On Tue, Jun 07, 2005 at 10:15:03PM +0100, Patrick Leahy wrote:

> >>>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.
> But the observer is *generated* by the interpretation! Until you have an 
> interpretation, you have no observers. And until you have an observer, you 
> have no interpretation (at least that's how I read the sentence quoted 
> above).

No the observer is somehow primary. As are the descriptions. If it
weren't for the anthropic principle, there would be no connection
between the two, and we'd have a genuine "brain-in-the-vat".

> How can structures which exist as some sort of pattern inside a bit string 
> (or am I supposed to say in the "meaning" integer output by some (other) 
> O(x)?) read a separate bitstring which exists as a parallel universe in 
> Platonia?

That is what they do, by definition. Observers observe. Platonia is a
collection of all possible observations, hence what observers observe
is in Platonia.

> So you find it a mystery that you have a face, eye etc??  If so, what does 
> the AP have to do with this mystery? Actually, maybe it would clarify 
> things if you said what you mean by the AP; it certainly doesn't seem to 
> be very like the AP that I know about.

The AP is a statement that observed reality must be consistent with
the observer being part of that reality.

> I'm not sure whether your "my reality" refers to the external world or 
> your internal representation of it. I guess the latter, otherwise your 
> body would be you, not a token representing you.

I'm not entirely sure I distinguish your difference between "external
world" and "internal representation". We're talking about observations
here, not models.

> >>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!
> Why does this follow? Your "observers" are maps O(x) from prefix strings 
> to the integers. Why can't you have two inconsistent maps... or rather, 
> how can you possibly avoid such?  And since two different maps don't 
> interact at all (how can a mapping interact with another mapping?) each of 
> your observers seems to be sealed in his own little universe. In which 
> case having >1 observer appears to be an unverifiable speculation, which 
> is why I say it seems like solipsism.

It follows from the Anthropic Principle. If O_1 is consistent with its
observed reality, and O_2 is consistent with its observed reality,
and O_1 observes O_2 in its reality, then O_1 and O_2 must be
consistent with each other (at least with respect to their observed realities).

> >>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.
> Well, if you are making an ontological proposition, you are ipso facto not 
> just explaining appearances. In your model your "bitstrings" *are* the 
> noumenon (in Kant's terminology). 

Sorry, I don't see this. The bitstrings are phenomena. No noumenon
appears. It is possible we are arguing semantic differences only though.

> >
> >>In this case "where they live" is crucial because it
> >>defines the environment the SAS find themselves in.
> >
> >Why?
> An intelligent system is "intelligent" by virtue of the way it interacts 
> with its environment. Think about the Turing test again: we conclude that 
> the computer is (not) intelligent because of the way it interacts with us. 
> To put it another way, you define these things as "observers". This 
> implies something observed. Obviously your model had better account for 
> people (observers) like us observing something like the world we see 
> ("where we live"), and preferably interacting with other people who are 
> granted equal status your ontology.

Does it not? OK, it is not exactly explicit about it, but this
situation should appear somewhere in Platonia.

> >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.
> If that's the *only* reason it's not solipsism, then I would say you just 
> don't have the courage of your convictions. Bruno's "shared dreaming" 
> sounds very like Leibniz's pre-established harmony, but that only works if 
> you believe in a provident deity (if it ever worked for anyone but 
> Leibniz!).

I'm not especially interested in Lebniz's thoughts on this
subject. But if it involves a provident deity, it sounds nothing like
either my theory or Bruno's.

> The acid test is this: Can your observers exchange information with each 
> other, and if so what is the data channel?

Yes. You will observe in your description other observers making
"marks" on the universe. This is a communication channel. There are
some subtleties to do with free will and so on, but this is
definitely stepping outside the remit of "Why Occam's paper".

> >
> >>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? :)
> I hope this is a bit clearer now. My problem is that you are trying to 
> make your observers work at two different levels: as structures within the 
> universes generated (somehow!) by your bitstrings, but also as an 
> interpretive principle for producing meaning by operating *on* the 
> bitstrings.  It's a bit like claiming that PCs are built by "The Sims".

Yes it is a bit like that. Obviously, the Anthropic Principle (or its
equivalent) does not work with "The Sims".

> >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.
> >
> I'm actually very sceptical of this claim.  Obviously you can encode a 
> meaning in a number, but the meaning is then carried at least partly by 
> the code, and not just by the number.

Of course, but that is of no importance. For the purposes of the
argument, all one does is perform an arbitrary enumeration of meanings
(which of course implies that this should be possible). The numbers do
not carry any meanings at all.

> >
> >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.
> >
> Is there a mathematical theory of meanings that could make the notion of a 
> "space of meanings" well-defined? Last I heard, philosophers were still 
> arguing about what "meaning" means!

By saying that meanings are enumerable sidesteps all these
difficulties. I have no problem with enumerable meanings, in fact I
think it is self-evident - but maybe not.

> >>
> >>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.
> In your private language, maybe. I shudder to think what bizarre ideas it 
> would put in the heads of my students if I used this definition!

Presumably when discussing this with your students, you are in the
context of quantum systems. In that context, superposition has the
usual linear sum of state vectors.

According to Oxford dictionary, "superposition" means multiple things
occupying the same place. This is obviously a far more general usage
than the QM meaning. And last time I looked, English was not a private

In the context of descriptions, a set of descriptions is a
superposition of descriptions. Where the descriptions disagree with
one another, the situation is indeterminate. Where they agree, that is
the information encoded by that set. If you want a mental image, use
Borges's library of Babel. Each book is a description. A set of books
has less information than each individual book due to inconsistencies
between them.


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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
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