René Descartes is remembered as the prototypical dualist, proposing two substances or domains of existence: res extensa (stuff in space), and res cogitans (the stuff of thought/imagination/experience): matter and mind. Despite rejecting dualism, our culture is deeply cartesian.
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@Plinz Have you looked into the wirk of @stephen_wolfram ? IMO formalising "functional space" may give physics a method to describe the triplet of space-time-function. Functions certainly seem to be their own "thing" in the same way space and time are "things".