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Not being a physicist I was wondering if there actually exist physical systems with equations which rely on lots of variables. Has anyone ever found anything like this? That is to say, found a joint system and set of descriptive equations such that the equations require at least, say, 10 independent variables? Or maybe some kind of proof that there will exist systems that cannot be described by less than a certain number of variables?

The counter-example he gave was of QTLs =. quantitative trait loci like height for example which are known to depend on lots of genes but no-one really knows how. But then dependency on lots of genes in an unknown manner might be funneled through some common mechanism such that the actual number of important variables is much smaller than expected.

Sorry if it's a bit philosophical...