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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 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.

`I agree most numbers are incompressible, but I was using random in a`

`different sense than the unpredictability of the next digits of the`

`number given previous ones.`

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 to throw`

`the dart so that it lands on one.`

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 a random`

`number in that range (as it is a candidate to be output by some RNG),`

`but the problem is selecting it in a random (in the sense of not-`

`predictable) way.`

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

`While a number can be interpreted as random once, it might not be the`

`second time.`

`While selecting and using all possibilities is arguably a way to`

`achieve randomness (unpredictibilty), (from some points of view) it is`

`often not practical nor useful. Consider encrypting a message with`

`all possible keys and sending the recipient all possible messages.`

`Not only might you need to send 2^256 possible ciphertexts but any`

`eavesdropper could use the first possible key to decrypt it. This`

`achieves randomness from the POV of the cipher, but not for the user`

`or the attackers.`

`In quantum cryptography this is essentially what is done, but it`

`requires that the sender and reciever (and attackers) be duplicated`

`for each possible key. So they need to be embedded in that larger`

`program that provides all possible inputs for it to seem random. This`

`is just FPI though, is it not?`

Jason

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.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. 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,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 not anyprogram executes forever, and what all of its intermediate statesare. If these statements are true independently of you and me, thenthe executions of these programs are embedded in arithmetical truthand have a platonic existence. The first, second, 10th,1,000,000th, and 10^100th, and 10^100^100th state of the UD'sexecution are mathematical facts which have definite values, andall the conscious beings that are instantiated and evolve and writebooks on consciousness, and talk about the UD on their 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 email to everything-list+unsubscr...@googlegroups.com.To post to this group, send email to everything-l...@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 may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify senderimmediately 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-l...@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-l...@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 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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