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One can easily embed R into R^N with a dense image, so it's straightforward to see that one parameter is always enough. In the case of computable reals (which c
by madez 8y ago
One can easily embed R into R^N with a dense image, so it's straightforward to see that one parameter is always enough. In the case of computable reals (which contain everything we deal with when doing things numerically), the embedding is even bijective. This completely misses the point, though, because the "natural" number of parameters is important in understanding reality.
- laretluval 8y agoHow do you determine the natural number of parameters?
- madez 8y agoThat is generally an unsolved problem, and highly specific to the situation. Even the interpretation of the question depends on the context. To read more about it, I would look under the term "System Identification" and "Mathematical Modelling", but I might have different contexts in mind that you.