On 15 May 2015, at 22:07, John Clark wrote:
On Fri, May 15, 2015 Bruno Marchal <[email protected]> wrote:
>>> Why would Turing machine obeys the laws of physics?
>> Because a Turing Machine like all machines involves change.
> The change are injection in N.
So what? A injection is a function and a function is a machine that
MOVES from one element in a set to another and ASSOCIATES it with
elements of another set. All these things involve change.
A function is not a machine. There are a non enumerbale number of
function from N to N, but only an enumerable number of digital machines.
>> and determine if it is white or black, and a clockwork must
determine if it should change the color of that cell or not, and a
clockwork must determine if it should move the tape one space to the
right or one space to the left or just stop. And nobody knows how to
make clockwork without using matter that obeys the laws of physics.
Nobody, absolutely nobody.
> Oh, so you do assume primitive matter.
I assume nothing, I know for a fact that NOBODY knows how to make a
clockwork without using matter and the laws of physics, maybe
someday somebody will figure it out but as of today NOBODY has the
slightest idea of how to do it.
Turing machine are not material clockwork but purely mathematical
notion.
>>> You can implement Turing machine in Lambda calculus
>> No you can not!
> Then not only Turing and Church were wrong, as they will both
proves this.
Don't tell me show me.
It is long and technical, and you have the tone of the one decided to
not change its mind, when you can consult any textbook, and actually,
it is already in the basic paper of Turing, that you refer too. It is
a result quite standard in the field.
I think you're talking Bullshit but it would be easy to prove me
wrong, just make a Lambda Machine that makes no use of matter that
obeys the laws of physics and make a calculation, any calculation
with it.
(lambda x x)(lambda x x) = (lambda x x)(lambda x x) = (lambda x x)
(lambda x x) = ...
(example of a non stopping computation). That computation is a
mathematical object. It can be described as an infnite sequence of
"(lambda x x)(lambda x x)", each resulting from the substitution of x
in (lambda x x) by the argument (lambda x x).
Do that and you will have not only won the argument but I will
personally buy your airline ticket to Stockholm for your Nobel Prize
ceremony.
No, whatever I do, you will use hand waving to not recognize it.
> You confuse [...]
Enough with the "you confuse" crap! Every post of yours contains a
"you confuse", put a little variety into your phrases.
> if you agree that 2+2=4, and if you use the standard definition,
then you can prove that a tiny part of the standard model of
arithmetic run all computations.
The word " run" involves changes in physical quantities like
position and time. And what sort of thing are you running these
calculations on?
No: "run" is defined mathematically, without any reference to physics.
Just buy the davis book, and red the old original paper.
>> Nothing can divide all arithmetical truth from all arithmetical
falsehoods. Nothing can do it including arithmetic.
> Sorry Arithmetical truth does it, trivially.
What a steaming pile of Bullshit.
See Epstein & Carnielli chapter 22. Or just take a look on Gödel's
1931 paper.
Or see the book by Matiyasevic, where it is show how diophantine
polynomial can simulate a Turing machine.
> You just dismiss a whole branch of math.
I dismiss junk science.
You just show that you have no idea of computer science.
> you are a comp1 believer, and "comp" is comp1. Then it implies comp2
Oh for christ sake! As if "comp" wasn't bad enough now we have
"comp1" and "comp2" and I'm not even going to ask what the hell this
new form of babytalk is supposed to mean, assuming it means anything
at all.
See the recent Post by Liz who suggested that difference.
> you invoke a God for which we have no evidence.
Science is about evidence and what we have ZERO evidence of is
anybody making one single calculation without using matter that
obeys the laws of physics. Let me repeat that, we have zero
evidence, zip nada zilch goose egg.
You confuse a priori computation in the mathematical sense with the
physical implementation of computation. We know since a long time that
computations are also implemented (non physically of course) in a tiny
part of arithmetic (the sigma_1 part).
> Amen (you are a good Aristotelian Theologian).
Be creative think of a new insult, the one about me being secretly
religious and being an admirer of Aristotle is getting old.
> the set of true sentences is well defined,
The set of all true statements is contained within the set of all
statements, the trick is to separate the true from the false.
We cannot separate them mechanically, but we can separate them
mathematically, and indeed those sets are definable in theories like
ZF. You need only the third excluded middle.
I agree that the set of all true statements and no false statements
has a definition that is not gibberish, but we know that nothing can
produce such a set.
Produce effectively.
Few things in mathematics can be produced effectively.
The integer that is equal to 2+2 but is not equal to 4 is also well
defined, but nothing can produce that integer either.
>> in general there is no way to determine which statements it is
possible to prove to be right or wrong and which statements you can
not.
> Gödel and Post provided a constructive way to do exactly this.
So you think Turing was wrong when he claimed that he proved the
Entscheidungsproblem had no general solution??
You confuse Gödel and Post notion of relative undecidability of a
consistent theory T, where Gödel's proof appears to be constructive
(we can find the undedicable sentence algorithmically from the given
consistent theory T; and Turing absolute (with CT) unsolvability
result for a class of problem.
Bruno
John K Clark
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