Hi Stathis,
I answer you, but it is at the same time a test, because most of my
yesterday (sunday 22 october) posts seems not having been send
successfully.
(Some arrived at the archive, but not in my mail box, others nowhere, I
will wait a whole and resend them: it was message for Peter and David).
Le 23-oct.-06, à 04:35, Stathis Papaioannou a écrit :
>> Church thesis just assert that a universal turing machine can compute
>> all computable functions from N to N.
>> It relate a mathematical object with a human cognitive notion. It does
>> not invoke physical machine at all.
>
> In a sense that is true, but a TM is still a model of what could
> possibly be built
> in a physical universe such as ours. Of course the model is still
> valid irrespective
> of the existence of a physical machine or indeed a physical universe,
> but if you
> abandon the idea of a physical universe there is no need to constrain
> yourself to
> models based on one.
I am not sure why you say the TM model is based on what we can build in
the physical universe.
Both with comp and without, the physical universe is a priori far
richer than a UTM.
The UTM of Turing relies explicitly on an analysis of human capacity
for computations.
Post universal systems are based on analysis of mathematician
psychology.
> So I suppose the two questions I have (which you partly
> answer below) are, having arrived at step 8 of the UDA could you go
> back and
> say that the UD is not really necessary but all the required
> computations exist
> eternally without any generating mechanism or program (after all, you
> make this
> assumption for the UD itself), or alternatively, could you have
> started with step
> 8 and eliminate the need for the UD in the argument at all?
This is the way I proceed in "Conscience and Mechanism". I begin, by
using the movie graph argument MGA, to show that consciousness cannot
be attached to physical activities, and then I use the UD to explain
that the comp-physics get the form of a measure on all computations.
In my Lille thesis I do the opposite because the UDA is simpler than
the MGA. It is not so important.
UD is needed to justify and to make mathematically precise the ontic
3-observer moments. They correspond to its (the UD) accessible states.
>
>>> It seems that this is the computer you
>>> have in mind to run the UD.
>>
>> Only for providing a decor for a story. This assumption is eliminated
>> when we arrive (step eight of UDA-8) at the conclusion that universal
>> digital machine cannot distinguish any "reality" from an arithmetical
>> one.
>>
>>
>>> That's OK and the argument works (assuming
>>> comp etc.), but in Platonia you have access to hypercomputers of the
>>> best
>>> and fastest kind.
>>
>> Fastness is relative in Platonia. Universal machine can always been
>> sped up on almost all their inputs (There is a theorem by Blum and
>> Marquez to that effect). Then indeed there are the "angels" and
>> hierachies of "non-comp" machine. A vast category of "angels" can be
>> shown to have the same hypostases (so we cannot tested by empirical
>> means if we are such angels). Then they are entities very closed to
>> the
>> "one", having stronger hypostases, i.e. you need to add axioms to G
>> and
>> G* (or V, V* with explicit comp) to get them.
>
> Of course I was joking when I said "best and fastest". In Platonia
> there is
> no actual time and everything is as fast and as perfect as you want it.
OK. But of course there exist notion of relative time: a fast Fourier
transform is faster than a slow Fourier transform, even in Platonia. Of
course this can be said in term of number of steps in computations (no
need to invoke time).
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Oct 23 2006 - 12:42:59 PDT