It is also possible to make a similar analysis of the deductive method, that is to say, of formal axiom systems. This is accomplished by analyzing more carefully the new version of Berry's paradox that was presented. Here we only sketch the three basic results that are obtained in this manner. (See the Appendix).

1. In a formal system with n bits of axioms it is impossible to prove that a particular binary string is of complexity greater than n+c.

2. Contrariwise, there are formal systems with n+c bits of axioms in which it is possible to determine each string of complexity less than n and the complexity of each of these strings, and it is also possible to exhibit each string of complexity greater than or equal to n, but without being able to know by how much the complexity of each of these strings exceeds n.

3. Unfortunately, any formal system in which it is possible to determine each string of complexity less than n has either one grave problem or another. Either it has few bits of axioms and needs incredibly long proofs, or it has short proofs but an incredibly great number of bits of axioms. We say “incredibly”' because these quantities increase more quickly than any computable function of n.

见：Gregory J. Chaitin. Information-Theoretic Computational Complexity. IEEE Transactions on Information Theory, IT-20 (1974), pp. 10-15.

管窥蠡测

       管窥蠡测这个成语源自“以管窥天，以蠡测海”。原话表面的意思是：从竹管的小孔里看天，用瓠瓢量海水。它的引申义是：目光短浅，眼光狭小，对事物的观察和了解都很肤浅。类似“坐井观天”的意思。
       出自：东汉·班固《汉书·东方朔传》：“以管窥天，以蠡测海，以莛撞钟，岂能通其条贯，考其文理，发其音声哉。”

 

http://www.zdic.net/cd/ci/14/ZdicE7ZdicAEZdicA1291484.htm

 

       take a narrow view of sth;look at the sky through a bamboo tube and measure the sea with a calabash——restricted in vision and shallow in understanding.

       管中视天，以瓢量海水，喻眼光狭小，见识不广或不自量力。

 

成語：管窺蠡測
http://bookstrg.com/Readstory.asp?Code=SS205844

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