"Saibal Mitra" <smitra.domain.name.hidden> writes:
> I don't understand why you consider the measures of the programs that do the
> simulations. The ''real'' measure should be derived from the algorithmic
> complexity of the laws of physics that describe how the computers/brains
> work. If you know for certain that a computation will be performed in this
> universe, then it doesn't matter how it is performed.
I think what you're saying here is that if a mental state is instantiated
by a given universe, the contribution to its measure should just be
the measure of the universe that instantiates it. And that universe's
measure is based on the complexity of its laws of physics.
I used to hold this view, but I eventually abandoned it because of a
number of problems. I need to go back and collect the old messages
and discussions that we have had and put them into some kind of order.
But I can mention a couple of issues.
One problem is the one I just wrote about in my reply to Russell, the
fuzziness of the concept of implementation. In at least some universes
we may face a gray area in deciding whether a particular computation,
or more specifically a particular mental state, is being instantiated.
Philosophers like Hans Moravec apparently really believe that every
system instantiates virtually every mental state! If you look at the
right subset of the atomic vibrations inside a chunk of rock, you can
come up with a pattern that is identical to the pattern of firing of
neurons in your own brain. Now, most philosophers reject this, they come
up with various technical criteria that implementations have to satisfy,
but as I wrote to Russell I don't think any of these work.
The other problem arises from fuzziness in what counts as a "universe".
The problem is that you can write very simple programs which will
create your mental state. For example, the Universal Dovetailer does
just that. But the UD program is much smaller than what our universe's
physical laws probably would be. Does the measure of the UD "count" as a
contribution to every mind it creates? If so, then it will dominate over
the contributions from more conventional universes; and further, since
the UD generates all minds, it means that all minds have equal measure.
To reject the UD as a cheating non-universe means that we will need a
bunch of ad hoc rules about what counts as a universe and what does not,
which are fundamentally arbitrary and unconvincing.
Then there are all those bothersome disputes which arise in this model,
such as whether multiple instantiations should add more measure than
just one; or whether a given brain in a small universe should get more
measure than the same brain in a big universe (since it uses a higher
proportion of the universe's resources in the first case). All these
issues, as well as the ones above, are addressed and answered in my
current framework, which is far simpler (the measure of a mental state
is just its Kolmogorov measure - end of story).
> The algorithmic complexity of the program needed to simulate a brain refers
> to a ''personal universe''. You can think of the brain as a machine that is
> simulating a virtual world in which the qualia we experience exist. That
> world also exists independent of our brain in a universe of its own. This
> world has a very small measure defined by the very large algorithmic
> complexity of the program needed to specify the brain.
I agree with this, I think. The program needed to specify a mental state
a priori would be far larger than the program needed to specify the laws
of physics which could cause that mental state to evolve "naturally".
Both programs make a contribution to the measure of the mental state,
but the second one's contribution is enormously greater.
The key point, due to Wei Dai, is that you can mathematically treat the
two on an equal footing. As you have described it, we have a virtual
world with qualia being created by a brain; and you have that same
world existing independently as a universe of its own. Those are pretty
different in a Schmidhuber type model. The second case is the output of
one of the universe programs (a very very complex one). The first case
is a rather intangible property of a universe program much like our own.
To unify them we ask the question of how we can output a representation
of that virtual world with qualia, using the shortest possible program.
Assuming that there actually is a universe which naturally evolves
a brain experiencing this mental state, we can do it with a two-part
program: the first which creates and evolves the universe, and the second
which analyzes the output of that universe to output the virtual world
representation we seek. This second part basically translates the brain
activity, part of the universe created by the first part, into whatever
reprsentation we have chosen for the virtual world and qualia.
Given that the universe created by the first part does evolve the
brain states needed as input for the second part, the second part can
be a relatively simple translation from physical to mental states.
Therefore we can create a short program which outputs the virtual world
and qualia in all its glory, and this short, two-part program will be
the main contribution to the measure of that mental experience.
Keep in mind that in this framework, we do not start with this two-part
structure. The starting point is much simpler: all we want to know
is, what is the Kolmogorov complexity of a mental experience? It is
only once we begin analyzing the problem that we note as you did that
building that mental experience as a universe of its own would require
an enormously large program. And then we realize that we can make a
much smaller program - with exactly the same output! - that has the two
part structure I described here. We deduce that such a program is what
is actually responsible for the measure of the experience.
And from this we conclude that the contribution of a universe to the
measure of a conscious experience is not the universe's measure itself,
but that measure reduced by the measure of the program which outputs
that conscious experience given the universe data as input. This then
leads to the principle that a big brain in a small universe gets more of
that universe's measure; that multiple instantiations of a consciousness
within a universe mean more measure; and that fuzziness of the concept
of an instantiation is no problem because it only affects the size of
the numbers being multiplied together to get the measure contribution.
As for the question above about the Universal Dovetailer universe, it is
easily solved in this framework. The output of the UD is of essentially
no help in producing the mental state in question, because the ouput is
so enormous and we would have no idea where to look. Hence the UD does
not make a dominant contribution to mental state measure and we avoid
the paradox without any need for ad hoc rules.
Hal Finney
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Received on Wed Jun 21 2006 - 03:52:36 PDT