On 18 Oct 2014, at 19:48, John Clark wrote:
On Sat, Oct 18, 2014 at 1:22 AM, Bruno Marchal <[email protected]>
wrote:
> Gödel shows that there are solution of Einstein's equation of
gravitation with closed timelike curves, making them consistent.
But only if you assume that the Universe is rotating, and
experimental evidence proves that it is not. And only if you assume
that Einstein's General Theory of Relativity is 100% correct, and we
know it can't be, it's the best theory of gravity we have but it
can't be the final word because it doesn't take Quantum Mechanics
into account.
> I was alluding to the usual time. It tells you which machines stop
and which does not stop if you wait a long time enough
Turing showed exactly how his machine worked and then proved that
his machine can not tell if a arbitrary program will ever stop,
Yes I provided this more than once here. It is easy and Post saw this
too, before Turing.
but people proposing a Super Turing Machines are much more vague.
I was not proposing any Super Turing machines. I was alluding that the
simple algorithm consisting to run a machine and wait if it stops or
not, is enough toi compute the Halting oracle in the limit. This has
been proved by Schoenfiled, and is in all textbook on computability
(sometimes under the name "the modulus lemma": the limit-computable
functions are the one computable in the halting oracle.
If a machine performed one calculations in the first second, and one
calculation in the next 1/2 second and then one calculation in the
next 1/4 second etc then if you sum the geometric series you find it
has performed a infinite number of calculations in exactly 2
seconds. But the problem is (apart from not specifying how the
machine could actually work that fast) is that after 2 seconds the
machine is in a unspecified state.
Or you could make a computer that made use of the real numbers, it
could tell if a arbitrary program will stop or not but I'm not even
convinced that real numbers exist in abstract Platonia; and even if
they do it's very hard to see how such a machine could ever be
built. if a machine can't produce a non-computable number even
approximately, (and nearly all the real numbers are non-computable)
then it's hard to see how a a non-computable number could have any
effect on a machine.
> I don't not assume set theory, infinities, etc.
So you don't assume the real numbers exist?
Indeed.
If so then not everything that mathematics is capable of describing
exists, and the same is true of another language, English.
Computationalism implies the "arithmetical Platonia" is quite enough.
You can put the "real numbers" in the machine's epistemology. You
don't need ontological real numbers.
> you need to unstuck your mind in step 3
First you need to fix the first 3 steps.
You have already agreed with step 0, 1, 2.
Your refutation of step 3 confused the first person view (the diary
content of individual people going out of the reconstitution box) and
the third person views (the collection of all memory content). The
details are in the posts, or in the paper.
You did understand sometimes, but then you say it is not great, or not
important, but you fail to answer why you don't read the next step 4,
then.
Bruno
John K Clark
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