At 10:27 -0500 16/01/2003, Stephen Paul King wrote:
I think that I am more upset with Tim's unsubscription that you are since he seemed to understand my argument against your thesis, but be that as it may be, I would like to interleave some comments to your post.
BM: Thank you very much. What upsets me with Tim leaving the list is that there is nothing that I appreciate more than to discuss with people who disagrees. Apparently you are willing to play that role, so certainly you or me will learn something (non necessarily exclusive "or"!) if we pursue that correspondence deeply enough. SPK:
WARNING: Ranting and raving may occur.;-)
Ah? Here you are confessing that you have some emotional attachment
to some principle. It is your right of course. But don't look at me
as a defender of comp. Sure I am willing to defend that comp is interesting,
non trivial, worth scrutinizing, ... But I never pretend comp is true.
My personal relation with comp, if I may talk about it, can be described
by the bad days and the good days. The bad days I wake up believing comp
false and hoping it true, or believing comp true and hoping it false. The
good days I believe it true and I hope it true, or I believe it false and
hope it false. As you know my work could still lead to a refutation of
comp. For example if the physics which must be extracted from comp is
different from the empirical physics, this would give evidences that comp
could be wrong.
Now, about my thesis, the only thing which has been done, is an argument
(a proof) that IF comp is true THEN physics is a branch of machine psychology.
The expression "Machine Psychology" is defined by the collection of statements
machines can correctly prove and/or infer about themselves.
I recall that by definition comp is the conjunction of the following
1) The personal implication PI
This is the thesis that, not only I can survive with an artificial skin,
liver, kidney, but also with an artificial digital brain, once this artificial
brain is a faithful copy of my brain build from a description, done at
*some* level, of my brain. The meaning of words like "survive" and "I" are
based on some amount of "grandmother" psychology.
(Note that this used will be ultimately eliminated in the arithmetical
translation of the argument).
2) Church thesis:
All digital computer computes the same class of
computable function from N to N) N = set of natural numbers.
3) Arithmetical Realism.
All proposition pertaining on natural numbers
with the form Qx Qy Qz Qt Qr ... Qu P(x,y,z,t,r, ...,u) are true independently
of me. Q represents a universal or existential quantifier, and P represents a
decidable (recursive) predicate. That is, proposition like the Fermat-Wiles
theorem, or Goldbach conjecture, or Euclide's infinity of primes theorem are
either true or false, and this independently of the proposition "Bruno Marchal
exists". It amounts to accept, for the sake of my argument, that classical logic
is correct in the realm of positive integers. Nothing more.
COMP is PI+TC+AR. PI is an hypothesis in the cognitive science. CT and AR
are hypothesis in the foundation of mathematics.
Do you believe COMP is meaningless?
Now my thesis presents two things:
a) An argument, based on a thought experiment, showing that COMP entails
physics is a branch of machine psychology. This is the UDA.
b) And then AUDA, the arithmetical version of UDA.
You can see AUDA as UDA without the PI! AUDA is UDA with the folk-psychological
(or grandmother) "I" substituted by the Godelian self-reference. This provides
more information including the shadow of the quantum.
I, for one, DO believe that "we are being dogmatical". I see a lot of statements of "belief" and very few reasoned arguments. The infamous "arithmetical realism" is one of them! I may be severely mistaken and please point out my errors, but this notion of "arithmetical realism" seems to say that "counting is fundamental" and yet disallows for the existence of "objects" that are counted. We can forget about all the other problems that I have with such appeals to "Platonism", this one is the most agregious!
BM: The main motivation of my work is to explain either the existence of objects or the apparent existence of objects. So I don't postulate their existence at the start. I am open to the idea that objects are unconscious theoretical constructions, probably arising from very long and deep computational histories .... If you want to maintain those objects' existence in some absolute sense, then abandon comp, or find an error in UDA. SPK:
If by "measurement is not something special" you mean that there is nothing intrisically mysterious and unable to be represented mathematically about the process of measurement, then I agree. I even agree with the basic notion that "observation" and "simulation" are one and the same, assuming that you believe that notion... But it is one thing to say that measurement = observation = simulation and another thing to limit the class of simulations to only those that are recursively enumerable, by UDA, for example. The "pre-specifiability" criterion of UTMs is, IMHO, the greatest problem that you do not face.
BM: I see you have a problem with CHURCH thesis too. I will come back on this. But let me tell you that I do NOT believe AT ALL that physical reality, whatever it is, can be generated by a UTM. This idea is self-contradictory. If (physical) reality can be generated by a UTM, then the invariance lemma in the UDA (we will come back to this) forces reality to be much vaster than what a UTM can generated. It seems paradoxical, but that follows from the distinction between first and third person point of view. We will come later to that, only when you tell me you understand what I mean by COMP, and that you are willing to accept it if only for the sake of the argument. SPK:
I have a serious problem with the Kroneckerian dogma that you seem to espouse. I do not understand how you can believe that the totality of all existence is limited to those aspects that are one to one and onto with the TM enumerable numbers.
BM: You should not confuse "DOGMA" and hypothesis. Also, I am not Kroneckerian. I tend to accept the whole Cantor paradise. I postulate AR, but I am neutral about bigger form of mathematical realism. More: I believe most of math not only can make sense for machines, but even that most of math are necessary for the self-extending first person notion of machines. The Universal dovetailer dovetails on the reals from a 1-person point of view, the UD even dovetail on all element of any division algebra. This follows form the invariance lemma. You confuse perhaps my work with Schmidhuber or Wolfram type of approach. But they attach 1-person to 3-person in a naive way which is just incompatible with their own comp hypothesis. See the step 11 and 13 in the UDA in 15 steps: http://www.escribe.com/science/theory/m1726.html See also: http://www.escribe.com/science/theory/m2998.html SPK
I share you enthusiasm about Everett's paper and thinking but ...BM: But the misunderstanding between us is perhaps deeper. Everett deduced the MANY (branches, relative-alternative states, worlds, histories, .... call it like you want) FROM the Schroedinger Wave Equation (SWE) + the computationalist theory of mind. Perhaps it is comp which trouble you (you would not be the first!).[SPK] No, Bruno, you cannot make that claim without serious caveats. You seem to be claiming that SWE is the output of UDA and thus any and all QM phenomena is derived from UDA actions but do not consider mathematical formal and computational complexity issues that are inherent in such a notion. Unless I am mistaken, this is equivalent to claiming that one and all aspects of QM can be derived or generated by a UTM. I have pointed you to a paper that shows that this is impossible (for finite classical machines?) and yet you ignore it!
BM: Let us not confuse the UD, which is a program (existing by Church thesis) and the UDA which is an Argument, based on the "UD infinite work" (UD*). The UD has no output! it is a program which does not stop. All what I say is that IF comp is true, then if the SWE is true (or approximately true), then for a typical observer, which computational state is generated (infinitely often) by the UD, SWE must appear as a stable description of his apparent neighborhood. SPK:
That is not so problematic in itself, but there is the "small" issue of how it is that an abstract machine, existing in Platonia and exempt from all limitations such as thermodynamics, can compute a simulation of a SWE that is extremely sensitive to the order of operations - ala the non-commutivity of the canonically conjugate operators - and does not even consider the notion of concurrency.
BM: I just do not postulate the physical laws, for I show how to recover them from comp. SPK:
You are making the same mistake that Julian Barbour is making. You are using the notion of a priori orderings or measures without taking into consideration the non-enumerability and the infinite computational intractability implicit in such orderings and measures.
BM: I do take that into account, if only because the machine psychology is divided into a deductive (G) and purely inductive part (G* minus G). It is a consequence of Church thesis (as POST has discovered in the 1920!) that the universal machine's fate is inescapably related to incompleteness, infinite, innumerable structures, intractability, uncountable sets, etc...
[SPK] Oh, that paper that only French reading people can access? Please don't mention it until you at least post an English version of it! Please point us to a step-by-step argument that "whole quantum must follow from the comp hyp";
BM: I don't stop doing that (to the point I feel often a little ashamed boring the co-listers with that). Just look at http://www.escribe.com/science/theory/m1726.html or other links to this list in my web page. I propose explicitly a step-by-step argument. If you want we can go through it step-by-step, I mean one-step/one-post, like the one I proposed to Joel in ten steps. SPK:
I simply cannot see how this can be done given the Kochen-Specker and Gleason theorems.
BM: I suspect you have not yet well understood the difference between first and third person point of view. Here is what happens: you believe in a physical world. You believe that there are empirical evidences that the physical world (which you grant) is described by QM. Now Kochen-Specker have indeed proved that there is no boolean map on the quantum reality. I don't postulate a physical world, I show that with comp we must to recover the physical world *appearances* from the logic of some first person appearances. I do show that such logic is a sort of quantum logic. I too can show that machine's physical world appearance is necesarily non boolean. The distinction between 1-views and 3-views is fundamental to understand that comp entails the stability of indeterminacy, non-locality non-contextuality, *and* non-booleanity from all "inside view" (1-view) in UD*. SPK:
BM:My problem is this: How can a computation be said to "exist" if there is no "physicality" to the tape and read/write head, e.g. the physical objects which the formal UTM definition refers to?
From that specific point of view, Turing's paper are not to good. In an
excess of pedagogical concern, Turing describe its machine in a rather
physicalistic way. The UTM can be seen as a purely mathematical object.
It exists in many shape including purely arithmetical one (Turing's results
depend on that!). It exists like the number 187987 exists.
I explain, or at least go toward an explanation of, the "existence" of atoms
big bangs and galaxies, as stable memory-pattern, in the dreams (1-computations)
of typical arithmetical (and immaterial) universal machines. "Typical" is used
in a Everett-related sense.
I still remember your idea about David Bohm's notions in one of your papers that seemed to say that we don't need particles. While I agree with you in a very "hair splitting" way about the unreality of particles, we cannot just dismiss physicality.
BM: You cannot say I dismiss it when all I give is an argument explaining where such physicality comes from, in case of the comp hyp is true. I even show what no physicist (in the actual sense of the word) will ever be able to show. Indeed I show that physicality is necessary. It's a part of math (and even arithmetic + intensional logic for the inner views). The physical laws are psychological laws, which are basically the mathematical laws of correct self-references. All the rest is geography or history, which appearance can be explained, but which details cannot be explained. SPK:
There is a phrase in the Caves et al paper that comes to mind: http://arxiv.org/abs/quant-ph/0204157 "A Hilbert space gets its connection to the world we live in through the physical quantities - position, linear momentum, energy, angular momentum - of the system that is described by that Hilbert space. These physical resources arise naturally from spacetime symmetries and the system Hamiltonian, and they are the physical resources that must be supplied to access various parts of the system Hilbert space." We might be able to make some kind of hand waving appeal to the simulability of the properties of these physical resources by a UTM ...
BM: Absolutely not. If comp is true, then "physical reality appearances" are not emulable by any UTMs. Physical reality appearances with all its non-computable aspects (like indeterminacy) appears from the whole UD*. For example we cannot program a UTM to generate a single infinite random sequence. But we can program a UTM for generating all infinite sequences. By the invariance lemma that set of infinite sequences will make appear the appearances of non computable sequences in the neighborhood of the observers, from their point of views. Remember that with comp the mystery is the appearance of the computable, not the appearance of the uncomputable. A priori (without Godel's incompleteness) comp predicts uncomputable white rabbits and uncomputable white noise. That's part of the reversal. SPK:
... and assume that that is all we need but you seem to assume much more than you are telling us! I go back to my earlier statement: We cannot just have the ability to count without some kind of prior existence of "objects" to count.
BM: That is *your* postulate. But I don't postulate that, I prove it. Indeed most immaterial machine will believe their mathematical abilities stem from their empirical observations. But in the whole picture the couple observer/object emerges from the immaterial relation between numbers. SPK:
We can dismiss the Heisenberg cut without to many problems but we cannot hand wave the categorical distinction between subject and object (Cartesian cut?)!
BM: Yes we can! There are a lot of so-called materialist monist. I just show that comp leads to immaterialist monism. A good thing given that nobody has ever been able to just define what could be a material thing. Physicists does not even try. SPK:
Tim does not see this "agnosticism" and neither do I! I see a bunch of "True Believers" that are unwilling to contemplate the contradictions that are inherent in their thinking. I was raised by missionaries and have a keen sense of "religiosity" when it comes around!
The agnosticism comes from the fact that we try (at least) to put all our carts
(= the postulates, not the dogmas) on the table.
I suspect that the contradictions you see come from
the fact that you don't yet distinguish completely the 1-person and the
3-person. (like Schmidhuber or Wolfram, but unlike Tegmark, Rossler, Everett, etc.)
On the other hand, I totally agree that we, at least, need to understand "where we disagree". ;-)
BM: That's the most important meta-point :-) Don't hesitate to ask any questions. Best Regards, Bruno -- http://iridia.ulb.ac.be/~marchal/