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The laws of nature are but the mathematical thoughts of God.

  • -- Euclid 欧几里得

自然法则不过是上帝的数学思想。

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Mathematical Thoughts

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If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

如果真的如希尔伯特所言，数学是一场毫无意义的游戏，在纸上做着毫无意义的标记，那么我们唯一可以参考的数学经验就是在纸上做标记。

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Using a dog as a narrator has limitations and it has advantages. The limitations are that a dog cannot speak. A dog has no thumbs. A dog can't communicate his thoughts except with gestures.

用狗做叙述者有其局限性，但也有其优势。限制是狗不能说话。狗没有大拇指。狗只能用手势来表达思想。

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A pure mathematical series would be one in which each term is derived from the preceding term by a rule.

一个纯数学级数应该是一个每一项都由前一项根据规则推导出来的级数。

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How utterly are one's best thoughts invaded by this going out in society.

一个人的最好的思想是如何完全地被这个社会所侵入。

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