I found this both aesthetically objectionable and logically dishonest. I figured this was just their way of giving up without having to say so: to turn hard messy problems into flimsy but easy cartoon ones. But surely not. Surely, they being so much smarter and well informed than I, had good reason to resort to these tricks. They understood that those inconvenient portions of equations really didn't make that much of a difference, right?
Well, the minute I had access to the clunky mainframe computers of the time, coded up a lot of these systems of nonlinear equations as recursive functions, set them to running under various initial values, and seeing wildly different results from one run to the next, I realized that this was all bullshit. That pesky little nonlinear factor? That x squared? Or that x times y? It made all the difference in the world. This was years before the whole discipline was called Chaos Theory, but obviously that was what was going on there.
The deal with Chaos Theory, put in one sentence is that a completely deterministic process turns out to be wildly affected by just the smallest numerical change in your starting variable. You've heard of the Butterfly Effect, the idea that a butterfly flapping an errant wing in Brazil causes a hurricane in Texas? Well, that's the dumb media version. The actual interpretation is something more profound, that an equation with no surprises whatsoever, that runs like clockwork, can give you something completely different every time, with just the tiniest of nudges at the start. It's rather like finding a jewel knocked from the helmet of Satan in a battle fought with God at the dawn of time. Rerun the whole thing, and that jewel is sometimes a diamond, others a sapphire.
So, that thing called Fate? That thing called Destiny? Even in a clockwork universe, both are utter fictions. Delusional Fantasy. It shouldn't come as a surprise, given that the universe is a complex open system with many overlapping and interdependent factors.
Invariably, a peranoscope viewer will be tempted to examine all possible outcomes of his or her own existence. I advise against it.
The most disconcerting aspect of such an investigation is not the fact that your existence makes up just a tiny (and by tiny I mean tiny, like, not even a bug smear on the windshield of life, not even a greasy little paramecium smear on said windshield) little spot of all, on average 10500, possible worlds. Given all the absurd events that could have occurred over the past 13.5 billion years, it's a wonder that you and I are here at all. And the creepiest thing isn't that so many possibilities in our lives end up being coin-flip moments, moments that we agonized over and then it turned out that epic decision made spit for a difference. And it wasn't the Hairy Eyeball Effect - the feeling that, as you view all possible worlds through the peranoscope, you in turn are being viewed, which makes you squirm self-consciously and in turn makes you feel the discomfort of phantoms as they squirm self-consciously, all of it rippling through the quantum foam, and all embarrassed by existence itself. Nor is the creepiest thing finding just how little control you have over your life, how chance and contingency make nearly 99.99999% of everything that happens.
No the absolute creepiest thing is, that very large but finite number of universes with the Earth, and the Sun, and our galaxy, and us in them, that small cross-section of all possible worlds where we exist, our existential étendue can almost be seen, if you squint hard enough, to be visibly shrinking.
I figure we cease to exist an average of 1.8 universes per hour.
All of us, dreaming of the past, or living the present, or in anticipation of living in the next civilization after this one, wink out on a regular and, it seems, accelerating basis. Except for the Convergence. That ensemble of universes where we all of us continue to exist seems to be stable and linearly unchanging.
But I could be wrong.