从迭代到人类语言

迭代不只是程序的表达方式,有人认为这也是人类思考的基本形式. 讲编译原理都要提到乔木斯基文法:

Grammar Languages Automaton Production rules (constraints) Type-0 Recursively enumerable Turing machine (no restrictions) Type-1 Context-sensitive Linear-bounded non-deterministic Turing machine Type-2 Context-free Non-deterministic pushdown automaton Type-3 Regular Finite state automaton
and

0型语言是限定条件最少的语言, 也是最基本的语言, 其他类型的语言都是他的子集.

乔木斯基认为迭代(recursive)也是人类语言的基本特征之一.(不清楚乔木斯基文法有没有包括人类语言),比如:
    我是一只大灰狼
    我认为我是一只大灰狼
"我是一只大灰狼"这个句子是第二个句子的一部分(我在这里终于明白0型文法的含义了 :)).

没有迭代特性的语言就只能表达有限的信息.

赢得诺贝尔经济学奖的Herbert Simon在1962年的文章<The Architecture of Complexity>也指出迭代的结构是信息处理的基本结构, 当然包括语言的处理. 计数就是一种迭代: 1, 2,...n...

或许所有人类思考的有迭代的特性, 但并不是所有的语言都有迭代的特性. Daniel L. Everett 讲了这个. 他发现了一个没有迭代特性的语言: 亚马逊森林中Pirahã人的语言.他举了个例子,  我们表达:
    张三的弟弟有座的房子  
但这个特殊的人群说:
    张三有一个弟弟, 他弟弟有个房子
这个语言系统也确实没有计数的表达.

Pirahã人相信他们经验世界的事情: 拿出证据来.比如作者曾给他们讲圣经的故事, 但似乎对那些人没有什么影响. 终于有个Pirahã人点破了他: "耶酥是什么颜色的? 他有多高?他什么时候告诉你这些事情的?.." 作者当然不知道. Pirahã人回答他: 那你为什么告诉我们这个?(真是实事求是!) 一个第一次座飞机的piraha人对飞机, 对天空也没有什么觉得新奇的, 那不是他兴趣内的世界.

不由得惊叹世界真是无奇不有:  因为我们不认识, 所以觉得奇怪.

也可以看出这群人生活的很孤立, 并且很难自己发展, 也不能接受外界的输入, 不说会没落, 他们至少无法走出亚马逊. 一个和外界有交流, 有扩展能力的系统才能发展.

但这些人有传说中的隐士的味道: 不为外物所动. 也许, 那就是他们的幸福所在吧. 希望地震中的同胞能更多的被拯救出来, 享受他们的幸福.




全文在这里:RECURSION AND HUMAN THOUGHT: WHY THE PIRAHÃ DON'T HAVE NUMBERS A Talk With Daniel L. Everett : Dan Everett believes that Pirahã undermines Noam Chomsky’s idea of a universal grammar.

还有一些有趣的例子:

"I sat with a Pirahã once and he said, what does your god do? What does he do?  And I said, well, he made the stars, and he made the Earth. And I asked, what do you say?  He said, well, you know, nobody made these things, they just always were here.

The first time I took a Pirahã on an airplane, I got a similar reaction. I was flying a man out for health reasons; he had a niece who needed surgery and he was accompanying her. We're flying above the clouds, and I know that he's never seen clouds from the top before, so I point down and I say, those are clouds down there. Uh huh. He was completely uninterested; he acted like he flew in planes every day. The Pirahã are not that curious about what we have. They haven't shown interest in a number of things that other indigenous groups, even Amazonian groups, that have come out and had contact with in civilization for the first time are curious about. The Pirahã have been in regular contact for a couple of hundred years now, and they have assimilated almost nothing. It's very unusual."

The reason that I believe that the Pirahã are like this is because of the strong cultural values that they have—a series of cultural values. One principle is immediacy of experience; they aren't interested in things if they don't know the history behind them. If they haven't seen it done. But there's also just a strong conservative core to the culture; they don't change, and they don't change the environment around them much either. They don't make canoes. They live on the river, and they depend on canoes for their daily existence—someone's always fishing, someone's always crossing the river to hunt and gather—but they don't make canoes. If there are no Brazilian canoes, they'll take the bark off a tree and just sit in that and paddle across. And that's only good for one or two uses.

I brought in a Brazilian canoe master, and spent days with them and him in the jungle; we selected the wood, and made a dugout canoe. The Pirahã did all the labor—so they knew how to make a canoe, and I gave them the tools—but they came to me and they said, we need you to buy us another canoe. I said, well we have the tools now, and you guys can make canoes. But they said, Pirahã don't make canoes. And that was the end of it. They never made a canoe like the Brazilians, even though I know that some of them have the skills to do that.

"The crucial thing is that the Pirahã have not borrowed any numbers—and they want to learn to count. They asked me to give them classes in Brazilian numbers, so for eight months I spent an hour every night trying to teach them how to count. And it never got anywhere, except for a few of the children. Some of the children learned to do reasonably well, but as soon as anybody started to perform well, they were sent away from the classes.

It also doesn't explain their lack of color words, the simplest kinship system that's ever been documented, the lack of recursion, and the lack of quantifiers, and all of these other properties.

I remember one time sitting in a hut with the Pirahã and they came and they said, we understand that you want to tell us about Jesus and that Jesus tells us that we should live certain ways."