On 28 Dec 2013, at 04:56, Jason Resch wrote:

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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 are`

`already random (even incompressible).`

`I guess you know that. In the phi_i(j) in the UD, randomness can`

`appear in the many j used as input, as we usually dovetail on the`

`function of one variable. (but such input can easily be internalized`

`in 0-variable programs).`

`For a long time I got opponent saying that we cannot generate`

`computationally a random number, and that is right, if we want`

`generate only that numbers. but a simple counting algorithm generating`

`all numbers, 0, 1, 2, .... 6999500235148668, ... generates all random`

`finite incompressible strings, and even all the infinite 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 1p`

`indeterminacy (and that one is in the eyes of the machine).`

`Chaitin's results can also explain why we cannot filter out that 3p`

`randomness from arithmetic.`

Bruno

What method is deployed to ensure that a program is not just a"regular" random number and not some random number prefixed on a"real" halting program?It don't see how it makes a difference. Truth is not a measure zero set, or is it? I don't understand this question.. Could you clarify? JasonOn Fri, Dec 27, 2013 at 10:09 PM, Jason Resch <jasonre...@gmail.com>wrote:On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King <stephe...@provensecure.com> wrote:Hi Jason,Could you discuss the "trace of the UD" that LizR mentioned? Howis it computed? Could you write an explicit example? I have neverbeen able to grok it.Bruno has written an actual UD in the LISP programming language. Iwill write a simple one in pseudo-code below:List listOfPrograms = new List[]; # Empty list int i = 0; while (true) {# Create a program corresponding to the binary expansion of theinteger iProgram P = createProgramFromInteger(i); # Add the program to a list of programs we have generated so far listOfPrograms.add(P);# For each program we have generated that has not halted, executeone instruction of itfor each (Program p in listOfPrograms) { if (p.hasHalted() == false) { executeOneInstruction(p); } }# Finally, increment i so a new program is generated the nexttime throughi = i + 1; }Any program, and whether or not it ever terminates can be translatedto a statement concerning numbers in arithmetic. Thus mathematicaltruth captures the facts concerning whether or not any programexecutes forever, and what all of its intermediate states are. Ifthese statements are true independently of you and me, then theexecutions of these programs are embedded in arithmetical truth andhave a platonic existence. The first, second, 10th, 1,000,000th,and 10^100th, and 10^100^100th state of the UD's execution aremathematical facts which have definite values, and all the consciousbeings that are instantiated and evolve and write books onconsciousness, and talk about the UD on their Internet, etc. as partof the execution of the UD are there, in the math.Jason --You received this message because you are subscribed to a topic inthe Google Groups "Everything List" group.To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/sqWzozazMg0/unsubscribe.To unsubscribe from this group and all its topics, 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. -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 stephe...@provensecure.com http://www.provensecure.us/“This message (including any attachments) is intended only for theuse of the individual or entity to which it is addressed, and maycontain information that is non-public, proprietary, privileged,confidential and exempt from disclosure under applicable law or maybe constituted as attorney work product. If you are not the intendedrecipient, you are hereby notified that any use, dissemination,distribution, or copying of this communication is strictlyprohibited. If you have received this message in error, notifysender immediately and delete this message immediately.”--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. --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.

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