Paradoxical Poetry

An original poem on some of Zeno’s paradoxes:

I.
Traverse a line? Don’t make me laugh!
Each segment’s segment’s cut in half.
One cannot simply walk the line,
‘cross infinite halves in finite time.

II.
Swooping down from high above
The eagle catches fleeing dove,
Yet swift Achilles, to this day,
Cannot o’ertake his tortoise prey.

III.
We see the arrow fly through air,
But surely there’s no motion there.
The arrow, ne’er before it’s caught,
Moves where it is, nor where it’s not.

IV.
In the hippodrome they run their course,
Speeds are measured in length of horse.
Opposing directions they fly past,
Each to the next seems doubly fast.

At the risk of over-explaining, a quick note on the four paradoxes mentioned in the poem:

The first verse deals with a paradox known as the “dichotomy”. This is probably the most well known of Zeno’s paradoxes. For a runner to reach the finish line, he must first reach the midpoint. In order to reach the midpoint, he must first go half way to the midpoint. And so on. As a consequence, before any distance can be traversed, an infinite number of smaller distances must be covered. And to take an infinite number of steps must take an infinite time. Therefore, the runner cannot possibly run even a short distance.

The second verse deals with the paradox of Achilles and the tortoise. It is actually quite similar to the first. Although Achilles is much faster than a tortoise, he can never catch it because in the time that it takes him to reach where the tortoise was, the tortoise will have moved a little further away. Therefore, before Achilles can ever catch up to the tortoise, he must first reach all of the infinite points where the tortoise had already been.

The third verse is the paradox of the arrow. An arrow, just like any other physical body, always takes up a space equal to itself. So at any given instant the arrow cannot move inside that space because the space is exactly the size and shape of the arrow. But it also cannot move outside of that space because it is perfectly contained. Therefore, motion is impossible.

The final verse treats the paradox of the stadium. If two teams of horses, four horses long each, pass each other in opposite directions, an observer will notice that in the time that the lead horse has covered a total distance of two horse-lengths, it will have actually passed all four of the other team’s horses. Therefore the chariot, despite its constant speed, travels two different distances in the same amount of time, which is absurd.

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Beer of the week: Cerveza Monterrey – The term “Corona knock-off” gets thrown around a bit, and this isn’t the first beer I’ve reviewed that might merit that description. This extremely pale Guatemalan lager is very carbonated. On its own, it is fairly watery and tastes of corn. The addition of lime and sea salt, however, makes this a reasonably palatable hot-weather drink. With a lot of lime, it is rather refreshing.

Reading for the week: Lives of the Eminent Philosophers by Diogenes Laërtius, Parmenides, Melissus, and Zeno of Elea – Zeno’s own writings are lost to us. However, Diogenes Laërtius (among others) preserved some of his ideas. Diogenes also relates the gruesome details of Zeno’s death, including the part where Zeno bites off the ear (or nose) of a tyrant. To help give context to Zeno’s life, this reading includes the lives of his teacher (and lover?) Parmenides and his contemporary Melissus.

Question for the week: Are the paradoxes mere logic tricks, or do they point to some more profound truth?


You can never drink the same beer twice.

There is an undeniable appeal to the statement by Heraclitus that “you cannot step twice into the same stream.” Impermanence is perceived everywhere we look. People who spend any time along the banks of a river or the seashore know that change is constant. Waters rise and recede; sandbars form and wash away. And this is true about everything else around us. We are always in the midst of growth and decay. We see organic growth and decay in plants and animals, but we also see mechanical growth and decay in buildings, cities, and technology. And, although we are incapable of perceiving it at any instant (because it is constant rather than instantaneous,) we recognize change in ourselves and our loved ones.

But the mere observation that change is constant does not do justice to Heraclitus. What makes the stream metaphor really interesting is the fact that it is paradoxical. Yes, the stream is different from one moment to the next, but we still recognize it as the same stream. How can we know that the river is always changing, but at the same time recognize that it is the same river?

Joseph Conrad’s Heart of Darkness begins with a reflection on the history of the River Thames. The characters observe that it is the same river that Roman soldiers navigated as they pushed the dark and dangerous boundaries of the Roman Empire. Likewise, it was the same Thames down which Francis Drake and other “knights–errant of the sea” sailed as they carried the torch of the English Empire to dark new lands. But while holding on to this recognition of consistency, they also acknowledge that the river’s “tidal current runs to and fro” unceasingly and that that the shoreline and the people have all changed.

Although the bulk of the main story takes place in Africa, Heart of Darkness begins on a pleasure yacht in London, as a conversation among ex-seamen. To sailors, we are told, “One ship is very much like another, and the sea is always the same.” But even us landsmen know that there are high seas and calm seas, and that the conditions at sea are actually very changeable. Again, it appears that Conrad is hinting at the paradox that Heraclitus was interested in: in spite of all its vicissitudes, there is something constant about the sea. And, for that matter, the entire world.

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Beer of the week: Negra Modelo – A Heart of Darkness reading deserves either a dark beer or a tropical beer. Negra Modelo is something of a compromise in both respects. Although “negra” means “black”, this beer is actually more of an amber color. And although Groupo Modelo is based in Mexico City, (and therefore technically tropical,) this bottle was probably brewed north of the tropics in Piedras Negras. (This is due to a complicated anti-trust settlement that I do not fully understand.) As to the beer itself, it is a bit thinner and less flavorful than might be hoped. There are some good dark-roasted malt notes throughout, but this beer is mostly uninspiring.

Reading of the week: Heart of Darkness by Joseph Conrad – This novella is an excellent read, and raises a lot of interesting questions about empire, individuals, and the nature of human society. Conrad apparently based some of the book on his own experiences as captain of a steamboat on the Congo River.

Question of the week: Rivers, like all things, change with time. But civil engineers literally reversed the course of the Chicago River. We may say that the River Thames of today is same river as when the Romans first explored it, but is the Chicago River of today the same river as before it was reversed?