Tuesday, 12 October 2010
The world is finite. The chaotic process that spawned the universe has an end.
R.D. Smith's assertion
"A quantised space, however large, is effectively finite thus cannot provide for truly chaotic behaviour."
in 'Social Structures and Chaos Theory', article in Sociological Research Online, paragraph 3.10, stands.
What refers to continuous,
"In its most precise rendering chaos can only arise when the possibility of any given state repeating itself is potentially zero."
drawn out of the necessity of '.. any given state repeating itself is potentially zero' and ..
".. a situation in which the orbital pathway of a flow or flux can continue for an indefinitely long period of time (for eternity) without ever passing through the same point twice."
.. despite the flow been allowed to 'run for an eternity'. It should 'never pass through the same point twice'. Continuity, put down as a prerequisite for the flow to be chaotic, a flow that requires to have no end, and such an end is met at the boundaries of the very universe itself. Phase space meets its limits at the realm of quanta. That puts another twist to the saga of chaos.
The continuity of the chaotic process it is not possible, the space within which it flows is finite even though its boundaries are as enormous as the universe itself is. It is not that this enormous space is quantised which as such it makes the duration of the flow even more immensely enormous, so if it takes an eternity, by being quantised it takes double or many times that eternity but still it is finite as the boundaries of the universe are finite.
And to speak of it, the boundaries of the universe are continuously expanding that augments the space available but still it is finite even if, for a given time, but for any given time, no matter how this interval of time can be comprehended, it is still finite. To what this conclusion points to, is that for a chaotic process, or the chaotic process of the universe is not continuous. There is an end to the chaos that created this very universe. At some point there will be no more space to explore, or even a situation where the chaotic process is catching up with the expansion of the universe itself.
And to add to that, is the current phase space, which according to the account of ever diminishing phase space, as the phase space opens up, explored via the chaos-induced bifurcations, out of the pre-existing phase space, within the space that the creation of attractors has already drawn, their ultimate space available what lies deeper down to the microscales, the world of quanta, excluding from what lies out of the attractors already created, the worlds, the universe that could have been, if at a certain bifurcation in its past a different choice has been made, as by, a different cosmological constant had been chosen.