Dear Bruno,
Thank you for this kind and thoughtful reply and comment.
Interleaving my responses below. Please forgive me if I make mistakes here,
there are some very complicated ideas involved that I understand only a
little bit.
-----Original Message-----
From: everything-list@googlegroups.com
[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Thursday, September 30, 2010 2:22 PM
To: everything-list@googlegroups.com
Subject: Re: A paper for your Comments
On 30 Sep 2010, at 04:25, Stephen P. King wrote:
> A crude sketch of a computational model of Interaction.
>
> Stephen Paul King
> 9/29/2010
>
> Might it be possible to model the content of 1st person experience as
> a computationally generated "simulation"?
[BM]
Yes and no.
Yes: that is a way to express digital mechanism.
No: IF you express mechanism through "yes doctor", which makes it possible
to separate more clearly the first person from its "third person describable
bodies at the hopefully correct level", THEN, strictly speaking, the first
person become attached to all its possible bodies, below its substitution
level. So it can be argued that the first person and its content is
distributed in the whole space of all computations. This includes oracles
and is a priori not an enumerable space.
In a sense, all bodies are zombie, "we" are always elsewhere. In a sense, DM
makes the first person NOT being a machine, from her/his/its point of view.
[SPK]
The "no" part of your comment here is one that I agree with and it
is very important because it speaks to the idea that there is a
stratification of levels of sorts within which we get an approximation of
3rd person describable bodies that are instances of the possible relative
positions that physical objects can have to each other. This is the start of
the solution to the problem of space. We then consider the idea that we have
to consider that the absence of an object from locations in space is just as
informative as the presence of objects. Thus all of the possible places
where an object is not located becomes an empty place that has equal
ontological status as the place were an object is present. Thus we get a
full space and not just a nothingness with a disjoint dust in it. This in
turn might help us makes sense of the notion of "vacuum fluctuations"...
Remember, we are thinking of space in term of a computational
simulation. Have you played a video game where other players are involved,
such as MMORPGs? The idea is that each person has a client program that
generates a simulated world where that player has itself as being in the
center. The client programs communicate with each other via a central server
that acts to save choices and enforce rules of consistency and an entire
virtual world that can be explored and occupied obtains. I suspect that we
can think of our physical world in similar terms!
This has profound implications for science and would justify Plato's
assertion that what we observe as the world is mere "shadows on a cave wall"
projected from a higher "reality".
***
> We can point to the body of work by
> David Deutsch, such as that found in his book The Fabric of Reality,
> as providing some excellent reasoning to at least consider that the
> answer to our question might be: Yes.
[BM] Deutsch accepts mechanism. He seems to even accept classical mechanism
(the brain is a classical computer, roughly speaking). This is not
postulated in the UDA reasoning. The consequences of DM I point too does not
depend on classical or quantum mechanism in cognitive science.
[SPK]
Somehow I keep missing the UDA reasoning. :( But let's keep going.
> OK, given that, how might we model interactions between such
> "simulations" in a way that would give us something that covers many
> situations including those where we have events that cannot occur
> simultaneously? I think there is.
[BM] That seems obvious for me. Cellular automate interacts, subroutine
interacts, all computations are, or can be, defined as elementary actions
and interaction. They look more physical when linearity is introduced, which
give a notion of resource.
Sub lambda calculus and sub combinator algebra are similarly linear.
[SPK]
Yes, but the interaction that you are thinking of might be one that
occurs upon and/or within a single substrate that is at the same level or
stratum as the automata, subroutines, etc. For the quantum aspects we have
do not have a substrate in the same sense. This is part of the tensor
product problem. Yes, we can think of some Rigged Hilbert, Fock or Gelfand
space that has all of the separate quantum system as separate rays but this
fall apart when we try to make our interactions follow the Lorentz or
Poincare group of transformations. The space that those generate is not
closed under the boosts or accelerations of objects. We are looking at
relations between linear spaces/algebras and finite dust like spaces.
Another challenge is in recovering the calculus so that we can
reproduce to some degree the partial differential functions and so forth
that we need for physics. I don't think that it will be so hard since the
Pratt transition model seems to not have problems with variations in the
scale or "size" of the transition. It is similar to doing a lattice
approximation of a continuum.
> Let us first point out some features of computations and the
> simulations that they could generate. We know that computers can
> generate simulations of other computational systems.
[BM] Yes. Computers are universal simulators. Universal is really
*universal*, if we think twice on Church thesis.
[SPK]
The only problem that I have with the Church thesis is that it seems
too rigid and narrow. Maybe it is just a prejudice of mine...
> We see this when we consider how one computer can run software that
> emulates of some other computer.
> What about a computer generating a simulation of itself?
[BM] No problem. Well, there are some problems, or impossibilities. You
cannot write a stopping program with output its own complete trace of its
actual behavior. But you can write a program a which output a program b
capable of given the trace of the program a, in finite steps. Solovay,
inspired by Hofstadter, makes relation between virus, and a form of
constructive lobianity. The Löbian sentence is the sentence which says of
itself that she is provable: "I am provable".
Amazingly Löb showed those sentences to be true, and of course, then,
provable. Hofstadter Solovay virus not only asserts that they are true, but
try, some with success, to actually provide a proof of themselves.
[SPK]
Yes and the impossible situations are important for they tell us how
some situations do not obtain, like the idea that an entity can have full
knowledge of all of the outcomes of all of its choices before it actually is
in the situation to make those choices individually. Free Will anyone? Now
to give the Löb virus an environment to live and reproduce in. :)
> What about a
> computer X generating a simulation of some other computer Y that is
> running a simulation of X?
[BM] No problem with unbounded 'tape'. Your machine might ask for more
memory. Let her write on the wall.
[SPK]
Yes but in the situation that I am considering there is an upper
bound. We see this in the Bekenstein bound, "... upper limit on the entropy
S, or information I, that can be contained within a given finite region of
space which has a finite amount of energy—or conversely, the maximum amount
of information required to perfectly describe a given physical system down
to the quantum level." http://en.wikipedia.org/wiki/Bekenstein_bound
My thought is that my machines (I call them Monads following
Leibniz' idea...) can only write on that "tape" or "wall" that is in a
logical sense 'shared' with all of the other machines that it can bisimulate
each other down to the substitution level. This goes back to the proposed
solution to problem of space and a better substitute for the usual notion of
"substance" in philosophy.
> It seems that if we allow for unlimited computational resources, we
> could have a computer generating a simulation of a computer generating
> a simulation of a computer generating a simulation .
[BM] Yes. Like the universal dovetailer which runs all computations on all
oracles, including itself an infinity of times.
[SPK]
Yes! I am trying to get you to think about this fact a bit more
deeply. The fact that we obtain "itself an infinity of times" is the key.
What if all of these differ only in their 3rd person aspect of relative
location? Like your discussion of how one can teleport and copy to different
locations. Think of all motion or "trajectories" in space as successive copy
and erase operations. This is, after all, exactly what quantum teleportation
involves!
[BM]All the combinators equation admits always solution, but some can give
non terminating computations.
[SPK]
Yes, this is where I think the "measure" is found that we are
looking for, in the space of solutions. What we need to find is something
like a filter to pre-partition the space, similar to how a notion of a
course graining is used in thermodynamics to partition the state space of a
physical system. At this moment I suspect that this filter is related to the
space of "time" that is implied in a bisimulation ... umm, I need a word
here, something that means "a collected narrative of many monads such that
there is no two monads do not share a common scene or image". This follows
from considerations of what is required for the idea that one can travel
from any point in a physical world to some other point without
discontinuity. It is the logical dual to the notion of an invariant internal
in Relativity...
> What about a
> computer X generating a simulation of computer Y that is generating a
> simulation of X as it generates a simulation of Y . As so forth.
[BM]No problems.
[SPK]
Excellent! :)
> We can see that if there is a finite upper bound on the resources
> available to the simulation generating computers then such expressions
> of infinite regress cannot obtain,
[BM] It depends! In some case self-referential programs stop, with self-
referential information.
[SPK]
OK, could you elaborate on this a bit more?
> but the idea that one computational system can
> generate simulations of other computational systems is not
> problematic and
> maybe even useful to model interactions between computational system.
[BM] I don't see the problem with simulating interaction (with fortran,
lisp or just numbers with + and x).
The conceptual problem is the peculiar symmetrical multi-universal
ways interaction seems to occur in our neighborhood, and in the
neighborhood of the first persons.
[SPK]
OK, that is where I have to explain more part of my idea. I have to
be sure that all understand the basic idea of bisimulation first before I
can go to the next step where we chain bisimulations and deal with
concurrency.
> Now we need to ask how it is that we distinguish a simulation of a
> computational system from a "real" computational system in most
> discussions
> of this idea?
[BM] When I hear the word "real", I take my gun .... :)
[SPK]
Good! It is nice to talk to someone that is not a naïve realist.
> Given that we have the notion of Universal Computers and even
> Universal Virtual Reality Machines (1)
[BM] Assuming the physicalist "Church Turing principle", I think. Which I
think might be hard to maintain with digital mechanism.
Again, the problem is in the word 'reality'. David Deutsch seems to
believe that there is a machine capable to emulate all physical
phenomenon. Needless to say, that is an open problem with DM, but it
might seems unreasonable to believe that we could have both Church
thesis true and the Church Turing principle true too. Below our level
of substitution there are too many white rabbits. In my opinion
mechanism go in the direction that "matter, time consciousness, etc.'
are NOT computable things. You can run the universal dovetailer, but
there are no step at which you can say "that first person is
emulated" (only its relative bodies). the first person itself is
distributed in the whole UD*, and its internal logic reflects that
facts.
[SPK]
Why not? It would help if you read that paper by Svozil et al that I
referenced previously http://tph.tuwien.ac.at/~svozil/publ/1999-embed.pdf .
The point is that a single quantum logic can embed many different Boolean
logics and a single Boolean logic can only partially embed a single quantum
logic. This is result of linear super position. We avoid the white rabbits
when we consider that all of the Löbian monads can only be said to
communicate and interact with each other if they can effectively bisimulate
each other. This acts as a contradiction filter that prevents one monad from
being logically sound to one set of monads and incoherent or even insane to
others within the same collection of concurrent bisimulations. We are
getting ahead of my explanations here....
The substitution level is the point at which there is no difference
that makes a difference when it comes to physical system that can be said to
run our computations. This also applies to successive brain states and goes
to the experience of continuity of experience. Matter, time, consciousness,
etc. are not computable things only in the sense that there does not exist
an unique "pigeon hole" algorithm that will select all of the physical
dynamics of a world that a naïve realist would think is "Real" for the same
reason that Leibniz' Pre-ordained Harmony cannot obtain. One cannot solve an
infinite NP-Complete problem in less than 1 step. This is why I advocate of
the idea that the universe that we observe, our common world, is something
that is continuously generated and not some mechanism that was created in
some special and unique event. To use a theological language, God's
creativity is eternal and continuous and not restricted to a single special
event.
Stephen Wolfram points out this when considering the intractability
of computing simulations of physical systems:
http://www.stephenwolfram.com/publications/articles/physics/85-undecidabilit
y/2/text.html
" The behavior of a physical system may always be calculated by simulating
explicitly each step in its evolution. Much of theoretical physics has,
however, been concerned with devising shorter methods of calculation that
reproduce the outcome without tracing each step. Such shortcuts can be made
if the computations used in the calculation are more sophisticated than
those that the physical system can itself perform. Any computations must,
however, be carried out on a computer. But the computer is itself an example
of a physical system. And it can determine the outcome of its own evolution
only by explicitly following it through: No shortcut is possible. Such
computational irreducibility occurs whenever a physical system can act as a
computer. The behavior of the system can be found only by direct simulation
or observation: No general predictive procedure is possible. Computational
irreducibility is common among the systems investigated in mathematics and
computation theory.[2] This paper suggests that it is also common in
theoretical physics. Computational reducibility may well be the exception
rather than the rule: Most physical questions may be answerable only through
irreducible amounts of computation. Those that concern idealized limits of
infinite time, volume, or numerical precision can require arbitrarily long
computations, and so be formally undecidable."
> we find that the idea that we can
> distinguish a simulation from the real thing to require some kind of
> notion
> of a physical reality that is distinct from simulations of parts of
> it.
[BM] Right. But what could *that* mean? With DM that can only emerge from a
projection on infinities of computations.
[SPK]
OK, could you elaborate a bit on this notion of a " projection on
infinities of computations"? How is this projection constructed?
> In other words that there is something about "reality" that is not
> capable of
> being simulated by a computational system in principle.
[BM] That's right again. But then since sometimes we know that the
arithmetical reality is the union of the Sigma_1 (computable) with the
Pi_1 (already not computable), and the Sigma_2 (not computable) and
the Pi_2 , well all the non computable true Sigma_i
(ExAyEzArEsAtEuAj...P(x,y,z,j, ...) and Pi_i (AEAEAEA...P) propositions.
Arithmetical truth extends widely the computable. Only the sigma_1
reality is partially computable, (p -> Bp)
[SPK]
I think that this is too restricted a view. This goes to my
prejudice that existence is not limited to the Integers...
> In the work of Bruno Marchal (2), building on prior work in modal
> logic, we
> find some very good arguments that there does not exist a
> computational
> means to decide which computation might be the one that exactly
> matches the
> world of experience that I have as a 1-scape. We can conjecture that
> that
> something has to do with the Hard Problem of Consciousness (3), but
> we can
> set that aside for now since we are only considering those aspects
> that are
> computational.
[BM] Why? The whole problem is there. How could a first person (conscious)
attaches her consciousness to any particular bodies, given that (from
a DM third person view) she got an infinity of bodies, relatively to
an infinity of universal numbers.
The hard problem of consciousness, assuming DM, is shown to be an hard
problem of matter.
[SPK]
Why? Because we need to deal with the intractability and the
embedding problems!
We also have to explain how that attachment of a particular mind to
a body follows. This is explained, I hope, in the duality idea. We have to
get to the point where my explanation makes sense first. Yes, the hard
problem of consciousness is equivalent to the hard problem of matter; they
are the dual of each other!!!!!!! This is obvious in the Stone Duality and
what Pratt is trying to explain in his papers.
> Additionally there are some other reasoning as to why it makes sense
> to suspect that some kind of Cartesian-like dualism is involved is
> implied.(4)
> We could go further and borrow from the brilliant writer and thinker
> Greg Egan (5) the notion of a 1-scape; the landscape of the world as seen
> by 1 person and communicated about in the 1st person sense.
[BM]Hmm... that looks like telepathy. Communication are third person
things, emerging at some level from the many computations that we share.
{SPK]
Yes, it does seem like telepathy but only because we have not
discussed how the idea of "substance" can be obtained. It has to do with
that weird thing in quantum mechanics called "phase entanglement" and how
all of the properties that one can attribute to "substance" can be obtained
by considerations that involve concurrent interactions. This also goes to
the notion of Time. Additionally, we have not discussed how the notions of
Information and Entropy are involved. I beg your indulgence in this, it
should be clear eventually that there is no "action at a distance" or
"telepathy" in my model, but there is not an "objective" 4 dimensional
universe either. Again, try to think of 3rd person things as that which is
invariant over many monads within a single "gossiping". I will define this
term "gossiping" soon. :)
> 3-scapes would then
> be considered as emerging from the intercommunications between many
> 1-scapes.
[BM] OK.
> We now move to considerations of multiple separate computational
> simulations.
[BM]The UD does that. It makes the steps of the computations of all phi_i
on all numbers and numbers stream. But this includes all the
computational means of all possible forms of interaction too. Right?
This includes Romeo and Juliette type of interaction at the level of
quark and electrons, in some computations.
[SPK]
Yes, but we have not addressed the concurrency problem yet.
> I suspect that we can use the notion of bisimulation to enable
> us to figure out when and if separate systems can be said to
> communicate
> with each other if in the course of a conversation back and forth
> their
> successive simulations of each other match up with the internal
> simulations
> that they might have of each other.
[BM] All you need is some good tensor products. With the X and Z logic, I
have searched for Temperley-Lieb algebra rich enough for having
projective structures, braids and knots, but the emergence of space
remains quite a mystery. But you are already supposing some good
tensor products. I can' do that with the DM 'deontology' (that would
be treachery)
[SPK]
Yes, deontology would not go because of the problem that I mentioned
previously with Leibniz' Pre-ordained Harmony.
> In other words, if my simulation of you telling me that X occurred
> matched
> up with your simulation of yourself telling me that X occurred *and*
> if your
> simulation of me responding to the occurrence of X matches up with my
> simulation of my response to the occurrence of X then we can say
> that X is
> communicated to me by you.
[BM] OK. In a third person sense of communication.
I have to go now, but I send the message anyway. I may comment on what
you write below, if I succeed in making some sense of it.
How should I read A ~ B ~ A? as (A ~ B )~ A, or A ~ (B ~ A) ? I
guess A ~ (B ~ A)
A = (A ~ A) for all A? This would not be a simulation in the usual
computer science meaning of the word. A program which simulates a
simulation of itself by itself would be a very special program. But I
will read this at ease soon.
Bruno
[SPK]
Let me copy a reply that I made to another friend on this:
Hitoshi wrote:
Interesting, although I do not understand the meaning of A ~ B as well as I
do not recognize what
A = A ~ A
means. Does this mean
A = (A ~ A)
or
(A = A) ~ A ?
**
[SPK]
In English: the computer A is equivalent to a simulation of the
computer A by the computer A itself. The "~" symbol means "simulates". This
captures the idea that a computational system can generate the image of the
form of any physical system. Think of what we discussed about how Local
Systems have an Inside and an Outside aspect which are very different. What
I am considering here is the way to think about the "outside" aspects and
ways that Local Systems can process and relate those aspects. The internal
aspect of a local system is a form of computational act but it is such that
it cannot "see" itself as it truly is. On the other hand, the computation
can generate patterns of information that other computers could identify as
form and extension and mass, etc.
Think of this: When you are reading these words, become aware of
your minds act of reading the words. Do you see words as something other
than some pattern of tiny dots on a monitor screen? No, we not have the same
kind of internal content in our minds. When one seeks to be aware of one's
own mental act of reading words, there is nothing like patterns of dots,
there is just a sense of "what it is like to see dots" and the recognition
of a meaning that occurs in mind as one perceives the pattern.
**
As another example
A ~ A = A ~ B ~ A.
Does this mean
(A ~ A) = (A ~ B ~ A)
or
A ~ (A = A) ~ (B) ~ (A)
or anything else?
**
[SPK]
This is interesting, some other person asked this same question. If
we were to use the ( and ) symbols where would intend a different meaning. A
simulating itself is equivalent to A simulating B simulating A or A~A = A ~
B ~ A.
(A~A) = (A~B~A) would read: The act of A simulating A is equivalent to the
act of A simulating B Simulating A. The difference is that the first
expression is general and not limited to a particular circumstance while the
expression with the brackets represent a particular case of the general
form.
A~(A =A) ~(B)~(A) would not make any sense as an expression since we
distinguish the simulation as an action and the equivalence as a passive
identification between actions.
**
Another fundamental question.
You say that X simulates Y. In which you need to assume the "existence" of X
and Y as individual independent existence.
Then you try to explain what X sees by simulating Y and then X itself
through the simulation of Y which simulates X. If your explanation will be
successful, you seem to be able to explain the "existence" of X itself
without the existence of Y, as the existence of Y is itself a simulation by
X and you need only the existence of X. You then will obtain solipsism.
In a sense this agrees with Substance of Spinoza. He assumes that the
existence is unique and it is Substance. There is only one existence
necessary. Simulation then does not and cannot exist.
***
[SPK]
X and Y are computational or local systems; the unitary
transformation of a QM system is equivalent to a computation. Well, it is
much more but it is at least a computation. We always assume that something
exists is there is any possibility that we can ascribe some property to it.
Existence is fundamental and not a property that something can have. Either
something exists or it does not. Existence does not depend on anything. We
would say that X and Y have some properties such that some other can
distinguish them from each other. WE need to be careful that we do not
confuse the existence of something, which tells us nothing at all about it
except that that existence is necessary, from the properties that we might
perceive.
What I am discussing here is how sets of properties can be
considered. The use of the notion of a simulation is a way to see a set of
properties as the creation of a process and not some "thing" that is
definite independent of that generative process. What I am writing here is
against the ideas that we know as "realism".
I am claiming that there are metaphysical postulates within the
notion of realism that are preventing us from understanding how we can
escape from the problem of solipsism. Remember how we discussed that Local
systems do not have "windows" and that they cannot be considered to
"exchange substances" with each other? How then are we to have a theory of
their interactions if our own idea about how communication and interactions
assume that this only happens because some substance is exchanged? We need
an explanation that allows us to model interactions in such a way that all
of the features and aspects and properties that we might encounter in a
situation where communication and/or interaction takes place but does not
involve assumptions that are contradicted by other facts. The notion of
simulation and bisimulation is a way to develop the thoughts and ideas
needed to form a better explanatory model of our world and our thoughts.
Spinoza's notion of Substance is similar to the idea that I am
developing here, but I am going much further than Spinoza. Yes, there is
only one Existence necessary as Spinoza explained, but that single existence
has as many expressions and aspects that can be considered in terms of
separate simulations as there are possible minds.
The key is to understand two basic principles, among a few others.
1) That two entities that have identical properties are one and the same
entity. 2) That the notion of communication between systems is completely
explainable in terms of the coincidence of identical internal aspects and
the way that these aspects evolve. This notion of bisimulation is a way to
express this notion of "identity" and equivalence. I will be writing more
to explain this further.
***
I hope that you can comment on the rest of the post below at your
leisure.
Onward!
Stephen P. King
> I strongly suspect that this idea is consistent with Shannon's
> notion of
> information as the coincidence of joint allowed states between a
> pair of
> systems and if so it may help us to take a step beyond the usual
> account of
> communication between systems that assumes some kind of substance
> exchange.
> Some of the algebra (6) of this idea if bisimulation is as follows.
>
> Let "A simulation of B" be denoted A ~ B.
>
> Further, let ( B ~ A ) be called the "conjugate" of ( A ~ B ); since
> these
> are not equal, the simulation is not commutative in general.
>
> We see that A = A ~ A is the "real identity bisimulation" since the
> simulation is equal to its' conjugate.
>
>
> Then we state the "Woolsey identity":
>
> A ~ A = A ~ B ~ A
>
> That is: real identity bisimulation = simulation of the conjugate
> simulation.
>
>
> This is a law of identity for computational bisimulation that
> implies that a
> "real identity" occurs only when the conjugate of the bisimulation
> is equal
> to itself.
>
> This "law of real identity bisimulation" would then imply:
> A ~ B ~ C ~ A not= A ~ A, since A ~ B ~ C ~ A not= A ~ C ~ B ~ A ;
> the conjugate is not equal to itself and so does not form the real
> identity
> of A ~ A = A.
>
> But the law of real identity bisimulation would validate the following
> statement:
> A ~ B ~ B ~ A = A ~ A,
>
> and this is seen to be consistent with
> A ~ B ~ B ~ A = A ~ B ~ A = A ~A
>
> since B ~ B = B.
>
> Also, due to the law of conjugate bisimulation identity:
>
> A ~ A = A ~ B ~ C ~ B ~ A = A ~ B ~ A
>
> this is "retractable path independence": path independence only over
> retrace-able paths.
> This is consistent since B = B ~ C ~ B, and is the closest I can
> come to
> associativity.
> Note that retractable path independence does not necessarily imply
> closure:
>
> A ~ C not= A ~ B ~ C,
> since closure is assuming something beyond the law of real identity
> bisimulation. It seems likely that bisimulation between
> three observers (or more) is not in general closed.
>
> Notes:
> 1. http://everything2.com/title/Turing+principle
> 2. http://iridia.ulb.ac.be/~marchal/
> 3. http://en.wikipedia.org/wiki/Hard_problem_of_consciousness
> 4. See http://xxx.lanl.gov/abs/math.HO/9911150 and
> http://boole.stanford.edu/pub/ratmech.pdf for more.
> 5) http://gregegan.customer.netspace.net.au/
> 6) As developed and communicated to me by Paul Hanna.
>
>
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