[ 16/April/21 Time:
What is the nature of your definition of time:
Time is a necessary pre condition for the existence of complexity.
Time is that aspect of a system that delivers some probability of a system transitioning from one state to another state.
Without any sort of phase transition, then there can be no change.
Without a differential in the probability of a transition happening in one direction rather than another, there can be no complexity.
Time is what results from such asymmetry in phase transition matrices at any and all levels of complexity.
By the time you build enough levels of complexity to sustain a human level awareness, then time is necessarily deeply embodied in all the degrees of causality (state sequence relationship) present in such systems.
In a purely logical sense, time is necessary for the existence of complexity.
When one looks deeply at the evidence for relativity, time does in fact appear to be local, and to be mediated by light like quanta. And that is a deeply complex topic that demands the use of non-binary logic and fundamental uncertainty.
[Followed by – 19/4/21]
It seems clear to me that all complexity requires time to exist, so in that sense alone, of being a necessary pre-condition, then a proposition could be said to bear or embody time.
If there were no asymmetry in system state transitions, if every state were equally likely to go one way or another, then there could be no “arrow of time”, everything would be a simple mass of sub-atomic soup at some equilibrium temperature.
The arrow of time seems to result from such asymmetries.
It is easy to tell the film is running backwards if you see a mess of egg shell and mixed liquid suddenly assemble into a yolk sac then be surrounded by albumin then have the shell fragments assemble into an eggshell as they fly together and upwards. Such events are so improbable as to likely never have occurred anywhere in the history of the universe as we know it. The process of assembling an egg is much slower, much more complex, and very dependent on a large series of contexts involving multiple levels of chemistry and behaviour.
It seems clear to me that most interest in modelling happens in the phase transition matrices. How does a system change states?
If Garret Lissi is correct in his conjectures, that the phase transitions of the simplest structures known to quantum mechanics are some function of the geometry of most complex symmetry known to mathematics (the E8 Lie group), then it is a form of “simplest” that is not what most people would consider “simple” – even though it certainly has a degree of “elegance”.
Complexity demands time, and it demands directionality in time.
We are complex, and could only possibly exist in a universe that does in fact have such properties (or something reasonably approximating them at certain scales).