FUNCTION (Step)
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1358 ▶ |
| Object type | Methodology or model |
- “A function which ”has finite intervals of constancy separated by instantaneous jumps“ (W.R. ASHBY, 1960, p.87).
ASHBY gives some interesting examples:
- “1. The electric switch has an electrical resistance which remains constant except when it changes by a sudden jump.
…
- “3. If a piece of rubber is stretched, the pull it exerts is approximately proportional to its length. The constant of proportionality has a definite constant value unless the elastic is stretched so far that it breaks. When this happens the constant of proportionality suddenly becomes zero,i.e. it changes as a step function.
…
- “7. By quantum principles, many atomic and molecular variables change in step-function form” (p.89).
ASHBY concludes: “Any variable which acts only in ”all-or-none“ degree shows this form of behavior if each degree is sustained over a finite interval” (p.89).
This should be compared with THOM's elemental catastrophes.
However, as ASHBY himself points out, “…whether a variable of a real object behaves as a step-function cannot in general be decided until the details of the method of observation are specified” (p.90).
In other words, a variable may appear as varying continuously or step-wise according to the observation scale.
According to E.von GLASERSFELD, the step function corresponds to “… the unstable transition between two stable regions given the name of catastrophe by THOM. These appear to be reminiscent of the description of a step change function in ASHBY's homeostat and may represent for us the accomplishment of the all-important step function required by AHSBY for his model of a machine that was both stable and capable of learning” (1976, p.123).