On 05 Feb 2012, at 21:32, meekerdb wrote:

On 2/5/2012 8:19 AM, Bruno Marchal wrote:No. All universal numbers can interpret a number as a function onquantities, or as properties on quantities, which are notquantities themselves. Universal numbers can also transform, orinterpret numbers as transformation of transformation, propertiesof properties, up in the constructive transfinite, etc.When the quantities can add and multiply, soon their attributes arebeyond all quantities, and LĂ¶bian quantities are arguably alreadyknowing that about themselves.I don't understand this. Maybe I don't know what universal numberis. I thought it was a number whose representation in digits wassuch that every number appeared in the representation. But I don'tunderstand how such number does things: transform, interpret,...

`Let phi_i be an enumeration of the (partial and total) computable`

`functions from N to N.`

Let <x,y> be a bijection from NXN to N.

`A universal number u is a number u such that, for all x and y, we have`

`phi_u(<x,y>) = phi_x(y).`

`The equality means that the LHS and RHS are either both defined and`

`equal, or both undefined.`

`u, applied on x and y simulate the machine x on the input y. u is`

`called the computer, x the program (the machine to be emulated), and y`

`is the datum/data. u interpret x as a machine, and it simulates x`

`behavior on the input y.`

`You can see it as the number-code of a universal machine or`

`programming language interpreter.`

`u depends on the choice of the bijection and of the phi_i base, but if`

`you choose (N, +, *) as a universal system, you can make it intrinsic,`

`and for any bijection, you will have different but equivalent`

`universal numbers. This is not a problem because we have to consider`

`*all* universal numbers to retrieve the physics and psychology of`

`machines (this will include all such bijection).`

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.