RANDOMNESS (Constrained)
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2720 ▶ |
| Object type | General information |
The limitation in randomness which results from the scaling process.
The scaling process defines more and more precise limits for the possible position of any structural element in a system (which may be for example the bronchioles in the lung, or a fine detail in the representation of the WEIERSTRASS function).
At any level, it is still impossible to exactly pinpoint the position of the element. In other words, randomness never disappears completely, but can be evermore reduced in space as well as in time.
This gives a firm base to the concept of ergodic relation.
From the viewpoint of the WEIERSTRASS function, the remaining randomness at any level corresponds to the imposibility to differenciate the function at any time.
It should however be noted that this randomness constrained by scaling excludes the case of giant fluctuations in systems far away from equilibrium (or possibly, such giant fluctuations do manifest the emergence of scaling at a higher level).