Dear Bruno:

These are some of the things I want to explore as a result of formulating 
my question re the UD.

To start:

1) Are you saying that the UD contains all other computations as data?

2) By your comment "You confuse computability and provability." I think you 
mean the UD indeed contains all computations as data.  But for sake of 
covering all bases I thought "compute" = "prove" was established by 
Turing.  Though I know some want to expand beyond this.   Regardless, IMO 
even if it has all this data it is still an expression plus data plus 
self-delimiter that outputs [proves] a value.  That is the "sense" I am using.

3)  If in order to work the UD contains all other computations as data then 
the UD is a highly complex program.  A small expression with a lot of data 
and a very large self-delimiter.  If you have to put the data string in to 
get it out that is a sign you are working with a random string.  Random 
strings are complex and I thought "all Theorems" was a very low complexity 
object.  Or is it random?

4) Why not run a highly parallel computer rather than a UD? [That is rather 
like a part of my model.]

5) My meaning for "knowing" is at first order like proving.  Chaitin is 
actually talking about the complexity of the FAS's theorem checker as the 
complexity of the FAS.  The theorem  checker "knows" all theorems of the 
FAS.  If a proof is an elegant proof by default then the theorem checker 
also knows this proof or it would not know how to check the output for 
theorem hood.  It can prove this proof is elegant because there is no other 
choice.

Hal

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