Indeed, whereas two analogous objects are structurally the same, a metaphor is like a projection onto a lower dimensional space, because there is a loss of certain qualities when the mapping takes place. A metaphor relates a literal thing to an abstraction. For example, the dot product between 2 vectors gives a scalar. It is a mapping from R^2 to the real line, whereas a matrix preserves dimension.

“Indeed, whereas two analogous objects are structurally the same, a metaphor is like a projection onto a lower dimensional space, because there is a loss of certain qualities when the mapping takes place. A metaphor relates a literal thing to an abstraction. For example, the dot product between 2 vectors gives a scalar. It is a mapping from R^2 to the real line, whereas a matrix preserves dimension.” – Narek

Ooh, oh I really really like that.
I’d never thought of a metaphor as a projection onto a lower-dimensional space; because of the loss of qualities… I always thought of it in terms of choosing certain qualities and ignoring others; but yes, that amounts to a pruning of qualities and a pruning is a loss of qualities… I just didn’t finish thinking of the consequences

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