BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

FUNCTION (Step) 2)

← Back

"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).

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

We thank the following partners for making the open access of this volume possible:

© 2020 BCSSS Contact/Imprint