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Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that…
Michael Dickmann: Here's what the story is. There was this little tadpole and a fish that grew up in a pond, and they were always intensely curious about life outside the pond. And then, eventually, the tadpole grows into a frog and discovers that, because he's an amphibian, he can go out and see what life is like. So…
An early classic experiment by the Nobel Prize-winning embryologist Roger Sperry illustrates the principle perfectly. Sperry and a colleague took a tadpole and removed a tiny square of skin from the back. They removed another square, the same size, from the belly. They then regrafted the two squares, but each in the…