The Curse of Immortality

This essay is dedicated to my grandson, Owen Rotondi, whose insights

about the nature of time led me to these ideas.

It is fashionable these days to criticize Zeno (5th century BCE) and to make fun of his famous paradoxes. But not to worry: This has been going on for 2400 years and we’re in good company; Plato himself was among the first.

Every generation of philosophers and mathematicians has conducted its own assault on Zeno’s Castle. After all, there is no way a tortoise can beat Achilles in a road race; there is no way that an arrow shot into the air can remain resting on its bow string. Something has to be wrong; but what?

At the beginning of the 17th century two unrelated mathematicians (Newton and Leibniz) simultaneously ‘demolished Zeno once and for all’ when they discovered, independently, the Calculus.

Well, not quite! It took none other than Bertrand Russell 200 years later to point out that Zeno’s castle still stands, as impregnable as ever, undamaged by the Enlightenment’s assault.

Flashback: I spent a year of my life in a cold sweat. I had just realized that death is not something that any of us will ever experience. Of course, we may all be dead…but you’ll never know it because ‘death’ is defined as the absence of all awareness (consciousness). You cannot be aware of being

dead.

I reasoned, “If I don’t die, subjectively, then I must live, also subjectively, forever.” Sounds cool, but let me assure you, it’s anything but! The me that lives forever will not be me at the time of my greatest triumphs or at my one moment of clairvoyant lucidity; it will not be me “when I ruled the world.” (Coldplay) The me that lives forever will be me as I am during the final conscious moment of my life.

Before Vatican II, Roman Catholics used to pray for ‘the grace of a happy death’. Appropriately so! Today, Catholics still entreat the Mother of God, “Pray for us…at the hour (i.e. moment) of our death.”

Objectively, of course, I do not really expect to live forever. I expect to die just like everyone else (and too soon). But what if, subjectively, I never die? And what if it is the final moment of my life, the pain, the confusion, the regret, the despair, the fear that endures forever in my consciousness?

This universal fate is literally ‘Hell’ as it was preached in some churches before Vatican II. Suddenly, I’m back in 2nd grade, hearing for the first time about the flaming Inferno, the stench of rotting flesh and brimstone, the shrieks of the damned and the cacophony of Bedlam.

My life can’t end; what would come next? I cannot imagine myself not being. Once born, I can never die…to myself. I approach death, but as a limit, not as a destination. Just as Achilles is forever racing toward, but never reaching, Zeno’s finish line, so I may be hurtling toward my death, every instant ever closer, forever. 

Over a Sunday feast of pulled pork, sauteed field greens and corn on the cob, Owen pointed out to me that my existential problem was simply a new version of Zeno’s famous paradox.

I had not yet thought to connect my own fear of dying with Achilles’ fear of humiliation at the hands of Zeno and his pet reptile. Owen made the connection for me…and an eschatological cloud was lifted.

Zeno’s paradox cannot be resolved using Arithmetic (including calculus) and the set of Real Numbers…despite 2400 years of trying. Real Numbers are ‘dense’, i.e. continuous; between any two Real Numbers there is at least one other Real Number. Every interval is continuous.

There is, however, a very simple, and as far as I know uncontested, solution to Zeno’s Paradoxes! But it requires us to throw Arithmetic and the set of Real Numbers out the window…or at least to put them on a shelf. And no, I’m not just reading from some naively  hopeful 4th grader’s Christmas letter to Santa.

Suppose instead we approach Zeno’s dilemma assuming that the number line is not continuous but made up of a sequence of discrete units. Let’s further suppose that this set of Discrete Numbers, and the new math it inspires, adequately models the real, physical world, i.e. Zeno’s race track.

No matter how small we make the distance between these units, there will come a point at which the Tortoise will run out of runway; it will no longer be possible to cover half the distance to finish line because ‘halfway to the finish line’ would put him right in the middle of the abyss of non-being. 

Our contestants will reach the brink of annihilation and at that moment, in a ‘quantum leap’, Achilles will find himself across the line…at last. The introduction of discrete gaps, no matter how tiny, immediately resolves Zeno’s paradox and makes arithmetic linear again. 

Great, but how can we justify such a move? Real Numbers are called ‘real numbers’ because they’re supposed to be real, right? How can we justify pulling a set of Discrete Numbers out of thin air?

If we have to use Unreal Numbers to force the result we want, then Achilles is an unreal champion…which might be worse than simply losing. Better to be humiliated by a tortoise than to go down in history as a cheat!

But Achilles is no cheat! It turns out that the physical world in Athens and in New York, on Alpha Centauri and beyond, is discrete. In fact, only ‘discrete math’ (e.g. binary computer language) can adequately model real events. Achilles runs his race and collects his trophy; let everyone hold their peace.

We now know, or think we know, that spacetime is made up of very tiny discrete units. How tiny are they? About 10^-35 meters across? We call this the Planck Scale. And how small is that? It’s about 20 orders of magnitude smaller than a proton. So small!

Try this: the ratio of the observable universe to your slim and trim body is the same as the ratio of a hydrogen atom to the Planck length. So very, very small, like you, but big enough!

Turns out, size doesn’t matter at all! Regardless of how small we make the unit of discontinuity, the gap between numbers, the possibility of infinite regression immediately disappears and Zeno’s paradox is resolved.

So we will die both objectively and subjectively in ‘ordinary (linear) time’. Now, thanks to Owen, I can smugly dust off an iconic slogan from my preteen years: “What, me worry?” (Alfred E. Newman, Mad Magazine)

Now we just need to be sure some hot shot physicist doesn’t come along to prove Planck wrong. But I’m no longer losing sleep! We have invoked the aid of Mater Dei (‘now and at the hour of our death’) and we’re told her

intervention never fails.

Plus the great Achiiles has never lost a road race. Even Usain Bolt could not keep up. Rumor has it, though it is unconfirmed, that Achilles ran a 3.9 40 at the NFL Combine last year.

If Planck’s wrong, then the Virgin Mary is a fraud, and Achilles is the World’s Biggest Loser. So I think we’re safe. I can relax. Thank you, Owen!

 ***

Jack Tribeman’s Rise and Fall of Immortality (2014) is a large acrylic-on-canvas painting that contrasts humanity’s spiritual ascent—overcoming instinct to achieve creativity and freedom—with its potential decline under the weight of those same powers. The dual composition reflects both the promise of boundless ingenuity and the fragility of progress, inviting viewers to question whether immortality of spirit is sustainable or destined to erode.