Mark,
you asked interesting questions, but I think the fundamental ones are still
'out there':
MP:(bold and in bold):
"I mean the big and unanswered question is WHERE are numbers?
I would ask (joining your heresy):
1. Where did numbers come from? (an answer may be: They are GOD to believe
in).
2. How do they act?
Bruno wrote: the relationship between numbers. How does a "RELATIONSHIP"
act? it is an abstraction. Only substrates IN relationship act. The numbers
are abstractions (or: the contents we assign to them are abstractions?) so
here we face abstractions of abstractions. If one considers the
not-so-physical world (numbers?)
- a-spatial - (and of course - a-temporal -), your question is out
of whack.
*MP next:
" what I am saying is that numbers need something which is not numbers -
(to exist - my addition-JM)"
I believe it can be incorporated into the identification of
"n u m b er "
if you ask only about their existence. Anything exists what we think about -
if not otherwise: in our thought. (I just had some exchange on this with
Stathis in a different aspect.)
John M
jamikes.domain.name.hidden
On 4/2/07, Mark Peaty <mpeaty.domain.name.hidden> wrote:
>
>
> Bruno:
> > With comp, what holds 'your lot" together are the relation between
> > numbers. The apparent third person infinite regression stops at the
> > level of those relations. The first person is most probably confronted
> > with many infinities, but this should not be considered as
> > problematical.
>
> MP: But what *relation* is there really? I just feel like this
> kind of discussion goes round and round in endless convolutions.
> Platonia is some kind of Never-never land; that numbers exist
> anywhere except inside human skulls and nowadays within
> phenotypic prostheses like electronic computers is NOT a proven
> fact, it is a glorious assumption!
>
> I mean the big and unanswered question is WHERE are numbers?
> Mathematicians now seem to be very sophisticated with WHAT
> numbers could BE, and _do_ also apparently, but very very big
> numbers which could represent everything significant about
> you, me, or the likelihood of a self referencing computer
> working out that it knows that it knows something really
> important, how can these 'relate'? Surely they have to be
> related by someone or something else! I guess what I am saying
> is that numbers need something which is not numbers in which, or
> by means of which they can exist for each other. I call it
> 'existence', and use the name of Janus as my symbol or emblem of
> this. But I don't expect any such symbol or emblem to resolve
> the paradoxes of our existence and experience of existence. As
> far as I can see, which admittedly is not very far, all
> explanations that purport to be *ultimate* explanations are
> doomed to a process of infinite recursion and regression.
>
> There was an Englishman called Kenneth Craik, who wrote a little
> book called 'The Nature of Explanation'. Unfortunately he died
> in his early thirties in a car accident in 1945 I think. I go
> along with his thesis - as I remember it from reading the book a
> decade or more ago - that the representational power of
> mathematics stems from its evolution of complex mathematical
> objects out of the interactions of simple elements, which can
> mirror many significant aspects of the physical/noumenal world
> because the latter seems to be manifesting a closely analogous
> evolution of aggregations of fundamental chemical elements,
> sub-atomic particles and so forth.
>
> For better or worse I must advocate what is hereabouts a virtual
> heresy: that people can never be reduced to numbers. To be a
> person entails the experience of 'I' and 'thou', 'me' and 'you'.
> There can be no me without you and no 'us' without 'them'. If a
> modest Loebian machine cannot work this out, then it needs to go
> back to school. Perhaps it can though, [if all worlds are
> possible and must happen], maybe it is just a matter of time
> before one or more smart, introspective, self-sustaining
> processors/processes emerges from a BOINC type distributed
> system. My bet is that the Silico-Electric ONE [or two, ...]
> will coalesce around the control and accounting of money, money
> being the embodiment of negative entropy in the cultural world.
> For what it's worth I think that such a creature will realise
> that ethics is part of the foundation of its world: a
> fundamental tool for the maximising of 'negative entropy'.
>
>
>
> Regards
>
> Mark Peaty CDES
>
> mpeaty.domain.name.hidden
>
> http://www.arach.net.au/~mpeaty/
>
>
>
>
>
> Bruno Marchal wrote:
> >
> > Le 06-mars-07, à 09:44, Mark Peaty a écrit :
> >
> >>
> >> Thank you Bruno!
> >>
> >> You and Russell between you have managed to strike some sparks of
> >> illumination from the rocky inside of my skull. There is no beacon fire
> >> to report but I start to get a glimmering of why you want to *assume*
> >> comp and see where it leads.
> >>
> >> It seems that self-reference and recursion are fundamental properties
> >> of
> >> anything that is "interesting" in all this, which rather seems to be
> >> the
> >> flavour of the new millennium.
> >>
> >> Just in thinking superficially about the Many Worlds though, it seems
> >> to
> >> pose a 'binding problem'. Now, I know that might sound like a leakage
> >> of
> >> concept from objections to identity theory in brain and mind theory.
> >> But
> >> what I am thinking about is this bit:
> >>
> >> 6) this means that if I take the comp hyp seriously, then, to predict
> >> the results of any experiment/experience, I have to "localize" all the
> >> infinitely many instantiations of my current state in the UD, look at
> >> the uncountable comp histories going through that states, and compute
> >> the statistics bearing on all consistent first person
> >> self-continuation.
> >>
> >> A human life must be a compilation of all these including the creation
> >> of internal [synaptic change, etc] structure/record which endow the
> >> ability to *be* the story. But when looking at this as a/n
> >> [infinity^infinity] Many Worlds affair, none of the worlds could 'know'
> >> that they are like or identical to others, surely? So I am puzzled.
> >> What
> >> holds 'my lot' together? We seem always to be confronted by yet another
> >> infinite regression.
> >
> >
> >
> > With comp, what holds 'your lot" together are the relation between
> > numbers. The apparent third person infinite regression stops at the
> > level of those relations. The first person is most probably confronted
> > with many infinities, but this should not be considered as
> > problematical.
> >
> >
> >
> >
> >
> >
> >
> >> ******
> >> A quick aside, hopefully not totally unrelated: Am I right that a valid
> >> explanation of the zero point energy is that it is impossible *in
> >> principle* to measure the state of something
> >
> > Why can't we measure the state of something? Even with just QM, the
> > many-world idea has been invented for abandoning the idea that a
> > measurement pertubates what is observed.
> >
> >
> >
> >> and therefore *we* must
> >> acknowledge the indeterminacy
> >
> > We must acknowledge indeterminacy once we postulate comp, given that it
> > makes us self-duplicable, and indeed self-duplicated "all the time".
> >
> > Bruno
> >
> >
> >> and so must everything else which exists
> >> because we are nothing special, except we think we know we are here,
> >> and
> >> if we are bound by quantum indeterminacy, so is everything else [unless
> >> it can come up with a good excuse!]?
> >>
> >> [Perhaps this is more on Stathis's question to Russell: Is a real
> >> number
> >> an infinite process?]
> >>
> >> ******
> >>
> >>
> >>
> >> Regards
> >>
> >> Mark Peaty CDES
> >>
> >> mpeaty.domain.name.hidden
> >>
> >> http://www.arach.net.au/~mpeaty/
> >>
> >>
> >>
> >>
> >>
> >> Bruno Marchal wrote:
> >>> Le 05-mars-07, à 15:03, Mark Peaty a écrit :
> >>>
> >>>
> >>>
> >>>> Nobody here has yet explained in plain-English why we have entropy.
> >>>> Oh
> >>>> well, surely, in the Many Worlds, that's just one of the universes
> >>>> that
> >>>> can happen!
> >>>>
> >>>
> >>> Not really. That would make the comp hyp or the everything idea
> >>> trivial, and both the "everything hyp" and the "comp hyp" would loose
> >>> any explicative power. (It *is* the problem with Schmidhuber's comp,
> >>> *and* with Tegmark's form of mathematicalism: see older posts for
> >>> that).
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>> Except that, for plain-English reasons stated above, there
> >>>> are *and always have been* infinity x infinity x infinity of entropic
> >>>> universes.
> >>>>
> >>>> It doesn't make sense. Call me a heretic if you like, but I will
> >>>> 'stick
> >>>> to my guns' here: If it can't be put into plain-English then it
> >>>> probably
> >>>> isn't true!
> >>>>
> >>>
> >>>
> >>> I will try. I will, by the same token, answer Mohsen question here:
> >>>
> >>>
> >>>
> >>>
> >>> Mohsen:
> >>>
> >>>> I don't know if in the hypothesis of simulation, the conflict of
> >>>> Countable and Uncountable has been considered.
> >>>>
> >>>
> >>>
> >>>
> >>> 1) I assume the comp hyp, if only for the sake of the reasoning. The
> >>> comp hyp is NOT the hypothesis of simulation, but it is the hypothesis
> >>> that we are in principle self-simulable by a digital machine.
> >>>
> >>> 2) Then we have to distinguish the first person points of view (1-pov)
> >>> from third person points of view (3-pov), and eventually we will have
> >>> to distinguish all Plotinus' hypostases. With comp, we are
> >>> duplicable.
> >>> I can be read and cut (copy) in Brussels, and be "pasted" in
> >>> Washington
> >>> and Moscow simultaneously. This gives a simple example where:
> >>> a) from the third point of view, there is no indeterminacy. An
> >>> external
> >>> (3-pov) observer can predict Bruno will be in Washington AND in
> >>> Moscow.
> >>> b) from a first person point of view, there is an indeterminacy, I
> >>> will
> >>> feel myself in washington OR in Moscow, not in the two places at once.
> >>>
> >>> 3) Whatever means I use to quantify the first person indeterminacy,
> >>> the
> >>> result will not depend on possible large delays between the
> >>> reconstitutions, nor of the virtual/material/purely-mathematical
> >>> character of the reconstitution.
> >>>
> >>> 4) There exist a universal dovetailer (consequence of Church thesis,
> >>> but we could drop Church thesis and define comp in term of turing
> >>> machine instead).
> >>>
> >>> 5) Never underestimate the dumbness of the universal dovetailer: not
> >>> only it generates all computational histories, but it generates them
> >>> all infinitely often, + all variations, + all "real" oracles (and
> >>> those
> >>> oracles are uncountable).
> >>>
> >>> 6) this means that if I take the comp hyp seriously, then, to predict
> >>> the results of any experiment/experience, I have to "localize" all the
> >>> infinitely many instantiations of my current state in the UD, look at
> >>> the uncountable comp histories going through that states, and compute
> >>> the statistics bearing on all consistent first person
> >>> self-continuation.
> >>>
> >>> 7) A naive reading of this leads to predict white rabbits (indeed the
> >>> lewis Carroll one) and perhaps white noise, that is too much entropy
> >>> ... This leads to a cheap refutation of comp, ...
> >>>
> >>> 8) ... except that the math shows this is a bit too cheap. Now if comp
> >>> is correct, AND if the physical laws are (approximately) correct, then
> >>> we have to extract the physical laws
> >>> a) without assuming the existence of a physical universe,
> >>> b) from the comp statistics.
> >>>
> >>> My (more technical) result is that computer science and mathematical
> >>> logics gives already clues that indeed we can recover the physical
> >>> laws
> >>> from computer science, once we get the relevant description of the
> >>> different points of view.
> >>>
> >>> In particular, for Mohsen's question, the conflict between countable
> >>> and uncountable appears to be an unavoidable conflict between first
> >>> and
> >>> third person points of view. The first person is bound up to interact
> >>> with uncountable physical apparent reality.
> >>> But all self-referentially correct universal machine introspecting
> >>> herself can discover the unavoidability of that conflict, and somehow
> >>> "meta-solve" it, indeed by distinguishing explicitly those points of
> >>> view again. When she does this, she discover a more subtle tension
> >>> between recursively countable and non recursively countable. This
> >>> tension is creative and can be proposed as a beginning of explanation
> >>> of life and local neguentropy.
> >>>
> >>> All this makes comp, and its related "theology" (theory of everything
> >>> including persons, say), empirically testable: derive the comp-physics
> >>> and compare with empirical nature.
> >>>
> >>> Must go. Hope this helps, (see papers in my url for more, or just ask)
> >>>
> >>> Bruno
> >>>
> >>> http://iridia.ulb.ac.be/~marchal/
> >>>
> >>>
> >>>
> >>>
> > http://iridia.ulb.ac.be/~marchal/
> >
> >
> > >
> >
> >
>
>
>
> >
>
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Received on Mon Apr 02 2007 - 18:41:52 PDT