Choice of Model and Method

Most mathematical processes are suitable for describing the system on a scale and for observing effects on other scales as disruptions. We can compare this approach with a look through a microscope – it shows details at a certain scale of length, e.g., 1 micron. Markedly smaller distances / spaces / gaps cannot be closed and we loose sight of markedly larger structures.

Here's an example from IT. If we're interested in effects that occur on a time-scale of one second (performance, response times), then fluctuations on a much shorter scale (milliseconds) are described approximately as a weak rustling or are completely ignored and fluctuations on a greater scale as (quasi) stationary. When investigating and comparing SAP systems, on the other hand, it is important to look at all scales in the same way.

There are few mathematical models capable of describing complex systems with sufficient precision in which differing scales play a fundamental role. In theoretical physics, one conventional group of methods, of which there are many variations and which is applied to different problems, are re-standardization / renormalization processes.

Some examples of the use of re-standardization / renormalization processes in other fields than IT are (this is not a representative selection):

Critical Phenomena and Phase Transitions. See e.g. Ken Wilson, Nobel Prize 1982
(http://www.nobelprize.org/physics/laureates/1982/press.html)

Elementary Particles – see e.g. Gerardus t'Hooft, Martinus Veltman, Nobel Prize 1999
(http://www.nobelprize.org/physics/laureates/1999/press.html)

Disorder? (Chaos?) and Localization – see e.g. Franz Wegner, Max Planck-Medal 1986
(http://www.thphys.uni-heidelberg.de/home/info/preise_dir/wegner_MP.d.html)