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【旧闻轶事】惠勒与哥德尔,顺带爱因斯坦
2014-01-17 13:59:00  信息论  科学史 
以下引自Gregory Chaitin著《Information-theoretic incompleteness》:(翻译则来自本人)
In summary, let me tell a story from ten years ago, from 1979, which was the centenary of Einstein′s birth. There were many meetings around the world celebrating this occasion. And at one of them in New York I met a well-known physicist, John Wheeler. I went up to Wheeler and I asked him, “Prof. Wheeler, do you think there′s a connection between G¨odel′s incompleteness theorem and the Heisenberg uncertainty principle?" Actually, I′d heard that he did,so I asked him, "What connection do you think there is between G¨odel′s incompleteness theorem and Heisenberg′s uncertainty principle?"
总而言之,我讲个十年前的事情。那一天是1979年爱因斯坦诞辰纪念日,在纽约的庆典会议上我遇见了著名的物理学家,约翰·惠勒。我走上前去提问:”惠勒教授,您认为海森堡不确定性原理与哥德尔不完备性定理间有联系吗?“事实上,我听说他深以为然。所以我问了:”您以为这两者间的联系是什么呢?“
This is what Wheeler answered. He said, ”Well, one day I was at the Institute for Advanced Study, and I went to G¨ odel′s office, and there was G¨ odel..." I think Wheeler said that it was winter and G¨ odel had an electric heater and had his legs wrapped in a blanket.
Wheeler said, "I went to G¨odel, and I asked him, `Prof. G¨odel,what connection do you see between your incompleteness theorem and Heisenberg′s uncertainty principle?′ " I believe that Wheeler exaggerated a little bit now. He said, "And G¨odel got angry and threw me out of his office!" 
Wheeler blamed Einstein for this. He said that Einstein had brain-washed G¨ odel against quantum mechanics and against Heisenberg′s uncertainty principle!
惠勒的回答是这样子。他说:”喔,那天我正在普林斯顿高等研究院,到哥德尔的办公室会见过他本人。“我记得惠勒还说了时值寒冬,哥德尔把他的双脚裹在电热毯里。
惠勒回忆道:“我走上前去提问:‘哥德尔教授,您认为您的不完备性定理与海森堡不确定性原理间的联系是什么呢?’”我猜惠勒的话肯定有着夸大的成分,他说:“然后哥德尔勃然大怒,把我轰出他的办公室!”
惠勒将其归咎于爱因斯坦,认为爱因斯坦把哥德尔洗脑到了反感量子力学和海森堡不确定性原理的地步。

In print I recently saw a for-the-record version of this anecdote,which probably is closer to the truth but is less dramatic. It said, not that Wheeler was thrown out of G¨ odel′s oce, but that G¨ odel simply did not want to talk about it since he shared Einstein′s disapproval of quantum mechanics and uncertainty in physics. Wheeler and G¨odel then talked about other topics in the philosophy of physics, and about cosmology.
最近我读到了这则轶闻的书面记录,也许更接近事实,不过没那么戏剧化。据其记载,惠勒没有被轰出哥德尔办公室,而是哥德尔单纯地拒绝讨论这个话题。因为他和爱因斯坦一样不赞同量子力学和物理中的不确定性。惠勒和哥德尔随即转而讨论其他物理哲学和宇宙学方面的话题。
There is some little-known work of G¨odel connected with general relativity, some very interesting work, about universes where the past and the future is a loop, and you can travel into your past by going around. That′s called a G¨odel universe. It′s a little-known piece of work that shows the stamp of G¨odel′s originality and profundity.
哥德尔有件与广义相对论密切相关的工作,非常有趣,不过相对没那么出名。这就是所谓的哥德尔宇宙,其中过去与未来闭合成圈,允许你沿其返回过去。由此管中窥豹,哥德尔思想的原创性和深度可见一斑。
Okay, so what was the final conclusion of all this? I went up to Wheeler at this Einstein centenary meeting, and I asked him this question. Wheeler told me that he asked G¨ odel the same question, and G¨odel didn′t answer Wheeler′s question, and Wheeler never answered my question! So I′m going to answer it!
好的,那么以上的最终结论是什么呢?爱因斯坦诞辰时我问了惠勒这个问题,惠勒告诉我他问过哥德尔同样的问题,而哥德尔没有答出惠勒的问题,惠勒也从没回答我的问题!所以我将自己来解答它!


(译者:希望知道Chaitin如何解答这个问题的读者请阅读原著,然而建议读者不要抱太大的期待)

2014-01-19 01:17:31
   呵呵,看来你要给出这个问题答案?
2014-01-19 09:42:40
   回楼上jake:
这不是我说的,是Chaitin说的……
但他的答案真的很跌眼镜……XD
简单来说就是“我们应该以做物理的方式来做数学”


2014-01-20 01:12:28
   以做物理的方式来做数学什么意思?就像Wolfram的新科学那样研究数学是吗?
2014-01-20 04:22:38
   回楼上jake:
我不知道NKS的做法是怎样……
蔡廷对随机性本身有着奇特的执着,在这本书里他开始觉得不完备性的存在实质上是因为大部分数学事实就是随机的,所以不能从一组固定的公理中推导出来。(这就是为何他说“上帝不仅在微观世界中投骰子,在整数中他也投骰子。”)
例如预言蔡廷常数的第k位是0还是1的方法,完全不能从已有的知识中推导出来。
我们知道在蔡廷不完备性定理中出现了只依赖于形式系统的常数L,在该系统中无法证明任意s具有高于L的算法熵。蔡廷认为:这个常数定量化了该形式系统公理集的“信息量”,如果相应的数学事实的复杂度高于这个阈值,那么我们将不能从中推出它,而且我们也不能发觉这一点,即便它确实是真的。我们只能通过接受这些事实的方法来提升系统的信息量,即改进其证明能力。
蔡廷相信这个阈限对整体数学同样有效。所以他建议:对于那些有着重要意义的猜想,例如黎曼猜想,假如它的复杂度估计足够高而且又没有它会引起矛盾的充分证明,直接像接受一个被实验检验过的可证伪物理理论那样接受它。

2014-02-18 16:30:42
   Chaitin的好朋友Calude同志有个正面回答,但是个类比。
见这篇文章:Calude:From Heisenberg to G¨odel via Chaitin
2014-03-14 14:51:31
   哦,我读过这篇论文,不过它的答案还是略显模糊了。
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