"Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are.
this also captures every instance of random numbers as well. 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?
Truth is not a measure zero set, or is it?
On 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? How is it
>> computed? Could you write an explicit example? I have never been 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 the integer
> Program P = createProgramFromInteger(i);
> # Add the program to a list of programs we have generated so far
> # For each program we have generated that has not halted, execute one
> instruction of it
> for each (Program p in listOfPrograms)
> if (p.hasHalted() == false)
> # Finally, increment i so a new program is generated the next time
> i = i + 1;
> Any program, and whether or not it ever terminates can be translated to a
> statement concerning numbers in arithmetic. Thus mathematical truth
> captures the facts concerning whether or not any program executes forever,
> and what all of its intermediate states are. If these statements are true
> independently of you and me, then the executions of these programs are
> embedded in arithmetical truth and have a platonic existence. The first,
> second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
> execution are mathematical facts which have definite values, and all the
> conscious beings that are instantiated and evolve and write books on
> consciousness, and talk about the UD on their Internet, etc. as part of the
> execution of the UD are there, in the math.
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Stephen Paul King
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