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 called:

"On Computable Numbers, with an Application to the Entscheidungsproblem".

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 Darwinian advantage)

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 consequences.




> 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.

Bruno

http://iridia.ulb.ac.be/~marchal/



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