On Fri, 2 Jul 1999 hal.domain.name.hidden wrote:
First, I have to say that Hal's post was a rather good one by the
standards of what shows up on this list.
> I agree with Jacques that Chalmers' biggest problem is his simplistic
> assumption that physical subsystems must occupy specific regions of space.
> This would rule out people as conscious entities, since we move around.
> You could patch this up but it is still far too limited.
It's not quite as bad as that, the regions of space could be a
function of time. But the elements could never pass through each other,
which rules out some possible computers. Also, in QM wavefunctions always
overlap and positions are not well defined.
> I think that Chalmers' basic strategy of looking at substructure
> of the mathematical process which is being instantiated, and trying to
> map them to physical substates of the physical system which claims to
> instantiate it, still works even with inputless systems. So I think his
> whole discussion of the need for input is in the end a red herring, but
> does not ultimately detract from his basic argument.
He does not actually require input but does waste a lot of time
talking about it. I agree that input is irrelevant, but it could be
useful at some later stage as a way of talking about only part of a
system.
> This approach includes Chalmers' as a subcase, where the SMA would
> simply choose a fixed location for each substate.
Not quite. I operate in phase space. (For QM, that would be the
space of all possible wavefunctions.)
> The main problem that I see with this approach is that Jacques proposes
> to use Kolmogorov complexity to judge the simplicity of the SMA. We want
> the SMA to be uniquely defined, and in fact he has to add a few ad hoc
> rules to deal with some possible ambiguities in order to get uniqueness.
> We therefore need a measure over algorithms which describes simplicity,
> so that we can take the simplest algorithm which satisfies the mapping
> constraints.
> [...non-problem snipped]
> However I think there is a worse problem. That is that K. complexity is
> not uniquely defined. K. complexity is defined only with regard to some
> specific universal Turing machine (UTM). Two different UTMs will give a
> different answer for what the K. complexity is of a string or program.
> In fact, given any particular string, you can construct a UTM which gives
> it an arbitrarily large or small K. complexity as measured by that UTM.
>
> I think this objection is probably fatal to Jacques' idea. We need the
> SMA to be uniquely defined. But this cannot be true if there exist UTMs
> which disagree about which mapping algorithm is simplest. Within the
> mathematical framework of K. complexity, all UTMs are equally valid.
> So there is no objective preference of one over the other, hence there
> can be no objective meaning to the SMA.
>
> In order to fix this, we have to identify a particular UTM which we will
> use to measure the K. complexity. There has to be some particular Turing
> machine which is preferred by the universe. You could choose one and
> produce an "objective theory of consciousness", but this would be yet
> another ad hoc rule which would make the theory less persuasive.
I don't think it's as bad as that! I do agree that the ambiguity
is a problem, and this is the main reason I say it needs to be made more
precise.
First, some UTMs are more complex than others. There are various
different ways to measure this, but two possible choices are to use the
'standard numbering' (see Li & Vitanyi), or to use a machine which
mimimizes a criterion such as number of head x tape states. I'm not
looking at the book right now so this may not be exactly right but there
are criteria that are not completely arbritrary if one is looking for
simplicity.
The other thing one might do is to try to average the complexity
over all possible Turing machines. The problem is that since there are
infinitely many the result may not be unique - order can matter. If so
it's possible that an iterative criterion might help, i.e. choose the
distribution of UTMs (if there is such a unique distribution) which when
operated to name all Turing machines, produces the same distribution.
BTW does anyone know if this is the case, or know someone who might?
OK so I just named two or three possible ways, but that's the
problem, isn't it? Too many possibilities? Well, the averaging idea may
or may not work depending on the math. I think if it does work, use it,
if not, that helps narrow it down :-)
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Fri Jul 02 1999 - 12:15:40 PDT