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.

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

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.

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