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Gödel, Turing and Cantor: The Math

132 点作者 jamesmiller5将近 12 年前

7 条评论

wicknicks将近 12 年前
Oh wow! This is a great write up on Godel&#x27;s work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read.<p>Slightly related: Although a more technical&#x2F;deeper discussion, but the book &quot;Godel&#x27;s Proof&quot;[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems.<p>[1] <a href="http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814758371" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;G%C3%B6dels-Proof-Ernest-Nagel&#x2F;dp&#x2F;0814...</a>
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6ren将近 12 年前
There&#x27;s a translation of Gödel&#x27;s paper linked via his wikipedia entries <a href="https://docs.google.com/viewer?url=http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf" rel="nofollow">https:&#x2F;&#x2F;docs.google.com&#x2F;viewer?url=http:&#x2F;&#x2F;www.research.ibm.c...</a> [google docs viewer]<p>curious facts: he died of starvation; he was a theist <a href="http://en.wikipedia.org/wiki/Kurt_G%C3%B6del#Later_years_and_death" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Kurt_G%C3%B6del#Later_years_and...</a>
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mvp将近 12 年前
This article took me to another from the same author<p>&#x27;<a href="http://skibinsky.com/godel-incompleteness-for-startups/#footnote-4&#x27;" rel="nofollow">http:&#x2F;&#x2F;skibinsky.com&#x2F;godel-incompleteness-for-startups&#x2F;#foot...</a><p>and I found the below statement and laughed out aloud. Although in the context, this statement makes sense, in general, I trust books that don&#x27;t belong to human-related matters (technical etc), because in human-related matters it is mostly one&#x27;s opinion against others.<p>&quot;As soon as these popular books leave the domain of human-related matters you are totally on your own.&quot;
Cacti将近 12 年前
Chaitin is cool, too.
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bitdiddle将近 12 年前
What I find interesting are the claims Penrose[1] and others make about human versus machine intelligence based on Godel&#x27;s results.<p>[1] <a href="https://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence#Lucas.2C_Penrose_and_G.C3.B6del" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Philosophy_of_artificial_intel...</a>
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stanonyime将近 12 年前
It would be interesting to speculate the consequence of Godel&#x27;s Incompleteness deductions on the quest for Grand Unified Field Theorems in theoretical physics
brisance将近 12 年前
Does this mean that the antivirus industry is nothing but a scam?
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