On 09 Jan 2009, at 20:12, Günther Greindl wrote:

>
> 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 don't understand what you mean by computations being infinitely far  
away. In the UD deployment, which I will wrote UD*, all computations  
begins soon or later (like all dominoes falls soon or later in the  
infinite discrete dominoe-sequences). All computations reach any of  
their relative computational state soon or later always after the UD  
makes a finite number of steps.   *Some* subcomputations can be  
interpreted as dovetailing on the constructive ordinal, but they still  
reach any of their computational step in finite time.




>
>
> I am skeptical of actual infinities in the "real=physical" world (in  
> my
> 1-OM in only believe in potential infinities.


I recall that the "physical" world is a *first person* plural  
observation, so with comp with have to expect "things behaving like if  
there was actual infinities". The "physical world" is just unreal, if  
we decide to say real = the ontological, in which case something is  
real if it belongs to the UD*, or if its existence can be proved in  
Robinson Arithmetic.




>
>
> 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).

Well, the UD has existed and has run in time 1991 and space Brussels :)

UD* does not exist "in" time and space, given that with comp it is  
"time and space" which *appears* from the point of view of the  
observers generated by the UD. It is an open problem if we can make  
sense with a notion like Bekenstein bound or just balk hole with comp.




>
>
> 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.

I can be OK with this. But the multi-verse emerge from the collective  
multiplication. It is difficult to talk on this because all talks are  
done at third person point of view level, even when we talk about the  
first person, and the first personal plural.



>
>
> 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.

Hmmm... The phrasing "reconstitution at infinity" does not make sense,  
I think. All reconstitutions are done after a finite number of steps  
of the UD. But you are right that for (the third person description)  
of the first person probable experience we have to take into account  
the infinite union of the computations going through the relevant  
state. The reals appears here and now, because they are generated at  
the limit, as a infinite union of finite computations, or finite  
pieces of infinite computations.



>
>
> 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.

OK. But it is the union which is infinite. The reconstitution can be  
numbered (by a God).


> And, as the infinity is completed in Platonia,

I *prefer* not. No actual infinities in the Arithmetical Platonia.  
Analytical and physical truth belongs to the epistemology. It makes  
things far simpler.



>
> they contribute to the measure of 1-OMs - with the power of the full
> continuum.


Yes. But those things appears in the discourse of the Lobian Machines,  
generated by the Robinson Machine (the arithmetical UD). Those machine  
have to use them because they can understand that theior histories are  
distributed in the whole UD*.



>
>
> Would you agree?

If my comments above makes sense.



>
>
>
>> 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?


Because in the UD, between two specific computational state of a  
computation, their will be an infinity of computations going through  
the computational states.




>
>
>> 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 ;-))


No problem for him, but what if he proposes to your daughter a wedding  
travel using a high-level computational band? Your daughter, or what  
you think will remain from your daughter (cf you are supposed to be  
low-level mechanist) will be a high-level computationalist version of  
your daughter. You are OK with that? If you are really low-level  
computationalist you could think your daughter is a zombie or just  
plain dead.
Among the very *high*-level computationalist some accept artificial  
brain with half their current number of neurons, and some accept brain  
with one neuron, and some accept brain with zero neuron ... (they  
identifies themselves with *the* arithmetical universal machine).

>
>
>> It is a complex puzzle because although they share the same basic
>> theology they will have quite different theotechnologies.
>
> Absolutely - I agree.


So you are *very* tolerant with your daughter. OK. In religious  
matter, this attitude is rare. Well you were joking I think :)



>
>
>> 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?


We agree. But in the context where I use "3-OM", I prefer to use "1- 
OM", to insist on the difference and prevent that people think "OM" is  
a short for "3-OM". Despite 3-OMs are finite and 1-OMs are infinite,  
the confusion is easy to do.

I have to go,
Best,

Bruno

http://iridia.ulb.ac.be/~marchal/




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