Godel

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thinkandmull

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Hello,

Has Gödel’s incompleteness theorems been disproved by universal computers? Has anyone here heard of Stephen Wolfram’s rule 110? Does it relate to Godel? I am not a math wiz but I like to read about it
 
thinkandmull said:
Hello,

Has Gödel’s incompleteness theorems been disproved by universal computers? Has anyone here heard of Stephen Wolfram’s rule 110? Does it relate to Godel? I am not a math wiz but I like to read about it
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Not for sure what you mean by universal computers, I assume you simply mean machines that are Turing Complete. But if you do, your question does not quite make sense. They are related, but not quite directly. Gödel’s theorems address whether there are mathematical statements which cannot be proven. Turing machines are more related to the issue of there are problems which cannot be computed.

Nevertheless, they have not been disproved. His proofs are solid, they will stand the test of time.

I am not an expert on rule 110 (came after my time of studying computability theory). They are Turning Complete (ie a version of a universal computer, to use your terminology), so again they are related to Gödel’s work, but not quite directly.
 
Mathematician John Allen Paulos says that Stephen Wolfram has a rule 110 in his book A New Kind of Science that “,as Wolfram proves, it is capable of performing all possible calculations”. Are you saying that because of Gödel’s principles it can’t determine if any of the premises of the calculations are true? Or am I still way off
 
thinkandmull said:
Mathematician John Allen Paulos says that Stephen Wolfram has a rule 110 in his book A New Kind of Science that “,as Wolfram proves, it is capable of performing all possible calculations”. Are you saying that because of Gödel’s principles it can’t determine if any of the premises of the calculations are true? Or am I still way off
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A Turing complete machine is a machine that can compute everything done by a Turing Machine, a theoretical computer defined by Alan Turing in the 1930s (IIRC). It is a universal computer. Except for finite limits of memory, all computers today are Turing complete.

A rule 110 machine is anither type of Turing Complete machine. I am not familiar with the book you refer to, I will check it out.
 
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