Galileo in his 1638 Discorsi (Two New Sciences) points out that weight scales with size as a cube while the cross-sectional area of bones supporting the weight scale as a square. When animal size increases, if the composition and therefore breaking resistance of bone remains the same, then weight-bearing bones must get relatively thicker. Thus the same weight in 3 dimensions results in the corresponding 2 dimensional system growing disproportionately. Call this the principle of dimensional capacity.
A similar dimensional approach occurs in the 1838 paper of Sarrus and Rameaux on the effects of size on the rate of breathing for constant temperature animals
This seems to apply to the 1998 astronomical observations of expanding space, so called dark energy. Space plus light motion is a 4 dimensional system. When the energy of the 4 dimensional system appears in the corresponding 3 dimensional space, like Galileo’s weight-bearing bones, the 3 dimensional system grows disproportionately.
Are there other historical instances of the principle of dimensional capacity? Are there earlier examples?
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