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.

However, as the cardinality of "my" ensemble is actually "c" (cardinality of the real numbers), it is quite probably a completely different beast.

There you go again with your radical compression. Without the reading I've been doing in the last two weeks, I wouldn't have been able to decode this statement as meaning:

2^\aleph_0 = \aleph_1 (by definition)

To assume c = \aleph_1 is the Continuum Hypothesis, which is unprovable (within standard arithmetic).


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.

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... 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.

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.


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. 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.

BTW I'm with Kant: you can't have an appearance without an underlying reality, even if that is unknowable.

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? In this case "where they live" is crucial because it defines the environment the SAS find themselves in. 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. 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? In this case it's unhelpful to call these meta-entities "observers"; rather, in effect, they constitute the (meta-)laws of physics. 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 page then goes on to make some comments about measure applied to
universes.  Here again I am confused about how to relate it to all that
has been descibed.  What are the analogs of universes, in this model?
Is it "descriptions", the infinite bit strings?  From what has been
presented so far, I don't understand how to relate our experience of
reality to this model.

Each description is a possible universe, composed of an infinite
amount of information. Any observer will of course only comprehend a
finite amount information, and hence be in a superposition of a subset
of universes corresponding to that finite information. Admittedly the
usage of the term "universe" is slightly strange here.

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.

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.

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? 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"?

(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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