On 28 Dec 2013, at 17:30, Stephen Paul King wrote:
Dear Bruno,
On Sat, Dec 28, 2013 at 6:53 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 28 Dec 2013, at 04:39, Stephen Paul King 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?
The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.
The space of all programs (that do halt of do not halt) *is*
accessible.
Could you elaborate on this claim. I wish to be sure that I
understand it. Is it really a "space"?
It is a recursively enumerable set.
Would it have metrics and topological properties?
As a set, you can endow it with some structure, if you have the
motivation.
All what happen is that we have no general systematic,
computational, means to distinguish the programs that halt from the
programs that does not halt (on their inputs), and that is why the
universal dovetailer must *dovetail* on the executions of all
programs.
Not having a "general systematic, computational, means to
distinguish.." has not stopped Nature.
Nor the FPI. Right.
She solves the problem by the evolution of physical worlds.
That's too quick, especially that we don't assume "nature".
I propose that physical worlds ARE a form of non-universal
computation.
Then brain and computers cannot exist in those physical world.
I still think that the UD lives only in Platonia and is timeless and
static.
That's correct.
Only its "projections" (to use Plato's cave metaphor) are run as
physical worlds
OK. The "FPI" projections. But they are not "run", only selected. The
computation are run, not the projection from inside.
Bruno
if they can survive the challenge of mutual consistency.
Bruno
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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