On 13 Aug 2012, at 06:42, meekerdb wrote:

On 8/12/2012 1:57 AM, Bruno Marchal wrote:Let phi_i be an enumeration of the (partial) computable function.u is universal if phi_u(x, y) = phi_x(y). (x,y) = some numbercode for the couple (x, y)So can y be some number code for a pair (a,b) and b a code for apair (c,d),...?

`Why not? It can make sense in some circumstance, but by (x,y) I meant`

`just a bijection between NxN and N. What the machine will do with the`

`numbers is up to them.`

`It is indeed frequent to code list of numbers like (x, y, z) by the`

`couple (x, (y, z)). Similarly for longer sequence, by iterating that`

`procedure.`

You wrote in another post:

Evgenii: What does intelligence means in this context that life isunintelligent? Let us compare for example a bacterium and a rock.Where there is more intelligence?Bruno: Bacteria are provably Turing complete, rocks are not.Brent: Bacteria a certainly smarter than rocks by any reasonablemeasure. But I don't think a bacterium has a semi-infinite tape.

`All machines, including the universal one, are finite object. Turing`

`discovery is really the discovery of a finite Turing machine u such`

`that phi_u(x, y) = phi_x(y).`

`Wolfram's problem consisted in finding the smallest possible Turing-`

`universal machine coded in cellular automata language. Again he asked`

`for something finite (even if needing an infinite plan to do any of`

`its possible work).`

`The infinite tape is only a rather misleading pedagogical folklore.`

`Example of universal "number" are brain, computer, programming`

`language interpreters, etc. Universal pattern in the game of life are`

`finite pattern. The infinite tape here is the infinite plan. The`

`infinite tape of the human has been provided by the wall of the`

`cavern, the pebble, knots, the papers, the books and diaries, the`

`magnetic tapes, the physical reality itself, etc. The infinite tape`

`plays the role of a potential infinite neighborhood in which the`

`memory of the machine can extend itself. It is not part of any`

`machine, as the notion of machine requires finiteness.`

`And in that sense bacteria have infinite tapes: the soil, or liquid,`

`or gel in which they multiply.`

`That is why I use the label "universal *number*", to always keep in`

`mind that those Turing universal being are finite entities. (By number`

`I always mean natural number 0, 1, 2, ...).`

`The universal machines are not God. In the arithmetical translation of`

`Plotinus, they play the role of "man", or "discursive reasoner" in`

`Plotinus. yet, their canonical first person person attached with them`

`(by incompleteness; or by the distinction between Bp and Bp&p) is a`

`sort of God, at least from the machine's point of view (it is`

`infinite, in some sense, and not arithmetically definable).`

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.