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.
WOB in CA
Allometric law in
cancer
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