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© Copyright 1993 Mario Hilgemeier

Models and Metaphors

      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.

Stop and Think

      Look again at figure 1. Is it possible to iterate the matrix 
in ways similar to figures 4 and 7? Which conceptual slippage [16] 
is needed for such an operation? Can semantic nets [15] be used for 
prediction or scenarios?

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