Frank, Steve, My favored approach is to say that *space is like a manifold*. For me, space is a *thing* and a manifold is an *object*. The former I can experience free from my models of it, I can continue to learn facts(?) about space not derived by deduction alone (consider Nick's posts on inductive and abductive reasoning). I concede here that we talk about an objectified space, but I am not intending to. I am using the term space as a place- holder for the thing I am physically moving about in. OTOH manifolds are fully *objectified*, they exist by virtue of their formality. Any meaningful question *about a manifold* itself is derived deductively from its construction. Neither in their own right are metaphors, the metaphor is created when we treat space *as if it were* a manifold. Just my two cents.
At the beginning of MacLane's *Geometrical Mechanics,* (a book I have held many times, but never found an inexpensive copy to buy) MacLane opens his lecture's with '*The slogan is: Kinetic* *energy is a Riemann metric on configuration space*'. What a baller. Glen, I love that you mention the <placeholder>, ultimately reducing the argument to a *snowclone*. Because the title of the thread actually implicates a discussion of metaphor, and because I may have missed your point about *xyz,* please allow me this question. Do you feel that *snowclones* are necessarily templates for making metaphors, or do you feel that a snowclone is somehow different? Jon
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