Re: Bisimulation Algebra

```On 8/25/2012 2:41 AM, meekerdb wrote:
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```On 8/24/2012 11:19 PM, Stephen P. King wrote:
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```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??
```
```
Dear Brent,

Good question! It matters at the interface - the input location vs. the output
location, but not for the internals of the computation itself. You have to stop thinking
of a computer as an isolated system. Bruno does this and he wonders why I complain that
he does not understand implications of the body problem when it is reduced to arithmetic.
We have a "reality" full of separate minds that needs to be explained.
Explaining a single mind is easy; why we can construct beautiful Peano arithmetic and
Robinson Arithmetic models of it, but a plurality of separate minds; that's hard!
We have diary entries and discussions of being at Washington or Helsinki or
Moscow, but that do these names mean to an isolated computation? Locating a
place is not the same as locating a number.

```
```
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.
```
```
B~C is not a system, B~C is system B simulating C. If D is a system
simulating B simulating C then it is its own self with its own identity D which
includes the ability to simulate B simulating C. This does not make D into a
system B~C. Sorry. Stop thinking off things as isolated from each other, the
entire idea of interaction becomes mute when you do that!

```
```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.
```
```
But you did assume that D was a particular computation and not a simulator
capable of many simulations, not just B~C. I didn't define that possibility, so
where did it come from?

```
```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.
```
```
It helps to check to see if one's conjectures about a idea are consistent
with all of the idea, not just pieces of it. Naming conventions are very tricky
and lead us into all sorts of temptations. ;-)

```
```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.
```
```
But there is a difference! A simulating B simulating A is the internal map
of a single program, A. A simulating B while it is simulating A is a internal
map (in A) of another program's (B) simulation. A slight difference. Can we
untangle computations from each other such that they can have seperate
identities or localizations? There is a good point to your critique here and it
is that the two versions are equivalent to a separate computer that has A, B
and C as subroutines such that the input and outputs are the same. But this
equivalence is strictly internal to that seperate system that might be, in
words like Bruno's, evaluating the difference.
What I am trying to set up here is the map-territory difference and where
it vanishes. When does my mental image of you and your mental image of yourself
differ? When might it be the same?

```
```I don't find your notion of system and simulation very clear.
```
```
Good point, I am an amateur at this and I am learning. I do appreciate your
interest! :-)

```
```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?
```
```
I am just following Deutsch's idea of a universal simulator. I am not sure
if this ties to functional equivalence yet, I'm exploring and reading lots of
Chalmer's stuff (and Bruno's -again).

```
```
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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