On 8/29/2012 10:52 AM, meekerdb wrote:

On 8/29/2012 5:18 AM, Stephen P. King wrote:On 8/29/2012 2:17 AM, meekerdb wrote:On 8/28/2012 11:08 PM, Quentin Anciaux wrote:Hi Brent,## Advertising

Until there is a precise explanation of what this phrase"generation by the UD" might mean, we have just a repeatedmeaningless combinations of letters appearing on our computer monitors.Seems pretty precise to me. The UD executes all possiblecomputations, one step at a time. If 'you' are a computation, thenit must eventually generate you.Brent --Hi Brent,Yes it will "eventually" generate me, but with a measure zerochance. The UD seems to be ergodic on the Integers.Not zero, only zero in the limit of completing the infinitecomputations. So at any stage short the infinite completion theprobability of "you" is very small, but non-zero. But we already knewthat.Brent

`I agree but the details of this are being crudely glossed over and`

`they are of utmost importance here! We need a precise definition of the`

`"at any stage short of the infinite completion" term. I suspect that we`

`can capture this using the uncountable infinity of non-standard models`

`of arithmetic`

`<http://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic> and`

`relations between the models to give us a nice formal model.`

`"The existence of non-standard models of arithmetic can be`

`demonstrated by an application of the compactness theorem. To do this, a`

`set of axioms P* is defined in a language including the language of`

`Peano arithmetic together with a new constant symbol x. The axioms`

`consist of the axioms of Peano arithmetic P together with another`

`infinite set of axioms: for each numeral n, the axiom x > n is included.`

`Any finite subset of these axioms is satisfied by a model which is the`

`standard model of arithmetic plus the constant x interpreted as some`

`number larger than any numeral mentioned in the finite subset of P*.`

`Thus by the compactness theorem there is a model satisfying all the`

`axioms P*. Since any model of P* is a model of P (since a model of a set`

`of axioms is obviously also a model of any subset of that set of`

`axioms), we have that our extended model is also a model of the Peano`

`axioms. /The element of this model corresponding to x cannot be a`

`standard number, because as indicated it is larger than any standard`

`number/."`

`The x would play the role of the inverse of the epsilon of`

`proximity to infinite completion.`

-- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- 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.