Hi Stephen,
On 13 Apr 2011, at 02:35, Stephen Paul King wrote:
Hi Bruno,
"Once more unto the breach, dear friends, once more"!
-----Original Message-----
From: Bruno Marchal
Sent: Sunday, April 03, 2011 1:03 PM
To: [email protected]
Subject: Re: Causality = 1p Continuity?
>> On 03 Apr 2011, at 05:15, stephenk wrote:
snip
>>
>> [SPK] That logical structures alone are insufficient to model our
>> existence.
> Correct. But arithmetical structure are enough (or please mention a
> flaw in UDA).
[SPK]
I wish to be doubly sure that I am not arguing against a straw
man, therefore I will be quoting from and commenting on:
http://groups.google.com/group/everything-list/browse_thread/thread/4c995dee307def3b
“COMP is the hypothesis that there is a level such that I
survive a digital functional substitution of my generalised body/brain
made at that level, + Church Thesis (CT: digital = turing) +
Arithmetical
Platonism (AR: the belief that arithmetical propositions obeys
classical logic, and this independently of my own cognitive ability).
To sum up: COMP = \exists n SURV-SUBST(n) + CT + AR “
OK. Since that time I do no more assume AR. The reason I assumed
explicitly AR was for reason of clarity, but AR is redundant, given
that you need it to make sense of Church thesis. As it is written in
sane04, and in the text you quote AR is just the idea that classical
logic can be applied to arithmetic.
“b) CU: there is a Concrete Universe, whatever it is. This is need
for the decor.
c) CUD: there is a Concrete running of a UD in the concrete universe.
Those are supplementary assumptions to ease the reasoning, and are
explicitly eliminated later.
d) 3-locality: computations are locally implementable in the
concrete universe. That is it is possible to separate two
implementations of two computations in such a way that the result
of one of these computations will not interfere with the result
of the other one. Computations can be independent.
More generally the result of a computation is independant of
any event occuring a long way (out of the light cone) from that
computation.”
...
“12) A Universal Dovetailer exists. (Extraordinary consequence of
Church thesis and Arithmetical Realism). The UD simulates all
possible digital devices in a quasi-parallel manner).
(Adding a line in the code of any UD, and you get a quasi-
computation of its Chaitin \Omega number).
13) So let us assume CU and CUD, that is let us assume explicitly
there is a concrete universe and a concrete running of a UD in it.
This need a sort of steady state universe or an infinitely expanding
universe to run the complete infinite UD.
Suppose you let a pen falls. You want predict what will happen.
Let us suppose your brain is in state S at the beginning of the
experiment. The concrete UD will go to that state infinitely often
and compute all sort of computational continuations. This is
equivalent to reconstitutions. It follows from 11 that your
expectation are undetermined, and the domain of the indeterminism
is given by the (infinite) set of reconstitutions. To predict,
with COMP, what will happen you must take into account all
possible histories going through the state S of your brain.
And here clearly the NEURO hypothesis is not used. Even if your
real brain state is the state of the actual concrete universe,
with COMP that state will be generated (infinitely often) by the
UD. Same reasoning if your brain state is the quantum state of
the universe, so the reasoning works even if the brain is a
non local quantum object (if that exists). So the physics is
determined by the collection of your computational continuations
relatively to your first person actual state.”
14) If 'that' physics is different from the traditional empirical
physics, then you refute COMP. But with COMP you will not refute
COMP, isn't it? So with COMP you will derive the laws of physics,
i.e. invariant and similarities in the 'average' continuations of
yourself (defining the measure on the computationnal continuations).
Exercice: why should we search a measure on the computational
continuations and not just the computational states? Hint: with
just the computational states only, COMP predicts white noise for
all experiences. (ok Chris ?). With the continuations, a priori
we must just hunt away the 'white rabbit' continuations.
You can also show that Schmidhuber's 'universal prior' solution
works only in the case the level of substitution
is so low that my generalised brain is the entire multiverse.
(see below).
15) Once you explain why arithmetical machines are statistically right
to believe in physical laws without any real universe, such a real
universe is redundant.
By Arithmetical Realism and OCCAM razor, there is no need
to run the concrete UD, nor is there any need for a real concrete
Universe.
(Or you can use the movie graph argument to show that a first
person is not able to distinguish real/virtual/and *Arithmetical*
nature of his own implementations, and this eliminates OCCAM.)”
OK, my problem is that SURV-SUBST(n) requires that the UD
actually run on some form of a CU as a CUD.
?
This contradicts the point 15 above.
You account for this by introducing CUD (CUD necessitates the
existence of CU). The CU and CUD involve a measure of change that
can be identified with “time” that is invariant under
parameterizations (by the teleportation with delay argument), or
equivalently there must exist a spatial distance interval, because
there must be some arbitrary parameter to distinguish 3-localities
from each other. If all 3-localities are exactly isomorphic in their
content then by the law of indiscernibles they are all one and the
same. All that one would have, maybe, is endomorphic maps from the 3-
local to the 3-local, but even those would require the existence of
a concrete structure that is their dual.
?
But this invariance does not eliminate the fact that the UD must
be run to be said to generate the digital simulations that are
equivalent (under 10 –13 of UDA) to 1p and their continuations.
AR makes the UD already executed in elementary arithmetic. The only
time we need is given by the sequence 0, s(0), s(s(0)), etc.
This parameterization invariant notion of time (or space) is
necessary for any expression/implementation of AR.
That would make all physical theory circular. But more deeply, there
is no reason to make an arithmetical truth (like s(0) + s(0) =
s(s(0))) dependent of physics. If you do really believe this, you
should explain and describe the dependence, and this without using
arithmetic in your physics.
AR must be expressible as some belief in each 1p (modulo coherent
and soundness):
Why? It is true, but I don't see the relevance.
for AR to exist
What do you mean by "AR exists"? That is ambiguous. And what you are
saying begin to look like "archeology is needed for dinosaur to
exist". The very idea of AR is that 1+1=2 does not need a human for
being true. Of course, a human or some alien is needed to say that
"1+1=2" is believed.
then it is necessary that a 1p believe that AR exists and the
statement “AR exists” is true. If the belief that AR exists cannot
be expressed by a CUD then AR cannot be said to exist since it would
be impossible to express the statement “AR exists”. Diagonalizations
require some form of CU support or else they all collapse into
Nothing.
Why does diagonalization need a CU?
You then argue that AR + OCCAM allows you to eliminate CUD and
thus CU.
Yes, and the movie graph can be used to eliminate 99,9% of OCCAM. The
remaining of OCCAM needed is the part needed in *any* applied theory.
But there is a problem with this! AR necessitates CUD to be distinct
from Nothing (per R. Standish’s definition and argument http://www.amazon.com/Theory-Nothing-Russell-Standish/dp/1921019638/)
!
AR presuppose only the existence of 0, and its successors. Actually it
presupposes only addition and multiplication, because you can derive
the existence of zero and its successors from it.
Just because “Real” and “Virtual” are 1p indistinguishable (which is
an isomorphism) does not necessitate that Arithmetic representations
of the 1p = 1p (which is an identity).
A main result is that the machine's 1p CANNOT be represented in
arithmetic. The closer we can go to this is given by the "Bp", but 1p
are given by Bp & p, and this can be shown to be non representable in
arithmetic. Machines cannot know that they are machine, and their
'inner god" has no name (like the ONE).
To do this is to violate the Representation theorem because an
isomorphism is not an identity, it is a mapping between two distinct
entities.
1) SURV-SUBST(n) implies the existence of 1p
Why?
2) SURV-SUBST(n) necessitates CUD.
Why?
3) 1p necessitates CUD.
Why?
4) if CUD does not exist, then neither does SURV-SUBST(n) and thus
1p does not exist.
5) if 1p does not exist, then AR cannot be expressed since AR/1p =
Nothing.
6) If AR cannot express on any 1p, then AR cannot exist.
7) Thus if CUD does not exist, then AR does not exist.
This makes no sense for me. I' sorry.
QED.
You are assuming that AR can exist and be expressive without any
support or supervenience. How is this so? Consider how AR must exist
as distinct from Nothing otherwise AR is equivalent to Nothing
Comp entails 'nothing primitively physical', and explains how to
recover physics and psychology (and theology) from arithmetic,
including a justification why we cannot really believe in comp, from
the first person perspective.
and have no properties or orderings or valuations or distinguishing
features or properties at all. We see in the Representation theorem
that “every abstract structure with certain properties is isomorphic
to a concrete structure (such as a transformation group on some
set.).” http://en.wikipedia.org/wiki/Representation_theorem
The "concrete" in the CU and CUD is far more concrete than the
"concrete" in the representation theorem. In category theory, a set
(as opposed to a point in a category) is said to be concrete, but that
is mathematical terminology and has nothing to do with the usual
notion concreteness in real life (which I presuppose for making easy
the first thought experiments).
For AR to exist as distinct from Nothing then there must exist a
concrete structure, a CU,
I doubt this.
that it is isomorphic to and yet is distinct from by any 1p. This is
especially important in light of the fact that the CU that is
necessary for the UD
Do you think that a physical universe is needed for the existence of
the number PI?
requires a parameter invariant notion of interval and this
requirement cannot be achieved if AR = Nothing. This kind of flaw
flows, in my humble opinion, from the mistake of assuming that
because we can map the sequencing of events in a 1p history to the
positive Reals then the sequence of events of all 1p = the positive
reals. This reasoning fails because of the requirements of general
covariance that is an empirically verified fact of our
experienciable reality.
Physics is not among the hypothesis. You cannot invoke it to show a
flaw in the reasoning. Also, I don't use real numbers at all anywhere,
so it is hard to make sense of what you seem to argue.
General covariance demands that for all of the representations
of the symmetry groups of the CU there exists a smooth
diffeomorphism between them for all 1p; all observers must see the
same form of physical laws otherwise there is a preferred frame of
reference. A preferred frame of reference is equivalent (via your
“real is indistinguishable from virtual” argument!)
Of course, here "real" just means "concrete" or "physical", and this
in the usual sense (and not necessarily in the "primary" sense of
Aristotle).
to a special 1p that can act as a computational oracle to decide
whether or not any given generic 1p contains self-contradictory
information, white rabbits, cul-de-sacs, etc. I believe that the
“measure” that you keep referencing is just another form of this
oracle. If that oracle exists then P=NP! See: http://en.wikipedia.org/wiki/P_versus_NP_problem
I am currently explaing the UD Argument on the FOR list. You might
intervene at each step. I have already explained that P = NP has
nothing to do with neither UDA nor AUDA.
In conclusion: Unless one has something to be mindful of there is
no need to have a mind at all. A mind at least must have a concrete
implementation of itself to be able to exist for some other mind. A
mind that does not exist for any other Mind has not means to define
itself as distinct from Nothing.
Which nothing? AR gives all you need to have a concrete (even if
immaterial) implementation of the UD. In a sense, it arguable that AR
is more concrete than anything suggested by physical experiments and
physical theories.
>> We need the physical world to be the interface between our
>> separate minds,
> Eventually with comp, the physical world is recovered by defining it
> as an interface between our different minds, or as the gluing dreams
> processes. We need a physical world. No doubt on this. The point is
> that we don't need a primary physical world.
[SPK]
I agree 100%. We do not need a “primary physical world”.
OK. Then. my modest result is just that comp makes this obligatory. No
primary physical world, and physics has to be derived entirely from
the number relations.
But by my argument above we do need some non-primary form of CU to
run the UD so that AR can be expressed.
You might try to formalise a bit your theory so that we could really
see the argument, and have a clear idea of your assumption. The whole
idea is that a non-primary something don't have to be assumed. If not,
it is no more non-primary.
Unless there exists a CU there cannot be a AR since AR is isomorphic
to some CU per the representation theorem.
The representation theorem is a theorem in pure mathematics. You
confuse the notion of concreteness in catgeory theory, and the usual
concreteness of life.
It is necessary for both Abstract and Concrete structures to exist
as distinct from Nothing.
With comp AR is enough to have both, and they are distinguished
naturally by the internal arithmetical observers.
snip
>> It is a young bipolar genius, of the kind "perishing (not
>> publishing)". His only work are notes that he wrote to me with the
>> solution of the first open math question in my thesis. I have put
>> them
>> on my web pages. Here is the link:
>>
>> http://iridia.ulb.ac.be/~marchal/Vandenbussche/AxiomatisationZ.html
>>
>> The solution of the open problem is in the first three slides. It
>> shows also that G and Z are bisimulable. The other slides comes
from
>> some questions I asked to him. It includes a pretty result showing
>> that the sentences asserting their own Sigma_1 truth are false (a
>> sort
>> of anti-Löbian phenomenon).
>
> [SPK] Could you elaborate on this bisimulation?
The B of the logic Z can be define in G by Bp & Dt, and the D of Z, by
Bf v Dp (the D of Z is really the usual logican's notion of relative
consistency).
Vandenbussche found that you can dually reverse that translation: the
B of G can be defined in Z by Bp v Df, and the D of G can be defined
in Z by Dp & Bt.
Be careful to interpret the B and D in the right logic. I should
perhaps write this in the following less ambiguous (but less readable)
way:
B_z A == B_g A & D_g t
D_z A == D_g A v B_g f
B_g A == B_z A v D_z f
D_g A == D_z A & B_z t
The two lines above are the usual definition of the Z box (the second
follows by duality on Bp & Dt)
The two last lines are Vandenbussche inversion. It leads toward an
axiomatization of Z, Z1, Z* and Z1*.
So despite their very different semantics, and "hypostasic role", G
and Z are variants of each other. The same for G1 and Z1, G1* and Z1*.
Unfortunately there is no such transformation available for the logics
X. (X, X1, X*, X1*)
We conjecture that G and X are not bisimulable, nor probably S4Grz and
X.
[SPK]
It is my conjecture that if a bisimulation does not exist for a
given logic that can be expressed in a 1p then that logic (and its
derivations) are purely “subjective”, e.g. given a pair of 1p it is
not possible for 1p_1 to communicate anything about a non-
bisimulatable logic to 1p_2 and vice versa. So by your comment G and
X are purely subjective logics, aka pure solipsisms.
I don't see this, nor can I make any sense of what you say here.
Bruno
http://iridia.ulb.ac.be/~marchal/
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