# Re: Ascension (was Re: Smullyan Shmullyan, give me a real example)

```
Quentin Anciaux wrote:
> Hi,
>
> >From what you've said about dovetailing before, you don't have to have
> >
> > just a single sequence in order to dovetail.  You can jump among
> > multiple sequences.  I have yet to understand how you could dovetail on
> > something that is not effective.
>
> I think dovetailing is possible because the dovetailer only complete sequences
> at infinity. So when you construct the matrice on which you
> will "diagonalize", you are already diagonilizing it at the same time.
> Example: when you have the first number of the first growing function, you
> can also have the first number of the diagonalize function (by adding 1) and
> the first number of the diagonalize*diagonalize function and ... ad recursum.
> By dovetailing you execute in fact everything in "parallel" but all infinites
> sequences are only completed at infinity.
>
> Quentin Anciaux```
```
OK.  Thanks.  But so far we have done only effective diagonalization.
I'll follow along as Bruno goes step by step.  Also, it seems to me
even with non-effective diagonalization there will be another problem
to solve:  When we dovetail, how do we know we are getting sufficient
(which means indefinite) level of substitution in finite amount of
computation?  (Also, I am waiting for a good explanation of how Church
Thesis comes into this.)  Again, I'll wait for the step by step
argument.

Tom

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