On 13 Jan 2012, at 17:30, John Clark wrote:
On Thu, Jan 12, 2012 Bruno Marchal <marc...@ulb.ac.be> wrote:
> I am not entirely sure what you mean by computable numbers (I
guess you mean function).
A computable number is a number that can be approximated by a
computable function, and a computable function is a function that
can be evaluated with a mechanical device given unlimited time and
storage space. Turing's famous 1936 paper where among other things
he introduced the idea of what we now call a "Turing Machine" was
"On Computable Numbers, with an Application to the
Turing showed that a very few real numbers, like the integers and
the rational numbers, have formulas to calculate their value as
closely as you'd like, but for the vast majority of numbers there is
no way to do this. There are a few more numbers like PI that are
computable with algorithms like PI= (4/1)-(4/3)+(4/5)-
(4/7)+(4/9).... , but for most numbers there is nothing like that
and no way to approximate their value. In fact he showed that almost
all the numbers on the real number line are non-computable. There
are LITERALLY infinitely more non-computable numbers than there are
computable numbers; Turing proved that these numbers exist but
ironically, despite their ubiquitous nature, neither Turing nor
anybody else can unambiguously point to a single one of these
numbers because there is no way to derive such a number from the
numbers that we can point to, the computable numbers.
So numbers, at least the numbers we or computers can use, cannot be
the only fundamental thing, non-computable numbers must be too. My
point was that if there are 2 general classes of fundamental things
that can not be simplified then there might be more. I think the
intelligence-consciousness link is a third fundamental thing, but
unlike Turing I can not prove it. And there may be fundamental
things that we can never prove are fundamental, truth and proof are
not the same thing.
OK, but today we avoid the expression "computable number". All natural
number are computable, and we use the term computable function, and we
represent computable real number by computable function from N to N.
With mechanism it is absolutely indifferent which fundamental finite
object we admit. I use numbers, but combinatoirs or java programs
would be equivalent with that regard. So many things can be judged
fundamental, but once we chose the basically ontology, the other
things becomes derived notions.
> We can even ascribe it [consciousness] a role (explaining its
There is no way consciousness can have a direct Darwinian advantage
so it must be a byproduct of something that does have that virtue,
and the obvious candidate is intelligence.
I disagree. Consciousness has a "darwinian role" in the very origin of
the physical realm. This is not obvious, and counter-intuitive, so I
don't expect you to grasp this before getting familiar with the UD
> like relative universal self-speeding.
I don't know what that means.
It means making your faculty of decision, with respect to your most
probable environment, more quick.
> I suggest that the quantum nature of the observable reality might
reflect the discovery that we are in that 'digital matrix'.
I don't know if that's true or not, but I do know that if I get too
close to even the most beautiful and detailed picture on my computer
screen I start to see individual pixels; and sometimes late at night
I speculate that somebody made a programing mistake and tried to
divide by zero at the singularity in the center of a Black Hole.
> I think that here you miss the UDA point.
That is entirely possible because I am unable to follow what you
call your dovetailing argument; I really don't think you have stated
it as clearly as you could.
I have stated in 100 step version, 15-step version, 6 step version,
but since many years I stick on the 8-step version for it is the one
which people understand the more easily. It is in the sane04 paper,
and you can ask any question. The seven first step are rather easy and
most people understand it without problem. It already show the
reversal. If you want I can re-explain it step by step.
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