Monday, 10 September 2007

Boundary Puzzles

Imagine ourselves traveling from Maryland to Pennsylvania. What happens as we cross the Mason-Dixon line? Do we pass through a last point p in Maryland and a first point q in Pennsylvania?

Consider Aristotle's own riddle about motion: At the instant when an object stops moving, is it in motion or is it at rest?

Or consider the dilemma raised by Leonardo in his Notebooks: What is it that divides the atmosphere from the water? Is it air or is it water?

Or, again, consider Peirce's puzzle: What color is the line of demarcation between a black spot and its white background?

When exactly did the industrial revolution begin? When did it end? (Where did it take place?)

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