In a previous post in reply to Hal Finnay, I have suggested the use of a particuliar case of additional conditions to the hypothetical set of equation that would rule ou universe. This is an attempt to clarify it while taking it out from the computation perspective with which it has nothing to do.

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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. This is a way to narrow down the set of solutions that offers several advantages: a) It removes the asymmetry in the choice of initial versus final (or any other combination of) conditions. b) It is consistent with boundaryless universes as proposed by Stephen Hawking for instance. c) It is able to make the flow of time appear as an emergent property instead of being postulated and built upon. d) This kind of condition is very well appropriate to select those in which SASs have chance to emerge. This condition does not seem alone enough to define a unique mathematical structure but there might be a little number of ways according to which the remaining symmetries could be canonically broken. 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. 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. A prediction with a weaker version of 2) would be that the set of global parameter that we observe must be consistent with any constraint we can obtain from the maximization constraint. It might be possible to solve problem 2) (finding the optimal sets of global parameter or some constraints on them) from high level considerations without being able to solve problem 1) finding the corresponding optimal universes. 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. Finally, the hypothesis of the maximization of the gradient of order within universes could offer the additional advanatges: e) It does not involve any arbitrary parameter. f) It might help not to require that a choice be arbitrarily made within an infinite set. Do all of this make sense ? Has it already been considered ? Georges Quénot.