© Copyright 1993 Mario Hilgemeier
What is the difference between a model and a metaphor? A metaphor carries meaning beyond the obvious, therefore a metaphor is more than a theory. A metaphor can be a kind of guiding principle for thought. One could explain a metaphor as a kind of high-level analogy. For instance, the Gleichniszahlenreihe can be seen as a curious mathematical object - as just another string-rewriting system. However, we have already seen some of its metaphorical qualities in the introduction. Here are some exemplary metaphorical meanings of the Gleichniszahlenreihe: - a metaphor for an iterated system producing a chaos of fractals - a mind looking at itself and bringing a "world with elements" into being - a meta-metaphor that shows what a metaphor is. A metaphor for a metaphor, for "jumping out of the system" and looking at it from the outside. - ... The title was intentionally set in quotes to be distinguished as an example (metaphor) for the view that there is something like a "world formula." Is it really possible to capture the phenomena of the physical and mental world in a finite set of mathematical models? The evidence of the last centuries looks promising. Scientific fields like celestial mechanics, quantum theory, genetics etc are good models in their domains. And I feel iterated systems (IS, fractals) to be a most promising candidate for what the Pythagoreans of today (physicists, geneticists and artificial intelligence researchers) are after, with some caveats described in the next sections.
Look again at figure 1. Is it possible to iterate the matrix in ways similar to figures 4 and 7? Which conceptual slippage  is needed for such an operation? Can semantic nets  be used for prediction or scenarios?next page content page
© Copyright 1993, Mario Hilgemeier, email: contact