Re: Questions on Russell's Why Occam paper

[Russell Standish]

I'm not sure I follow your reasoning, but it wouldn't surprise me if
the Turing subset of my world has additional constraints - namely the
worlds seen by observers whose O(x)'s are prefix machines, not just maps.

On Fri, Jun 10, 2005 at 05:56:50PM +0200, Bruno Marchal wrote:
 
 Le 10-juin-05, ? 14:59, Patrick Leahy a ?crit :
 
 Russell Standish:
 If the AP applies to the Sims Mark VII, then their reality will be a 
 description containing a body corresponding to their intelligences. 
 They will not be aware of the PC that their description is being 
 generated on. We, who inhabit the world with the PC will not be aware 
 of the countless other PCs, Macs, Xboxes, Eniacs, Turing machines, 
 pebbles in Zen monasteries etc running Sims Mark VII. So the PC 
 itself is actually irrelevant from the internal perspective of the 
 Sims.
 
 Well at least we agree on that.  No strange loops in this picture, so 
 it is unlike the picture you outline in your paper.
 
 
 
 Aargh  Bad luck! A point where I disagree with both Schmidhuber 
 *and* Standish, at least here apparently.
 
 To explain I must assume comp and ... (for one) explicitly the *result* 
 of my thesis. In a nutshell: it is that, if comp is assumed, then the 
 correct law of physics are derivable from comp. (it makes comp 
 testable: derive physics from comp and compare with empirical physics).
 I will call the physics derived from comp: the comp-physics.
 
 Please admit this if only for the sake of the argument.
 
 Suppose I build a simulated city with some self-aware entities evolving 
 in that simulated environment. Then
 
 Either I simulate the correct comp physics, then apparently the 
 simulated entity cannot know they are simulated by me, but actually 
 this sentence has no meaning, because they are simulated by 2^aleph_0 
 immaterial stories (constituting arithmetical truth), so it is only in 
 a weak sense that they are failed. (actually it is not even possible to 
 simulate comp physics except in the ridiculous sense of running 
 (really) the universal dovetailer.
 
 Or I simulate incorrect comp physics, then the only way we could say 
 the simulated entity are failed is
 1) either by killing them (in some absolute way) when they discover 
 discrepancies between the comp-physics they can find by herself and 
 their fake environment. But in that case their story is finite and its 
 measure can be shown equal to 0. Or
 2) eithert I keep up correcting the simulation, but then in the limit I 
 don't fail them. Or I limit the cognitive ability of the entities, but 
 then either I will failed to genuinely fail them, or I will make them 
 inconsistent (and here too the measure can be shown equal to zero, and 
 that is related to the non-cul-sac phenomenon).
 
 
 It is an amazing positive consequence of machine's incompleteness that 
 you cannot genuinely failed any (relatively simulated or not) machine 
 having enough introspection power for a very long time.
 
 Apparently, In machine's platonia, all lies leads soon or later to a 
 (recognizable) catastroph.
 
 Tp prevent falling into an inconsistency, this last conclusion follows 
 from comp, and remember that if comp is correct we cannot know it is 
 correct, and we cannot probably know that all lies leads soon or later 
 to a (recognizable) catastroph. But if you *bet* on comp, you can bet 
 on it!
 
 Bruno
 
 
 http://iridia.ulb.ac.be/~marchal/

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Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Fri, Jun 10, 2005 at 01:59:16PM +0100, Patrick Leahy wrote:
 
 On Thu, 9 Jun 2005, Russell Standish wrote:
 
 Yes, if you think there is a concrete reality in which everything exists 
 (your question of where does the observer live?), then the AP is a 
 tautology.
 
 What I meant by where does the observer live, in more formal language, 
 is how do you account for the (apparent) sense data we have?. 

Perhaps you ask too much. Your question is something along the lines
of what explains qualia, or what breathes fire into the
equations. 

I could state baldly that descriptions can conscious. This is no more
preposterous than Tegmarks mathematical systems can be
conscious. Maybe that satisfies you, maybe not. What can be stated
more convincingly is that all experience (including internal conscious
experience) is a description, a bunch of data interpreted by an
observer. Consequently, the set of all descriptions will contain a
description of your current conscious experience. Hence we can make
strong claims about appearances - the phenomenon. As to whether there
is a Noumenon - I take Laplace's rather agnostic point of view - I have
no need of that hypothesis. Perhaps you do.

 I also 
 have a strong preference for an account where the description of at least 
 our world doesn't privilege one particular observer. In particular, this 
 is hard to square with your insistence that the observer provides the 
 interpretation of each of your bitstring universes.
 

The situation is symmetric with respect to all observers. That is
hardly priveleging  an observer.

 As both Hal and I keep trying to emphasise, we are interested in how, or 
 whether, your theory can account for our own existence and the reality (or 
 appearance, if you prefer) that we see around us. So the case of 
 disembodied intelligences is a total a red herring. I don't really care 
 whether these feature in your theory or not, but I do care whether you can 
 account for (apparently) embodied intelligences.
 

Apparently embodied intelligences are part of the space of all
descriptions by definition. The anthropic principle accounts for the
fact that we observer them, and not (say) flying white rabbits.

 
 Instead, one can take the Anthropic Principle as an assertion of the 
 reality we inhabit...
 
 Again, you are using a private language... the AP is not regarded as any 
 such assertion by anyone else I've ever heard of. Most people regard their 
 existence as proved by their own subjective experience, not some invented 
 principle. 

Of course - Decartes and all that. The AP applies to what we see in
the world around us, not a proof or otherwise of our own existence.

 
  ... and experimentally test it. In all such cases is has been shown to 
 be true, sometimes spectacularly.
 
 If we know experimentally the reality we inhabit (?!), which I guess 
 I've just claimed that we do, why do we need a principle to assert it?
 
 Likely you mean something completely different, in which case please 
 explain (with examples of said experiments!).

The experiments are the usual suspects showing fine tuning of physical
parameters in the universe. Tegmark's paper is a good review of the
topic. As is Barrow and Tipler's book.

 
 snip Quoting me:
 
 Then you are implying that the observer can, in a finite time, read and 
 attach meaning to a full (space-time) description of itself, including 
 the act of reading this description and so on recursively.
 
 
 Not at all. Consistency is the only requirement. If the observer goes 
 looking for erself, then e will find erself in the description. It 
 doesn't imply the observer is doing this all the time.
 
 I think here we have run into the same inconsistency that you admitted in 
 your discussion with Hal. In your first reply to Hal you assert that the 
 observer O(x) attaches a unique meaning to the description string. Which 
 would imply processing all bits of the string up to the start of the 
 don't care region. A later reply suggest that we should in different 
 contexts assume (a) this and (b) what your paper actually says, i.e. the 
 meanings are updated as further bits are read.  Now you have changed this 
 again, and the observer is not (modelled by) a simple mapping but is a 
 free agent who can choose to apply mappings to different regions of the 
 bitstring at will.

Yes, as I've further clarified to Hal, O(x) is actually a function of
time. One imagines that in general the region of sigificant bits of x
expands as a function of (psychological) time. 

In my defence, the paper was written over a period of 4 years, and the
O(x) was a later addition to try to clarify points in section 2. I
didn't realise at the time that it introduced some ambiguities into
section 3.

 
 And even that doesn't actually answer my problem: let's assume the 
 observer *does* go looking for erself. You claim he will find himself, 
 but if the description is *complete* my original problem remains: he will 
 never finish 

Re: Questions on Russell's Why Occam paper

[Bruno Marchal]

Le 10-juin-05, à 14:59, Patrick Leahy a écrit :


Russell Standish:
If the AP applies to the Sims Mark VII, then their reality will be a 
description containing a body corresponding to their intelligences. 
They will not be aware of the PC that their description is being 
generated on. We, who inhabit the world with the PC will not be aware 
of the countless other PCs, Macs, Xboxes, Eniacs, Turing machines, 
pebbles in Zen monasteries etc running Sims Mark VII. So the PC 
itself is actually irrelevant from the internal perspective of the 
Sims.


Well at least we agree on that.  No strange loops in this picture, so 
it is unlike the picture you outline in your paper.





Aargh  Bad luck! A point where I disagree with both Schmidhuber 
*and* Standish, at least here apparently.


To explain I must assume comp and ... (for one) explicitly the *result* 
of my thesis. In a nutshell: it is that, if comp is assumed, then the 
correct law of physics are derivable from comp. (it makes comp 
testable: derive physics from comp and compare with empirical physics).

I will call the physics derived from comp: the comp-physics.

Please admit this if only for the sake of the argument.

Suppose I build a simulated city with some self-aware entities evolving 
in that simulated environment. Then


Either I simulate the correct comp physics, then apparently the 
simulated entity cannot know they are simulated by me, but actually 
this sentence has no meaning, because they are simulated by 2^aleph_0 
immaterial stories (constituting arithmetical truth), so it is only in 
a weak sense that they are failed. (actually it is not even possible to 
simulate comp physics except in the ridiculous sense of running 
(really) the universal dovetailer.


Or I simulate incorrect comp physics, then the only way we could say 
the simulated entity are failed is
1) either by killing them (in some absolute way) when they discover 
discrepancies between the comp-physics they can find by herself and 
their fake environment. But in that case their story is finite and its 
measure can be shown equal to 0. Or
2) eithert I keep up correcting the simulation, but then in the limit I 
don't fail them. Or I limit the cognitive ability of the entities, but 
then either I will failed to genuinely fail them, or I will make them 
inconsistent (and here too the measure can be shown equal to zero, and 
that is related to the non-cul-sac phenomenon).



It is an amazing positive consequence of machine's incompleteness that 
you cannot genuinely failed any (relatively simulated or not) machine 
having enough introspection power for a very long time.


Apparently, In machine's platonia, all lies leads soon or later to a 
(recognizable) catastroph.


Tp prevent falling into an inconsistency, this last conclusion follows 
from comp, and remember that if comp is correct we cannot know it is 
correct, and we cannot probably know that all lies leads soon or later 
to a (recognizable) catastroph. But if you *bet* on comp, you can bet 
on it!


Bruno


http://iridia.ulb.ac.be/~marchal/

Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Thu, Jun 09, 2005 at 01:55:32AM +0100, Patrick Leahy wrote:
 
 [Russell Standish wrote]:
 
 The AP is a statement that observed reality must be consistent with
 the observer being part of that reality.
 
 Famously, this can be interpreted as either a trivial tautology (Brandon 
 Carter's original intention, I think), or an almost-obviously false 
 principle of necessity (Barrow  Tipler's SAP). If you think there's a 
 mystery here it suggests you go for the necessity version, but given your 
 infinite ensemble the tautology would suffice perfectly well.

Yes, if you think there is a concrete reality in which everything
exists (your question of where does the observer live?), then the AP
is a tautology. 

However, if you are prepared to allow for the possibility that
observers exist nowhere, then things are not quite so simple. One
can always imagine being the brain-in-the-vat observer a reality which
does not contain a body, or a brain, in a vat or anywhere
else. Usually in this scenario, the observer will conclude that there
must be a body somewhere else, and so concludes that it is inhabiting
some kind of virtual reality. However, this implicitly assumes there
has to a brain somewhere, and so implies a reality somewhere else for
the brain to inhabit. But what if the brain is not required?

Obviously, the last conclusion is full blown solipsism, but that is
hardly a knock down argument.

Instead, one can take the Anthropic Principle as an assertion of the
reality we inhabit, and experimentally test it. In all such cases is
has been shown to be true, sometimes spectacularly. With the AP, one
recovers some of the properties of a concrete reality, without all of
it. In particular, Marchal's shared dreaming follows as a
consequence, and it contradicts solipsism.

 
 You also said:
 
 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? snip
 
 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).
 
 Ah. Just to be sure, do you mean that the string the observer attaches 
 meaning to is the one which describes the very same observer? This seems 
 to be implied by your comment above; but you don't say it or clearly 
 imply it in your paper.
 
 Then you are implying that the observer can, in a finite time, read and 
 attach meaning to a full (space-time) description of itself, including the 
 act of reading this description and so on recursively.
 

Not at all. Consistency is the only requirement. If the observer goes
looking for erself, then e will find erself in the description. It
doesn't imply the observer is doing this all the time.

 Which is impossible, of course.
 

Of course.

 You also said:
 
 I'm not entirely sure I distinguish your difference between external
 world and internal representation. We're talking about observations
 here, not models.
 
 I'm sure you can distinguish *my* mental representation of the world from 
 your own. Hence if we share a world, and you can't distinguish between 
 that world and your internal representation, then you are not granting 
 equal status to other observers such as me.
 

I'm not sure that is the case. I have a theory of your mind. I get it
most economically by observing my own mind, hence I'm self-aware. My
theory of the mind says that you are doing the same thing. Isn't this
symmetric? 

 You also said (quoting me):
 
 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.
 
 Actually I don't see why not. The existence of The Sims implies a universe 
 compatible with the existence of Sims. But granting this is not so for the 
 sake of the argument, presumably the AP *will* apply to the Sims Mark VII 
 which will be fully self-aware artificial intelligences. 

If the AP applies to the Sims Mark VII, then their reality will be a
description containing a body corresponding to their
intelligences. They will not be aware of the PC that their description
is being generated on. We, who inhabit the world with the PC will not
be aware of the countless other PCs, Macs, Xboxes, Eniacs, Turing
machines, pebbles in Zen monasteries etc running Sims Mark VII. So the
PC itself is actually irrelevant from the internal perspective of the Sims.

 But it will still 
 be absurd to claim that the Sims are responsible for construction of PCs 
 (assuming they are not connected to 

Re: Questions on Russell's Why Occam paper

[Hal Finney]

Russell Standish writes:
 On Mon, Jun 06, 2005 at 01:51:36PM -0700, Hal Finney wrote:
  In particular, if an observer attaches sequences of meanings to sequences
  of prefixes of one of these strings, then it seems that he must have a
  domain which does allow some inputs to be prefixes of others.  Isn't that
  what sequences of prefixes would mean?  That is, if the infinite string
  is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
  010, 0101, 01011,   Does O() apply to this sequence of prefixes?  If
  so then I don't think it is a prefix map.

 Yes I agree this is vague, and seemingly contradictory. I'm not sure
 how to make this more precise, but one way to read the paper is to
 treat observers as prefix maps for section 2 (Occam's razor), and then
 for section 3 (White Rabbit problem) ignore the prefix property.

 It could be that the way of making this more precise is to assume
 observers have some internal state that is constantly updated (a time
 counter perhaps), so actually going through a sequence of prefix maps
 in (psychological) time, but at this stage I don't have an answer.

Unfortunately I still don't understand this.  You agree that it is a
seeming contradiction but that doesn't help me to see how to interpret it.

Here's an idea.  Would it be possible for you to explain how this
page is meant to be understood, in an INformal way?  Often when people
present concepts they do a formal writeup, but if they give a seminar
or explanation they will depart from the formalism and explain what is
really going on behind the scenes.  That's the kind of explanation I think
I need.

Could you explain how these concepts relate to the actual experiences
we have as human observers?  What are descriptions and meanings
in terms of our sensory and mental experiences?  Which descriptions
does an observer observe?  What are the sequences of prefixes and
how do they relate to our day to day lives?  What is the point of the
equivalence classes and what does that have to do with what we observe?

I think an informal explanation of these topics would help me, and
perhaps Paddy, to better understand the structure that you formally
describe.  At this point I am still failing to see how it all relates
to my experience of the world as an observer.

Thanks -

Hal Finney

Re: Questions on Russell's Why Occam paper

[Patrick Leahy]

[Russell Standish wrote]:


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


Famously, this can be interpreted as either a trivial tautology (Brandon 
Carter's original intention, I think), or an almost-obviously false 
principle of necessity (Barrow  Tipler's SAP). If you think there's a 
mystery here it suggests you go for the necessity version, but given your 
infinite ensemble the tautology would suffice perfectly well.


You also said:

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? snip


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).


Ah. Just to be sure, do you mean that the string the observer attaches 
meaning to is the one which describes the very same observer? This seems 
to be implied by your comment above; but you don't say it or clearly 
imply it in your paper.


Then you are implying that the observer can, in a finite time, read and 
attach meaning to a full (space-time) description of itself, including the 
act of reading this description and so on recursively.


Which is impossible, of course.

You also said:


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


I'm sure you can distinguish *my* mental representation of the world from 
your own. Hence if we share a world, and you can't distinguish between 
that world and your internal representation, then you are not granting 
equal status to other observers such as me.


You also said (quoting me):

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.


Actually I don't see why not. The existence of The Sims implies a universe 
compatible with the existence of Sims. But granting this is not so for the 
sake of the argument, presumably the AP *will* apply to the Sims Mark VII 
which will be fully self-aware artificial intelligences. But it will still 
be absurd to claim that the Sims are responsible for construction of PCs 
(assuming they are not connected to robot arms etc, for which no analogs 
exist in your theory). Let alone for them to construct the actual PC on 
which they are running, as apparently implied by your last message... even 
robot arms wouldn't help there.


Paddy Leahy

==
Dr J. P. Leahy, University of Manchester,
Jodrell Bank Observatory, School of Physics  Astronomy,
Macclesfield, Cheshire SK11 9DL, UK
Tel - +44 1477 572636, Fax - +44 1477 571618

Re: Questions on Russell's Why Occam paper

[Russell Standish]

If we're allowing ourselves a little informality, then I'd appeal to
the notion of observer moment. Within any observer moment, a finite
number of bits of the bitstrings has been read, and processed by the
observer. Since only a finite number of bits have been processed to
determine the meaning of reality at that moment, the
observer map O(x) is a prefix map. Hence at any point in time the
arguments in section 2 of the paper hold.

The meaning O(x) could also be called the observer moment. If
observer moments are enumerable, one can inject OMs into the set of
natural numbers.

Observers find themselves embedded in a psychological time. I have not
been explicit about exactly what this time is, however I envisage it
to probably be what mathematicians call a time scale, which is a
closed subset of the real numbers. Time could be continuous, or it
could be discrete (eg the set of natural numbers). It could be
something else, eg rational numbers or the Cantor set. All of these
are example time scales. The exact nature of time is something to be
settle later (if possible), but if you are more comfortable witrh
discrete time (as many are on this list), then you are welcome to use integers.

How this feeds back to our original observer map is that we'd expect
the map O(x) to be dependent on time, ie O(t,x). This is consistent
with time being psychological. The description or universe x is
independent of time. It would correspond to what David Deutsch calls a
block universe.

Now perhaps section 3 makes some sense. What I call robustness of
the observer, ie that observers will not be fooled by a little noise
on the line - lions in camouflage are still observed to be lions for
instance constrains the form of time evolution of O(t,x). I haven't
formalised exactly what this constraint is, but it is something along
the lines of continuity of |O^{-1}(t,O(t,x))|, or continuity of the
observed complexity of the world. 

On Wed, Jun 08, 2005 at 09:09:04AM -0700, Hal Finney wrote:
 Russell Standish writes:
  On Mon, Jun 06, 2005 at 01:51:36PM -0700, Hal Finney wrote:
   In particular, if an observer attaches sequences of meanings to sequences
   of prefixes of one of these strings, then it seems that he must have a
   domain which does allow some inputs to be prefixes of others.  Isn't that
   what sequences of prefixes would mean?  That is, if the infinite string
   is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
   010, 0101, 01011,   Does O() apply to this sequence of prefixes?  If
   so then I don't think it is a prefix map.
 
  Yes I agree this is vague, and seemingly contradictory. I'm not sure
  how to make this more precise, but one way to read the paper is to
  treat observers as prefix maps for section 2 (Occam's razor), and then
  for section 3 (White Rabbit problem) ignore the prefix property.
 
  It could be that the way of making this more precise is to assume
  observers have some internal state that is constantly updated (a time
  counter perhaps), so actually going through a sequence of prefix maps
  in (psychological) time, but at this stage I don't have an answer.
 
 Unfortunately I still don't understand this.  You agree that it is a
 seeming contradiction but that doesn't help me to see how to interpret it.
 
 Here's an idea.  Would it be possible for you to explain how this
 page is meant to be understood, in an INformal way?  Often when people
 present concepts they do a formal writeup, but if they give a seminar
 or explanation they will depart from the formalism and explain what is
 really going on behind the scenes.  That's the kind of explanation I think
 I need.
 
 Could you explain how these concepts relate to the actual experiences
 we have as human observers?  What are descriptions and meanings
 in terms of our sensory and mental experiences?  Which descriptions
 does an observer observe?  What are the sequences of prefixes and
 how do they relate to our day to day lives?  What is the point of the
 equivalence classes and what does that have to do with what we observe?
 
 I think an informal explanation of these topics would help me, and
 perhaps Paddy, to better understand the structure that you formally
 describe.  At this point I am still failing to see how it all relates
 to my experience of the world as an observer.
 
 Thanks -
 
 Hal Finney

-- 
*PS: A number of people ask me about the attachment to my email, which
is of type application/pgp-signature. Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.


A/Prof Russell Standish  Phone 8308 3119 (mobile)
Mathematics0425 253119 ()
UNSW SYDNEY 2052 [EMAIL PROTECTED] 
Australia

Re: Questions on Russell's Why Occam paper

[Bruno Marchal]

Le 06-juin-05, à 22:51, Hal Finney a écrit :


I share most of Paddy Leahy's concerns and areas of confusion with
regard to the Why Occam discussion so far.  I really don't understand
what it means to explain appearances rather than reality.



Well this I understand. I would even argue that Everett gives an 
example by providing an explanation of the appearance of a wave 
collapse from the SWE (Schroedinger Wave equation) and this without any 
*real*collapse.
And I pretend at least that if comp is correct, then the SWE as an 
*appearance* emerges statistically from the interference of all 
computations as seen from some inner point of view of the mean 
universal machine.
But, as I pointed a long time ago Russell is hiding (de facto, not 
intentionally I guess :) many assumptions.
There are a lot of derivation of the SWE in the literature, it would 
be interesting that Russell compares them with its own. My favorite one 
is the one by Henry and another one by Hardy.
Note the incredible derivation of QM from just 5 experiments + a 
natural principle of simplicity by Julian Swinger in his QM course 
(taken again by Towsend in its QM textbook). I will give reference once 
less busy.


I agree with Hal and Paddy about the lack of clarity in many passages.
Note that my result is infinitely more modest (despite the 
appearance!). I just prove that if comp is assumed to be correct then a 
derivation of the SWE *must* exist, without providing it. Well, in the 
interview of the Lobian machine I do extract some 'quantum logic' from 
comp, but it is too early to judge if the SWE can be extracted from it. 
But it should be, in principle, if comp is true. Advantage: I just 
assume natural numbers and classical logic, I don't assume any geometry 
or temporality, which for me are really the miraculous things in need 
to be explained.


Bruno



It's hard to
get my mind around this kind of explanation and what to expect from it.
Also the way the Anthropic Principle applies to infinite strings seems
extremely vague until we have a clearer picture of how those strings
relate to reality.

One area I differ:

Paddy Leahy writes, quoting Russell:

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).


Actually Russell did not bring aleph_1 into the picture at all.  All 
that

he referred to was aleph_0 and c which by definition is 2^aleph_0.
c is the cardinality of the reals and of infinite bit strings.  This is
all just definitional.  Whether c is the next infinite cardinal after
aleph_0 is the Continuum Hypothesis, but that is not relevant here.

Another area I had trouble with in Russell's answer was the concept of
a prefix map.  I understand that a prefix map is defined as a mapping
whose domain is finite bit strings such that none of them are a prefix
of any other.  But I'm not sure how to relate this to the infinite bit
strings that are descriptions.

In particular, if an observer attaches sequences of meanings to 
sequences

of prefixes of one of these strings, then it seems that he must have a
domain which does allow some inputs to be prefixes of others.  Isn't 
that
what sequences of prefixes would mean?  That is, if the infinite 
string

is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
010, 0101, 01011,   Does O() apply to this sequence of prefixes?  
If

so then I don't think it is a prefix map.

I want to make it clear by the way that my somewhat pedantic and 
labored

examination of this page is not an attempt to be difficult or stubborn.
Rather, I find that by the third page, I don't understand what is going
on at all!  Even the very first sentence, In the previous sections, I
demonstrate that formal mathematical systems are the most compressible,
and have highest measure amongst all members of the Schmidhuber 
ensemble,

has me looking to see if I skipped a page!  I don't see where this is
discussed in any way.  So I hope that by pinning down and crystalizing
exactly what the first page is claiming, it will help me to see what
the more interesting third page is actually able to establish.  I think
Paddy is in much the same situation.

Hal Finney



http://iridia.ulb.ac.be/~marchal/

Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Tue, Jun 07, 2005 at 08:29:57AM +0200, Bruno Marchal wrote:
 
 Le 06-juin-05, ? 22:51, Hal Finney a ?crit :
 
 I share most of Paddy Leahy's concerns and areas of confusion with
 regard to the Why Occam discussion so far.  I really don't understand
 what it means to explain appearances rather than reality.
 
 
 Well this I understand. I would even argue that Everett gives an 
 example by providing an explanation of the appearance of a wave 
 collapse from the SWE (Schroedinger Wave equation) and this without any 
 *real*collapse.
 And I pretend at least that if comp is correct, then the SWE as an 
 *appearance* emerges statistically from the interference of all 
 computations as seen from some inner point of view of the mean 
 universal machine.
 But, as I pointed a long time ago Russell is hiding (de facto, not 
 intentionally I guess :) many assumptions.

It would be nice to expose these hidden assumptions. As far as I'm
aware, all my assumptions are exposed and upfront, where at least you
as a reader can decide if you agree, but there is always the
possibility of some that I've missed.

 There are a lot of derivation of the SWE in the literature, it would 
 be interesting that Russell compares them with its own. My favorite one 
 is the one by Henry and another one by Hardy.

The only thing I was aware of by Henry was a derivation of the
correspondence principle from gauge invariance in a paper you sent me,
something I think that Stenger does better in his book (which is
almost published now!).

And as for Hardy, I never found his axioms terribly reasonable,
unfortunately. 

 Note the incredible derivation of QM from just 5 experiments + a 
 natural principle of simplicity by Julian Swinger in his QM course 
 (taken again by Towsend in its QM textbook). I will give reference once 
 less busy.


Sure - I'm not aware of that.
 
 I agree with Hal and Paddy about the lack of clarity in many passages.
 Note that my result is infinitely more modest (despite the 
 appearance!). 

Hardly infinitely more modest. You start from a slightly different
basis (COMP thesis vs all descriptions ensemble), derive the
existence of what I assume, and end up not quite where I end
up. Perhaps if you adopted Kolmogorov probability axioms, you could
get the full QM theory to result. The other things I assume tend to be
assumed by you also - COMP = TIME, and I think you assume PROJ. Not
sure where your work stand with the Anthropic Principle.

 I just prove that if comp is assumed to be correct then a 
 derivation of the SWE *must* exist, without providing it. Well, in the 
 interview of the Lobian machine I do extract some 'quantum logic' from 
 comp, but it is too early to judge if the SWE can be extracted from it. 
 But it should be, in principle, if comp is true. Advantage: I just 
 assume natural numbers and classical logic, I don't assume any geometry 
 or temporality, which for me are really the miraculous things in need 
 to be explained.
 
 Bruno
 

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A/Prof Russell Standish  Phone 8308 3119 (mobile)
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Re: Questions on Russell's Why Occam paper

[Bruno Marchal]

Le 07-juin-05, à 09:20, Russell Standish a écrit :

On Tue, Jun 07, 2005 at 08:29:57AM +0200, Bruno Marchal wrote:
Le 06-juin-05, ? 22:51, Hal Finney a ?crit :

I share most of Paddy Leahy's concerns and areas of confusion with
regard to the Why Occam discussion so far.  I really don't understand
what it means to explain appearances rather than reality.


Well this I understand. I would even argue that Everett gives an 
example by providing an explanation of the appearance of a wave 
collapse from the SWE (Schroedinger Wave equation) and this without any 
*real*collapse.
And I pretend at least that if comp is correct, then the SWE as an 
*appearance* emerges statistically from the interference of all 
computations as seen from some inner point of view of the mean 
universal machine.
But, as I pointed a long time ago Russell is hiding (de facto, not 
intentionally I guess :) many assumptions.

It would be nice to expose these hidden assumptions. As far as I'm
aware, all my assumptions are exposed and upfront, where at least you
as a reader can decide if you agree, but there is always the
possibility of some that I've missed.


OK. it seems to me that (equation 14 at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html  )

 inline: img75.gif

is really presupposing a lot. Where does that come from? It presupposes a space/time geometry, continuity, derivability notion for H, topological notion, etc.

To begin with.

Bruno

http://iridia.ulb.ac.be/~marchal/

Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:
 
 OK. it seems to me that (equation 14 at 
 http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html  ) 
 
 ?
 

In LaTeX, this equation is

\frac {d\psi}{d t}={\cal H}(\psi)

It supposes time, but not space (TIME postulate). Moreover, it
supposes continuous time, but I do suggest in the paper how it might
be generalised to other possible timescales. Perhaps it also supposes
continuity in time for \psi, although this probably flows from
assuming continuity of time. I do not think time is necessarily
continuous - I think it is interesting to explore alternative QMs
without this assumption.

The question is whether this is the most general evolution equation
for continuous time, or whether there is some more general
equation. Remember, we do have already that \psi is a member of a
Hilbert space, so we can write things like:

\psi(t')-\psi(t) = ...

What do you mean by derivability notion for H, and topological notion?

  
 
 is really presupposing a lot. Where does that come from? It presupposes 
 a space/time geometry, continuity, derivability notion for H, 
 topological notion, etc. 
 
 To begin with. 
 
 Bruno 
 
 http://iridia.ulb.ac.be/~marchal/ 
 
 


-- 
*PS: A number of people ask me about the attachment to my email, which
is of type application/pgp-signature. Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.


A/Prof Russell Standish  Phone 8308 3119 (mobile)
Mathematics0425 253119 ()
UNSW SYDNEY 2052 [EMAIL PROTECTED] 
Australiahttp://parallel.hpc.unsw.edu.au/rks
International prefix  +612, Interstate prefix 02



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Description: PGP signature

Re: Questions on Russell's Why Occam paper

[Bruno Marchal]

Le 07-juin-05, à 12:28, Russell Standish a écrit :


On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:


OK. it seems to me that (equation 14 at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html  )

?



In LaTeX, this equation is

\frac {d\psi}{d t}={\cal H}(\psi)

It supposes time, but not space (TIME postulate). Moreover, it
supposes continuous time,



Yes but that is a lot of assumptions. Why a linear time capable of 
being represented by the very special line with the usual topology of 
the reals? I can imagine many topology on the reals.





but I do suggest in the paper how it might
be generalised to other possible timescales.



yes but if you pretend to derive your equation, I don't understand what 
you mean by generalizing your conclusion (if only by: I have not derive 
it and it remains some work to do).





Perhaps it also supposes
continuity in time for \psi, although this probably flows from
assuming continuity of time.



Why should a function be continuous just because it is defined on a 
topological space (which is what I assume you are saying when you say 
continuity of time).





I do not think time is necessarily
continuous - I think it is interesting to explore alternative QMs
without this assumption.



Sure. But again how to talk on derivation then. I mean if someone 
pretend to derive B from A, then if someone else derive something mùore 
general than B from A, it is a critic of the assertion that B has been 
derived from A. If from facts I can derive the murderer is among John 
and Charles, I am not so interested in  knowing the derivation can be 
generalized into leading that the murderer is among John, Charles, Lee, 
Bruno and Nicole!






The question is whether this is the most general evolution equation
for continuous time, or whether there is some more general
equation.



Absolutely.




Remember, we do have already that \psi is a member of a
Hilbert space, so we can write things like:



OK, but you assume Set theory (that by itself is huge in our context). 
I show only that you have a preHilbetian space (why should cauchy 
sequence of vectors converges).






\psi(t')-\psi(t) = ...

What do you mean by derivability notion for H, and topological notion?



Topological notion are needed for talking of continuity (a continuous 
function is just a function from topological space into a topological 
space such that the inverse image of open set is an open set).. You 
assume the familiar topology of reals, complex number, etc.
Derivability is a stronger requirement (although some algebraist would 
introduce many nuances). Someday I will show you make also assumption 
on consciousness, but that is more subtle, and then all physicist if 
not almost scientist are doing them when they pretend to solve the 
consciousness problem like Dennett, or when they put it under the rug 
(a little bit like Lee in his last posts, I would say).


Look Russell, as I said I appreciate your attempt, it is just that, as 
Hal and Paddy mentionned, there remains quite a lot of work to make it 
thoroughly communicable. You should really put more clearly your 
assumptions. You assume a vast part of mathematics, and I would say of 
physics, mainly with your time postulate and your equation. Compare 
your work with those I have mentionned (I will give the reference for 
those you don't have yet). Don't compare it to quickly  to mine where 
the assumptions are made still at a much more basic (logical and 
arithmetical) level. I assume less than Peano arithmetic. I know I 
could seem a little bit presomptuous, but nuance would make the post 
more long and more boring. Hope you don't mind, (actually I would be 
glad someone criticize the most severely possible my work),


Bruno

http://iridia.ulb.ac.be/~marchal/

Re: Questions on Russell's Why Occam paper

[Patrick Leahy]

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!).

Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Tue, Jun 07, 2005 at 05:57:17PM +0200, Bruno Marchal wrote:
 
 Le 07-juin-05, ? 12:28, Russell Standish a ?crit :
 
 On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:
 
 OK. it seems to me that (equation 14 at
 http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html  )
 
 ?
 
 
 In LaTeX, this equation is
 
 \frac {d\psi}{d t}={\cal H}(\psi)
 
 It supposes time, but not space (TIME postulate). Moreover, it
 supposes continuous time,
 
 
 Yes but that is a lot of assumptions. Why a linear time capable of 
 being represented by the very special line with the usual topology of 
 the reals? I can imagine many topology on the reals.
 

I thought the definition of the reals defined its topology? Perhaps
you're using topology somewhat differently.

It is a good question as to why time should have a topological
dimension of 1, and I admit to not having a good answer to that. All I
can say is that computationalism also introduces a time with
topological dimension of 1. Tegmark has some arguments as to why the
topological dimension is 1, and not any other number, but these are
not overly persuasive (the argument depends on properties of 2nd order
PDEs, which already carries a greater amount of baggage)

I only assume continuity to make contact with standard QM. It is an
arbitrary assumption in my opinion, and should rightly be viewed with
suspicion. 

 
 
 but I do suggest in the paper how it might
 be generalised to other possible timescales.
 
 
 yes but if you pretend to derive your equation, I don't understand what 
 you mean by generalizing your conclusion (if only by: I have not derive 
 it and it remains some work to do).
 

Of course there remains some work to be done.

 
 
 Perhaps it also supposes
 continuity in time for \psi, although this probably flows from
 assuming continuity of time.
 
 
 Why should a function be continuous just because it is defined on a 
 topological space (which is what I assume you are saying when you say 
 continuity of time).
 

Because then it wouldn't be an evolution. For a state \psi(t') to
depend on the state \psi(t), there must be a corresponding limit
\psi(t')-\psi(t) as t'-t. Of course if t were not continuous, then
this condition is no longer necessary.

 
 
 I do not think time is necessarily
 continuous - I think it is interesting to explore alternative QMs
 without this assumption.
 
 
 Sure. But again how to talk on derivation then. I mean if someone 
 pretend to derive B from A, then if someone else derive something m?ore 
 general than B from A, it is a critic of the assertion that B has been 
 derived from A. If from facts I can derive the murderer is among John 
 and Charles, I am not so interested in  knowing the derivation can be 
 generalized into leading that the murderer is among John, Charles, Lee, 
 Bruno and Nicole!
 

To use your analogy, the situation is more like:

Assuming the murderer is John, Charles, Fred or Diana, I have shown
that the murderer must be one of John or Charles. However, if we also
consider Lee, Bruno and Nicole ... there is more work to be done.

The assumption of J,C,F or D corresponds by analogy to the continuity
assumption. 

L,B and N are not continuous - does that sound right? :)

 
 
 
 The question is whether this is the most general evolution equation
 for continuous time, or whether there is some more general
 equation.
 
 
 Absolutely.
 

I think it is, for the reason above. I willing to stand corrected
should that not be the case.

 
 
 Remember, we do have already that \psi is a member of a
 Hilbert space, so we can write things like:
 
 
 OK, but you assume Set theory (that by itself is huge in our context). 
 I show only that you have a preHilbetian space (why should cauchy 
 sequence of vectors converges).
 
 

Yes I do assume set theory. That is stated.

I prove Cauchy sequences converge in the paper. It requires the use of
Kolmogorov axiom no. 6. Hence the space of states is a Hilbert space.

 
 
 \psi(t')-\psi(t) = ...
 
 What do you mean by derivability notion for H, and topological notion?
 
 
 Topological notion are needed for talking of continuity (a continuous 
 function is just a function from topological space into a topological 
 space such that the inverse image of open set is an open set).. You 
 assume the familiar topology of reals, complex number, etc.

Ah yes, you're talking about topological spaces. I just did a quick
refresher course on these using Wikipedia. Indeed, when I make the
arbitrary continuity assumption of time, it is an assumption that time
is a subset of the reals, which has the usual metric and topology
defined. When you say you can imagine many topologies on the reals,
what you are really saying is that you can imagine sets isomorphic to
the reals (1-1 corrspendence), that have many different topologies, eg
the trivial or the discrete topology for instance, or anything defined
by an arbitrary metric. For instance the set of descriptions which is
isomorphic to the 

Re: Questions on Russell's Why Occam paper

[Russell Standish]

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!).
 

Re: Questions on Russell's Why Occam paper

[Patrick Leahy]

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).


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.



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.


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. 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).


snip


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

Re: Questions on Russell's Why Occam paper

[Russell Standish]

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 

Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Mon, Jun 06, 2005 at 01:51:36PM -0700, Hal Finney wrote:
 
 Another area I had trouble with in Russell's answer was the concept of
 a prefix map.  I understand that a prefix map is defined as a mapping
 whose domain is finite bit strings such that none of them are a prefix
 of any other.  But I'm not sure how to relate this to the infinite bit
 strings that are descriptions.

A prefix map attaches the same output to all strings that share a
common finite length prefix.

 
 In particular, if an observer attaches sequences of meanings to sequences
 of prefixes of one of these strings, then it seems that he must have a
 domain which does allow some inputs to be prefixes of others.  Isn't that
 what sequences of prefixes would mean?  That is, if the infinite string
 is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
 010, 0101, 01011,   Does O() apply to this sequence of prefixes?  If
 so then I don't think it is a prefix map.
 

Yes I agree this is vague, and seemingly contradictory. I'm not sure
how to make this more precise, but one way to read the paper is to
treat observers as prefix maps for section 2 (Occam's razor), and then
for section 3 (White Rabbit problem) ignore the prefix property.

It could be that the way of making this more precise is to assume
observers have some internal state that is constantly updated (a time
counter perhaps), so actually going through a sequence of prefix maps
in (psychological) time, but at this stage I don't have an answer.


 I want to make it clear by the way that my somewhat pedantic and labored
 examination of this page is not an attempt to be difficult or
 stubborn.

Even being difficult and stubborn has its place (to help winkle out
subtle errors of logic eg), so long as you relax enough at other times to
obtain understanding. I appreciate the effort in any case.

 Rather, I find that by the third page, I don't understand what is going
 on at all!  Even the very first sentence, In the previous sections, I
 demonstrate that formal mathematical systems are the most compressible,
 and have highest measure amongst all members of the Schmidhuber ensemble,
 has me looking to see if I skipped a page!  I don't see where this is
 discussed in any way. 

This is pretty much a tautology. Formal mathematical systems are a
means of compressing data in the form of facts about numbers. If one
were to include all such possible compression schemes, rather than
just the systems studies by mathematicians to date, one would end up
with the set of Turing machines, or equivalently of computable
functions. The Occam's razor result clearly relates measure to the
amount of compressibility in the description.

Perhaps such a view of mathematics is strange. Certainly I find it
strange when Stephen Wolfram says mathematics is incapable of
understanding complex phenomena, and one should cellular automata
instead. To me, cellular automata are just another example of a
mathematical system.

 So I hope that by pinning down and crystalizing
 exactly what the first page is claiming, it will help me to see what
 the more interesting third page is actually able to establish.  I think
 Paddy is in much the same situation.
 
 Hal Finney

I hope so too.

-- 
*PS: A number of people ask me about the attachment to my email, which
is of type application/pgp-signature. Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.


A/Prof Russell Standish  Phone 8308 3119 (mobile)
Mathematics0425 253119 ()
UNSW SYDNEY 2052 [EMAIL PROTECTED] 
Australiahttp://parallel.hpc.unsw.edu.au/rks
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Re: Questions on Russell's Why Occam paper

[Russell Standish]

On Fri, Jun 03, 2005 at 04:22:07PM -0700, Hal Finney wrote:
 Russell Standish recently mentioned his paper Why Occam's Razor which
 can be found at http://parallel.hpc.unsw.edu.au/rks/docs/occam/ .  Among
 other things he aims to derive quantum mechanics from a Schmidhuber type
 ensemble.  I have tried to read this paper but never really understood it.
 Here I will try to ask some questions, taking it slowly.
 
 On this page, http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html ,
 things get started.  Russell describes a set of infinite bit strings he
 calls descriptions.  He writes:
 
 By contrast to Schmidhuber, I assume a uniform measure over these
 descriptions -- no particular string is more likely than any other.
 
 This surprises me.  I thought that Schmidhuber assumed a uniform measure
 over bit strings considered as programs for his universal computer.  So
 what is the contrast to his work?

Nowhere in Schmidhuber (1997) does he propose a measure over the input
programs. What he does is is justify the appearance of a universal
prior in the set of descriptions by passing the raw data through a
reference UTM. Presumably the set of descriptions is sampled uniformly
by the observer.

In Schmidhuber (2000), the set of descriptions is generated by a
machine which has resource bounds. This leads to the notion of speed
prior which differs from the universal prior in several important
respects. I sometimes refer to the two different ensembles as
Schmidhuber I and Schmidhuber II.

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. However, as the cardinality of my ensemble is
actually c (cardinality of the real numbers), it is quite probably a
completely different beast. It is also not generated by a program,
Schmidhuber style, it simply is (in the sense of being the simplest
set - equivalent to nothing).

 
 It seems that the greater contrast is that while Schmidhuber assumed that
 the bit strings would be fed into a computer that would produce outputs,
 Russell is taking the bit strings directly as raw data.
 

Quite true.


 But I am confused about their role.
 
 Since some of these descriptions describe self aware substructures...
 
 Whoa!  This is a big leap for me.  First, I am not too happy that mere bit
 strings have been elevated with the title descriptions.  A bit string on
 its own doesn't seem to have the inherent meaning necessary for it to be
 considered a description.  

Many apologies for deploying terminology in a different way to you
expect. A description (in my terminology) does not necessarily have
meaning. It is simply data. This is in accord with how I use the term
in casual English usage too - a description is simply a string of
letters, and may or may not be meaningful. Meaning is attached by an observer.

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. Why should an observer expect to see a token of erself
embedded in reality? That is the mystery of the AP.

 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.

 It's especially confusing to read the introductory word since as though
 this is all quite obvious and need not be explained.  To me it is very
 confusing.
 

Sorry for not going slow enough. The habits of concise expression are
hard to shake.

 The page goes on to identify these SAS's as observers.  Now they are mappings,
 or equivalently Turing Machines, which map finite bit strings to integers.
 These integers are the meanings of the bit strings.

Not equivalently. Not all maps can be represented by a Turing machine,
only computable ones.

 
 I believe the idea here is that the bit strings are taken as prefixes
 of the description bit strings in the ensemble.  It is as though the
 observers are observing the descriptions a bit at a time, and mapping
 them to a sequence of integer meanings.  Is that correct?
 

Indeed that is one interpretation. The most important point is that
the observer map is a prefix map, in the sense of prefix machines of
Algorithmic Information Theory. In reading a bit string one bit at a
time, once a meaning is attached to the string, that is the meaning
for evermore - the observer cannot change er mind after reading a few
more bits.

Schmidhuber (2000) deals with machines that do change their mind, so
perhaps there is some extension possible in this direction.

 So here is another confusion about the role of the 

Questions on Russell's Why Occam paper

[Hal Finney]

Russell Standish recently mentioned his paper Why Occam's Razor which
can be found at http://parallel.hpc.unsw.edu.au/rks/docs/occam/ .  Among
other things he aims to derive quantum mechanics from a Schmidhuber type
ensemble.  I have tried to read this paper but never really understood it.
Here I will try to ask some questions, taking it slowly.

On this page, http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html ,
things get started.  Russell describes a set of infinite bit strings he
calls descriptions.  He writes:

By contrast to Schmidhuber, I assume a uniform measure over these
descriptions -- no particular string is more likely than any other.

This surprises me.  I thought that Schmidhuber assumed a uniform measure
over bit strings considered as programs for his universal computer.  So
what is the contrast to his work?

It seems that the greater contrast is that while Schmidhuber assumed that
the bit strings would be fed into a computer that would produce outputs,
Russell is taking the bit strings directly as raw data.

But I am confused about their role.

Since some of these descriptions describe self aware substructures...

Whoa!  This is a big leap for me.  First, I am not too happy that mere bit
strings have been elevated with the title descriptions.  A bit string on
its own doesn't seem to have the inherent meaning necessary for it to be
considered a description.  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?

It's especially confusing to read the introductory word since as though
this is all quite obvious and need not be explained.  To me it is very
confusing.

The page goes on to identify these SAS's as observers.  Now they are mappings,
or equivalently Turing Machines, which map finite bit strings to integers.
These integers are the meanings of the bit strings.

I believe the idea here is that the bit strings are taken as prefixes
of the description bit strings in the ensemble.  It is as though the
observers are observing the descriptions a bit at a time, and mapping
them to a sequence of integer meanings.  Is that correct?

So here is another confusion about the role of the description bit
strings in the model.  Are they things that observer TM's observe and
map to integers?  Or are they places where observers live, as suggested
by the Since line quoted above?  Or both?

Now it gets a little more complicated: Under the mapping O(x), some
descriptions encode for identical meanings as other descriptions, so
one should equivalence class the descriptions.

The problem I have is, O takes only finite bit strings.  So technically
a description, which is an infinite bit string, does not encode a
meaning.  What I think is meant here, though, is that two descriptions
(i.e. infinite bit strings) will be considered equivalent if for every
finite prefix of the strings, the O() mapping is the same.  So if we
think of O as observing the description bit strings one by one,
it will go through precisely the same sequence of integer meanings
in each case.  Is that right?

In particular, strings where the bits after some bit number n are
``don't care'' bits, are in fact equivalence classes of all strings that
share the first n bits in common.

I think what this considers is a special O() and a special string prefix
such that if O sees that particular n-bit prefix, all extensions of
that prefix get mapped to the same meaning integer.  In that case the
condition described in my previous paragraph would be met, and all
strings with this n-bit prefix would be equivalent.

One can see that the size of the equivalence class drops off
exponentially with the amount of information encoded by the string.

That seems a little questionable because the size of the equivalence class
is infinite in all cases.  However I think Russell means to use a uniform
measure where the collection of all strings with a particular n-bit
prefix have a measure of 1/2^n.  It's not clear how well this measure
really works or whether it applies to all sets of infinite strings.

Under O(x), the amount of information is not necessarily equal to the
length of the string, as some of the bits may be redundant.

Now we have this new concept of the amount of information which has
not previously been defined.  This sentence is really hard for me.
What does it mean for bits to be redundant?  We just discussed strings
where all those after bit n are don't care, but this sentence seems
to be envisioning other kinds of redundancies.

The sum P_O(s) = [sum over p such that O(p)=s of] 2^(-|p|)
where |p| means the number of bits of p consumed by O in returning s,
gives the size of the equivalence class of all descriptions having
meaning s.

Boy, that's a tough one now.  We consider all bit strings p such that O(p)
= s.  Now, is this supposed to just be those cases described earlier where
the bits after |p| are don't care bits?  Or is it all strings p such
that