[randcraw]

I disagree. Many problem spaces are not continuous and can involve incomplete information that make a continuous model like a curve useless.

For instance, a linguistic model that lacks definitions for some words, or which allows too much ambiguity can leave sentences unparsable or uninterpretable. Disruptions to word order in sentences can lose sufficient information that no curve or fitment can recover it. A curve has to capture sufficient information for fitting it to be useful. I think not all concepts or relations are amenable to N-dimensional cartesian representation. (Though I'd like to see a reference confirming this.)

And hidden interdependence between dimensions can make any curve drawn in that coordinate space a misrepresentation of the actual info space, and any curve fit in it, dysfunctional.

Any mapping of info onto a cartesian coordinate space presumes constraints that limit the utility of any function that across that space. So no curve is guaranteed to be meaningful in "the real world" unless those assumptions are conserved upon reentry from the abstract world.

George Box's "All models are wrong, but some are useful" suggests that while fitting curves in wrong models may be possible, it well may be form without function.