David Cowles
Oct 15, 2024
“Achilles is still sulking, humiliated by a…tortoise; but at least we have a universe and…we can be assured that its ultimate trajectory is toward Good.”
You know the story of the famous tortoise who beat the great Achilles in a road race, and you may have heard about the arrow that remains suspended in mid-air over Athens, but you may not know about Zeno’s latest paradox. Here’s how it came about:
One day Zeno of Elea and I were reclining on freshly mowed grass in the shade of a eucalyptus tree. Then Zeno had one of his bright ideas. (That’s when you knew that you could be in trouble. Another day without lunch!)
“Let’s build a universe,” Zeno began. Zeno didn’t suffer from false humility.
Naively I replied, half napping, “What will we use for materials?”
“Our minds, of course, dear boy, our minds.” How foolish of me! BTW, he always called me ‘dear boy’ even though I was many years his senior.
“Let’s make it a good universe,” he said. “Let’s fill it with variety and intensity. Everything’ll be a ‘happening’, an event. Let’s have people in this world, let’s give them freedom to do as they will but let’s make sure they’re aware of themselves and their surroundings at all times. And we’ll fill the world with other living things and with enduring objects to boot.”
“Sounds good, Zeno,” I muttered as soon as I heard him pause for air; but he paused longer. I hate his pauses. Hope that he’s not working up another one of his famous paradoxes…but prepare to be disappointed.
Finally, he broke the silence: “This won’t work!”
Wait for it! Will he let it drop? Or will I, by which I mean you, have to listen to a long, boring lecture explaining just exactly why it won’t work – as if anybody cared.
“There’s no incentive, we’re missing motivation!” Yup, we be doomed! “Why would a world like this ever will itself to be? Why would any event ever happen?”
“I dunno, Zeno, why not create an incentive? Give events a reason to happen, like a reward or something… something ‘good’.”
“That’s it! The ‘Good’. I’ll add goodness to my world. Everyone prefers what’s better over what’s worse. So that will work. Thank you.”
Another pregnant pause. The rabbits stop hopping, the birds stop chirping, the meadow is in a state of suspended animation. “No it won’t; it won’t work!”
“My friend,” Zeno began in an avuncular tone inconsistent with his youth, “In the real world, things do not follow straight lines. If I build Good into the world, like I did gravity, events in my world will naturally tend toward the Good so my World Line will have (-y/x) as its overall slope. But that slope will not be uniform. It will be more steeply negative (‘negative’ is a positive thing in this context, i.e. closer to Good) over some intervals, less so over others.
“At some point(s) along the way, my World Line will arrive at a ‘local minimum’, a point from which all slopes are positive, i.e. uphill. To continue, my World Line would have to move away from the Good and that is not possible in my model.
“Nothing can ever freely elect to move in any direction other than toward the Good (∞, є). All events must bring the world closer to the Good. Therefore, no event with a positive slope is possible. But my model inevitably includes such pseudo-events; therefore my model is defective. It won’t work.”
Ever the optimist, I venture, “So, it doesn’t work all the time, so what? It works most of time; isn’t that good enough?”
I’ve never seen Zeno more exasperated…and I’ve seen him exasperated many times, often with me, sometimes with other muggles. (Yup, there were ‘muggles’ even then, in the 5th century BCE.)
“After all our time together, do you still not understand?” His Jesus’ complex was kicking in, 400 years before the Nativity. Some Advent!
“Real numbers are continuous. 2 is ½ of 4, 1 is ½ of 2. Every interval on the Real Number Line (RNL) is a fractal of every other interval. So if there is even one point where the World Line can assume a positive slope, then any point on the World Line is potentially ‘slope-positive’.
“Yes, it works most of the time, but we can’t know when it’s working and when it isn’t so it’s useless. Wherever slope > 0, my world ends; and if my world ends, it is as if it never began in the first place. Simply put: ‘It is not.’ But slope may be greater than 0 at any point on my trajectory. Therefore, since my world can ‘not exist’…it cannot exist.”
This reminds me of the time many centuries later when my best friend’s family got the first TV in our neighborhood. Of course, I ran over to his house. We stared at the screen forever. Hmm, not much happening. “Is it turned on,” I ventured. “I don’t know,” he replied, “It always looks like this.”
All of Zeno’s paradoxes take a similar form: “Either Real Number Theory and therefore the rules of arithmetic are wrong, or there is no world as we know it. But of course, there is a world, and it is as we know it (Descartes meets Wittgenstein), so arithmetic must be invalid.”
What’s going on here? My Life Ball is rolling along the World Line, heading toward the Good. Suddenly, I hit a randomly occurring dip and enter a ‘local minimum’. My next step, in any direction, is ‘up’; it requires me to invest energy to overcome the gravity-like attraction of the Good. But that’s impossible according to my model. Therefore, the world as we know it is impossible,,,but the corollaries are even worse:
Any world similar to the world we know is impossible if it allows even a single quantum of ‘anti-good’, a single point, t, where y/x > 0, a positive slope.
A world in which there could be even a single quantum of ‘anti-good’ is impaled on the horns of Manichean, gnostic dualism.
Any possible world, including our world and all worlds like our world, must uniformly tend toward Good. But that does not seem consistent with experience.
Even Augustine, who did not believe in the existence of evil per se, did not insist that every moment, t, be uniformly good.
Therefore, the world as we know it can’t be a real world; it must be some sort of grand illusion.
So we’ve gone from trying to create a World to realizing that no World can exist. “This is a fine mess you’ve got us into,” Zeno.
Surprisingly though, there is a way out (though Zeno might not have realized it); it’s called Quantum Mechanics (c. 1920 CE). Was Zeno 2,500 years smarter than Bohr & Co.? Maybe, maybe not; either way, here’s how it works:
My Life Ball is rolling uniformly along the World Line, tending constantly in the direction of the Good. Then I hit a randomly occurring ‘pot hole’. My negative slope suddenly goes ‘super-negative’ and now I will need to travel on a positive slope to get back up to my World Line.
According to classical physics, this is impossible. I have fallen into an ‘energy sink’, a spot where potential energy is minimized, aka a ‘local minimum’. Any next step must be ‘up’, but it can’t be because there is no ‘up’ in my world…according to classical physics.
But in a quantum world, my Life Ball has a positive probability of being anywhere in its universe. So when my Life Ball seems to fall into a local energy sink, there is in fact a finite probability that that ball is not located in this cul-de-sac at all; it may still be on the World Line, or even above it.
Of course, the probability is miniscule but that’s irrelevant. According to the Many Worlds Interpretation of QM, every event with a non-zero probability does happen…in some universe. Therefore, at any time, t, there is a finite probability that my Life Ball will be on or above the World Line. Therefore, there always exists an extension of the universe as I know it that conforms to my model.
Athens still trembles under the threat of Zeno’s suspended arrow, and Achilles is still sulking, humiliated by a lazy good for nothing tortoise; but at least we have a universe and it’s the universe we know and love. And, all evidence to the contrary, we can be assured that it’s ultimate trajectory is toward Good.
David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at dtc@gc3incorporated.com
ress, Literary Journal Spring 2023.
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