On 06 Feb 2012, at 19:34, meekerdb wrote:

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On 2/6/2012 1:50 AM, Bruno Marchal wrote: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 attributesare beyond all quantities, and LĂ¶bian quantities are arguablyalready knowing 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 Idon't understand how such number does things: transform,interpret,...Let phi_i be an enumeration of the (partial and total) computablefunctions 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, wehave phi_u(<x,y>) = phi_x(y).The equality means that the LHS and RHS are either both defined andequal, or both undefined.Thanks. So it is not literally that the number does things, it justpicks out the function that is universal for a given bijection and agiven enumeration of the functions.

`You are right. Technically we could bypass the bijection, and use only`

`function with one argument, but this leads to the combinators (or`

`numbers with some other operations). But a number per se do nothing.`

`It needs a universal numbers to be interpreted, or ... the fixed`

`universal base and in that case the * and + laws are enough, so that`

`the choice of the universal (Sigma_1 complete) initial system endows`

`the numbers with a "natural operational interpretation" by that`

`universal basic system. From inside, the numbers will still not know`

`the difference between a base (UD-like) computations, and any higher`

`level one (and for the physics he has to take them all into account).`

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.