JS:
>>Then there is your "invariance lemma: the way you quantify 1-indeterminacy
>>is independent of (3-)time, (3-)place, and (3-)real/virtual nature of the
>>reconstitution." This does not make sense, because if the (3-) probability
>>distribution on the possible futures and reconstitutions does depend on
>>time or place or other things (why not?) then 1-indeterminacy does so,
>>too. Under most distributions, some futures are less likely than others.
>>Hence there are nontrivial, distribution-dependent, probabilistic
>>1-predictions as well as "quantifications of 1-indeterminacy" that depend on
>>time/space/other things.
BM:
>I see you genuily fail to understand the invariance lemma. No problem. We
>will come back to this until you get the TILT, (if you agree).
Bruno, I am usually skipping those of your paragraphs that contain
sentences such as "physics is a branch of machine's psychology" because
I have no idea what that is supposed to mean. Still, I feel you do have
something nontrivial to say, I just have not been able to figure out
what exactly it is. Maybe if I knew why "I genuinely fail to understand
the invariance lemma" - please show me!
JS:
>>Not uncomputable. Any past is finite.
BM:
>I was talking about the immediate next futur.
But any finite future is computable by a long program as well.
The problems arise with infinite futures.
JS:
>>I am prejudiced against claims of rigorous proof when even the
>>assumptions are unclear; and against statements that are plain
>>wrong, such as "the UD generates all real numbers".
BM:
>I am not claiming I am rigorous, except when you say I am vague
>and when you ask me precisions which are not relevant.
>The sentence "the UD generates all real numbers" is ambiguous.
>Either you interpret it as
> "The UD generates (enumerates) the set of all real numbers"
>This does indeed contradict Cantor's theorem.
>Or you interpret it as
> "All real number are (individually) generated by the UD".
>In which case, with the usual definition of "generating a
>real (generating all its prefixes)" it is just correct. Isn't it?
No, it isn't, since "generating an individual real" is not equivalent to
"generating all prefixes of all reals." "Generating an individual real"
means "generating all prefixes of that individual real, AND NOTHING
ELSE". Generating a real means you somehow have to be able to identify
and completely describe that particular real. If you cannot do this
without describing lots of other things then the individual real does
not exist from any constructive perspective.
The trivial algorithm ALPHABET
( http://rapa.idsia.ch/~juergen/toesv2/node27.html )
whose outputs are 0,1,00,01,10,11,000....is
not generating a description of any individual infinite real because it
never creates a complete representation thereof. Ambiguity arises because
each of the outputs is just a prefix of many infinite reals.
The best you can achieve is an algorithm that outputs at least the
computable infinite reals in the sense that it outputs their
finite descriptions or programs.
BM:
>So I ask you again: do you agree that comp entails the existence of
>first person indeterminacy, as it is shown by the self-duplication
>thought experience?
If it just means you don't know in advance in which possible future you'll
end up, provided there is a nontrivial distribution on the possible
futures, then this is ok (and trivial). Do I need any additional
preliminaries to realize why I "genuinely fail to understand your
invariance lemma"?
Juergen
