Allometric law and complexity

Complex systems may be divided into three qualitative groups:

1. The whole is the sum of its parts, e.g. molecules of an ideal gas, or the set of integers.
2. The whole is more than the sum of its parts:
2a Like water in a container (at room temperature). Its molecules are not dispersed randomly. Each water molecule is a dipole, and tends to partially align itself with other molecules.
2b Or the following sentence :” My information content is more than the sum of the letters in me”
2c Wolfram CA classes 3 and 4 (p. 231)
3. The whole controls its parts  (and is obviously more than the sum of its parts). Such systems obey the allometric law , or power law, which describes the relationship between the whole (W)  and its parts (p). Like in the following equation:  p = a * W ^ b  or  Log[p] =  Log[a] +   b * Log[W].

Kleiber (1930) described the relationship between the mass (M) of an  organism and its basal metabolic rate (BMR) which applies to the majority of animals,  BMR= a * M ^ 0.75  . Thus a cat, having a mass 100 times that of a mouse, will have a BMR roughly 31 times greater than that of a mouse. 

Since all living systems obey similar relationships, the allometric law may be regarded as their attribute. However it is observed also in some non-living complex systems. The law indicates that living systems are constrained by a relative shortage  of vital substances like oxygen which drives the basal metabolic rate (BMR) and determines the size of an animal. Since oxygen is scarce,  the  organism controls its distribution among the organs.  Brain is the most privileged, then come the kidneys, heart  muscles and bones. The power law thus indicates that the whole actually controls its parts. It has a wisdom which is called here Wisdom of the Body (WOB).

WOB has two meanings: 1. It is the set of interacting processes, and 2. It is an optimizing principle. Processes in the body interact so as to keep it  optimal.

Allometric law in cancer

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