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 (Iguess you mean function).A computable number is a number that can be approximated by acomputable function, and a computable function is a function thatcan be evaluated with a mechanical device given unlimited time andstorage space. Turing's famous 1936 paper where among other thingshe introduced the idea of what we now call a "Turing Machine" wascalled:"On Computable Numbers, with an Application to theEntscheidungsproblem".Turing showed that a very few real numbers, like the integers andthe rational numbers, have formulas to calculate their value asclosely as you'd like, but for the vast majority of numbers there isno way to do this. There are a few more numbers like PI that arecomputable with algorithms like PI= (4/1)-(4/3)+(4/5)-(4/7)+(4/9).... , but for most numbers there is nothing like thatand no way to approximate their value. In fact he showed that almostall the numbers on the real number line are non-computable. Thereare LITERALLY infinitely more non-computable numbers than there arecomputable numbers; Turing proved that these numbers exist butironically, despite their ubiquitous nature, neither Turing noranybody else can unambiguously point to a single one of thesenumbers because there is no way to derive such a number from thenumbers that we can point to, the computable numbers.So numbers, at least the numbers we or computers can use, cannot bethe only fundamental thing, non-computable numbers must be too. Mypoint was that if there are 2 general classes of fundamental thingsthat can not be simplified then there might be more. I think theintelligence-consciousness link is a third fundamental thing, butunlike Turing I can not prove it. And there may be fundamentalthings that we can never prove are fundamental, truth and proof arenot 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 itsDarwinian advantage)There is no way consciousness can have a direct Darwinian advantageso 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 mightreflect 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 tooclose to even the most beautiful and detailed picture on my computerscreen I start to see individual pixels; and sometimes late at nightI speculate that somebody made a programing mistake and tried todivide 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 youcall your dovetailing argument; I really don't think you have statedit 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/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.