Principia Cybernetica Web

Trial-and-error in a Metasystem Transition

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 level.

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)

Copyright© 1999 Principia Cybernetica - Referencing this page

V. Turchin,

Aug 6, 1999


Metasystem Transition Theory

The Metasystem Transition

Prev. Next


Add comment...