在去年的《 关于标准化，答一方水 》一文中，我介绍了我关于离散化与系统发展关系的思想，大意是：稳定而复杂的系统得以建立的前提是，其构成元素的离散化（或曰数字化）。当时我列举了元素、分子、基因、生物体、音乐、语言、文字、期货等等例子。刚刚看到Steven Pinker在The Language Instinct中表达了类似的意思，他把基于离散化元素的系统叫做“离散组合系统”（discrete combinatorial system），把与此相对的系统叫做blending system（我想把它翻译成“掺和系统”或“烂泥系统”），以下摘自该书第4章How Language Works： The principle underlying grammar is unusual in the natural world. A grammar is an example of a "discrete combinatorial system." A finite number of discrete elements (in this case, words) are sampled, combined, and permuted to create larger structures (in this case, sentences) with properties that are quite distinct from those of their elements. For example, the meaning of Man bites dog is different from the meaning of any of the three words inside it, and different from the meaning of the same words combined in the reverse order. In a discrete combinatorial system like language, there can be an unlimited number of completely distinct combinations with an infinite range of properties. Another noteworthy discrete combinatorial system in the natural world is the genetic code in DNA, where four kinds of nucleotides are combined into sixty-four kinds of codons, and the codons can be strung into an unlimited number of different genes. Many biologists have capitalized on the close parallel between the principles of grammatical combination and the principles of genetic combination. In the technical language of genetics, sequences of DNA are said to contain "letters" and "punctuation"; may be "palindromic," "meaningless," or "synonymous"; are "transcribed" and "translated"; and are even stored in "libraries." The immunologist Niels Jerne entitled his Nobel Prize address "The Generative Grammar of the Immune System." Most of the complicated systems we see in the world, in contrast, are blending systems, like geology, paint mixing, cooking, sound, light, and weather. In a blending system the properties of the combination lie between the properties of its elements, and the properties of the elements are lost in the average or mixture. For example, combining red paint and white paint results in pink paint. Thus the range of properties that can be found in a blending system are highly circumscribed, and the only way to differentiate large numbers of combinations is to discriminate tinier and tinier differences. It may not be a coincidence that the two systems in the universe that most impress us with their open-ended complex design—life and mind—are based on discrete combinatorial systems. Many biologists believe that if inheritance were not discrete, evolution as we know it could not have taken place. 这一思想虽然萌生已久，但始终感觉不够成熟，需要继续发酵，所以一直没单独成文，下面是一段我向朋友鼓吹该思想的聊天记录： (2008-06-13) 23:38  辉格  z3  我前段时间在考虑一个新的问题 23:46  z3  辉格  哦，什么问题？ 23:53  辉格  z3  符号化，或者叫数字化 24:44  辉格  z3  我发现进化过程中 26:11  辉格  z3  每一次的系统跃迁，就是从下层系统发展出上层系统时，有个前提 26:20  辉格  z3  就是下层元素的数字化 26:31  z3  辉格  需要个例子说明一下。 26:42  辉格  z3  比如音乐 26:56  辉格  z3  音节、音素是下层结构 27:23  辉格  z3  要进化出复杂的乐曲， 27:33  辉格  z3  必须先有音阶 27:42  辉格  z3  音阶就是数字化的音素 27:57  辉格  z3  文字也是 28:06  辉格  z3  没有数字化之前是图画文字 28:09  z3  辉格  数字化是概念化的过程。降低复杂性。 28:27  辉格  z3  图画文字不可能产生复杂文学作品 28:33  z3  辉格  恩 28:34  z3  辉格  对头 28:37  辉格  z3  必须先有字母表 28:43  辉格  z3  就是数字化 28:48  辉格  z3  基因也是 29:06  辉格  z3  四种碱基对就是四个字母 29:09  辉格  z3  数字化了 29:15  z3  辉格  对。没有数字化无法进化。 29:25  辉格  z3  然后是64种氨基酸 29:39  辉格  z3  这是小分子层面的数字化 29:43  辉格  z3  然后是基因 29:44  z3  辉格  没准兔子传四代就变成老虎了，这就没法搞了。呵呵。 29:49  辉格  z3  对 30:07  辉格  z3  文化也是如此 30:24  辉格  z3  传说故事中的英雄人物 30:31  辉格  z3  或者小丑 30:35  辉格  z3  都是脸谱化的 30:47  辉格  z3  否则文学结构无法建构 30:53  z3  辉格  呵呵。要不然没法承载概念了。 30:57  辉格  z3  对 31:09  辉格  z3  符号化过程无处不在 31:22  辉格  z3  是每一次系统迁跃的前提 31:41  辉格  z3  这一层符号化了，就有可能向上一层迁跃 31:57  辉格  z3  否则基础就是松软的 32:09  辉格  z3  任何结构都会垮掉 32:14  辉格  z3  维持不久 32:26  z3  辉格  我曾经想过把那个变形虫的核心概念用基因的方式表达。 32:33  辉格  z3  嗯 32:35  z3  辉格  而不是继承。 32:37  辉格  z3  机械发展也是 32:58  辉格  z3  标准件通用件就是符合化或者说数字化的 33:13  z3  辉格  我觉得还是信息处理的问题。 33:26  辉格  z3  对， 33:33  辉格  z3  数字化有两个含义： 33:38  辉格  z3  1）离散化， 33:46  辉格  z3  2）有限小集合 33:54  z3  辉格  恩。 34:10  辉格  z3  离散化是指各离散值之间高容错性 34:10  z3  辉格  无限集合是上帝他老人家的地盘。 34:24  辉格  z3  高容错性保证了复制不会失真 34:38  z3  辉格  恩。 34:44  辉格  z3  第二是小集合 35:10  辉格  z3  我在想代码如何符合这样的条件？ 35:13  z3  辉格  智能的极限。 35:35  z3  辉格  再高的智能也只能处理很小的集合。 35:43  辉格  z3  是的 36:03  辉格  z3  大脑某些缓存区很小 …… 40:17  辉格  z3  财报把上市公司的表现符号化了 40:39  辉格  z3  否则大规模交易不大可能 40:46  z3  辉格  恩。 40:55  辉格  z3  期货市场也是 41:01  z3  辉格  简化。要不然就要学很多门行业。 41:02  辉格  z3  标准期货合约 41:31  辉格  z3  还有贸易合约 41:46  辉格  z3  什么CIS、FOB ……