On 20 Jun 2012, at 20:23, Stephen P. King wrote:
On 6/20/2012 3:39 AM, Bruno Marchal wrote:
On 19 Jun 2012, at 19:41, John Clark wrote:
On Tue, Jun 19, 2012 at 6:01 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>> Unlike the proton and neutron nobody has found any
experimental evidence that the electron has a inner structure,
that it is made of parts.
> The primitive matter I talk about is the idea of primary matter
in the Aristotle sense
Aristotle was a great logician but a dreadful physicist.
> If I say that electron is not primitive, I don't mean it is made
of part, almost the contrary, that it is a mathematical reality,
or that it is reducible to a non physical mathematical or
theological reality, an invariant in our sharable computations.
I don't know what that means. What experiment would I need to
perform, what would a electron need to do to prove it was
"primitive".
The electron cannot do that, but my pet amoeba cannot prove they
are unicellular, despite they are.
It is just that if matter is primitive (not explainable from non
material relation) then we have to make it infinite to
singularize consciousness.
Dear Bruno,
I am parsing your comments here as I want to fully and clearly
understand them.
Do you stand by that implication, that "matter is primitive" =
"not explainable from non material relation"? This implies that:
"matter is not primitive" = "explainable from non material
relation". No? I would like to better understand how the notion of
ontological primitives is defined in your dictionary.
Something is not primitive if you can derive it from something
simpler. Put in other word, something is not primitive if its
existence or its appearance can be proved in a theory which does not
postulate it in the basic assumption. It is emergent, in some large
sense.
Exemple: if comp is true then matter is not primitive (by UDA). Like
"life" is no more considered as primitive by most biologist, as it is
consider as being a chemically emergent reality for them.
With comp, we just abandon the idea of singularize consciousness in
bodies, and then the bodies have to be explained in term of number
relation.
Why would we have to "singularize consciousness in bodies" at
all? What premise or postulate is it that consciousness is
"singularized" in a body? I am assuming that "singularize" means "to
make singular" in the sense of either a singularity or a singleton.
I am not sure which of the latter you are assuming.
It is the way we experience our consciousness. We feel to be unique in
only one body, and universe. Of course we know better, once we assume
comp or even just QM (without collapse).
It is more easy to understand that reversal at the epistemological
level. Physical concepts are not primitive means that we can reduce
them to non physical concepts, like those coming from theoretical
(mathematical) computer science. It means that physics is not the
fundamental science. Exactly like we can reduce biology to physics,
we can reduce physics to the study of machine dreams.
At the epistemological level we are assuming that there already
exist conscious entities, therefore a reversal cannot be run in a
consistent manner if the reversal implies the non-existence of
conscious entities.
OK.
You are now equating "reducible" to "explainable". Is an explanation
a "constructive" process in your thinking?
Not necessarily, and usually necessarily not.
>> To calculate the first 100 digits of Chaitin's constant you'd
need to feed all programs that can be expressed in 100 bits or
less into a Turing Machine and see how many of them stop and how
many of then do not. Some of them will never stop but the only way
to know how many is to wait a infinite number of years and then
see how many programs are still running. So you'd need to be
infinitely patient, in other words you'd need to be dead.
> Only to be sure of the decimals obtained.
Well yeah, it's easy to calculate Chaitin's constant if you don't
mind getting it wrong.
After BB(100) computation steps, the decimals will be correct. I
will not know it, but they are correct.
Is this correctness that occurs after the BB(100) steps capable
of being "forced" to hold for the infinite case, as discussed in
this paper http://arxiv.org/abs/math/0509616? I would like to better
understand how you leap the gap between the finite case and the
infinite case.
? (The infinite case is no more a case of "computation").
> If I relax that constraints, then I need only to be *very
patient*. The non computable, but well defined Buzzy Beaver
function (BB) bounds the time needed to wait. Of course it grows
*very* fast. But I don't need an *infinite* time to get the 100
first digits correct. Any time bigger than BB(100) will do.
If we wait a googoplex to the googoplex power years some 100 bit
programs will still be running, some of them could be Busy Beaver
programs but others could just be very long finite programs. And
in the same 1962 paper where Rado introduced the idea of the
beaver he proved that a general algorithm to tell if a program is
a Busy Beaver or not does not exist.
That is true for all programs. There is no algorithmic way to see
if a program compute the factorial function. Again, this does not
change anything in the argument.
What if a factorial is involved in the explanation of
consciousness?
1) Nothing special about factorial. What I said is true for any program.
2) The fact that there is no algorithm to decide if a program compute
some function does not ential that we cannot recognize what do some
program.
3) But this is not relevant, as comp ^prevent any chance to know for
sure what program run us. That is why the "yes doctor" asks for an act
of faith.
It's true that if you knew the numerical value of Chaitin's
Constant then you would know that if a 100 bit program had not
stopped after a Turing Machine had run n number of finite
operations then it never will; but the trouble is you don't know
Chaitin's Constant and never can, so you can never know how big n
is. So even though they have been running for a googoplex to the
googoplex power years one of those programs could stop 5 seconds
from now.
Not if I waited, by chance or whatever, a time bigger than BB(100).
If a decimal change after that, then we got a computable function
growing more quickly than BB.
You do realize that this dependence upon a number of steps in a
computational process is not equivalent to the notion of time in a
strict way simply because time is not just the number of steps, it
is also the transitional flow from one step to another.
In which theory?
And a Busy Beaver program grows faster than any computable
function but to my knowledge it has not been proven that all non-
computable functions grow as fast as the Busy Beaver.
That would be false. There are many non computable predicate, with
non growing values.
What would be the ration of computable to non-computable
predicates? Are you considering an ensemble or a space of predicates?
I was considering here all first order logical predicates;
> Lawrence Krauss in his book "A Universe From Nothing" says that
someday something close to that might actually be possible.
> You mean? Deriving addition and multiplication from physics?
No, Krauss talks about deriving physics from addition and
multiplication, or at least from logic; he talks about proving
that in the multiverse only certain fundamental laws of physics
are logically self consistent. He even talks about the distant
dream of showing that "something" is consistent but "nothing" is
not.
OK. Nice.
Is not the proof (showing) that "something" is consistent and
"nothing" is not consistent a triviality because "nothing" cannot be
exactly defined such that a proof can be constructed.
It depends on the theory which is used.
> That is impossible.
I think both Krauss and I would give the same response to that,
maybe.
> Why do you use "gibberish" to condemn free will, and not to
condemn event without cause?
Because the meaning of "a event without a cause" is clear and no
circularity is involved.
Cause is a fuzzy notion, and so "non causal" is even more fuzzy.
I agree! This is why the entire discussion of free will is
incoherent if it involves notions of cause and effect given an
ambiguous notion of cause.
OK.
Even the meaning of the question "what caused a event without a
cause?" is clear, although it is a stupid question
because the answer is so obvious. But the meaning of "free will"
is anything but clear and circularity abounds.
In computer science, circularity is not a problem. We can eliminate
it with the second recursion theorem of Kleene. Free-will seems to
me rather clear, except that some philosopher defend a
contradictory notion of free-will. I gave my definition of c-free-
will, and I don't see why we should reject it.
I would like to better understand how this elimination occurs.
Could you point us to a good discussion of Kleene's second recursion
theorem? Would you recommend this article http://www.math.ucla.edu/~ynm/lectures/2009csl.pdf
?
The wiki article defined the 2nd theorem as: "The second
recursion theorem. If F is a total computable function then there is
an index e such that <1ae7ce28ce024bddd11f90588fb3816c.png>.
Here <1ae7ce28ce024bddd11f90588fb3816c.png> means that, for each n,
either both <888eb19b7b9a5e48762a5df7aeb98890.png> and
<855a06a79f43f1c1b63e789553f981df.png> are defined, and their values
are equal, or else both are undefined."
I will prove it on the FOAR list.
The point here is that either a fixed point obtains or the
functions cannot be defined (aka are non-constructable). What is
instructive to me is that fixed points have certain requirements to
exist when we are thinking of them in the case of physics. For
example, in the Brouwer fixed point theorem, we see that closure and
convexity of a set of points is required. Exactly what would play
the role of these in the computable function case?
The analogy break because we don't have to use geometry or topology.
And "why do we have free will?" is not a stupid question, its not
smart and its not stupid and even though it contains a question
mark it's not even a question, it's just a sequence of ASCII
characters.
We agree that nc-free-will does not make sense, but you have not
succeeded in convincing me that all notion of free-will is non
sensical.
I would really like to understand why it is that John Clark
insists on this elimination attitude toward the referent of that
"sequence of ASCII characters". It seems that he does not understand
the ramifications of such a postulate! IMHO, it makes anything that
claims to be produced by his mind to be a meaningless "sequence of
ASCII characters" as it clearly cannot be the result of an act of
"his" will. He can have no will and thus there is not really a "his"
associated with the supposed entity that is denoted by the sequence
of ASCII characters : "John Clark". There is no such thing as a
possessive modifier for universes accessible by "John Clark" if we
are to be consistent with claims.
I think John has a problem with "nc-free-will", not with c-free-will,
which in my opinion is just will in a case of degrees of freedom, non
coercion, etc. It is what make responsibility and moral behavior
possible.
Bruno
http://iridia.ulb.ac.be/~marchal/
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