4 metabolic scaling. The 4/3 fractal envelope of Brownian motion in Lawler 2001. Brittin and Gamow 1961 on photosynthesis, an implicit reference. In cosmology energy density varies with distance as 1/a^3 for matter and 1/a^4 for radiation. Jafar and Shamai 2007, perhaps, on cell phone transmission towers. The 4/3 law has two guises. First, a system with 4 dimensions has 4/3 the degrees of freedom of one with 3 dimensions. Second, lengths in a 4 dimensional system are 4/3 longer in the 3 dimensional system. The 4/3 law may account for dark energy.

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