At 01:19 27/01/04 -0500, Kory Heath wrote:
At 1/26/04, Stephen Paul King wrote:
The modern incarnation of this is the so-called
4D cube model of the universe. Again, these ideas only work for those who
are willing to completely ignore the facts of computational complexity and
the Heisenberg Uncertainty principle.
I think you and I are living in two completely different argument-universes here. :) I'm not arguing that our universe is computable. I'm not arguing that our universe can definitely be modeled as a 4D cube. I'm not arguing that only integers exist. The only reason why I keep using CA models is that they're extraordinarily easy to picture and understand, *and*, since I believe that SASs can exist even in very simple computable universes like CAs, it makes sense to use CA models when trying to probe certain philosophical questions about SASs, physical existence, and instantiation. Quantum physics and the Heisenberg Uncertainty principle are simply irrelevant to the particular philosophical questions that I'm concerned with.
Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the "future" as well as one tick in the "past". Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc.
This simple thought experiment generates some fascinating philosophical questions. Are those SASs actually conscious? If so, at what point did they become conscious? Was it at the moment that our testing algorithm decided that that particular 4D block followed our specified CA rule? Or is it later, when we "animate" portions of the 4D block so that we can watch events unfold in "realtime"? These are not rhetorical questions - I'd really like to hear your answers, because it might help me get a handle on your position. (I'd like to hear other people's answers as well, because I think it's a fascinating problem.)
Anyway, the point that I'm really trying to make is that, while these thought experiments have a lot of bearing on the question of mathematical existence vs. physical existence, they have nothing at all to do with quantum physics or Heisenberg uncertainty. The fact it seems so to you makes me think that we're not even talking about the same problem.
I understand Kory very well and believe he argues correctly in this
post with respect to Stephen.
But at the same time, I pretend that if we follow Kory's form of
reasoning we are lead to expect a relation with (quantum) physics.
This can seem a total miracle, ... but only for someone being both
computationnalist and physicalist, and that has been showed
impossible (marchal 88, Maudlin 89, ref in my thesis).
Let me try to explain shortly.
The reason is that if the initial CA is universal enough the (and that
follows for theoretical computer science) "universal CA" will
dovetail on an infinite number of similar computations passing through
each possible SAS computational state, and then ...
... remembering the comp 1-indeterminacy, that is that if you are duplicate
into an exemplary at Sidney and another at Pekin, your actual
expectation is indeterminate and can be captured by some measure,
let us say P = 1/2, and this (capital point) independently of the time
chosen for any of each reconstitution (at Pekin or Sidney), giving that the
reconstitution cannot be perceived (recorded by the first person)).
So if we run an universal dovetailer (implemented in CA, or FORTRAN,
or even just arithmetical truth), each SAS will have an indeterminate futur
and his/her/its expectation (from his 1-person pov) will be given by
a measure on all its computational continuation, runned, or even just defined,
in the complete procession of the universal CA.
Now, that measure on those computations must fit the SAS's physical law,
if not the SAS will correctly infer that comp is false, which, we know,
must be true (we runned the CA, for exemple).
So the physical laws must result from a relative (conditional to a state S) measure
on all computations continuing S. (and actually this looks like Feynman formulation
OK, I was short, please look at (where UDA = Universal Dovetailer Argument)
UDA step 1 http://www.escribe.com/science/theory/m2971.html
UDA step 2-6 http://www.escribe.com/science/theory/m2978.html
UDA step 7 8 http://www.escribe.com/science/theory/m2992.html
UDA step 9 10 http://www.escribe.com/science/theory/m2998.html
UDA last question http://www.escribe.com/science/theory/m3005.html
Joel 1-2-3 http://www.escribe.com/science/theory/m3013.html
Re: UDA... http://www.escribe.com/science/theory/m3019.html
Joel's nagging question http://www.escribe.com/science/theory/m3038.html
for previous post where I explain the thing step by step;
or look at http://www.escribe.com/science/theory/m1726.html
For a one-post presentation of the argument.
I would be very interested if you, or anyone in the list (btw apology for
the minority who would have already see the point), could tell me at which
step of the reasoning you would disagree (in either presentation).