Nine out of ten kids come home from a baseball game having seen their favorite
player win the game with a home run, and want to play baseball and make
spectacular plays. The tenth kid is instead inspired to do a brilliant
science fair project: "Excel at what you love, do best, and are expected to
do."
(The kid wins the prize at the science fair, and the teacher says, "You really
hit a home run with that one.")
The kid has done analogical quadrature, mapping the relation between the
baseball player and his on-field expertise in a deeper way than the other
kids did.
In AQ, the idea is to construct a mapping or transformation so that A does B
can be mapped into C does D, typically starting with A, B, and C and finding
D. Once done, there is a clear analogy (as pointed out by the teacher)
between B and D.
A blend is more like designing a helicopter by combining a dragonfly and a
car. You take the general shape and behavior of the dragonfly, and the size,
interior seats, driver controls, etc, from a car.
In general in a blend you start with B and C without an A. Both relations B->D
and C->D are analogies, mappings from one concept to another. (You could, if
you wanted, complete the square ("quadrature") and find an A -- but it's
typically the opposite of what you want. In the example you'd get a beetle,
with the size and provenance of the dragonfly and the shape and behavior of
the car!)
The key to either of these is finding the right mapping(s). I claim that
virtually all of intelligence consists of finding useful mappings. Feynman
put it, "The glory of science is that we can find a way to think such that
the law is *evident*."
Josh
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