On 17 Feb 2014, at 15:07, Richard Ruquist wrote:
Edgar,
We recently learned on this list that a Turing machine does not halt
based on real numbers and apparently can only halt for the natural
numbers.
It is the contrary. On real numbers, the proof of first order logical
statement always halt. the theory is decidable (that is a theorem due
to Tarski).
But on the natural numbers, the simple first order theory is
undecidable, and many proofs will never halt, without us being able to
know why (well this assumes comp, really).
From a logical point of view, the real numbers are much more simple
than the natural numbers. Think about the difference of complexity to
solve x^17 + y^17 = z^17 on the real numbers and on the natural numbers.
Now, with the real number, and the sinus function, you can define the
natural numbers, and become Turing universal, on the natural numbers.
What about the notion of computation on the real number? Well, there
are many such notions, and they are not equivalent. On the reals,
there is no Church thesis, and I a remain unconvinced by most attempt
to generalize computability on the reals. This does not deprive some
notion of computation on the reals to be useful for some application.
I wonder if that may correspond to your claim of the computations of
nature being different from the computations of humans. If I
remember correctly you referred to the former as R computations and
the latter as H computations.
Unfortunately Edgar has not yet explain what he meant by computation.
It cannot be the standard sense, as he explicitly dismiss the
existence of computation, or of all finite pieces of computations
(which includes the pieces of the non stopping one) in arithmetic
(which is a relatively "standard" theorem).
He refers also to "reality" like if we knew what it is at the start.
Logic provides tools to avoid such commitment, in any subject matter,
even theology.
Bruno
Richard
On Mon, Feb 17, 2014 at 8:49 AM, Edgar L. Owen <edgaro...@att.net>
wrote:
Russell,
And, as I mentioned, there is exhaustive evidence from cognitive
science, and the sciences of physiology and perception, of the many
specific different ways that humans DO model an external reality in
their internal mental models of reality.
Why do you just reject all this well documented science out of hand?
Edgar
On Sunday, February 16, 2014 6:54:48 PM UTC-5, Russell Standish wrote:
On Sun, Feb 16, 2014 at 01:40:15PM -0800, Edgar L. Owen wrote:
> Russell,
>
> Well, there is overwhelming evidence of many sorts. The very fact
that you
> and I can even communicate about this issue is one proof, unless
you think
> I'm just a pesky figment of your imagination!
It is evidence only of an intersubjective reality. That there is a
common reality (to us) that we can agree on. Indeed, COMP, to take one
theory of consciousness, predicts the existence of such an
intersubjective
reality. But, it is not evidence of a reality independent of all
observers.
>
> And of course that can't possibly be true since I was here just
fine before
> I ever met you....
>
> The obvious fact that we have to eat and breathe to survive,
unless you
> believe that just imagining food and oxygen is enough to sustain us.
>
That is evidence of the Anthropic Principle (there is much stronger
evidence of that too), ie what we observe as reality must be
consistent with our existence within that reality. The Anthropic
Principle
does not imply an observer independent reality - that would be a
reverse syllogism fallacy.
> So again I would say you are confusing the internal simulation of
reality
> that all minds produce, and that everyone thinks is the real world
he lives
> in, with the real external reality that all minds simulate each in
their
> own way.
>
Keep going. You still haven't provided any evidence that this "real
external reality" actually exists! Until you do so, I will state that
there is nothing here to confuse. Of course, if you actually succeed,
not only will many people be surprised, you will undoubtedly be the
most famous philosopher since Aristotle and Plato.
Cheers
--
----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpc...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
