Is Einstein's geodesic a metaphor or an idiom?
I am applying semantic theory to physical theory to bridge the two realities and have found the discussion on metaphor and odium illuminates this purpose.
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An idiom is a lexical and/or syntactic fixed phrase that does not work like normal phrases, and does not mean what it looks like it should mean. For example, no buckets, books, or hands are involved in these examples:
Any fixed phrase, or construction like let alone, is an idiom. Note that this describes the form of an idiom, not its meaning. And the meanings are almost always very metaphoric.
There are no books necessarily involved in making book, but there is a careful record of the bettors, like a book. There are no hands necessarily involved in giving me a hand, but they might be involved, and they function as a metaphor of human activity.
Returning to Einstein's geodesic, first one has to decide whether mathematics is composed of metaphors, or not. My own take is that any idea that exists only in human minds is much more likely to be metaphoric than not. Since math has its own communicational systems, it's hard to say that any given chunk of it is idiomatic, because it's not language. But math can certainly be metaphoric, especially since most of our thought is metaphors.