Monday, June 26, 2017

Infinities, Eternities, And Free Will: A Belated Rumination

     Dystopic’s recent piece on fate has caused me to revisit several questions that have baffled theologians and philosophers for millennia. The confusion of those earlier thinkers was understandable: they approached questions about the nature of God, His relation to Creation, and the destiny of the human soul from the vantage of a time-bound creature. However, as with all inquiries into matters beyond the reach of human senses and the extent of human intellect, the postulates make all the difference. Those baffled thinkers started from a premise that guaranteed that they’d never escape the maze they’d entered.

     Among the reasons I write fiction is that I can “put words in the mouths” of my protagonist characters: convictions and sentiments that might seem inappropriate coming from me. As my protagonists are usually several hundred percent larger than life, the trick makes them more persuasive than they’d otherwise be. Yet they’re still my words – my conjectures and reasoning – and it’s only proper that I stand behind them.

     Besides, this is some of the most intellectually exciting material ever entertained by a human mind. So let’s get excited! (To the Balmer level, at least.)

     “I never really got that part,” Christine said.
     Ray nodded. “Understandably so. It seems paradoxical. I don’t really think we’re expected to ‘get’ it. Just accept it on the evidence.”
     The room had grown dim. It had gotten quite late, but neither Ray nor Christine was in any hurry to conclude their chat.
     “What makes it hard for most people,” Ray said, “is that we tend to think of God as just a very powerful temporal entity, like some sort of super-magician. But He’s not. He created time. He looks down on it from above, the way you or I would read a map. He knows the path we follow because He knows all the paths we might follow, and what might flow from every one of them.” He sat back and reflected for a moment. “So our time-dependent language about ‘choosing’ and ‘knowing’ gets us into trouble when we try to apply it to God.”

     [From Shadow Of A Sword]

     Yes, that’s me expressing a personal conviction through a character – a Catholic priest, at that – that I could never, ever “prove:” that our wills are free and our choices are unconstrained by anything but the laws of physics. It arises from postulates about the Supreme Being that I regard as most plausible:

  1. That God exists;
  2. That all we sense or experience (and possibly a whole lot more) is His deliberate creation, including time;
  3. That He stands outside it all, capable of viewing it “from above.”

     A time-bound mentality has a great deal of difficulty coping with the implications of those assumptions. We’re not equipped for it. That can cause us to overlook the possibility of the assumptions themselves. But without them, we strain to cope with the paradox of human free will versus the existence of an omniscient Creator. We start pondering “fate:” more specifically, whether we’re predestined to make the choices we make. And we find ourselves trapped in an inescapable maze.

     In other words, the postulates, whether we accept them or not, predetermine the success or failure of our attempts to find a satisfactory explanation.

     Despite the human mind’s difficulties at coping with infinities and eternities, the concepts are critically important to several fields. We deal with irrational and transcendental numbers, which cannot be expressed in a finite number of digits. We deal with a variety of number systems, each of which has an infinite number of elements. We conceive of “space” itself as being infinite in extent. Moreover, we silently assume that “space” – i.e., nothingness – will “exist” forever.

     An exercise familiar to physics students nicely illustrates the utility of infinity. Imagine yourself floating motionless in space, looking at a perfectly flat, featureless plane infinitely long and wide. How would you determine your distance from that plane?

     You couldn’t. Even if you were to set yourself into motion, you wouldn’t be able to do it. Without features whose perceived size would change as you move, you’d have no way to do so. By postulate, the plane itself is infinite in extent, so you wouldn’t be able to judge by the perceived motion of its edges; it doesn’t have any.

     Important exercises in calculus ask us to evaluate the limit of an algebraic expression as its dominant variable goes to infinity, and the numerical values of integrals that range over infinity. It’s possible even though the mind can’t really cope with anything that’s unbounded in extent.

     Cosmologists struggle to cope with the phenomenon of unidirectional entropy vis-a-vis unidirectional gravity. Their speculations are temporally unbounded: they deal comfortably – well, more or less – with the problems of black hole formation versus quantum evaporation: Those phenomena imply the possibility of an alternation between an ever-expanding, featureless sea of radiation and a Big Bang-style monobloc that gives birth to a “new” alternation that repeats eternally.

     Unbounded things appear to be as important to human conjectures about “reality” – a word I like almost as much as “should” – as they are to our conceptions of God.

     Contemporary physics has begun, tentatively and with much trepidation, to toy with the theoretical possibility of the “multiverse:” an expanded conception of existence that includes “universes” that are separated from one another by differences in the “fundamental constants” that define their physical laws. Some exceptionally daring thinkers are exploring the possibility that the “fundamental constants” aren’t constant at all. I exploited that concept in Freedom’s Scion:

     “The experimental results from our test crystal are consistent with a fifteen percent increase in the speed of light.” Althea grinned again. “That’s fifteen percent over the speed of light in a vacuum.”
     A gasp circled the group.
     “What can you do with that?” Teodor asked.
     “With that alone? Not much. But that’s just from the power we have from one eighteen-century-old fission reactor that spends most of its juice keeping us alive up here. If my equations are sound, with a terawatt of power I can get raw space to accept passage at approximately Michelson eighty. Give me a terawatt more, and I can drag a fifty-ton mass up to that speed in about two months.” She pulled a mock innocent face. “Hope to Earth in four months or a little better. That fast enough for you?”
     She swept her eyes over the stunned guests.
     “Rothbard, Rand, and Ringer,” Valerie breathed. “You actually did it.”
     Althea nodded. “We think so, Mom.”
     “Wait a moment,” her mother said. “What about reaction mass?”
     “Don’t need it.”
     “How, then?”
     “Basically, the same technique that allows me to increase the speed of light,” Althea said. “Alteration of the permittivity constant, applied differentially—a front-to-back gradient—over an ovoid volume enclosing the mass to be propelled. A properly distributed effusion of gamma rays and W-plus bosons is all it takes to get the process started. Put a negative charge on the outer surface of the vessel, and you're off. That gives you a reactionless drive and the next best thing to perpetual motion. Only works in a hard vacuum, though, so don't expect to use it for anything groundside.”
     The genesmith appeared near to apoplexy. “You altered a fundamental constant of physics?”
     Althea nodded again. “Should I have asked permission first?” She grinned. “I had to, Granduncle. The only way to breach what we call the lightspeed barrier is to alter the conditions that determine lightspeed. The only way to do that is to increase the permittivity of the vacuum. And the only possibility of doing that lay in Althea's Axiom.”
     “Which is?”

     Yes, it’s speculation – but it’s speculation that illustrates the utility of conceptions about infinity and eternity to our inherently limited minds. In our universe, the Planck Constant is terribly small: about 6.63 x 10-34 Joule-seconds. Its tininess allows us to employ a cause-and-effect-based physics at macroscopic scale. But imagine a universe whose Planck Constant is a whole Joule-second! Causality would appear to reign only at scales so incredibly large that the behavior of objects as large as stars and planets would appear indeterminate. Life of our sort could never exist there.

     If it “exists” – whatever that word “really” means – the Lord God made it all.

     Yes, these are the sort of things I think about when I have time for the “longest thoughts:” the ones that trail off into infinity, that can’t reach a firm conclusion on this side of the veil of Time. They’re among my reasons for looking forward to the afterlife...assuming (of course) that there is one, that it won’t be awful, and that God will deign to answer a few questions in His free moments.

     Max Born once said that he had two questions for God:

  1. Why relativity?
  2. Why turbulence?

     As that great mind has gone to his reward, I hope the Almighty has gratified his curiosity...and that when my time comes, He’ll deign to gratify mine, should I have the opportunity to ask Him about the subjects addressed above. But should He be willing to help me with those, I must admit that I’ll have another: “Lord, why the Boston Red Sox?

     Jesus said to the Twelve, “Fear no one. Nothing is concealed that will not be revealed. What I say to you in the darkness, speak in the light; what you hear whispered, proclaim on the housetops. And do not be afraid of those who kill the body but cannot kill the soul; rather, be afraid of the one who can destroy both body and soul in Gehenna.” [Matthew 10:26-28]

     May God bless and keep you all!


Cordolf said...

Terrific stuff as usual, Francis!

I was unfamiliar with the Balmer levels you were referring to, but was happy to be educated.

When I had first read your note, I mistakenly thought you were referring to the "Ballmer level" of excitement instead.

JWM said...

The last series of posts have kept me up night thinking. I've read through Dystopic's post a couple times also: Anger, Fear, Guilt, and now (thankfully) Awe at the limits of what we can know. You have addressed these issues in the macro- large cracks forming under the foundations of Western Civilization, and I, at least, have responded in the micro-I've taken yet another look at the frustration, and subsequent rage as the effects of this mass idiocy impinge on my daily life. It comes down to the question of meaning. You see everything going to hell in a handbasket, and what can any of us actually do? It does no good to be just one more old man angry with the world. One must do *something*. But what? Your answer is to write, to keep these ideas circulating though the minds of others, letting those of us in the blue-state ideological ghetto know that there are like minded folks out there. And as I sit watching the cursor blink- this thought comes wingin' into my head (coffee!). Remember the old sci-fi movie, "The Incredible Shrinking Man?" At the end, when the hero shrinks away into the infinitesimal, his final epiphany is realizing that to God, he still exists. He still matters. That is the perspective that becomes so difficult to maintain.