On 30 Dec 2013, at 09:01, meekerdb wrote:

## Advertising

On 12/29/2013 11:42 PM, Bruno Marchal wrote:On 29 Dec 2013, at 20:25, meekerdb wrote:On 12/29/2013 5:56 AM, Bruno Marchal wrote:On 28 Dec 2013, at 22:23, meekerdb wrote:On 12/28/2013 4:09 AM, Bruno Marchal wrote:For a long time I got opponent saying that we cannot generatecomputationally a random number, and that is right, if we wantgenerate only that numbers. but a simple counting algorithmgenerating all numbers, 0, 1, 2, .... 6999500235148668, ...generates all random finite incompressible strings,How can a finite string be incompressible? 6999500235148668 inbase 6999500235148669 is just 10.You can define a finite string as incompressible when the shortercombinators to generate it is as lengthy as the string itself.This definition is not universal for a finite amount of shortsequences which indeed will depend of the language used (herecombinators).Then you can show that such a definition can be made universal byadding some constant, which will depend of the universal language.It can be shown that most (finite!) numbers, written in any base,are random in that sense.Of course, 10 is a sort of compression of any string X in somebase, but if you allow change of base, you will need to send thebase with the number in the message. If you fix the base, thenindeed 10 will be a compression of that particular number base,for that language, and it is part of incompressibility theorythat no definition exist working for all (small) numbers.Since all finite numbers are small, I think this means the theoryonly holds in the limit.The definition will work for all numbers reasonably bigger than thecode of the universal machine used. That is what determine theconstant. Not all numbers are small relatively to the size of theuniversal number/machine used to compress information.Maybe you can clarify this point which seemed to arise in mydiscussion with JR. Are you talking about numbers or about stringsof digits that name numbers?

`I am talking about string of digits (naming or not numbers). Sometimes`

`I call them number, as all strings on a fixed alphabet can be seen as`

`a number written in the base defined by that alphabet. But compression`

`is a notion concerning strings of symbols.`

Bruno

Brent --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.