Post number 33 of 33 in The Ganymede Progression.

This is the final exercise in the progression, and tellingly it asks me to examine patterns. Why study the Force? Why examine that which is chaotic, as the chaotic nature of the thing makes it virtually impossible to predict and practically unlikely that the fruits of our labours will produce lasting change? That’s what chaotic means, right? Luck? Only being able to trace causation after the fact?

The reason that’s not the case is that even massively chaotic systems show patterns. I’m going to talk a little bit about fractals and a little about strange attractors. Here’s a definition of the latter:


strange attractor
noun MATHEMATICS
an equation or fractal set representing a complex pattern of behaviour in a chaotic system.

Strange attractors are elements, subsystems within chaotically large systems which, whilst not really “predictable” to a classical degree, still give us a working model of the likely state of things. They are the limits of the chaos, perhaps. For example we might not be able to say Bob is in his seat, but we may be able to reasonably, heuristically (an important concept which I touched on long ago), assume he is in the office. This is a massive oversimplification but it gives the general idea – plot the path a person takes 50 times, they’re unlikely to set foot in the same atomically precise place even once, but we get a consistent pattern that they moved from roughly point A, to roughly point B. The chaos of them doing so has predictable constraints. Bob is unlikely to be 15 feet outside the 3rd floor window (unless it was a really bad day).

The universe does this, too. We call these roughly predictable patterns “strange attractors”. Things are attracted to certain courses and certain trends of behaviour. Once we realise this, we learn that the system in question is complex, that is, very very hard to predict with meaningful accuracy. But it is not random, nor is it so chaotic as to be entirely unpredictable.

This is a model of a strange attractor:

Strange+Attractor

There is a pattern above. There is a lot of “blank space” and a lot of coloured space. The “results” form the coloured space, and the blank space is therefore fairly predictable. It’s not a line chart, not a simple two-dimensional map of probability. But it shows a trend, a disposition (this is an important concept); a pattern.

What we learn about the Force is similarly rooted in strange attraction. We learn the dispositional facts of the universe, and of our interactions with things, and with others. We learn the “basic principles”. Sure, when people try and pin us down to this or to that, we may err. We may not know if we are on the upswing or the down-stroke, the in or the out, the draw or the release. We may learn to predict these things and recognise them, however, and we may learn to accept and understand their limitations. We can learn the rules of the game, even if we can’t predict the actions of every player well enough to win a bet on the superbowl.

Moving on to fractals:

fractal
noun MATHEMATICS
a curve or geometrical figure, each part of which has the same statistical character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation.

Fractals are complex and definitions vary, but the essential principle is that they describe elements where the very smallest aspect of the system mirrors the very largest. This macro/microcosmic symmetry is inherent in strange attractors, too. Strange attractors and fractals are intimately linked.

 

The strange attractor at the heart of this is not a simple thing. For instance, the moon orbits the earth, and the earth orbits the sun. These orbits are regular and predictable, round things going in round orbits around other round things, with limited interference from other strong external forces. But bouncing a tennis ball on a pebbly beach introduces a huge number of variables. The round thing is affected by many semi-round things, by gravity, by angles and winds and shapes and the whole thing becomes chaotic and unpredictable. That’s not to say we wouldn’t see a trend, if we bounced the ball roughly the same way a million times.

Now. Fractals are like the pebbly beach. They have something non-simple at their heart (the strange attractor), but that doesn’t mean they are chaotic. They aren’t. They are deterministic and to an extent, therefore, predictable. And, crucially, they are symmetrical. What’s true for the wider system is true for the subsystem, down to the tiniest, finest-grained level imaginable.

Whew. Still with me?

Jedi are tiny, tiny specks in the vast expanse of the wider Force. They are crystallisations of the whole, in a specific space and time, for a while. Grains of sand on a beach as wide as time itself They live and die, much as the universe lives and dies. They face the pressures of change and stagnation, of push and pull, in and out, yin and yang. They change, they grow, they meet entropy and then they pass on into a new form. “What’s good for the goose is good for the gander”. “As above, so below”. What is true of the whole is also true for part. Each tree models a leaf, each leaf models a tree.

By learning about ourselves, we understand the Force.
By learning about the Force, we come to know ourselves.

This concludes this Progression.

Thank you for reading, and may the Force be with you, always.