On Mon, Jun 06, 2005 at 12:06:06PM +0100, Patrick Leahy wrote:
>
>
> On Mon, 6 Jun 2005, Russell Standish wrote:
>
> >I am beginning to regret calling the all descriptions ensemble with
> >uniform measure a Schmidhuber ensemble. I think what I meant was that
> >it could be generated by a standard dovetailer algorithm, running for
> >2^\aleph_0 timesteps.
>
> It can't! Timesteps are denumerable, hence this statement is just a
> contradiction in terms. You better postulate your ensemble without
> reference to any algorithm to generate it.
Indeed I do. Only Schmidhuber uses the dovetailer. Hence my "regret".
...
>
> 2^\aleph_0 = \aleph_1 (by definition)
>
Hal dealt with this one already, I notice. 2^\aleph_0 = c. \aleph_1 is
something else entirely.
> <snip>
> >
> >Now an observer will expect to find a SAS in one of the descriptions
> >as a corrolory of the anthropic principle, which is explicitly stated
> >as one of the assumptions in this work. I make no bones about this - I
> >consider the anthropic principle a mystery, not self-evident like
> >many people.
>
> Very few supporters of the AP would "expect to find a SAS" in a bitstring.
> Until you *specify* a way of interpreting the string, it contains nothing
> but bits.
The observer specifies the interpretation.
>
> >Why should an observer expect to see a token of erself
> >embedded in reality? That is the mystery of the AP.
>
> What ARE you talking about? Observer's don't see tokens of
> themselves...
I can see that I have a body - if I look in the mirror I can see a
face, eye etc, all of which appear to be under my control. This is a
token embedded in my reality that represents me.
> if anyone (God?) has a 3rd-person/bird's eye view, it is certainly not
> someone who is included in any particular reality. No way is anything like
> this implied by the AP. All the AP requires is that there *be*
> observers/SAS in (real) universes, which is true in our case at least.
>
Sorry - you lost me here ... oh well.
> >
> >>And now we find not only that the bit string is
> >>a description, but it is a complex enough description to describe SAS's?
> >>How does that work?
> >>
> >
> >The bitstrings are infinite in length. By reading enough bits, they can
> >have arbitrarily complex meanings attached to them.
> >
>
> In particular, any bitstring can be "interpreted" as any other bitstring
> by an appropriate map. Hence until you specify an interpreter you are
> simply not proposing a theory at all.
>
The observer _is_ the interpreter. There may well be more than one
observer in the picture, but they'd better agree!
> <snip>
> >
> >All that is discussed in this paper is appearances - we only try to
> >explain the phenomenon (things as they appear). No attempt is made to
> >explain the noumenon (things as they are), nor do we need to assume
> >that there is a noumenon.
>
> Most readers of your paper would take it that you are making a strong
> ontological proposition, i.e. that the basis of reality is your set of
> bitstrings.
This is the case.
If this is *not* the case, and you think the bitstrings may be
> represented in some deeper reality (or maybe are just metaphors), then
> what is the motivation for your proposal? Why do we need to think about
> this intermediate layer of bitstrings? The original simplicity goes out
> the window.
This latter extrapolation is not the case.
>
> BTW I'm with Kant: you can't have an appearance without an underlying
> reality, even if that is unknowable.
>
I'm not sure Kant says this, but in any case that's not important. I'm
with Marchal, who says if there is an underlying reality which is not
only unknowable, but also unnecessary to explain phenomena, then why
assume that particular hypothesis? It makes no sense.
> >Bruno Marchal has a detailed discussion on this in his thesis, and
> >concludes that he "has no need for this hypothesis" (what he calls the
> >extravagant hypothesis).
> >
> >So the former statement is true :[the description strings are] things
> >that "observer" TM's observe and map to integers. It is also true that
> >descriptions of self aware observers will appear within the description
> >by the Anthropic Principle. The phenomenon of observerhood is included.
> >However where the observers actually live is not a meaningful question
> >in this framework.
>
> I think either your terminology or you model has now got very confused.
> Are your "observer" TMs the observers (SAS) whose experiences your theory
> is trying to explain?
Yes.
> In this case "where they live" is crucial because it
> defines the environment the SAS find themselves in.
Why?
> If you are not
> careful your theory becomes effectively that we are all "brains in
> bottles" or Leibnizian monads, which is solipsism by another name.
It is not solipsism, if only for the reason that multiple observers
exist in our observed reality. They are all as real as our own consciousness.
Bruno Marchal calls this "shared dreaming". It seems apt.
> Or are
> your "observers" the missing "interpreters" in your theory which give it
> meaning, and allow us to find (in principle) the SAS within the bitstrings
> that represent actual observers like us?
Yes. I wasn't aware of them being missing though. Where did you find
them? :)
In this case it's unhelpful to
> call these meta-entities "observers"; rather, in effect, they constitute
> the (meta-)laws of physics.
Hmm... I'm not sure what your point is here.
Incidentally, a TM by itself can't generate
> meaning, as it is only a map from integers to integers. You still have to
> specify externally how to interpret the code as something more than a mere
> number. (E.g. in the Turing test the output bits have to be processed into
> English language text).
>
The use of TM was to connect with computationalists. Computationalists
would say that all observers could be represented by a TM, and
observers do attach meaning to bitstrings. The meanings themselves can
be enumerated, ie embedded in N.
Of course not all TMs are observers - we're not trying for a complete
theory of consciousness here!
And the theory works even if the observers were not TMs, but simply
some prefix map from the space of descriptions to the space of meanings.
All you give up is the compiler theorem, or some universal complexity
measure. Grounding complexity with respect to the observer suffices.
>
> Not to mention the terms "observer" and "superposition". In QM, which is
> the natural context, superposition implies that it is possible sometimes
> to observe (and predict) interference effects. I don't see how this can
> happen in your sense, since there is no interaction between descriptions.
I disagree. Superposition simply means that something is true and not
true simultaneously, it is indeterminate. It is true in QM that the
complex Hilbert space structure allows for interference effects, but
the term superposition surely has a broader meaning.
>
> >Alterantively, one could talk about "observer moments" as corresponding
> >to the equivalence classes of descriptions. This interpretation would be
> >more natural to many here on this list.
>
> Surely not equivalence classes of *descriptions*? If a description =
> universe, some will contain many different observers and hence OMs.
>
These are orthogonal ways of interpreting mathematical
objects. Descriptions may contain multiple observers (according to the
given observer, of course). And sets of descriptions (which we're
identifying as OMs) contain descriptions as set members.
However the word "contains" has two distinctly different mathematical
meanings here. It is probably better to replace it with the word
"belongs" when referring to OMs, ie "Set A contains description x"
whould be translated as "Observer moment A belongs to universe x". By
logic, of course, OMs in general belong to many universes. Also "a
universe x having many OMs" corresponds to "description x being an element of
multiple sets".
> >
> >In section 3 of the paper, I now introduce a temporal dimension, with
> >the observer repeatedly sampling the set of all descriptions, with the
> >proviso that successor states can only differ by a finite number of bits.
> >
>
> So are you saying that your "descriptions/universes" in Section 2 don't
> contain a representation of time?
No - its just it hasn't been made explicit. Since all descriptions are
in the ensemble, some will naturally have a description of time.
>why shouldn't they? If they don't, how
> can they represent "universes" in any sense at all? If they do, what's the
> point of introducing a second, independent "time dimension" in your
> meta-world of "observer" processing "universes"?
>
To make it explicit to deal with subsequent issues - failure of
induction and quantum mechanics.
> (And no, I havn't managed to work all the way through you "QM" section.
> After a while you just lost me completely. I'm hoping Hal's questions
> will help clarify things enough for me to get a grip on it.)
>
> Paddy Leahy
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Received on Mon Jun 06 2005 - 20:49:49 PDT