On 8/24/2012 11:19 PM, Stephen P. King wrote:
On 8/24/2012 11:33 PM, meekerdb wrote:
On 8/24/2012 7:05 PM, Stephen P. King wrote:

"...due to the law of conjugate bisimulation identity:

          A ~ A   =   A ~ B ~ C ~ B ~ A   =   A ~ B ~ A

this is "retractable path independence": path independence only over retractable paths.

I don't understand this. You write A~(B~A) which implies that B~A is a "system" (in this case one being simulated by A).

Dear Brent,

The symbol "~" represent simulate, so the symbols A~(B~A) would be read as "A simulating B while it is simulating A". A and B and C and D ... are universal simulators ala David Deutsch. The can run on any physical system capable of universality.

  But then you write

A~B~A=A~A

These would read as: "A simulating B simulating A", which is different from "A simulating B while it is simulating A", a subtle difference. The former is simultaneous while the latter is not.

The idea of simultaneity seems out of place in simulation. A simulation simulates the event relations that define time. Your distinction implies some external time that makes an essential difference within the simulation??


and also

A~B~C~A =/= A~C~B~A =/= A~A

This seems inconsistent, since A~B~C~A = A~D~A where D=B~C,

How do you get D=B~C from? That is inconsistent with the Woolsey identity rule .

It's just defining a symbol "D" to denote the system B~C.

For example C could be capable of simulating B in the process of it simulating A, which is different in content from C simulating A while A is simulating B. Simulators do not commute the way numbers do.

I didn't assume commutation.  I denoted B~C by D and C~B by E, making no 
assumption that D=E.

BTW, a simulation relation is not necessarily an identity like "=".


but then A~D~A=A~A. And A~C~B~A = A~E~A where E=C~B, and then A~E~A=A~A. But then A~B~C~A = A~C~B~A.

I seem to be assuming a natural ordering on the symbols A, B, C, D, etc.

No I just followed the arbitrary convention of picking the next letter when I needed a new name. Put X for C and S for E if you like, they are just names of systems.

Of course for real computers running simulations it is not necessarily the case that A~B~A=A~A, which would equal A, although that's the most efficient way for A to simulate B simulating A. I don't find your notion of system and simulation very clear. I suppose by "system" you mean a some definite set of things which are evolving by a defined process, some set of states which can be computed by an algorithm (or possibly including randomness?). Then a simulation is a different set of things evolving through states that are isomorphic to the system simulated?

Brent

and a notion of being at the same level in the ordering with the "(..)" symbols. I should have made this clear. My apologies! Does the comment about telescope property not make sense?


You drop the parentheses, implying the relation is associative, but then you treat it as though it isn't??

Not having pointed out the ordering caused a confusion. My apologies. Thank you for pointing this out! This idea still needs a lot of work, that I do admit!


Brent



--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
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