Hi Bruno,
> and Cantor get a contradiction from that. You assume the diagram is
> indeed a piece of an existing bijection in Platonia, or known by God.
No, you misunderstand me there - I just meant that we need to take the
step to infinity - see below.
> that you get by flipping the 0 and 1 along the diagonal of the matrix
> appearing on the right in the diagram. That sequence, thus, exists in
> Platonia, but definitely cannot belong to the list described above.
snip
> So you have to look at it, in the third person point of view as
> computations which bifurcate (or differentiate by the rule Y = II), and
> bifurcate again, and again, and again, OK?
Yes, I'm with you so far.
> And now, what you are missing. I think. It is the distinction between
> third and first person point of view. As defined in the first and second
> step of UDA (not the Theatetical one used in AUDA).
>
> Looking at the generation of the UD, or dovetailing on all computations,
> you can see the many computations being generated and you can see them
> differentiate or bifurcating all the "time", where here time is defined
> by the succession 1, 2, 3, 4, 5, ... itself. If you universal base is
> two dimensional (like with the Conway Game of Life) you can see the
> deployment as a static three dimensional conic structure.
>
> Everything there, is enumerable. At each UD step, everything is even finite!
snip
> But things changes when you adopt the first person point of view, due to
> the fact that the first person point of view cannot be aware of the
> dovetailing delays, nor of the extreme multiplication and redundancy of
> the computations. And if you are OK with, well, mainly here the step 4,
> you see that the "intuitive" measure will have to be made on the union
> of all computations going through the "current" state.
Agreed.
> 0...
>
> I have already begin the generation of a continuum of binary "history":
> Indeed, all those beginning by 0. Then I write
>
> 1...
>
> So I have begin the generation of the binary sequence beginning by 1. As
> you see I am dovetailing (not universally though!).
>
> Then i generate all possible extensions, which give me two time more work.
> First the possible continuation of the one beginning by 0.
>
> 00...
>
> 01...
>
That is how I visualized it, yes.
>
> Now, if you interpret the 1 or 0 as results of a self-bifurcation in the
> UDA, then by the unawareness of delays, the first person indeterminacy
> of those "in front of a never stopping UD", where your computations are
> dovetailed, in particular on the binary infinite sequences, bears on
> set with cardinalities of continua, despite mathematically the third
> person description does not leave the enumerable.
And here is where we seem to "disagree" - but maybe only in a trivial
sense - maybe we mean the same thing actually.
I agree that everything is still enumerable from a third person point of
view, and that the "continuum" arises from a 1st person point of view,
but also only if I imagine all computations of the UD - also the ones
infinitely far away.
I am skeptical of actual infinities in the "real=physical" world (in my
1-OM in only believe in potential infinities.
http://en.wikipedia.org/wiki/Potential_infinity
see Bekenstein Bound, and Seth Lloyd's work on the limits of
computation), but when we say that physics is emergent from 1st person
point of view of the third person UD, we are also aware that this UD
does not exist "in" time and space (but generates it for inside observers).
So no problem with infinities there - I only have a problem with local
physical (1-OM) infinities (as presupposed in textbook physics when
using calculus for finite volumes of spacetime)- but then again, where
they appear locally I think they are also indicative of the multiverse,
as in Max Tegmark's suggestion that natural constants could be viewed as
indexicals into the Multiverse). So, actual infinity (as opposed to
potential) is always a multiverse-feature.
To return to the question at hand: the full continuum, also from a first
person perspective, appears only when I also take into account
reconstitutions "at infinity" - because, for every finite section I
consider (however large), I only have _stubs_ of full reals - and not
all the reals.
I think a bit along the lines like when one takes an ordinal, say
"omega", and imagines that it is infinity "completed". In the same
sense, we need _completed_ infinity for a real continuum (as opposed to
only a subset) to arise. And, as the infinity is completed in Platonia,
they contribute to the measure of 1-OMs - with the power of the full
continuum.
Would you agree?
> only low levels (not necessarily the "bottom"). Also, I can sometimes
> speculate that comp could predict there is no bottom.
In what way do you think this follows from comp? Because there are
histories for every arbitrarily deep probing of "physical" reality?
> The real question is what will you think if you, "low-level"
> computationalist father have a daughter falls in love with a high-level
> computationalist?
I would only allow them to get married after he was scanned, teleported
to Mars, and returned back again ;-))
> It is a complex puzzle because although they share the same basic
> theology they will have quite different theotechnologies.
Absolutely - I agree.
> OM are Nick Bostrom's subjective "observer moment". Basically,
> momentaneous qualia of feeling to be "in space-history".
That is how I always use OM.
> I use sometimes OM in that sense, although I tend to write 1-OM for it.
> By 3-OM I mean either a computational state "of a brain or of a
> universal machine "vehiculating" that experience, that quale"
> Or, in probabilistic context, a 3-OM is identified with all its
> occurence in the UD deployment. It is the many 3-OM, corresponding to
> the same experience (qualitatively, and this exists in infinity in the
> UD deployment, quantitatively, assuming comp).
Ok - could we agree to use OM for 1-OM in the future and 3-OM for the
other variant?
Best Wishes,
Günther
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Received on Fri Jan 09 2009 - 14:15:11 PST