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复杂方法在实际中往往用途不大(在有噪声的情况下)
阿诺德(Vladimir Igorevich Arnold,1937-06-12 ~ 2010-06-03)说:
推导的链(即所谓的“证明”)越长越复杂,最后得到的结论可靠性越低。复杂的模型几乎毫无用处。
特斯拉(Nikola Tesla,1856-07-10 ~ 1943-01-07)说:
Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
今天的科学家们用数学替换了实验,并且他们从方程到方程来回地推导,最终建立了一个和现实世界没有任何关系的数学结构。
对四色定理计算机证明的批评:
一个好的数学证明应当像一首诗——而这纯粹是一本电话簿!
A good mathematical proof is like a poem - this is a telephone directory!
所以,在带有噪声和变化较快的实际情况下,复杂方法往往用途不大。线性方法往往比(高阶)非线性方法更有效。
相关链接:
[1] 张永祥,2014-06-27,顶级科学大师丝语: 俄罗斯玩不玩CNS? 精选
http://blog.sciencenet.cn/blog-1076418-806951.html
http://blog.sciencenet.cn/blog-1076418-806951.html
[2] Nikola Tesla Quotes on Life, Energy & Inventions to Inspired
http://cutelovequotesforher.org/nikola-tesla-quotes-on-life-energy-inventions/
[3] Kenneth Appel, From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Kenneth_Appel
[4] Gregory J. Chaitin [1974] Information-theoretic computational complexity. IEEE Transactions on Information Theory, IT-20, pp. 10-15.
[5] 杨东屏[1993] 哥德尔不完全性定理剖析, 曲阜师范大学学报:自然科学版, 19(1): 31-36.
[6] 2013-10-04,数学证明的长度:与公理系统能力负相关 精选
http://blog.sciencenet.cn/blog-107667-729907.html
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