Georges Quenot writes:
> Considering the kind of set of equation we figure up to now,
> completely specifying our universe from them seems to require
> two additional things:
>
> 1) The specification of boundary conditions (or any other equivalent
> additional constraint.
> 2) The selection of a set of global parameters.
>
> My suggestion is that for 1), instead of specifying initial
> conditions (what might be problematic for a number of reasons),
> one could use another form of additional high level constraint
> which would be that the solution universe should be "as much as
> possible more ordered on one side than on the other". Of course,
> this rely on the possibility to give a sound sense to this, which
> implies to be able to find a canonical way to tell whether one
> solution of the set of equations in more "more ordered on one
> side than on the other" than another solution.
I think this is a valid approach, but I would put it into a larger
perspective. The program you describe, if we were to actually implement
it, would have these parts: It has a certain set of laws of physics; it
has a certain order-measuring function (perhaps equivalent to what we know
as entropy); and it has a goal of finding conditions which maximize the
difference in this function's values from one side to the other of some
data structure that it is modifying or creating, and which represents
the universe. It would not be particularly difficult to implement a
"toy" version of such a program based on some simple laws of physics, and
perhaps as you suggest our own universe might be the result of an instance
of such a program which is not all that much more large or complex.
In the context of the All Universe Principle as interpreted by
Schmidhuber, all programs exist, and all the universes that they generate
exist. This program that you describe is one of them, and the universe
that is thus generated is therefore part of the multiverse.
So to first order, there is nothing particularly surprising or
problematical in envisioning programs like this as contributing to the
multiverse, along with the perhaps more naively obvious programs which
perform sequential simulation from some initial conditions. All programs
exist, including ones which create universes in even more strange or
surprising ways than these.
By the way, Wolfram's book (wolframscience.com) does consider some
non-sequential simulations as models for simple 1- and 2-dimensional
universes. These are what he calls "Systems Based on Constraints"
discussed in his chapter 5.
Where I think your idea is especially interesting is the possibility that
the program which creates our universe via this kind of optimization
technique (maximizing the difference in complexity) might be much
shorter than a more conventional program which creates our universe
via specifying initial conditions. Shorter programs are considered
to have larger measure in the Schmidhuber model, hence it is of great
importance to discover the shortest program which generates our universe,
and if optimization rather than sequential simulation does lead to a
much shorter program, that means our universe has much higher measure
than we might have thought.
However, I don't think we can evaluate this possibility in a meaningful
way until we have a better understanding of the physics of our own
universe. I am somewhat skeptical that this particular optimization
principle is going to work, because our universe's disorder gradient is
dominated by the Big Bang's decay to heat death, and these cosmological
phenomena don't necessarily seem to require the kinds of atomic and
temporal structures that lead to observers. If you look at Tegmark's
paper
http://www.hep.upenn.edu/~max/toe.html which lists a number of the
physical-constant coincidences necessary for life, not all of them would
have cosmological importance and change the order-to-disorder gradient
of the universe.
> It might well be that this additional constraint can also be
> used for selecting the appropriate set of global parameter for
> the set of equations considered in 2). It does not seem
> counter-intuitive that the sets of global parameters that
> allows for the maximization of the gradient of order among all
> possible solutions considering all possible values for global
> parameters be precisely those for which SASs emerges and
> therefore those we see in our universe: universes not able to
> generate complex enough substructures to be self aware would
> probably equally fail to exhibit large gradients of order and
> vice versa.
Certainly an interesting suggestion. Again, when we look at the larger
view of all possible programs, we have optimization programs which
have some parameters fixed; and optimization programs which allow the
parameters to vary as part of the optimization process. The latter
programs would tend to be smaller since they don't have to store the
value of the fixed parameters; but on the other hand the need to allow
for varying the parameters may add some complexity, so it might be that
particularly simple values of parameters can be accommodated without
increasing program size.
> The hypothesis of the maximization the gradient of order seems
> even Popper-falsfiable. At least one prediction can be made:
>
> Given the set of equation that describe our universe and the
> corresponding set of global parameters, if we can find a canonical
> way to compare the relative global gradient of order within the
> universes that satisfy this set of equations:
>
> 1) It could be possible to determine the subset of universes
> that maximize the gradient for each set of global parameters
> (comparing all possible universes for a given set of global
> parameters), these being called "optimal" for this set of
> global parameters.
>
> 2) It could be possible to determine the sets of global parameters
> that maximize the gradient in an absolute way (comparing
> optimal universes for all possible sets of global parameters).
>
> The prediction is that the set of global parameter that we observe
> is one of those that maximizes the gradient of order within the
> corresponding optimal universes.
Yes, that's a good prediction, and you may be right that we could already
take some steps towards testing it. Tegmark's paper can be interpreted
as providing some such tests.
> Maybe also the constraint could be used at a third level if it
> can remain consistent as a mean to select the appropriate set of
> equations.
Yes, or at least for part of the equations. As with the case of
parameters, all different versions of such programs would exist, and
the real question is which one is shortest.
>From Wolfram's book, though, I can't escape the suspicion that no such
programs will turn out to be the shortest ones; but that there will be
some much smaller program that lacks the logic and clean division of
function that I describe above (the three parts, etc) but which still
manages to create our universe. Once we move away from sequential
simulation and start considering optimization and other more exotic
techniques, it is difficult to avoid taking the next step and considering
random programs. Wolfram's first few chapters amount to a taxonomy
of how random programs behave, and his tentative conclusion is that
a substantial fraction of them generate complex-looking structure.
It may be a leap of faith to suppose that our highly intricate and ordered
universe could be generated by some incomprehensible mess of a program,
something much smaller and tighter than any human programmer could
create or perhaps even understand. But there is some historical basis
for the idea that random programs can be more efficient in size than
human-designed ones; I recall that in one of the early Artificial Life
experiments, the original replicator carefully designed as the initial
seed soon self-improved to be even smaller than the human designer had
thought possible.
Hal Finney
Received on Sat Jan 10 2004 - 21:16:28 PST