有人說，實際是理論的延伸；也有人認為，理論是實際的抽象表達。那些聰明又有名氣的思想家，不管是支持哪一種論點，都能產生許多「有用」或「影響深遠」的思想或學說。而自己工作了這些年，卻只有一些不成熟的經驗：理論與實際雖然在許多「概念層次」的地方很相似，但是在許多「現實層次」上的建議卻常有衝突。
這完全是現實社會的成本考量嗎？似乎也不是如此。有時，對於實際很重要的許多性質（例如「軟體品質」、或者資訊檢索中的「相關概念」），似乎連理論都難以界定清楚。
在一本關於 "Distributed Systems" 的書上看到右上方的這張圖。很喜歡它對「當理論遇上實際」的描繪。藝術作品就是這樣，對現實常有詼諧幽默的表達，富有詩意，又餘味盎然。
..... in 1686 ..... Leibniz's philosophical essay ..... Discourse on Metaphysics, where Leibniz discusses how we can distinguish between facts that follow a law, and lawless, irregular, chaotic facts. How can we do this? Leibniz's idea is very simple and very profound. It's in section VI of the Discours. It's the observation that the concept of law becomes vacuous if arbitrarily high mathematical complexity is permitted, for then there is always a law. Conversely, if the law has to be extremely complicated, then the data is irregular, lawless, random, unstructured, patternless, and also compressible and irreducible. A theory has to be simpler than the data that it explains, otherwise it doesn't explain anything. ..... Here is the basic insight, the basic model. It's a software view of science: A scientific theory is a computer program that computes our observations, the experimental data. And these are our two fundamental principles, originallydue to William of Occam and to Leibniz: The simplest theory is best (Occam's razor). This means that the smallest program that calculates the observations is the best theory. Furthermore, if a theory is the same size in bits as the data it explains, then it's worthless, because there is always such a theory (Leibniz).
回覆刪除摘錄自Irreducible Complexity in Pure Mathematics by Gregory Chaitin
印象中，irreducible complexity 和 Kolmogorov complexity 似乎很類似...
回覆刪除只是想拿Leibniz的想法當"散文"看看, 又因為偷懶, 所以借Chaitin的東西來引述. 並沒有在意(也沒有能力)區隔Chaitin和Kolmogorov的complexity measures有何異同 ..... 唉唉 ..... 學長總是能教人用功.....
回覆刪除哎哎哎～不要這樣說啦。
回覆刪除我對 irreducible complexity 與 Kolmogorov complexity 都沒有什麼了解的。
應該說，是 Ankh 自己對於這些理論的東西，一直保有好奇的求知心吧 :)