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整理图书,又看到那本8开的Escher版画集,收图29幅,都配有作者的解说。这回才注意到,原来那幅著名的《瀑布》,是根据彭罗斯的“不可能三角形”(tribar)画的——而老彭的那个图,却是受了Escher的启发——老彭在接受媒体采访时,回忆了那段故事:
When I was in Cambridge reading mathematics, I went to Amsterdam for the International Mathematics Congress. There I saw M.C. Escher's fascinating work. That inspired me to try my hand at drawing such impossibilities. The result was the 'impossible triangle', which looks three-dimensional, but actually it is not. My father saw it and made some other stuff. We published a paper on all that acknowledging Escher. He, in turn, drew upon the impossible triangle to create the 'Waterfall', and an impossible staircase made by my father to create 'Ascending and Descending' - monks ascending and descending a staircase.
Escher也引用了老彭父子发表在The British Journal of Psychology (Vol.49, part 1, Feb. 1958) 的的文字:
Here is a perspective drawing, each part of which is accepted as representing a three-dimensional, rectangular structure. The lines of the drawing are, however, connected in such a manner as to reproduce an impossibility. As the eye pursues lines of the figure, sudden changes in the interpretation of distance of the object from the observer are necessary.
老彭从小就对“不可能”的东西感兴趣。假如有什么东西看似不可能,那一定有更深层的东西。I have certainly enjoyed puzzles since an early age and things that look like impossible things are often particularly intriguing. You see something in the real world that gives the appearance of being impossible, yet it has to be a possible because it is in the real world. Quantum mechanics is a good example where you see things that are intriguingly, seemingly impossible. 现实世界里看似不可能的东西一定是可能的——因为它已经在了。这一点,有点儿像我前些天引用的Dawkins的magic of reality,而且是诗意的那种,甚至还带点儿“禅意”。
这个三维的不可能在高维空间是不是可能呢?如果是,那个瀑布会不会成为一个永动机?那么,我们的物理法则是不是还可能?
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