2008/11/16 Brent Meeker <[EMAIL PROTECTED]>:

>> But if any computation can be mapped onto any physical state, then
>> every computation can be mapped onto one physical state; and why not
>> the null state?
> I'm not sure that works.  In the original idea the mapping was to be
> one-to-one (which is possible since a stone or other physical object has
> many microscopic states).

I don't see why the mapping can't be
one(physical-state)-to-many(computation-states). This wouldn't work if
you actually tried to keep track of the computation - in that case you
would need some sort of index variable - but that isn't a problem if
you don't require that the computation interact with the world at the
level of substrate of its implementation.

> If the mapping is something like:
> computation-state1---map1---->physical-state0
> computation-state2---map2---->physical-state0
> computation-state3---map3---->physical-state0
> ...
> then the inverse mapping,
> physical-state0---1map--->computation-state1
> physical-state0---2map--->computation-state2
> physical-state0---3map--->computation-state3
> ...
> has to implicitly provide it's own order.  So for the physical-state0 to
> implement the computation there would have to be another index variable,
> like time, to order the inverse mapping.  Then it would really be
> physical-state0@ t=1---1map--->computation-state1
> physical-state0@ t=2---2map--->computation-state2
> physical-state0@ t=3---3map--->computation-state3
> ...
> Right?
> Brent.

Stathis Papaioannou

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