# Re: Simple proof that our intelligence transcends that of computers

```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.
```
Brent
--
```
```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.
```
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