On 28 Dec 2013, at 17:35, Stephen Paul King wrote:

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Dear Bruno,On Sat, Dec 28, 2013 at 7:09 AM, Bruno Marchal <marc...@ulb.ac.be>wrote:On 28 Dec 2013, at 04:56, Jason Resch wrote:On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King <stephe...@provensecure.com> wrote:Hi Jason,"Any program, and whether or not it ever terminates can betranslated to a statement concerning numbers in arithmetic. Thusmathematical truth captures the facts concerning whether or not anyprogram executes forever, and what all of its intermediate statesare. "this also captures every instance of random numbers as well. It is not clear to me what "random" means in arithmetical truth.Randomness can appear from the perspectives of observers, but Idon't see how it can arise in arithmetic.?It appears in all numbers written in any base. Most numbers arealready random (even incompressible).I guess you know that. In the phi_i(j) in the UD, randomness canappear in the many j used as input, as we usually dovetail on thefunction of one variable. (but such input can easily be internalizedin 0-variable programs).OK, I must agree, but can you see how this removes our ability touse the natural ordering of the integers as an explanation of theappearance of time?

`Of the physical time? yes, that is right. That is a consequence of the`

`delay invariance of the FPI. But we can still use it indirectly. It`

`is part of the additive-multiplicative structure of the numbers that`

`we assume (through the numbers laws).`

Since there are multiple and equivalent (as to their properties)sequences of integers that have very different orders relative toeach other, if we use these ordering as our "time" we would have adifferent dimension of time for every one!

?

`On the contrary. As you just said, the appearance of time is not`

`dependent on that order.`

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, and even all theinfinite one (for the 1p view, notably).In that (trivial) sense, arithmetic contains a lot of 3p randomness,even perhaps too much. Then 1p randomeness appears too, by the 1pindeterminacy (and that one is in the eyes of the machine).Chaitin's results can also explain why we cannot filter out that 3prandomness from arithmetic.Have you had any more thoughts on the "book keeping" problem we havediscussed in the past?

Can you remind me? Thanks. Bruno 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.