On 28 Dec 2013, at 04:52, Jason Resch wrote:
On Fri, Dec 27, 2013 at 10:39 PM, Stephen Paul King <stephe...@provensecure.com
> wrote:
Dear Jason,
ISTM that the line " For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms)" is buggy.
It assumes that the space of "programs that do not halt" is
accessible. How?
We never know a prior if a program will halts or not. However, once
a program has reached a halted stated it is immediately apparent.
If the function name was "willThisProgramHalt()", then I agree it
would be a buggy program. :-)
The UD as I wrote it executes all programs, whether they will halt
or not, but it never wastes time trying to run another instruction
of a program that has halted. This is only an optimization, and I
added it only to reduce the ambiguity of "running another
instruction of a program that has halted".
OK. The LISP UD is even more optimized, and the small UD I just gave
is not optimal at all. Of course, to optimize a UD is a bit like pure
coquetry :) (it should not change anything in the measure conflicts,
a priori).
Bruno
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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