On 28 Dec 2013, at 16:51, Jason Resch wrote:

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On Dec 28, 2013, at 6:09 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 notany program executes forever, and what all of its intermediatestates are. "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.I agree most numbers are incompressible, but I was using random in adifferent sense than the unpredictability of the next digits of thenumber given previous ones.

`OK. But in the iterated self-duplication, both form of indeterminacy`

`can be mixed.`

In the phi_i(j) in the UD, randomness can appear in the many j usedas 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 generatecomputationally a random number, and that is right, if we wantgenerate only that numbers.Right, all the random numbers are there, the question is how tothrow the dart so that it lands on one.

Of course. And here the 1-indetermlinacy provides one answer.

but a simple counting algorithm generating all numbers, 0, 1,2, .... 6999500235148668, ... generates all random finiteincompressible strings, and even all the infinite one (for the 1pview, notably).I think we are using the term in a slightly different sense.Certainly any number in the range 1 - N can be considered as arandom number in that range (as it is a candidate to be output bysome RNG), but the problem is selecting it in a random (in the senseof not-predictable) way.

`Yes. here I just point on the fact that random number (with random`

`digits) exists.`

There was a joke cartoon of some computer code: int getRandomNumber() { return 4; // this number was determined by a random die roll }

Lol Close to my favorite infinite binary random sequence: 00000000000000000000000000000000000000000000000000000000... The term "random" is very large.

While a number can be interpreted as random once, it might not bethe second time.While selecting and using all possibilities is arguably a way toachieve randomness (unpredictibilty), (from some points of view) itis often not practical nor useful. Consider encrypting a messagewith all possible keys and sending the recipient all possiblemessages.Not only might you need to send 2^256 possible ciphertexts but anyeavesdropper could use the first possible key to decrypt it. Thisachieves randomness from the POV of the cipher, but not for the useror the attackers.In quantum cryptography this is essentially what is done, but itrequires that the sender and reciever (and attackers) be duplicatedfor each possible key. So they need to be embedded in that largerprogram that provides all possible inputs for it to seem random.This is just FPI though, is it not?

Yes. Bruno

JasonIn that (trivial) sense, arithmetic contains a lot of 3prandomness, 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 3prandomness from arithmetic.BrunoWhat 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.I will 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,execute one 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 betranslated to a statement concerning numbers in arithmetic. Thusmathematical truth captures the facts concerning whether or notany program executes forever, and what all of its intermediatestates are. If these statements are true independently of you andme, then the executions of these programs are embedded inarithmetical truth and have a platonic existence. The first,second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state ofthe UD's execution are mathematical facts which have definitevalues, and all the conscious beings that are instantiated andevolve and write books on consciousness, and talk about the UD ontheir Internet, etc. as part of 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 emailto 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 ormay be constituted as attorney work product. If you are not theintended recipient, you are hereby notified that any use,dissemination, distribution, or copying of this communication isstrictly prohibited. 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