Metaphors

One of my college math professors encouraged us to find ways in which we could use mathematical ideas as metaphors for aspects of our lives. In his case, he used changes of basis in a vector space as a metaphor for how useful it can be to change one’s point of view on things. “You can change the world by changing how people look at it”, he said.

I think that finding connections between different ideas and experiences can be an entertaining and useful exercise, regardless of where they come from.  Sometimes the metaphors are insightful, sometimes they break down when stretched too far, but as long as we are aware of their limitations there can be value in these mental games.  I recall another professor telling me that much of science develops by analogies, and some (for instance, Douglas Hofstadter) would go further and say that most reasoning is analogy-making.

Thinking and working accross disciplines should often be very fruitful.  By stepping outside of one’s field one can gain new inspirations, insights and ideas.  Of course, there are dangers of doing this: if we go to far as to assert that “A=B” (rather than “A is like B”), we can end up in a mental confusion (I have known people that assert a connection between quantum mechanics, “collective consciousness”, and their past lives).

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