Leibniz

顯然 Leibniz 也是個 computer scientist！請看聰明的文章（ext-link）：

他在 1666 年（當時 20 歲）寫出《組合學的藝術》（Art of combinatorics）之論文。在前言中他預測這門新知識可以延拓應用到邏輯、歷史、倫理學、形上學，乃至整個科學。他又說：

假設我們可以用一些基本的字來表達人類的思想，因此可以想像有一系列的字，各代表了簡單的概念，那麼任何複雜的概念都可以用這些字組合起來。從而奇妙的「發明術」（the Art of invention）就變成可能了：即所有可能的概念與命題都可以機械地產生。據此我們不但可以探討已知，而且也可以追尋未知，進一步從事更深刻的研究。

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Leibniz 也夢想著要建立一套普遍的數學，他稱之為「Characteristica Universalis」，使得思想也可以化約成計算。他解釋說：

如果有了這樣的數學，那麼我們探討形上學與道德規範時，就可以如同幾何學與分析學之論證推理一般。兩個哲學家萬一發生意見衝突，他們的爭吵就不會嚴重過兩個會計員，這時只需拿起筆，平心靜氣地坐下來，然後互相說（必要的話可找個證人）：讓我們計算一下。

Leibniz 對於發明術一直深感興趣，他說：

沒有什麼東西比看出發明的根源更重要，我認為這比發明出來的東西更有趣。

他計劃寫一本書來探討發明術，可惜從未實現。發明術也許只是人類永遠無法實現的一個夢想…

上面的描述完美呼應 Knuth 在 DDJ interview 時所講的這段：

There were computers in the 19th century, the 17th century... I imagine there are computer scientists in the pygmy forest. I haven’t really carried this out as an experiment, but I imagine that people may not have machines but one in fifty of them, wherever you go, has this profile, this ability. I’m not a sociologist, nor an anthropologist, but reading publications, reading literature, I can sense how much people think like I do, even if they were writing from a different century.

我最想做的事情幾乎就是 Leibniz 的夢想了。當然，在二十世紀數學與邏輯的發展下，我們發現通往這個夢想的路困難重重、荊棘遍佈，幾乎令人絕望。其實我不敢相信這樣的一條路存在，只能「希望」它存在 XD。

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難怪 Gödel 要崇拜 Leibniz XD。

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補充另一個例子。這次是 Robert E. Tarjan 的 ACM Turing Award Lecture 裡面的一段：

I graduated from CalTech in June 1969 with a B.S. in mathematics, determined to pursue a Ph.D., but undecided about whether it should be in mathematics or computer science. I finally decided in favor of computer science and enrolled as a graduate student at Stanford in the fall. I thought that as a computer scientist I could use my mathematical skills to solve problems of more immediate practical interest than the problems posed in pure mathematics. I hoped to do research in artificial intelligence, since I wished to understand the way reasoning, or at least mathematical reasoning, works. But my course adviser at Stanford was Don Knnth, and I think he had other plans for my future: His first advice to me was to read Volume 1 of his book, The Art of Computer Programming.

當然我不知道 Knuth 拿 TAOCP 給 Tarjan 看的動機是什麼，不過應該是因為這樣，使得後來 Tarjan 做的工作和他踏入 CS 的初衷之間有點距離 XD。