"It isn't a circle--it is simply a long line--as in geometry, you know, one that reaches into infinity. And because we cannot see the end--we also cannot see how it changes. And it is very odd by those who see the changes--who dream, who will not give up--are called idealists...and those who see only the circle we call them the "realists"!"

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Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But in order that this work merit the name of Geometry, it is necessary that these hypotheses or postulates express the result of the more simple and elementary observations of physical figures.

— Giuseppe Peano