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  • 33 + 1 Vignettes on the History of Scalar Inversion
  • John Durham Peters

i. zeno's arrow

Modernity has no monopoly on the imagination of infinitely small things. The ancient Greek philosopher Zeno of Alea designed several paradoxes to show that plurality and motion were illusions. One of them posits the vertigo of an infinitely subdivisible line. An arrow flying through space must reach the halfway point before it reaches its destination. It must also reach the halfway point between the halfway point and the destination, and so on in an infinite series. The catch is that space never runs out of halfway points. As the arrow flies it runs up against an ever-thickening wall of smaller distances and grinds to a halt as if bouncing off an asymptotic forcefield. The infinite supply of minute distances shows movement to be an illusion; subdivisibility (of space) proves impossibility (of motion).1 But everybody knows that real arrows fly in blithe indifference to mathematical conundra. Even the most committed pre-Socratic wouldn't walk into battle expecting philosophical contradiction to protect them from the onslaught of oncoming arrows. Rough material scale has a way of overpowering superfine imagined scale. This is the difference between the mathematical and physical, imaginary and real, theoretical and practical. With math, you can vary quantities any way you please as long as you are true to the mathematical rules. You can always add one more number to any supposed infinity. With physics, however, you eventually run aground on natural constraints. Those constraints have grown finer and smaller since the Greeks. Ancient thought abounded in invisible and ineffable things, but for immediate contact, their smallest things were sand, seeds, dust, and grain, a droplet of water, a flea.

ii. aristophanes's fleas

Aristophanes's The Clouds molds the template for academic satire. Perhaps the first comedy of ideas, it features a head-in-the-clouds [End Page 305] (literally) intellectual charlatan, a new educational institution promising wisdom and influence, credulous student wannabes willing to fork over adulation and cash, and abstruse research that looks absurd to outsiders. Socrates, as the buffoonish charlatan, is the butt of the joke, and cuts quite a different figure than the noble lover of wisdom and pesky questioner of Plato's dialogues. (Plato would later blame The Clouds for contributing to Socrates's eventual condemnation.) The absurdity of Socrates's inquiries in The Clouds is marked by his interest in the high and the low, the big and the small—that is, celestial or atmospheric matters (ta meteMra pragmata) on the one hand and the smallest things, fleas and gnats, on the other. Socrates is quite the clever methodologist and figures out how to measure the distance that fleas can jump by making wax tracings of their feet which look like miniature Persian slippers. He also discovers that gnats phonate by using their anus as a kind of trumpet.2 (Trey Parker and Brad Stone, creators of South Park and The Book of Mormon, must have learned much from Aristophanes.) Socrates's research in The Clouds is unquestionably silly, but any inquiry that seeks genuinely new knowledge risks the rebuke of failure or the risk of illegitimacy. Without the benefit of hindsight all basic research can seem vain. (The Nobel Prize for Medicine in 2017 went to scientists studying circadian rhythms in fruitflies—research promising to reveal much about sleep disorders and even jetlag among humans.) Aristophanes not only played philosophy for laughs but ruled out the sky and the very small as worthy objects of inquiry. His bathos knew no size but our current one, no senses but our own; he stayed in the safe middle human range.

iii. archimedes's grains of sand

In one of the first works of popular science, Archimedes, the mathematician-engineer, wrote to his mathematically-minded patron Gelon, the king of Syracuse, and calculated how many grains of sand it would take to fill the known universe. The work, called Psammites in Greek or Arenarius in Latin, is translated as The Sand-Reckoner, but its title more literally means Of Sand. It is a pun, as sand was both the matter and the medium of...

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