**Next message:**Max More: "Re: ECON: The Fed's Y2K Recession of 2001"**Previous message:**hal@finney.org: "Investing in artists to get a share of later success"**In reply to:**zeb haradon: "Re: Unprovability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

zeb haradon wrote:

*>
*

*> I missed the beginning of this thread, but it seems like you're talking
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*> about whether the Goldbach conjecture could fall into the class of
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*> undecidable theorems. I don't know if anyone has pointed this out yet, but
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*> the Goldbach conjecture cannot fall into that class.
*

The beginning of the thread,

http://www.lucifer.com/exi-lists/extropians/1811.html

described an article in the March 10 issue of _New Scientist_ that

contains an informal description of the work of mathematician Gregory

Chaitin of IBM's Thomas J. Watson Research Center, who is interested in

randomness and its implications for the rest of mathematics, especially

the provability of assertions in number theory. The article mentions a

number Chaitin defined called Omega which is apparently an embodiment of

randomness, and other numbers called Super Omegas which exemplify some sort

of hierarchy of randomness.

Later posts by Samantha Atkins, Eliezer, and others harrumphed at

the article, e.g.:

http://www.lucifer.com/exi-lists/extropians/1811.html

The only mention I see in the _New Scientist_ article of anything that

even looks like the Goldbach Conjecture (not by name) or the Riemann

Hypothesis (by name) is the paragraph:

"Take the problem of perfect odd numbers. A perfect number has divisors

whose sum makes the number. For example, 6 is perfect because its

divisors are 1, 2 and 3, and their sum is 6. There are plenty of even

perfect numbers, but no one has ever found an odd number that is

perfect. And yet, no one has been able to prove that an odd number can't

be perfect. Unproved hypotheses like this and the Riemann hypothesis,

which has become the unsure foundation of many other theorems (New

Scientist, 11 November 2000, p 32) are examples of things that should be

accepted as unprovable but nonetheless true, Chaitin suggests. In other words,

there are some things that scientists will always have to take on trust."

Jim F.

**Next message:**Max More: "Re: ECON: The Fed's Y2K Recession of 2001"**Previous message:**hal@finney.org: "Investing in artists to get a share of later success"**In reply to:**zeb haradon: "Re: Unprovability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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