Generality?

睡前聽聰明昨天的雜談，哭了一點。Computer Science 現在根本無法和 Mathematics、Physics、Biology 等研究自然的科學比「美」。聰明說著說著，數學那統和單純的優美華麗，CS 目前的理論難以望其項背。當然，要讓任何一門學問的美感勝過 Mathematics 是極端艱鉅的任務：To challenge Mathematics (or Physics or Biology or...) is to challenge the "background structure" created by God. 此處先天就有個極大的限制條件：無論我們如何努力地讓抽象層級提升，實作、甚至思想上，我們都無可避免受限於這個 "background structure"，e.g. we can hardly imagine a 4-dim or 5-dim space, or 2-dim time, or a world in which 1 plus 1 gives 3. Gauss' Divergence Theorem can be (maybe deceptively) easily extended to n-dim spaces, but Stokes' Curl Theorem can't. The latter is inherently 3-dim. Is it possible for us to escape from the "background structure" (if we can be sure that we have completely escaped from it) and reach the highest level of abstraction (if we can be sure that we are absolutely at the highest level)? Horribly hard.

Why thinking about "escaping from the 'background structure' ?" Because we don't know whether this "background structure" is unique & universal. In effect, we are simply guessing everything, and luckily the guesses seem right. We cannot even prove the guesses by logic, which itself is also unprovable.

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A famous movie trilogy refers to the "background structure" as "the Matrix," and of course, the concept in the movies is much simpler.