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Fifth dimension of life and the 4/5 allometric scaling law for human brain
Author(s) -
He JiHuan,
Zhang Juan
Publication year - 2004
Publication title -
cell biology international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.932
H-Index - 77
eISSN - 1095-8355
pISSN - 1065-6995
DOI - 10.1016/j.cellbi.2004.07.011
Subject(s) - allometry , fractal dimension , scaling , brain cell , fractal , dimension (graph theory) , exponent , radius , curse of dimensionality , scaling law , human brain , mathematics , physics , statistical physics , geometry , mathematical analysis , combinatorics , biology , neuroscience , statistics , computer science , philosophy , ecology , linguistics , computer security
Brain cells are not spherical. The basal metabolic rate ( B ) of a spherical cell scales as B ∼ r 2 , where r is the radius of the cell; that of a brain cell scales as B ∼ 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.