By Martin Gardner
Aha! perception demanding situations the reader's reasoning strength and instinct whereas encouraging the improvement of 'aha! reactions'.
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Extra resources for Aha! Insight
The earliest reference known is a book published in China in 1803. Its title, The Collected Volume ofPatterns of the Seven-Piece Puzzle, suggests earlier books. Most scholars believe the game originated in China about 1800, became an Oriental craze, and then spread rapidly to the West. The earliest Western books, says Read, were little more than copies of Chinese rice-paper booklets. The Western books even copied errors in the Chinese illustrations. One of the earliest English books on tangrams, originally owned by Charles Lutwidge Dodgson (better known as Lewis Carroll), came into Dudeney's possession.
The top row shows that a third of the voters prefer candidates A, B, and C in the order ABC. The middle row shows that another third rank them BCA, and the bottom row shows that the remaining third rank them CAB. Examine the matrix carefully NONTRANSITIVE PARADOXES 1 RANK ORDER 2 57 3 Figure 26 T h e voting paradox (left) and the tournament paradox based on the magic square (right) and you will find that when candidates are ranked in pairs, nontransitivity rears its head. Two-thirds of the voters prefer A to B, two-thirds prefer B to C, and two-thirds prefer C to A.
Many books, and even a few encyclopedias, declare that tangram play is about 4000 years old. In my Scientijc American column for September 1959, I called tangrams the oldest of dissection games and said that the Chinese had been amusing themselves with it for several thousand years. This is totally wrong. The man responsible for the myth is none other than Sam Loyd. In 1903, when Loyd was sixty-one and at the height of his fame, he published a little book (now extremely rare) called The Eighth Book ofTan.
Aha! Insight by Martin Gardner