Hi Dan,
On 30 Mar 2016, at 07:26, Dan wrote:
Bruno, I always anticipate your thoughtful replies. I seem to
transcend my own logical capabilities each time you introduce some
concept which, at first, seems paradoxical to me. Resolution of
paradox (due to language ambiguity or sensory illusion) seems to me
to be an essential growth mechanism. It causes the integration of
some new subtle distinction/pattern into a learner's knowledge base.
I'd sometime mentioned Schmidhuber's formal theory of discovery/
creativity (scientific, artistic, etc.) as subjective compression
progress. This is what deep learning accomplishes- dynamically
improving compression of sensory input data (e.g. http://people.idsia.ch/~juergen/compressednetworksearch.html
). I was searching for more information about Post's number when I
stumbled on a report on metamathematics by Chaitin (http://arxiv.org/html/math/0203002v2
) with the claim: "We need a dynamic, not a static metamathematics,
one that deals with the evolution of new mathematical concepts and
theories. Where do new mathematical ideas come from? Classical
metamathematics with its incompleteness theorems deals with a static
view of mathematics, it considers a fixed formal axiomatic system.
But mathematics is constantly evolving and changing! Can we explain
how this happens? What we really need now is a new, optimistic
dynamic metamathematics, not the old, pessimistic static
metamathematics."
Dynamic metamathematics... is this not what Schmidhuber's
compression progress (i.e., the whole endeavor of deep learning
AFAIK) is essentially about- automated theory formation? A Darwinian
asymptotic approach towards minimum description length? I had read
some article on psychology which said that subjective time for an
observer slows down whenever it is presented with "interesting"
sensory data (i.e., data with patterns that are neither too random
or too simple in relation to existing knowledge). [http://mindhacks.com/2011/04/18/time-flies-when-youre-having-fun/
] Perhaps it is why life seems to pass more quickly as we age: we
make less compression progress (unless we continue to place
ourselves in new sensory environments and try new experiences).
I have no problem with this, at least if time remains conceived
phenomenologically.
But for the computationalist mind-body problem, a big part of this
must be derived from the "static", non dynamical, arithmetical reality
(which needs to be assumed if only to define what we mean by
computation). Now, that dynamical aspect or phenomenology appears in
the two intensional of Gödel's beweisbar predicate ([]): []p & p, []p
& <>t & p. The first one gives an intuitionist logic, and the second
one a sort of quantum intuitionistic logic (perhaps fully quantum when
p is restricted on the universal dovetailing).
It is too early to address your question (on compression and the
feeling that times flies more quickly in front of deep data) in that
setting (which interest relies only in the fact that we get different
logic for the "knowable" and the "justifiable" part. But the idea
seems reasonable to me.
Now, I am not sure why Chaitin qualifies "static" as pessimistic. It
think that is personal philosophy. Its own work seems to me illustrate
the contrary. Like many scientists, he believes that philosophy is the
place where we can defend personal opinion. One of my goal was to
illustrate that *some* philosophy (the one based on digital mechanism,
actually) and theology/metaphysics can be done with the scientific
attitude, which of course does not please to some philosophers.
Bruno
On Tuesday, March 29, 2016 at 12:55:01 PM UTC-4, Bruno Marchal wrote:
Hi Dan,
On 29 Mar 2016, at 01:36, Dan wrote:
Bruno, I don't understand your arguments fully. Specifically,
I don't understand how the fact that the propositional logic of
true but unprovable sentences can be structured by "modal logic G*
minus G" (??) is useful to provide distinction between qualia and
quanta.
Because G* is decidable, so the machine looking inward, or the
machine talking about herself (and remaining silent if necessary)
can (in fact cannot not) discover truth about itself which escapes
its ability to justify rationally.
Then it is not just G* \ G, but the intensional variants (Z1* \ Z1,
X1* \ X1, and S4Grz1). So there is a simple algorithm which can be
selected by evolution, or that a machine can just discover by
looking inward, which the machine can use to "intuit" many non
provable truth about itself, and then change itself into a new
machine by incorporating the new formula, or using them in many
other ways.
When you say Godel incompleteness result is "constructive" rather
than the non-constructive Chaitin "relative complexity" result, do
you mean that it provides a way for some entity to precisely
identify elements from the set of empirically evident emergent
truths which it is unable to describe formally (e.g., with finite
set of differential equations or a sequence of instructions in some
universal description language)? In other words, are you saying
Godel-type incompleteness is the mechanism by which some observer
is able to recognize emergent complex phenomena (e.g., measurements
of social/economic systems characterized by scale-free power-law
distributions, generated with preferential attachment processes,
and modeled by minimization of Fisher information) even though it
is beyond ability of observer to describe deterministically using
equations, programs, etc.? If this is what you mean, I don't
understand how the Godelian result is "constructive" in this sense
or why the Chaitin result is by comparison "non-constructive."
Chaitin shows the existence of infinitely many sentences which are
undecidable, like this long string of symbols is incompressible, but
the machine is unable to prove them for any specific strings. In the
case of GOdel's incompleteness, the machine can find the specific
undecidable statements, and indeed a transfinite number of them.
In no case is that related to anything empirical. the empirical
reality is eventually explained in term of a statistics on all
computations supporting consistent extension of "myself". I can't
explain here the details, but if you tell me if you understand the
Universal Dovetailer Argument (like in the paper sane04, or
comp-2013) we can build from that.
I am not criticizing the Kolmogorov-Chaitin approach, just that it
uses an incompleteness which does not help to explain why we can be
aware of things that we can hardly explain or justify, like
consciousness and qualia, or the intuition of the transcendental
truth, ...
How are the Chaitin-type results using inequalities of algorithmic
complexities (of the observer and observed) "eventually emergent on
the Gödel-Löbian sort of limitation?" This would be an argument of
ontological primacy and so it should have no assumptions.
?
All universal numbers suffer from both limitations. We have them
both, and just as a consequence of elementary arithmetic. We don't
need to assume a primary physical universe. Actually I argue that we
cannot use it to singularize or stabilize the conscious experiences,
which is why at some point physics is reduced to computer science/
arithmetic.
When we say true but unprovable, it makes me think of relative
algorithmic complexity.
That is correct. Chaitin does show the existence of true but non
provable sentences, (the one similar to those found by E. Post
manybyears ago), but it does not give a criteria which makes the
machine able to find them and produce them as output. That is
contrary to the case of Gödel's type of incompleteness. Both are
interesting, but the second one can be used to put light on the
qualia/consciousness problem: how do we "know" non provable
sentences? The constructive aspect of Gödel's incompleteness
explains why the machine is confronted to such truth all the time,
and how that enrich its mental space, even before she bet on some
world.
A "self-aware [mathematical] substructure," in Tegmark's terms, of
given Kolmogorov complexity cannot recognize patterns which have
greater Kolmogorov complexity than itself. When we say a truth
(i.e., pattern in nature) is unprovable, this claim is relative to
some particular observer and it is not an objective claim.
Yes, and the invocation of some Nature is not really working, for
conceptual reason explained in the UDA, especially step 7 and 8
(which are not so easy).
Indeed, deep learning techniques like neuroevolution and clustering
by compression enable an agent with different channels of
perception from a human to be able to make decisions by discerning
patterns it observes (intelligent decisions that will maximize
entropy, future possibilities) without any need to store any
explicit analytical, symbolic, or linguistic expression of the
patterns themselves.
I have no problem with this.
Further, these may be patterns which the machine's channels of
perception would enable it to symbolically represent, but perhaps
which could not be symbolically expressible for a human.
That necessarily happens. In fact consciousness happens for such a
reason, although it uses both Gödel's constructive incompleteness,
and Tarski's constructive (in a weaker sense though)
inexpressibility (of truth and semantic of oneself) theorem.
I am partial to Tegmark's terms when it comes to channels of
perception: "frog" perspective (first person, subjective),
"consensus" (first person, collective), and "bird" (third person,
objective).
Well, I extracted those notion directly from number's self-reference
(first person is given by []p & p, first person plural from []p &
<>t, third person is just []p). But then, the splitting of G and G*
splits in two each of those points of view. Eventually I have 8 such
notions, if not 4 + 4*infinity, because the logics with "<>t" are
graded, which is useful for having some nice correspondence between
the quantum and space to be recovered in the quantum logic of the
machine's observable extracted from self-reference. Tegmark is on
the right track, in a different direction (as he comes from
physics). I start directly from the mystical (eyes closed) machine's
interview. the fact that it matches is a good sign for digital
mechanism (computationalism).
Estimation theory probably has not received enough attention in the
philosophies of mind, science, and language (at least until Frieden
and Romanini quantified the semiotic philosophy of CS Pierce using
Extreme Physical Information).
Reviewing your paper "COMP (2013) - by Bruno Marchal", I see the
following: "An argument against the comp hypothesis has to
speculate on some unknown non-computable, and non-first person comp-
recoverable (as explained later) function in Nature, and this has
never been observed."
If so, is this following recent discovery an argument against comp?
Does first person indeterminacy come to the rescue in this case, as
you showed it does for collapse of QM wave function? http://arxiv.org/abs/1502.04573
No, if they could show that the spectral gap is Turing complete (and
thus undecidable, but with a complement complete for the halting
problem) then this would more confirm comp than be a problem. A
priori, comp make the machine confronted to something too much
complex, with an a priori too much information (from white rabbits
to white noise). in QM, already the 0-body problem is Turing
universal. IF QM is the "correct" comp physics, the spectral gap
result will not change many thing, on the contrary, it add some more
level of universality in physics, and provides hopes for some more
Turing complete, even quantum-Turing complete, subsystems in the
physical reality. Very interesting paper, but, well, if you think
you could refute computationalism from there give some clues.
I have just come across and ordered your book "The Amoeba's Secret"
and am looking forward to reading it. Have you seen the Youtube
playlist created by Sante Fe Institute on Complexity? It raises
questions in my mind about validity of COMP; I mention one example
in my blog which references the following paper, where genetic
algorithms are used to evolve locally interacting agents of
cellular automata to coordinate and perform some global task:
But saying this means that you are using comp, especially with
cellular automata, which can be emulated with a sequential
"stubborn" Turing-von Neuman type of universal machine. Not in real
time, but normally after the UDA, you know there is no real time:
just pieces of machines dreams glued or not by universal numbers.
(paper: http://rundle.physics.ucdavis.edu/PHYGEO30/MitchellCAsandGAs.pdf
, video: https://www.youtube.com/watch?v=hdRTcrTYfiQ&index=99&list=PLF0b3ThojznRyDQlitfUTzXEXwLNNE-mI
). As I learn more about information transfer in complex systems
(as in biosemiotics), I increasingly begin to question the validity
of COMP or at least am unable to see how the hypothesis explains
such information-theoretic descriptions of nature. EDIT: Actually,
it seems quite obvious now that COMP is valid in such a case... the
cellular automata rule which evolves from the genetic algorithm is
the simple computation.
OK. Nice you see this now. You save my time. yes, all the Santa Fe
approach uses comp. "My" comp is the weakest comp hypothesis in the
literature, and all I want to share is that it fits much better with
Plato theology than with Aristotle theology (which assume a primary
material universe).
Note that the comp ethics does not fit well with Plato's politic, as
someone made me realize, and I see now that even Plato made the
"machine's blasphem" error, (mixing philosophy/theology with human
practical affairs).
The real recent progress (the working democracy, i.e. the voting
system), does avoid the argument by authority on the fundamental
satisfying machine (human) aspirations). The antic greeks have
missed the genuine notion of democracy, or altered it at the start.
A recurrent human mistake.
From the perspective of any one agent in the cellular automata,
however, the description of the overall system behavior is beyond
symbolic expression (the system is Relatively, not Absolutely,
complex because indeed the researchers were able to codify the
emergent patterns using a "particle physics" framework).
Nice it is a bit like the comp explanation of free-will. the system
is globally determined, but in no way accessible to the system, yet
the system can codify emergent set of possible choice/solution, and
ponder which one will satisfy it more relatively to some short term
or longer term goal.
But again, to attach a qualia to such "set of pattern", the
constructive undecidability makes this automatic: it is just true
that from that position the machine get a type of undoubtable
certainty but without any means to justify its presence rationally.
I don't think there is any problem between the possible physical
motivation in computer science complexity theory. But for the mind
and the theological ultra-basic questioning (on the nature of
reality), the constructive incompleteness of Gödel gives all the
answers (well at the propositional logical level) through the
intensional nuances (whose existence and non triviality is given by
the incompleteness) of machine's provability. It is a super-ideal
case. real life, and applied physics uses more our non-monotonic
paraconsistent super-layer of Belief revision system, natural
languages, ... but this, I assume, play no part in the origin of
the physical laws (that would be like assuming an incompetent God,
or a toxic Glass-of-Milk at the start. Like assuming miracle, this
does not help to solve the fundamental problem, but it can provide
jobs and money, which is part of the game.
Algorithmic complexity is a very interesting subject. I do not
exclude that it will play some role in the derivation of the physics
from arithmetic, that we have to do if we assume digital mechanism.
But to express first and solve genuinely if sketchy the psycho and
theo logics part of the problem, the royal road is the Gödel one,
especially after Solovay offered the arithmetically sound and
complete formalization (at the propositional level) of many entities
self-reference logics G and G*.
We get a logic of observable from some of its intensional variants,
and the complexity is more related to the hamiltonian(s), and to the
depth of the infinitely many computations which support us "here and
now". I can guess the hamiltonian is something highly symmetrical
and plausibly linear, but not much more.
But my goal is not solving a problem in physics, but in "theology"
or "philosophy of mind", when assuming a precise quite general
version of (digital) mechanism, i.e. without hiding the
consciousness aspect under the rug.
Have you read Everett? Tegmark starts from Everett, but has clearly
not see the importance of the first person indeterminacy in the
computer science frame, and is not really aware of the importance of
the universal (in the sense of Church-Turing) machine. At least
Chaitin exploits this. Both are unaware that Everett's move needs to
be extended in elementary arithmetic, and the wave itself must be
accounted phenomenologically.
...
I don't find a good reference of a paper by Calude which shows
almost directly why algorithmic randomness hides a bit of the
"meaning" in the Post "information" number, or in Gödel's
provability predicate.
For exemple the ith decimal of "Post number" is 0 or 1 if phi_i
stops or not, with phi_i an enumeartion of the program without
input. (It is a view of the Halting Oracle). That sequence is more
or less random, but with some extreme redundancy that the Chaitin
omega number completely abstracts itself from. But Calude's point
was deeper than this, ... I will tell you when I found this back.
Bruno
On Thursday, March 24, 2016 at 12:56:01 PM UTC-4, Bruno Marchal
wrote:
On 24 Mar 2016, at 05:15, Dan wrote:
Paper discussing exact mapping between renormalization group and
deep learning: http://arxiv.org/abs/1410.3831
It seems interesting, thanks.
Another paper relating Kolmogorov complexity to geometry, with
focus on spacetime / causality: http://arxiv.org/abs/1206.2893
I will dig on this more when I have more time, but I am less
convinced at first sight.
Have you read my arguments? You would better see if some ideas
there could help or not to extract physics from arithmetic through
machine's self-reference. Some caution have to be taken to get the
distinction quanta and qualia properly.
In this list most people defend ensemble of universe or dreams type
of theories, which generalize Everett conceptually, and which
maintain 3p determinacy and 3p locality. We can exploit the fact
that machine have the means to grasp that the truth about them
extends properly what they can justify rationally, yet such truth
is still very well structured, and incompleteness forces it to obey
different logics for each mode. You might appreciate, given that
you seem to appreciate Chaitin's work, which also relies mainly on
the recursion theorem in computer science. The learning theory of
Gold, Blum, Case and Smith, Osherson, Stob, Weinstein (to name a
few) is also very interesting (and non constructive like Chaitin).
The usual "Godel" result is constructive and this is what I exploit
to put some light on the "body" problem that the mechanist
philosopher is confronted too.
Bruno
On Monday, March 21, 2016 at 9:12:33 AM UTC-4, Bruno Marchal wrote:
On 17 Mar 2016, at 16:26, spudboy100 via Everything List wrote:
Wolfram would agree with this paper in some ways.
https://www.youtube.com/watch?v=Re9eB_j6m-0
The main content gets very interesting, for me, at 1hr 8 minutes
in, and 1 hr 12 minutes in to Wolfram's SETI lecture.
-----Original Message-----
From: Dan <[email protected]>
To: Everything List <[email protected]>
Sent: Wed, Mar 16, 2016 11:13 pm
Subject: Can Space-Time Be Based on Logic and Computation?
Paper:
http://arxiv.org/abs/1602.06987
Comments:
Lossless compression of an image or audio file approximates its
Kolmogorov complexity and reveals its "compressibility," or
"interestingness." If it's not at all compressible it is too
random to be aesthetic or enjoyable, whereas too much
compressibility is associated with oversimplicity. Many classical
works have been analyzed in this way and show to be in the
middle. Schmidhuber mentions a theory of creativity, fun,
motivation based on compression progress. Compression progress
seems to be essential to theory of general AI- I refer to
neuroevolution techniques, Cilibrasi and Vitanyi's paper
Clustering by Compression for inference, as well as Wissner-
Gross's simulations showing tool-usage behavior upon entropy
maximization. Was a paper recently giving exact mapping between
renomalization group and deep learning.
Do you have the reference of that paper?
Paper I link to above takes idea of data compression / Kolmogorov
complexity even beyond a relationship to statistical mechanics or
deep learning to explain the causal appearance of spacetime
itself. I want to understand how Extreme Physical Information
fits in to all of this.. it provides observer dependence and
derivation of so many physical and nonphysical laws. It also
encapsulates limits of knowledge using any particular channel of
perception.
Of course the Gödel type of limitation (as opposed to Kolmogorov
or Chaitin type of limitation) is independent of even the
existence of a channel of perception (which are eventually
emergent on the Gödel-Löbian sort of limitation). A big difference
between both is that the algorithmic information limitation is non
constructive: you get an infinity of undecidable sentences, but no
means to individually recognize them. On the contrary, the Gödel-
Löbian limitations is constructive, and gives the means to the
machine to build the undecidable sentences, and perhaps to extends
itself from them. Indeed the whole (propositional) logic of the
true but non provable sentences is structured by the modal logic
G* minus G and its intensional variants. This is useful to get the
qualia and the general qualitative feature associate to
consciousness.
Bruno
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