On 20 Jun 2012, at 19:37, John Clark wrote:

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On Wed, Jun 20, 2012 at 3:39 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:>> It's true that if you knew the numerical value of Chaitin'sConstant then you would know that if a 100 bit program had notstopped after a Turing Machine had run n number of finite operationsthen it never will; but the trouble is you don't know Chaitin'sConstant and never can, so you can never know how big n is. So eventhough they have been running for a googoplex to the googoplex poweryears one of those programs could stop 5 seconds from now.> Not if I waited, by chance or whatever, a time bigger than BB(100).Then it will never stop but you don't know it will never stop, soyou'll still be looking to see if it stops in the next 5 seconds orthe next 10 seconds or the next googoplex to the googoplex poweryears.

Correct.

Godel was a Platonist, he thought things were true or they were nothe just said sometimes we can't know which, and Turing certainlybelieved all programs will come to a stop or they will not,

Yes. That is part of Arithmetical Realism.

but he was investigating if we can always obtain that one bit ofinformation for any program and he proved we can not.

Indeed.

Neither the Busy Beaver nor Chaitin's work on the Omega Constantchanges that fact and is just more confirmation that Turing wasright, not that more confirmation was needed, the proof is ironclad.

Sure.

> If a decimal change after that, then we got a computable functiongrowing more quickly than BB.As I've said if a program of a given size has not stopped by acertain finite number of operations it never will, but that factdoes you no good at all because to know what that finite number isyou'd have to know Chaitin's Constant and you don't know that andnever will.

`Yes. But nowhere I said that we would knowingly get the decimals`

`correct, only that we would get the decimal correct after a finite`

`(even if unknown) time.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.