On 28 Dec 2013, at 05:01, Stephen Paul King wrote:
How do we distinguish a program from a string of random numbers.
(Consider OTP encryptions).
In which language?
A program fortran will be distinguished by the grammar of Fortran.
In some language all numbers will be program.
Then , for all language question like "does that progream compute this
or that" are non algorithmically solvable (and undecidable in most
theories).
Bruno
On Fri, Dec 27, 2013 at 10:56 PM, Jason Resch <jasonre...@gmail.com>
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 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.
It is not clear to me what "random" means in arithmetical truth.
Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.
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?
Jason
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 i
Program 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 it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}
# Finally, increment i so a new program is generated the next
time through
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.
Jason
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