Modelling the Theory

[ianmw]

Health warning! - wild thinking ahead! (I'm not sure where to put this, but maybe this is the best place.)

I've been playing with ideas trying to develop a quasi-mathematical model to incorporate Tony's ideas. I say "quasi" because it's many years since I've done any serious mathematics, and I've very little idea where to start. My hope is that such a model might make it easier to intuit the consequences of such ideas, and to show where they need modification, if they do. This intention of this post is merely to raise questions which others far better qualified than myself may be able to answer. I must also apologise if my reasoning is less than clear, due to the need to condense many pages of sketches and thoughts.

It does seem to me that it should be possible to model any life as a set of experiences, or events, and link them to others by means of an information carrier mechanism. This eventually leads to the fairly intuitive and hardly original observation that we are all connected in some way, however small, although obviously most of the information-type connections will be at second and more remote hand. (Like the brain? Holographic?)

We can therefore consider the sum of the life-sets so defined to constitute all human history (since lives overlap), or our universe perhaps, or some such fairly broad system. However, this immediately raises the question of the stability and equilibrium of such a system. Would it be like the trusty ideal pendulum, or at least one with energy input equal to energy loss, where small disturbances are damped, and the system always returns to its original state? This would imply that any alternative universes would quickly return to the original, and could effectively be disregarded. It would also have implications for any daemonic replay, since a life unchanged would imply a completely static system (due to its connections with everything else), but changes might or might not affect the stability of the whole (even in an apparently chaotic system it seems to be the case that there are always pockets of stability at any scale). Could the system act like a fluid, stable under certain conditions, but becoming turbulent and unpredictable under others? How do the initial parameters (the Big Bang?) affect the subsequent behaviour of the system as defined - in other words not merely the physical development of the system?

Lastly - and at this point I come to a puzzled halt - if we postulate our universe (or whatever we want to call our larger system) as a point in phase space of infinite dimensions, would its path over time be fixed (assume the common understanding of time), with a distinct start and end, would it be recurrent, or would it be fractal? If it has a distinct start and end, then by definition this seems to rule out alternate universes, or daemonic replays, since the system would effectively be fixed for all time. If recurrent, this seems to have the same consequence, since a fixed or a recurrent path are equally determinate. Do the first two alternatives (fixed and recurrent) therefore illustrate a Newtonian view, and is the third (fractal) model Quantum? If fractal, which may be the only case to allow free will, what is the equivalent of the enclosing area, and how, if at all, can we conceptualise the attractor(s)?

If you don't know what I'm talking about that probably makes two of us! Otherwise any suggestions will be gratefully received.