Formal or mathematical models can be continuous or discrete. Historically, continuous models based on differential equations have been the accepted methodology for modelizing in science.
However, since the development of digital computing, "discrete models are influencing our conception of real world systems and the role classical mathematical methods are to play in modelling them" and: "In many applications of these discrete concepts the availability of theoretical results is replaced by the computational power of digital computers" (A.G. BARTO, 1978, or in G. KLIR (ed), 1991.p. 377).
Computers, becoming a kind of experimental laboratory tool, and being digital, offer (and require) a new class of models, frequently called "simulations". This offers at the same time, new variety and new constraints to modelization. BARTO, after a careful discussion, concludes that: "… computational power alone is not a substitute for the careful simplification and theoretical generalization that have helped make classical methods so fruitful" (p.395).
This clearly is a more polite, but still powerful caveat carrying the same meaning as the famous "Garbage in, garbage out".
In any case, both type of models are useful in their own right. Neither, however, tell us the ultimate "truth" about reality.
It is also possible that connection machines will introduce still another type of models in the future.
- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented
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: