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,

Until there is a precise explanation of what this phrase "generation by the UD" might mean, we have just a repeated meaningless combinations of letters appearing on our computer monitors.

Seems pretty precise to me. The UD executes all possible computations, one step at a time. If 'you' are a computation, then it must eventually generate you.

Hi Brent,

Yes it will "eventually" generate me, but with a measure zero chance. The UD seems to be ergodic on the Integers.

Not zero, only zero in the limit of completing the infinite computations. So at any stage short the infinite completion the probability of "you" is very small, but non-zero. But we already knew that.


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.




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 
For more options, visit this group at 

Reply via email to