The trial and error method leads to metasystem transitions.
Consider the beginnings of biological evolution. Molecular
formations in the "primordial soup" emerge, and after some time,
disintegrate. Some have very short lives; we say that they are
unstable. Others may survive for a very long time; they are
called stable. In terms of our metaphor, nature creates various
arrangements of molecules and tries them for stability. It keeps
stable ("right") combinations, and discards unstable ("wrong") ones.
As the primordial soup is cooking, various formations come
in close contacts with each other, which creates bigger formations.
The stability of these new formations depends on the arrangement
of their components.
Typically, for one stable arrangement there will be a big number
of unstable arrangements. Assuming a random nature of
collisions and contacts between components, we conclude that
the number of trials necessary in order to come to a stable
configuration must be comparable with the total numberN
of all arrangements.
This number grows fast with the numbernof components.
For an illustration assume that components form a chain,
and stability is achieved when they are arranged
in a certain order. Then the number of possible
arrangementsNwill ben!. Supposenis a small number,
say,5. ThenN=120. This is quite a reasonable
number of trials. Translating back from the metaphorical language
to an exact one, we note that the finding of a stable arrangement
means that a metasystem transition took place, with integration
of5components into a whole.
This is fine. But ifn=50, thenNis more than 1023.
To find a stable arrangement by random choice becomes hopeless
even for Mother Nature.
Still, not all is lost. Stable formations of sizenbecome
building blocks for further construction. When a small number --
let it be5again -- of these blocks get together, it will take
a reasonable number120of arrangements to try; a new level of
a structural hierarchy emerges.
This mechanism works on all levels. In parallel with structural,
a control hierarchy grows up. Controlling factor is just the
laws of physics, but acting in various roles and leading to
various consequences. In particular, it may keep the numbern
of integrated blocks fixed, or allow integration of unlimited
number of similar blocks; the latter leads to
the branching growth of the penultimate
MST is a necessary step of evolution, both
biological and cultural; this is just a fact of combinatorics.
Evolution proceeds by random trial (spontaneous arrangement of
some building blocks) and error (elimination of unstable arrangements)
with an occasional hit: emergence of successful (stable) formation.
When nature or man tries this game with the number of blocks
greater than a few, the probability of a hit is practically
zero. But the divide-and-conquer method may work: choose among
arrangements of only a small number of blocks, and if the resulting
formation is stable enough, make an MST: use it as a new block
for the next structural level of the system. (see the Principle of Recursive Systems Construction)