On Tue, 7 Jun 2005, Russell Standish wrote:
Hal dealt with this one already, I notice. 2^\aleph_0 = c. \aleph_1 is
something else entirely.
d'oh!
<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.
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).
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?
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.
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.
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.
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.
<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.
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). Kant's point was that you can't infer
the nature of "things in themselves" from observation. He didn't say that
you can't speculate about their nature, and even guess right, by chance.
In effect, this mailing list discusses nothing but the nature of the
noumenon. (Kant would probably say this is a waste of time, of course).
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?
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.
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!).
The acid test is this: Can your observers exchange information with each
other, and if so what is the data channel?
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".
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.
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!
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!
It is true in QM that the
complex Hilbert space structure allows for interference effects, but
the term superposition surely has a broader meaning.
The most general meaning is the literal one: A & B are super(im)posed if
they are lying on top of each other. But it's rather a pointless
expression if a superposition can't be distinguished from either/or.
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".
OK, that's clearer.
<stuff on meta-time deleted as maybe this will make sense when we get on
to your QM section!>
Paddy Leahy
