Metaphor as Map

If a metaphor is a mapping from one conceptual domain to another, what are its properties?  In mathematics, the most interesting mappings are those in which preserve some structure, for example algebraic or differential structure.  Lakoff and Johnson haven't discussed this sort of mathematical notion - yet in the book anyway - but I suspect similar notions underlie our use of metaphor.

Conceptual understanding is clearly a critical element of thought, and not surprisingly, it is tightly wrapped with metaphor.  One metaphor is seeing is understanding.  We often use the verbs interchangeably.  Here we are mapping the conceptual domain into the physical sense of sight.  Some properties of sight are faithfully replicated in the metaphor: seeing clearly, for example, means being able to distinguish and identify the parts of an image, and conceptual understanding is strongly analogous.  Other related visual metaphors abound - a "foggy memory" for example.  Clearly the mapping is not one to one - some visual concepts are rarely found relevant, like color.

Of course the very word "understand" is itself a metaphor, with the root meaning of "standing in the midst of" (rather than physically under).  Another synonym is "grasp" a mapping on to the physical acting of holding something in one's hand.  Here again, the sensory-motor associations are clear.  Add the word "comprehend" to the list.  One of its original Latin meanings (hold tightly) has been lost, but the other one that we use survives.


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