# Re: No(-)Justification Justifies The Everything Ensemble

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Le 17-sept.-07, à 14:22, Russell Standish a écrit :```
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> Sorry my fingers are slipping. Machines (computable functions) are a
> type of map, but not all maps are machines (or perhaps you prefer the
> word function to map).

OK. You know I like your little book as an introduction to the field,
but, as you have already acknowledge, there is some lack in rigor in
it, and it is not even clear if eventually you are of the ASSA type or
RSSA type, or if you accept comp or not. Use of Bayes and Prior, for
example, is a symptom of ASSA type reasoning. Distinction between 1 and
3 person points of view is symptom of the RSSA type of reasoning, (and
favored with comp).
RSSA reasoner does not necessarily condemn ASSA as useless or false for
the explanation of geographical and cosmological aspect of our physical
reality, but pure ASSA, without taking into account the 1-3 distinction
is bound up to fail on the mind body problem (with or without the comp
hyp.), that is ASSA could  explain things, but cannot explain the
nature of mind and the nature of matter and the nature of the relation
in between (and that is why they most often use "Aritotle like identity
theories".

>
> Not equivalent. Equivalent status. Assumption of the set of all
> infinite strings plays the same role as your assumption of
> arithmetical realism, and that is of the ontological background.

I don't know. Let us fix a simple alphabet: {0, 1}. Then an infinite
string like
111101000100111000000010100101100001101001 ..... (infinite on the
right) can be seen as the chracteristic function of a subset of N (the
first 1 in the string means then that 0 is in the set,, the second one
that 1 is in the set etc. The resulting set is
{0, 1, 2, 3, 5, 9, 12, 13, 14, 22, 24, 27, 29, 34, 35, 37, 40, ...}
So there is a bijection between the set of infinite strings on the
{0,1} alphabet, and the subset of N. So without putting any
extra-stcruture on the set of infinite strings, you could as well have
taken as basic in your ontology the set of subset of N, written  P(N).
Now, such a set is not even nameable in any first order theory. In a
first order theory of those strings you will get something equivalent
to Tarski theory of Real: very nice but below the turing world: the
theory is complete and decidable and cannot be used for a theory of
everything (there is no natural numbers definable in such theories).
From this I can deduce that your intuition relies on second order
arithmetic or analysis (and this is confirmed by the way you introduce
time). But then this again is really a strong assumption, far stronger
than arithmetical realism.
To be sure, I still don't know if your ontic base is just "nothing"
(but then in which theory?) or the infinite strings (again, in which
theory and as I said you will to use rich mathematics for that), etc.
As you know, I am trying to go a little beyond the UDA result so as to
give a little smell of the real thing. The trouble is that the basic
tools of logic and axiomatic are not very well known by anybody but the
professional logicians.

> It might seem like such uncountable sets are too much to assume, but
> in fact it is the simplest possible object. It has precisely zero
> information.

Zero information. Zero justification. Occam razor ... I do agree with
these major motivations for the everything idea, but I disagree with
the proposition saying that the the set of strings needs
zero-information. Why not the infinite strings on both right and left
(coding the integers), or infinite many-dimensional lattices fit with
zero and one on the vertex, or etc. ?
There is just a lack of enough precise definition so as to verify your
statements that strings needs zero-information, and as I say above,
from some standard and traditional view points, infinite strings needs
a lot of information to be define.

> No countable set has this property.

Why?

> I put your objection
> into the same category as those who claim the multiverse is
> ontologically profligate. Apologies to intuistionists out there.

Apologies to intutionists and also to constructivist like Schmidhuber,
but also to weak arithmetical platonist like, imo, digital mechanist
ought to be.

>>> Obviously I'm departing from
>>> Schmidhuber at that point, and whilst in "Why Occam's Razor" I use
>>> the
>>> term Schmidhuber ensemble to refer to this, in my book I distinguish
>>> between Schmidhuber's Great Programmer idea
>>
>>
>> (which you confuse some time with the UD, I think).
>>
>
> He does actually dovetail,

We have discuss this. In the first paper the "great programmer" is not
a dovetailer, and indeed there is nothing in the ASSA approach for
which dovetailing could play a role.

> so it is a universal dovetailer in all but
> name perhaps. But the ontological basis of the "Great Programmer"
> differs very much from COMP.

Again this is not corect. Schmidhuber and me do agree on comp (100%
agreement: we have the same hypothesis). And relatively to the comp hyp
and the importance of the universal machine Schmidhuber and me are much
closer than with Tegmark whi is just very naïve about notion of
mathematical reality. Now the problem is that, unlike many people in
this list, Schmidhuber does not address neither the mind body problem
nor the 1-3 person distiinction, and the relativity of states which
derives from that distinction. This forces him to literally defend the
idea that randomness in nature never really exist, which is hard to
justify in front of the physical branch of history we are living. This
does not makes his work wrong, but at least incomplete (and then he
should use Bennett notion of depth for the cosmological/geographical
aspect (like I do in Conscience et mécanisme: using just Kolmogorov is
not enough, but here I am going out topic.

> Of course, although you'd better say the Standish ensemble so as not
> to misattribute it to Bertie. Also, it is quite clearly a set (I think
> you've read enough English papers to know the difference between and
> ensemble and a set in English, I hope?)

Well, I hope you are not referring to the notion of "ensemble" as it
occurs in physical statistics. Again, this would mean that you endow
the space of infinite strings with a structure of a measure space
(boolean sigma-algebra, for example). because this means that your
basic ontology is much richer than just the strings. I am trying to
understand a bit more clearly how you view of the everything thing.

>>>>
>>> All of these concepts are more precise and have additional properties
>>> to the set of all infinite strings. For instance, the reals have
>>> group properties of addition and multiplication that the strings
>>> don't.
>> But as sets, they are isomorphic, and if you don't have
>> extra-structure
>> on your "ensemble", the relation between your "observers" and your
>> "ensemble"  is even more obscure, it seems to me.
>>
>
> You've lost me here.

I'm the one saying that I'm lost here. I am just asking: how do you
define "observer" in the infinite strings setting. (Actually with or
without extra-strcuture, like what you need to have a measure space).

>> So here you do explicitly accept extra-structure, a measure, on your
>> ensemble, making them again quite close to the reals.
>> You cannot derive the existence of a measure from just a definition of
>> a set. (There are *many* possible measures on any set).
>>
>
> Yes of course. The uniform measure has always been part of the
> definition.

This was not clear, sorry. Now you definitely need analysis or second
order arithmetic. This is everything but nothing!

>>> see Li & Vitanyi example 4.2.1 for a detailed
>>> discussion. The idea is simple enough, however.
>>
>>
>> ... where they describe how to put a measure on some set of *subsets*
>> of an uncountable sets. You have to define a Borel structure on it,
>> etc.
>> It is indeed explained in Li & Vitanyi (page 214q).
>>
>
> We must have different editions. On mine its page 243 :). So there
> must be some non-measurable subsets.

This is not even provable in formal set theory like ZF (Zermelo
Fraenkel). You need the axiom of choice, if I remember well. This means
you presuppose set theory (a vastly bigger and richer ontology than
arithmetic).

> But I fail to see how these can
> be inverse images of an observers interpretation (O^{-1}(n)) must be
> measurable). But then I admit I am acting like a physicist in glossing
> over these sorts of details.

I would not have dare to call you a physicist, but now that you admit
you are acting a bit like them, I can understand better :)

>>>>> It is the interpretation of the observer, but it
>>>>> isn't arbitrary.
>>>> Certainly not in Schmidhuber, as I remember (cf our discussions in
>>>> this
>>>> list). OK, with comp, but in some RSSA way, and not in any ASSA way
>>>> based on an ensemble.
>>> Schmidhuber downplayed the role of the observer, as is typical of a
>>> scientist.
>>
>>
>>
>> (OK, but only since 525 after J.C., and just because scientists have
>> been forced to let the fundamental questioning to authorities mixing
>> political and spiritual power ....).
>>
>
> What happened in 525 CE again?

The greek scientists, and after them all scientist, were forced to
abandon the scientific field known as "theology" to the political
authorities. 525 is the year where the Athenian Academy of Plato has
been closed by the Christian emperor. Since then the human science are
inexact at the roots,  making them inhuman at the roots too. Normal
science and theology will surive up to the eleven century, thanks to
the arabs, which will make it possible for the science to make a tiny
come back at the Renaissance (Enlightnment Period) later. But
scientific theology will not go through, and still today many scientist
are unaware of the beautiful rational contribution of the platonist and
neoplatonist in the human AND exact science. They are still putting
under the rug all the interesting questions addressed by the Greek
Theologian (To be sure most of these questions appeared also and before
in China and India, but I never sure of the exact dates and places;
many text are not yet precisely dated.

>>> Since this appears to be the point of departure between you
>>> and he, I'll state that I've always followed you in this point, that
>>> the 1st person pov (what I call the semantic level) is important.
>>
>>
>> OK. But again it could be misleading to call that "the semantic
>> level",
>> because a relation between "semantic" and first person would be a very
>> interesting things to dig on, but nobody has done that yet.
>> All hypostases (first person, third person, first person plural, etc.)
>> have syntax and semantics.
>
> Yes but again we're mixing terminologies. When I refer to syntactic
> level, I'm refer to what stuff is,

You can do that. I see the point. But it is not standard at all and has
to be explained in all detail, especially if you are not clear if you
follow comp or not. Even with comp this is highly ambiguous.

> and when I refer to semantic level,
> I mean how it is interpreted.

This is even less standard, and although I could put sense on it, this
is only because I have tools for doing that. A term like
"interpretation" can be seen as syntactical at some level and
semantical at some other level.

> This can be applied to all situations
> where emergence is occurring.

I knwo a lot of people who are searching their gun when they hear the
word "emergence".  I mean this is a word which can be used once you
take many precautions. Also, if comp is correct, as you know, it is
matter (stuff) which emerges from consciousness/meaning (cf the
reversal result).

> So in the case of an ideal gas, the
> molecular description is syntactic, and its thermodynamic description
> is semantic.

Hmmm....  I cannot really accept this. Here is a case where emergence
is far better than semantics.

>  In the Game of Life, the update rule is syntactic, the
> description in terms of gliders, puffers and guns is semantic.

This is contrary to the standard use of those terms. You can do that,
but you have to explain explicitly why and how. Logic is the science
which is specialized in defining notion like syntax and semantics, both
through mathematical structures.
Frankly a glider is still a finite syntactical object. A moving glider
is a bit more ... dynamical, and this can be related through some
"operational" semantics. Again, the point is to choose definition (no
one are the best one) and then to stick on those definitions. I suggest
to always use the original definition from the field which use the
notion the most. And then you can modify them to suit your context, but
it helps the reader if you do that explicitly.

> It may
> not be the best terminology, but it is the best I've come across to
> date.

I doubt that. Perhaps be careful by using Wkipedia (it could be the
best and the worth), verify perhaps on Stanford dictionnary, etc.

Another point where your fuzziness does not help is that you are not
clear on the comp hyp. Schmidhuber is clear on comp, even if he has
disagreed when discussing online in the list with the consequences I
derive from it. But the disagreement comes not from what comp means,
but from the 1/3 distinction, which Schmidhuber does not consider.
Tegmark does introduce an embryo of 1/3 distinction (but quite
different from mines (see below)), but Tegmark still uses some identity
thesis implicitly for making observer belonging to universe, and minds
to brain. Such identities have just no meaning at all once you
postulate the comp hyp (or even strong weakening of it btw). OK? (by
UDA). Yes?

Bruno

>
>> I have given in this list and in all my papers on the subject two main
>> definitions of the first person. In UDA it is the memory content of a
>> diary that a candidate for self-multiplication keep with him, and in
>> AUDA I define the first person by the "knower" (and thus the knower
>> modal logic S4(*)) by using the more abstract theaetetical notion of
>> knowledge given in the Theaetetus by Plato (they are related through
>> the usual platonist "dream argument").
>>
>>
>> Bruno
>>
>> (*) knowing p   ->   p  (incorrigeability)
>>       knowing p   ->  knowing(knowing p)  (introspection)
>>      knowing (p  ->  q)  ->  [(knowing p) -> (knowing q)]
>> (rationality or weak omniscience).
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>>

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

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