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
