Allometric law an the NKS
Three kinds of complex systems were introduced in the previous section:
1. The whole is the sum of its parts. (Reductionism)
2. The whole is more than the sum of its parts (Aristotle)
3. The whole controls its parts. (Life) These 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].
The three types may be regarded as stages in the evolution of scientific discourse, aimed at understanding reality.
1. Atom and force are the basic concepts of Cartesian
reductionism according to which the whole is the sum of its atoms whose
properties are the same as that of the whole. The same applies to force
of the whole which is the sum of the forces of its parts. Essentially,
chemistry is reducible to physics, and biology is reducible to chemistry
However in the real world this simple relationship does not hold.
Galileo discovered the law of Free Fall, according to which acceleration of gravity g equals 9.8 m/s2 and is the same for all bodies. Yet daily experience teaches that the free fall of bodies varies. Galileo’s laws ignore the context in which they are applied. The context “distorts” (perturbs) the observed law randomly, and the deviation of the observed from the postulated is regarded as an error. The error may be reduced by repeating the experiment many times, whereupon measurements will approach the “true” limit postulated by the Law. This is the essence of the reasoning of physics. Its metaphysics was laid down by Plato. Laws inhabit the realm of ideas and represent the reality while the observed phenomena are distorted.
2. Aristotle realized the whole is more than the sum of its parts. The behavior of objects can be attributed to four kinds of explanation, which Aristotle called causes.
During the 19th century physical laws where applied to bio-medical reasoning introducing the error concept (or randomness) to medicine. Disease is defined as an error while the normal is health. This notion is highlighted by the Genetic fatalism. Genes are the blueprint of our healthy organism and when they mutate (change) we are sick. The task of the physician is to repair bad genes or even replace them.
Soon it became evident that many people with mutated genes are actually healthy. In order to save the reductionist view of disease geneticists conjured new genetic terms, and theories which explain why some people with mutated genes are healthy. They are discussed elsewhere
Geneticists fail to realize that the context in which
they observe disease cannot be ignored anymore. The context is our organism
in its entire complexity, and it cannot be reduced, or simplified like
it is done in physics. The organism may make us sick with “good” genes
and keeps us healthy with mutated genes.
3. Since the organism as a whole controls its parts new mathematical tools are needed in order to untangle its sophistication. All the nice mathematical tools applied in physics are of little help since they were designed to handle isolated and ideal situations devoid of any context, while processes in the organism are neither isolated, nor ideal and above all their context cannot be ignored anymore.
Cellular automata are the first step in the new direction. The main NKS message is that the iteration of simple CA may create any desired complexity. Which is still a reductionist approach. Yet this it not enough . Above all we need tools to simplify complexity without losing its essence which ought to be Wolfram’s concern. Twenty years ago he created the Mathematica package in order to explore the NKS ideas. Time has come for a new kind of Mathematica software, which will enable the end user to simplify complexity without losing its essence.
His name of the game is symbolic computing, which served for creating Mathematica. Why not start the computing from complex blobs obeying the allometric law, and simplify them more and more . . . ?
The allometric law points to a new era in science and philosophy. Cartesian reduction is dead, long live phenomenology.