In Two New Sciences, 1638, Galileo applies his analysis of the strength of a beam to an animal’s weight bearing bone. For a larger animal, weight scales by 3 when cross sectional area of bone scales by 2.
The relative dimensional capacity to contain or impress W varies by exponents 3:2, or (D+1)/D.
Question. Does (D+1)/D extend from D+2, Galileo’s case, to D+3?
Minkowski’s space time can be considered a D=3 example.
If extension to D=3 were valid, then the ratio of dimensions may explain 3/4 metabolic scaling, Stefan’s Law, Peto’s Paradox, brain weight scaling, the fractal envelope of Brownian motion, and expansion of cosmological space, among other problems.
An exploration of this question is in: Preprint From Galileo’s simple case to universal 4/3 scaling
What supports (D+1)/D working for D+3? What undermines it?
Is the extension to D= 3 valid?
A recent article with a flow chart shows how the question above arises.
Preprint Flowchart for deriving 4/3 scaling
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