Free Will .AND. Predestination

I've been thinking since mid-2012, a BLOG hiatus if you will, just not posting about it. I hate to just say something when I don't have anything _interesting_. But this particular musing I'm posting today, I've had before; perhaps it's time to air it, to see if the posting spurs new points of view.

This will not be your usual, tired posting about a subject that goes back at least centuries (John Calvin), perhaps millenia (Saint Augustine?). This is a different slant, spurred into recollection by listening to Beethovan's 4th Symphony on WKAR this morning.

When Beethovan wrote the 4th, he was free to start it on any pitch, duration, chord, whatever, that he wanted. By the time he got to the end, he had almost no freedom at all; an arbitrary note would have been discordant. Similarly, when the author starts a fictional story, it's a "blank sheet of paper". S/he can start anywhere, and go anywhere else. The author's task is to tell a pack of lies, and make the reader like it; suspension of disbelief is accepted, but not internal contradictions. But as the story progresses, the degrees of freedom for the narrative narrow; there are more and more things to not contradict. By the end, there's very little literary (or musical) freedom left.

Life is like that, too. When I was young, my options seemed unlimited. As I made decisions (or didn't...), as I committed myself to a path, to my "life trajectory", other options were lost in the past. Now that I'm old, I seem to have very few ones left. Soon, there will be only one. I'm not there yet, but I can see this all too clearly.

One of the most amazing things about this Big Place where we live, is that it's comprehensible, that we mere humans can come to understand the cosmos. Our gestalt is by no means complete; we're constantly learning, ever expanding our species knowledge. But that we can at all.... And the best tool that I know for this is mathematics. Here are three easy steps:

• Algebra, the use of symbols with rules for manipulation, goes 'way back, is of Arabic origin, multiple fathers, and centuries before the Renaissance. Almost everything in mathematics is expressed with algebra; it's hard to overstate the importance of this "general solution".
• Calculus (roughly, the instantaneous slope of a function, and separately, the area underneath a curve, co-discovered by Newton & Leibnitz) depended upon analytical geometry (the equivalence of algebraic functions and graphical 2-D curves, Descartes); all three were invented during the Seventeenth Century. Suddenly change was comprehensible, and predictable. That last bit is the key I want to maintain here.
• Quantum mechanics is a Twentieth Century invention, but it's a mathematics quite unlike calculus. Its conclusions are useful mainly in The Land of the Very Small, are probabilistic rather than deterministic, and are supremely accurate. However, there's a crucial departure from the "model" presented by calculus, and that's..., the model. Both predict future behavior; however, calculus gives us a mental model, "explains" the universe. Quantum mechanics does no such thing; there's no model, no comprehension, no understanding, just prediction unsurpassed. Indeed, when pitted against Einstein's General Relativity, QM wins (at least this is my interpretation of Bell Theorem experiments). I suspect that we'll be generations getting around this failure-to-model, understanding "what's it all about".

So back to my initial point, that options narrow as the story / symphony / life progresses. I've never even seen this mentioned elsewhere, let alone analyzed. Is there a mathematics for this, perhaps the Mathematics of Converging Trajectories? Well, the best I can say is, "not yet". For the aging process, that's easy, that's entropy. But this..., I don't think so.