On 28 Dec 2013, at 05:31, Stephen Paul King wrote:
Hi Jason,
On Fri, Dec 27, 2013 at 11:23 PM, Jason Resch <jasonre...@gmail.com>
wrote:
On Fri, Dec 27, 2013 at 11:09 PM, Stephen Paul King <stephe...@provensecure.com
> wrote:
Hi Jason,
"It is not a question of whether or not that binary string refers
to anything that is true or not, only what its particular value
happens to be." No no no! We can not make statements without showing
how their proof are accessible!
The proof is straight forward. Run the UD and see what the state is.
Run it, on what hardware? ??
Are you objecting that it does not have a definite value because you
or I are not capable of computing it?
Did the 100th digit of Pi not exist until the first human computed it?
Pfft, that is a red herring and you know it! Why even mention
humans? If numbers exist, then that existence has nothing at all to
do with humans or aliens of black clouds. It is merely the necessary
possibility that the numbers are not inconsistent. If they were
inconsistent, then all that would exist is noise. And we are back to
my question. What decodes the noise into "meaningful" strings?
The universal numbers, through the laws (in this case with arithmetic
beeing the base) of addition and multiplication. Arithmetic "dovetail"
on programs, and consciousness filter out the "meaningfull one" (as we
assume comp).
Consider the i-th through j_th values of pi's expansion in binary.
If it is a finite string, how do we know that it is a Turing machine
program?
All integers can be mapped directly to Turing machine programs.
Consider Java: it uses a byte-code where every byte is an
instruction for the Java virtual machine. Every string of bytes can
therefore be considered as a sequence of instructions for the Java
virtual machine to execute.
SO it is OK to include the java code that generates noise. There are
your oracles! Pick one. Whoops, how is the selection made?
Like in the WM duplication. By self-reference.
bruno
Jason
On Fri, Dec 27, 2013 at 11:06 PM, Jason Resch <jasonre...@gmail.com>
wrote:
On Fri, Dec 27, 2013 at 10:44 PM, Stephen Paul King <stephe...@provensecure.com
> wrote:
Hi Jason,
"The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ..."
Umm, how? Godel and Matiyasevich would disagree! If there does not
exist a program that can evaluate whether or not a UD substring is a
faithful representation of a "true theorem", then how is it "a fact"?
The mathematical fact to which I am referring is only a basic and
straight-forward statement like "the binary representation of the
state of UD after executing 100..00th steps is
'1010101111010...0010". It is not a question of whether or not that
binary string refers to anything that is true or not, only what its
particular value happens to be.
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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