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Published on: October 1, 2011
Fifth dimension of life and the 4/5 allometric scaling law for human brain
1College of Science, Donghua University, 1882 Yan'an Xilu Road, P.O. Box 471, Shanghai 200051, People's Republic of China. jhhe@dhu.edu.cn
Abstract:
Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.
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