On 04 Jun 2015, at 19:54, John Clark wrote:
On Thu, Jun 4, 2015 Bruno Marchal <marc...@ulb.ac.be> wrote:
>>> or A string which is not algorithmically compressible,
>> Yes, that is a very good example of an event without a cause.
> "Event" is a physical notion. Algorithmic non compressibility is
an mathematical notion.
Nothing caused the 9884th digit of a random number to be a 6 rather
than some other digit, and that is the one and only reason it is NOT
algorithmically incompressible. But something did cause the 9884th
digit of PI to be a 4 and not some other digit, and that's why PI IS
algorithmically compressible.
I have a counter-example to your claim. Fix a universal system. It
determines completely its Chaitin number, yet it is algorithmically
incompressible. Same with "Post number": that one is compressible, yet
most of its digital are not computable, although completely
deterlmined, if you agree that a close machine (a machine activated on
some input) either stop or does not stop.
>>>> But that is not yet proven too, as comp implies there is
something non computable, but it might be just the FPI and the
quantum FPI confirms this.
>> I don't care, I'm not interested in "comp" or of the Foreign
Policy Institute.
> If you don't care, you would abandon the idea of showing that
comp1 does not imply comp2
And I'm even less interested in "comp1" and "comp2" whatever the
hell they are supposed to be.
In some post you argued once that comp1 is trivial, and that we need
to be irrational to believe in the negation of computationalism.
So you start again your dismissive rhetorical maneuvers.
>>> Physics use a lot of non computable things in the background.
>> Name one.
> The set of real numbers.
If time or space is quantized as most physicists think it is then
the real numbers are just a simplified approximation of what happens
in the physical world.
Typically, physical quantization is defined by using complex numbers.
Even mathematicians are starting to have reservations about the real
numbers, even Gregory Chaitin has started to distrust them and
ironically his greatest claim to fame came from discovering (or
maybe inventing) a particular real number, the Omega.
Mathematicians have some problem with the real numbers since the
beginning. Most are solved by method usuallu judged to rough, like an
axiomatic set theory, etc. It is on analysis that intuitionist
mathematics and clmassical mathematics differ the most. In theoretical
computer science we can justify the needs of non constructive method,
as very often there is provably no constructive tools available, and
it is part of the subject. But again, the point was just that CT does
not refer to physics. And yes CT entails incompleteness and the
existence of non computable functions and of algorithmically non
soluble problems.
>>>> It is intuitively obvious that no computation can be made
without the use of matter that obeys the laws of physics.
>>> "made" is ambiguous.
>> Bullshit.
> Did you mean "made" in the physical reality, by a physical
universal machine,
Of course I mean that!
> or did you mean "made" by a immaterial universal machine, like
Robinson Arithmetic?
Of course I don't mean that, unless you know how to build a
immaterial machine with material! Couldn't you have figured this out
by yourself?
It is easy to implement an immaterial machine with matter, like you
can represent the abstract number 2 with two pebbles.
> I say that computationalism is false, because you use primitive
matter.
Computationalism says you can make matter behave intelligently if
you organize it in certain ways,
That is a rephrasing of computationalism, and what you say follow from
it, but the more precise and general version is that you stay
conscious (and don't see any difference) when simulated at the right
level (which existence is assumed), and that will entail that we can't
distinguish a physical computation from a purely arithmetical one, by
pure introspection (without clues from observation).
maybe that matter is primitive and maybe it is not but there has
been a enormous amount of progress in recent years with AI
demonstrating that Computationalism is probably true. There has been
zero progress demonstrating that mathematics can behave intelligently.
Mathematics does not belong to the category of things which can behave.
But mathematics, and actually just arithmetic, can define relative
entities behaving relatively to universal number, and that is known
since Post, Turing, etc.
> Why should we abandon computationalism, given that nobody has ever
show the existence of primitive matter?
Nobody has shown the existence of primitive mathematics either.
Primitive means that we have to assume it. Logicians have prove that
arithmetic, or universality, is primitive in the sense that you cannot
derive arithmetic, or the existence of universal numbers, without
assuming less than that.
People have shown the existence of computations made by matter
(maybe primitive maybe not) but nobody has shown the existence of
computations made by mathematics (maybe primitive maybe not).
Sorry, but repeating an absurdity many times will not help.
Computations have been discovered in mathematics. All textbooks in the
filed explains that. Read some book on the subject (like Mendelson,
Boolos and Jeffrey, Cutland, ...).
>> If you say non physical stuff can make a calculation, any
calculation, I'm not going to believe it until you show me some non
physical stuff that is actually calculating something.
> Well, any specification of any algorithm compute what it has to
compute in arithmetic. For example K computes the left projection in
arithmetic, when define in arithmetic.
You can't make a calculation with a definition!
You can. And if it is simple enough, you can do that mentally. You
will tell me that in this case we still need a physical brain, but
this can be a local relative notion, as it is shown obligatory at some
stage of the reasoning.
> You are the one saying that "compute" means "compute physically",
I say "compute" means figuring out an answer, nobody has ever done
this without using matter that obeys the laws of physics.
You are right, but this does not prove that the notion of matter is
used in the definition of computation. To do something materially we
need matter, but PA and formal systems compute things without doing
the computation physically. Kleene invented his famous predicate and
got his normal form theorem for the computable function by using the
arithmetical existence of the computations only.
If you know how to make such a calculation don't tell me about it
just make the calculation. Just do it.
KKK ===> K
(No use of matter, here, except to send you the description by mail,
but that is not part of the computation).
> To compute is defined mathematically, not physically.
You can't make a calculation with a definition!
See above. K is define by Kxy = x, and I can use that to compute KKK.
Then, PA does the same, using the same definition. The computations
are entirely and faithfully emulated through the number relations.
> It might be time you give your definition of computation, as we
still don't know it. Then I will show you that I use a different,
standard definition, which has no relation with physics at all. To
be frank, there is a tun of literature by people who search such a
physical definition, but usually recognize they still have not find
it.
You can't make a calculation with a definition!
>> Then have it do so and end this debate right now, have non-
physical arithmetical reality calculate the solution to a problem
from a first grade arithmetic book!
> I gave this as an exercise to Liz, sometime ago. I explained how
RA compute 2+3. No mention at all of physical device was used. Of
course, to verify this, as we live locally in a physical reality, we
use physical tools to describe all this,
In other words RA can't compute diddly squat.
> Again you are back to your Aristotelian assumption.
To hell with those damn idiot Greeks!
> If you agree that 2+2=4 independently of me and you, you can
certainly conceive that "2+2=4" is true independently of the universe,
That would be true if you and the entire physical universe were the
same thing, but I have a suspicion that might not be the case.
Then explain me what you mean by universe, and why that is needed to
make 2+2=4.
As I said, at some point, in this hard subject, it is nice if you
could list your assumptions.
> as "2+2=4" does not presuppose anything physical a priori.
Once more you are just asserting the very thing you're trying to
prove, that mathematics is more fundamental than physics.
I am not asserting that at all. I am saying that arithmetics does not
involve physical assumptions. That is different. That arithmetic is
more fundamental than physics will be a non trivial consequence of
computationalism. The point is that this is testable.
I don't know if that's true or not but unlike you at least I know I
don't know.
This is a lie, as I have often explained that I don't know if comp is
true. What I do know is that IF comp is true, then the notion of
primitive matter, or physicalism/naturalism/materialism is
epistemologically indefensible.
Bruno
John K Clark
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