There is a big difference between what mathematicians call a fallacy and what they call a paradox. A fallacy is a flawed proof, such as the “proof” on page fifty-four of the book under review, that all triangles are isosceles. A paradox is an assertion almost impossible to believe but nevertheless true. A good example is the famous twin paradox of relativity. If one twin travels a long distance from the earth, at a fast speed, then returns, she’ll be younger than her stay-at-home sister. The time difference can be arbitrarily large. If the traveling twin goes to a distant galaxy at a velocity near that of light, then returns, thousands of earth years could have gone by. Time travel into the far future (not into the past) is a genuine possibility!

The twin paradox, which incidentally has been empirically confirmed, is not hard to comprehend if one is familiar with the time dilation of relativity theory. Far more...


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