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 ~ Athis 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" (inthis case one being simulated by A).Dear Brent,The symbol "~" represent simulate, so the symbols A~(B~A) would be read as "Asimulating B while it is simulating A". A and B and C and D ... are universal simulatorsala David Deutsch. The can run on any physical system capable of universality.But then you write A~B~A=A~AThese would read as: "A simulating B simulating A", which is different from "Asimulating B while it is simulating A", a subtle difference. The former is simultaneouswhile 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, whichis different in content from C simulating A while A is simulating B. Simulators do notcommute 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 thenA~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. Ishould have made this clear. My apologies! Does the comment about telescope property notmake sense?You drop the parentheses, implying the relation is associative, but then you treat itas though it isn't??Not having pointed out the ordering caused a confusion. My apologies. Thank you forpointing 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 --You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

-- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.