The blue image is one trajaectory of the Lorenz system with (σ, ρ, β) = (10, 28, 8/3) started from the initial point (0, 0, 1). The yellow image is for the same parameters but a different initial condition, (0, 0, 1+ε) where ε = 10-5.
While it is true that you can understand the effects on macroscale, the micro dynamics is still somewhat of a issue in our determinations?
At best, a new computerer with the ability to imput extraodinary amounts of data for a model prediction, yet there is no method to detail where all microdynamic processes will lead to other then to assume it on a classical level?
I would like to think such encapsulation would have found value in as much as we move our understanding of macrosate happenings from quantum dynamcial ones, as well?
So Thales has to arise with some basic priniple? How you map this, is important.
He recorded: ‘Thales says that it is water’. ‘it’ is the nature, the archê, the originating principle.
Almost as important, as understanding the basis of discrete things, could manifest, “from other states of existance“?
Symmetry breaking realizations understand well that such a process is revealled from other phases of existance?
This is a Crucible. This is the standard model? Beyond it is the existance of dynamical world that is but one more phase transiton realized from the point symmetrical breaks into manifestation of universes, galaxies worlds, as concrete things?
Ancient alchemist understood it’s significance.
Processes hidden in Platonic forms, might have been of value assigned to astrological processes, while this process, could also exist in the human form, for perfection.
So the mentality, although couched in the alchemist view and widely encompassing, understood that such a crucible would have held the alchemist to a process of refinement. Usng water, as a example in this process was significant, in that the states of matter could have “other forms” in it’s expression where such “solidifications” held to discrete forms.
Kaluza and Klein’s thinking was a bit beyond the normal fourth dimensional realizations. Yet could have baez said this is the way of God. Why invoke, when it is a natural part of our existence to wonder, and what value assign to concrete things? meantal or otherwise in the discrete nature of things?