On 6/19/2012 5:39 AM, Bruno Marchal wrote:
On 19 Jun 2012, at 08:01, Stephen P. King wrote:
On 6/18/2012 5:13 PM, Bruno Marchal wrote:
Brent, Stephen,
On 18 Jun 2012, at 18:55, Stephen P. King wrote:
On 6/18/2012 11:51 AM, meekerdb wrote:
On 6/18/2012 1:04 AM, Bruno Marchal wrote:
Because consciousness, to be relatively manifestable, introduced
a separation between me and not me, and the "not me" below my
substitution level get stable and persistent by the statistical
interference between the infinitely many computations leading to
my first person actual state.
How does on computation interfere with another? and how does that
define a conscious stream of thought that is subjective agreement
with other streams of thought?
Brent
They interfere statistically by the first person indeterminacy on
UD* (or arithmetic).
Hi Bruno,
You seem to have an exact metric for this "measure" of "the first
person indeterminacy on UD* (or arithmetic)".
Not at all. I only reduce the mind-body problem (including the body
problem) into the problem of finding that metric. UDA must be seen as
a proof of existence of that "metric" from the comp hypothesis. Then
AUDA gives the logic of observable which is a step toward that metric
isolation.
Dear Bruno,
What I fail to understand is how the currently well known and
existing proofs of the non-existence of generic metrics on infinite sets
that are, AFAIK, identical to your concept of computations (as strings
of numbers) do not seem to impress you at all. It is as if your are
willfully blind to evidence that contradicts your claims. I am
sympathetic to your motivation and am interested in finding a path
around this serious problem that I see in your reasoning. My point here
is that this claim that "UDA must be seen as a proof of existence of
that "metric" from the comp hypothesis" has no epistemological "weight"
if it cannot be associated with the other aspects of mathematics. One
must show how one's new idea/discovery of mathematical
"objects/relations" are related to the wider universe of mathematical
objects and relations; or one is risking the path of solipsism.
I have tried to get your attention to look at various
possibilities, such as the axiom of choice, non-well founded sets, the
Tennenbaum theorem, etc. as possible hints to a path to the solution but
you seem to be trapped in a thought, like light orbiting a black hole,
endlessly repeating the same idea over and over. Would you snap out of
it and see what I am trying to explain to you?
What I need to understand is the reasoning behind your choice of set
theory and arithmetic axioms;
I don't use set theory. Only elementary arithmetic. At the ontological
level.
But Bruno, you are being disingenuous here. The phrase "only
elementary arithmetic" is not all that is involved! in order to have a
meaningful description of "only elementary arithmetic" one has to relate
to a wider univerce of concepts and one must connect to the physical
acts that support the experience of what numbers are.
At the meta-level I use all the math I need, like any scientist in any
part of science.
I am not sure what that means.
after all there are many mutually-exclusive and yet self-consistent
choices that can be made. Do you see a 1p feature that would allow
you to known that preference is not biased?
As I said, I use arithmetic because natiural numbers are taught in
high school, but any (Turing) universal will do.
Do you understand the idea that "natural numbers [as] ... taught in
high school" does not have special ontological status? I am trying to
get you to think of numbers in a wider context.
the point is that neither the laws of consciousness, nor the laws of
matter depend on the choice of the basic initial system, so I use the
one that everybody knows.
So, does a consensus of belief grant special ontological status?
What else am I to think of the implication of the phrase "... that
everybody knows". Closed sets of communications are (representationally)
studied in network, game and graph theory. From what I have read, finite
versions of these reach equilibrium in at least log_2 N steps and once
there never change again. This only illustrates the point that we have
to consider open systems and those are such that they do not allow for
exact closed form descriptions in math. This is a well known fact to any
competent engineer.
Sometimes I use the combinators or the lambda algebra. I don't use
geometrical or physical system because that would be both a treachery,
in our setting, and it would also be confusing for the complete
derivation of the physical laws.
Nice excuse! LOL!
And it remains to be seen if that defines a conscious stream of
thought that is subjective agreement with other streams of thought.
If it does not have "subjective argeement" with other mutually
exclusive then there would be a big problem. No?
No. It would be a refutation of comp+classical theory of knowledge (by
UDA). That would be a formidable result.
But the evidences available now, is that the physics derived from
arithmetic, through comp+ usual definition of knowledge, is similar to
the empirical physics (AUDA).
Exactly what does this mean? You keep repeating these words... How
about finding a new set of words that has the same meaning? Truths are
independent of particular representations!
Do you realize that you are asking Bruno the same question here
that I have been asking him for a long time now? Exactly how do
computations have any form of causal efficacy upon each other
within an immaterialist scheme?
By the embedding of a large part of the constructive computer
science in arithmetic.
What "part" is not embedded?
The non elementary, second order, or analytical part. It is not
embedded in the number relations, but it appears in the mind of the
universal numbers as tool to accelerate the self-study. It is
epistemological.
So exactly how are numbers embedded themselves such that this
second order aspect can have some measure of the logical analogue of
causal efficasy (aka significance)? You are not avoiding the "other
minds" problem here! One has to explain how minds can have any influence
or even synchrony with each other. Even Leibniz recognized this and
postulated a "pre-established harmony" to account for it. It was a good
try, but ultimately it failed for the simple reason that such a
"pre-established harmony" is equivalent to the solution to an infinite
NP-Complete computational problem. You simply cannot ignore the
implications of computational complexity!
There is a universal diophantine polynomial (I will say more on this
on the FOAR list soon). Once you have a universal system, you get
them all (with CT). I might identify a notion of cause with the
notion of universal (or not) machine. Some existing number relation
implements all the possible relations between all possible universal
machine.
Universality (of computations) requires the existence of an
equivalence class (modulo diffeomorphisms) of physical systems over
which that computation is functionally equivalent. No?
?
Do I underestimate your ability to understand the English language?
Do we need to go through the discussion of universality again? Really?
OK, I will try to step though my reasoning slowly for you.
What does computational universality means if not some form of
functional equivalence between a large (possibly infinite) set of
physical systems? When we study General Relativity we discover something
known as the "Hole Argument
<http://plato.stanford.edu/entries/spacetime-holearg/>". It ultimately
shows the notion of "*Leibniz Equivalence*. If two distributions of
fields are related by a smooth transformation, then they represent the
same physical systems."
(http://plato.stanford.edu/entries/spacetime-holearg/Leibniz_Equivalence.html)
I am assuming that the readers can understand that "sets of
physical systems" (as considered in the notion of computational
universality) are connected to representations of physical systems by
"distributions of fields" for my reasoning to be clear here. Perhaps I
have not explained this and made the mistake of just assuming that it is
understood that in physics we use mathematical objects to *represent*
the physical objects of experience. It is how *representation* works
that we seem to have differences in opinion.
How much more do I need to explain? You claim that universality is
completely separable from physical systems. I disagree.
If not, how is universality defined? Over a purely abstract set? What
defines the axioms for that set?
You don't need set. You can define "universal" in arithmetic. I am
starting an explanation of this on the FOAR list.
OK, I will continue to pay attention to your posts. :-)
You have to study the detail of Gödel's proof, or study Kleene's
predicate, which translate computer science in arithmetic. For the
non materialist, the problem is not to get interactions, the problem
is not having too much of them.
Correct! You get an infinite regress of "interactions"! Way too
many! In fact, I bet that you get at least a aleph_1 cardinal
infinity. But what about the continuum hypothesis? Do you take it as
true or false in your sets?
I don't care at all.
That is why I see your thesis as ultimately a failure. You are
ignoring the very thing that causes problems for your idea. You cannot
just assume that some kind of number is special without justification.
While it is true that a huge quantity of work has been done discovering
the properties of recursively enumerable functions and integers does not
by itself justify or offer a proof that they are somehow special, as
Kronecker and others seem to which with their statements such as : "/God
made theintegers <http://en.wikipedia.org/wiki/Integers>; all else is
the work of man/." http://en.wikipedia.org/wiki/God_Created_the_Integers
If you take it as false then you obtain a very interesting thing in
the number theory; it looks like all arithmetics are non-standard in
some infinite limit! You have to have a means to necessitate a limit
to finite sets. The requirement of Boolean satisfyability
<http://en.wikipedia.org/wiki/Boolean_satisfiability_problem>exactly
gives us this "rule".
? (unclear).
Where does the existence of non-contradiction in logic obtain from?
Mere or arbitrary postulation? No. It is necessary. But this necessity
in the axiomatic sense that we see when we consider logic as an abstract
entity does not transfer into or onto actual sets of propositions such
as those that would accurately represent physical systems interacting
with each other in our worlds of experience.
Keep in mind I submit a problem, for the computationalist. Not a
solution., but precise problems. You can use the arithmetical
quantization to test test the quantum tautologies.
We will see if there is or not some winning topological quantum
computer on the border of numberland, as seen from inside all
computations.
What physical experiment will measure this effect?
Well, here the physical events is the discovery of quantum
computations in nature. That is what remain to be seen in the
arithmetical physics. But we have already the quantization and a
quantum logic.
Have you tried this:
http://scholar.google.com/scholar?q=quantum+computation++photosynthesis&btnG=&hl=en&as_sdt=0%2C41&as_vis=1
But how does the implementation of quantum computation in "natural"
(as opposed to "man-made) systems prove your idea? So far I have shown
you that there exists proofs that one cannot extract quantum logics from
classical logics without serious moduli. On the other hand, we can
extract plenums of classical (Boolean) logical algebras from a single
quantum logical lattice (modulo sufficient dimensions). Why are you so
eager to extract quantum from the classical?
If there is no physical effect correlated with the difference, then
this idea is literally a figment of someone's imagination and nothing
more. The physical implementation of a quantum computer is a physical
event. I thought that your idea that computations are independent of
all physicality was completely and causally independent from such. =-O
My argument is that a computational simulation is nothing more
than "vaporware" (a figment of someone's imagination) until and
unless there exists a plenum of physical systems that all can
implement the "best possible version" of that simulation.
Arithmetic implements all computations already. And UDA explain that
the physical emerges from that, and evidence are that the comp
arithmetical physics can implement the quantum computations. They are
just not primitive.
Your use of the word "Implements" is nonsensical. Any concept of
implementation that is completely divorced from physical actions is
nonsense as it cannot imply things that it is unable to by its definition.
When we recall that Wolfram defines the "real thing" as the "best
possible simulation, we reach a conclusion. This "plenum" is the
trace or action (???I am not sure???) of (on?) an equivalence class
of spaces that are diffeomorphic to each *other under some ordering*.
I am not certain of the wording of the first part of this, but I am
absolutely certain of the latter part, "an equivalence class of
spaces that are diffeomorphic to each *other under some ordering*" I
am unassailably certain of.
Wolfralm is unaware of consciousness and first person indeterminacy.
So? We could equally claim that you do not understand the role of
complexity in computations and thus be dismissive of your ideas, but we
chose not to.
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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