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ZENO AND BOLTZMANN

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Life . . . presupposes its own change and movement,

and one tries to arrest them at one’s eternal peril.

—Laurens van der Post, Venture to the Interior (1951)

We should probably begin with Parmenides, who was born around 515 b.c.e. in Elea, on the Greek mainland. He is known for founding Eleaticism, which quickly became one of the leading pre-Socratic schools of Greek thought. But though only small fragments of his principal work—the lengthy, three-part On Nature—survive, there’s really no need to complicate what is essentially a simple worldview, one that very much jibes with biocentrism 2,500 years later.

Parmenides’ views were seconded and championed by Zeno, born in the same settlement twenty-five years later. Both men tirelessly argued that the apparent multiplicity of objects we see around us, along with their changing forms and motions, are but an appearance of a single eternal reality they called “Being.” This was actually very much in sync with what had been written in Sanskrit texts a thousand years earlier, although Parmenides and Zeno seem to have arrived at their perceptions independently.

The Parmenidean principle boils down to “all is one.” This may seem like idle philosophy, but it’s pregnant with vast experiential perceptions that affect everyday experiences then and now. A babbling brook, for example, would be apprehended by the Eleatics as an expression of the limitless energy and play exhibited by Being or existence, whereas the opposing school (almost universally embraced in our modern time) is that a multiplicity of separate, quasi-independent objects like water molecules and pebbles are exhibiting cause-and-effect-derived actions in a space- and time-based matrix in which these disparate items come and go individually. And although the multiple-causation versus the “single animated essence” views may at first seem philosophical and unimportant distinctions, each in turn leads to very different conclusions about what’s actually unfolding and what kind of reality we’re part of. It’s actually a life-changing topic.

Perhaps that’s why Parmenides and Zeno, almost obsessively embracing their stone-simple concept of Being, felt a kind of Paul Revere–like need to spread the word. Doing so, they insisted that their view didn’t require faith or perception but could be proven through logic. Because they said that all claims of change or of non-Being are illogical, Zeno in particular created a series of paradoxes designed to disprove all time- or motion-based arguments, which he maintained would lead inexorably back to the simplicity of the One Energy. Even today, Zeno’s paradoxes are taught, debated, and still generally considered valid.

More than that, Aristotle admiringly credited Zeno as being the inventor of the dialectic, a word that later became synonymous with formal logic. This was ironic in a way, since Zeno’s entire purpose was to support and recommend the Parmenidean doctrine of the existence of “the one” indivisible reality, which is about as unconvoluted a position as is humanly possible to take. So in looking at Zeno’s paradoxes, we should always remember that their goal was not to be clever or to pull the rug out from under the machinations of logical thought, but to contradict and disprove the widespread belief in the existence of “the many”—meaning individual objects with distinguishable time-based qualities and separate motions.

Zeno created many paradoxes to prove his point, but we’ll only list the three best known. Probably everyone has heard of the Achilles and the Tortoise tale, called by various other names as well. It starts by letting the slower-moving tortoise have a head start, and then Achilles attempts to catch up and pass it in a race. Let’s say the tortoise goes half the speed of Achilles. Well, as soon as Achilles reaches the place where the tortoise was positioned at the outset, the tortoise has meanwhile moved on by half that distance. When Achilles reaches this new position, the turtle has meanwhile slowly advanced to yet another new position, halfway beyond its initial advancement and Achilles’ new position. And when Achilles attains the new tortoise position, there’s no avoiding the fact that the animal has managed to move ahead by another half of that distance. The halves keep getting further halved, but Achilles can never catch the tortoise.

A second paradox is similar: If Homer wants to reach a man selling grapes from a cart, he must first advance to half the distance between his front door and the fruit vendor. Then, he must arrive at a point that is half of that distance. Then half of that. It’s obvious that half of the remaining distance will always have to be attained first, and this creates an infinite task that has no conclusion. Homer can never buy the grapes.

Our third paradox involves an arrow in flight. Obviously, at any given instant in time the arrow must be somewhere and nowhere else. It is no longer where it used to be, and it is not yet at its next possible point in its flight. In other words, at every instant there is no motion because the arrow is exclusively at one precise position and thus at rest. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

In our busy lives, there may be a tendency to dismiss such logic as mere puzzles, and brush them off as if shooing away a fly. But the greatest minds through the centuries have been tormented by Zeno’s paradoxes. Although some have grandly announced “solutions,” the consensus is that they’re still valid today. The paradoxes can actually be solved by biocentrism. By seeing that time and space are not actual commodities like coconuts, biocentrism says they cannot be divided in half again and again to produce such conundrums. Alternatively, one might see that the physical world is not the same as the abstract mathematics or even simple logic we might use to describe it. Logic demands symbolic thinking, where objects and concepts are represented by ideas, whereas the actual world doesn’t have to play by those semantic rules. By this reasoning, Zeno’s paradoxes arise because we’ve switched between the physical and the abstract. Since we’re so rooted in our thinking minds, we’ve forgotten how to recognize the difference. In the abstract world, those endless halvings are a stopper and prevent Homer from ever buying the grapes. But in the actual nonsymbolic reality of nature, he can simply walk over and hand the vendor a drachma.

For our purposes, however, it’s enough to show that space and time—the seemingly bedrock grid many of us assume to be a real framework for the universe—are fragile mental constructs whose logical existence can be shaken by the likes of Zeno. If he’s right and motion cannot actually exist, what is it that we experience when we watch a home run ball narrowly miss the foul pole? What’s going on there? Before we get to that, we have one more task in our demotion of time: to see if any area of science can support it.

This takes us to Austrian physicist and philosopher Ludwig Boltzmann, who was born in 1844. Beginning his study of physics when he was nineteen at the University of Vienna after his father died, he earned his PhD at age twenty-two and became a lecturer. It was a heady time for physics, and Boltzmann was particularly fascinated with developing a way to statistically figure out how to explain and predict the motion and nature of atoms, which let him accurately determine such properties of matter as viscosity—basically how gooey or runny liquids are.

Boltzmann struggled his whole life with wild swings in mood, which flowed like his beloved fluids at vastly different rates. Today he’d probably be diagnosed as suffering from bipolar disorder. It often made his relationships with his colleagues difficult, but it didn’t prevent him from making major advancements in explaining how matter behaves. In doing so, he was in a way anticipating the quantum mechanics that would arise decades later, which also rely on statistics to understand how the physical world operates. Before finally succumbing to depression and hanging himself at the age of sixty-two, he created three laws of thermodynamics, of which the second— commonly associated with the idea of entropy—remains the most famous.

Entropy enters our own reasoning because it is the single area of physics that seems to argue for the existence of time. In all others, whether the equations of general relativity, or Kepler’s laws of planetary motion, or quantum mechanics, everything is time symmetrical—stuff happens, but there is no external arrow or directionality that makes time an actual entity.

Boltzmann created a model of atoms in a gas that resemble colliding pool balls. He showed that if they’re all confined in a box, each collision causes a distribution of velocity and direction that becomes increasingly disordered. Ultimately, even if a high degree of order was the initial condition—say one side of the box contained hot, fast-moving atoms and the other side cold, slower-moving ones—this structure would vanish. Such an ultimate state of large-scale uniformity, or total lack of order even on the microscopic level, is called entropy. Given enough time, the final condition—a state of maximum entropy—is thus inevitable.

Notice the word “time” was central to the process. And that’s the point. The act of going from structure to disorder, of increasing entropy, is a one-way process. The eventual uniformity, and the obliteration of all temperature differences, appears to be time based because it’s not reversible. We see this in everyday life. The drawer in which we keep our socks never somehow gets more arranged, with matching pairs increasing their frequency no matter how long we rummage through them. Disorder happens naturally. And if this really is physical or mathematical evidence for a “direction” or “arrow” of time, then time is real.

Arrows of time are not taken lightly in physics. Stephen Hawking once argued that if the universe ever stops expanding and begins to collapse, the arrow of time would point in the opposite direction and physical processes would reverse themselves on every level. Presumably we’d never notice anything amiss, since our own mental workings and brain functions would be running backward, too. In any case, Hawking eventually decided that reversed time couldn’t happen, and he changed his mind as if to demonstrate the process.

We have no other hard evidence for time except for Boltzmann’s second law of thermodynamics. But this entropy is no small thing. It’s pretty inarguable. Is there any way out that can make us not seem like naive pleaders as we build our anti-time cathedral?

Fortunately, yes. Although many casually use entropy as an argument for time, Boltzmann himself didn’t see it that way. Entropy, he argued, is simply the result of living in a world of mechanically colliding particles where disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, the state of maximum disorder is simply the most likely to appear. Put another way, entropy is merely a matter of things slamming into other things in the here and now. No arrows exist. Randomization is a present-moment process. Sure, we humans can always peer at a dynamic scene, look away for a while, then look again, and things will be different. But different scenes, the fact of change, and randomization itself are not the same thing as time.

Boltzmann essentially said that a state of order in which molecules just happen to all move at the same speed and direction is the most improbable case we can imagine. In other words, the second law of thermodynamics is merely a statistical fact. Any gradual disordering of energy is like shuffling a deck of cards. What we called “order” when the deck was purchased, with each suit arranged in ascending array, was a special case. The act of randomization requires no ghostly magical external entity.

So if time does not actually exist, what do we experience in everyday life? We need to know before tackling the ultimate scary time-consequence, the apparent end to life. But more importantly, we need to know who experiences what, where these adventures take place, and how our lives unfold.