The earliest recorded thoughts about infinity come from ancient Greece, in particular from Anaximander and the idea of the apeiron (ἄπειρον). Anaximander was a philosopher who lived in Ionia, in present-day Turkey, in the 6th century BC. As is generally the case with the pre-Socratics, little survives of his work, so much of what we know comes from later testimonies.

Anaximander (source: Encyclopedia Britannica Online)

Apeiron is typically translated as “infinite,” “eternal,” or “limitless,” and the apeiron was posited by Anaximander as the source of the universe, a formless chaos out of which all else emerged. Xenophanes, later expanding upon Anaximander’s ideas, put forth the following picture of the world:

The upper limit of the Earth borders on Air,

The lower limit of the Earth reaches down to the Unlimited, {i.e. the Apeiron}.

-DK 21B28, translation by Karl Popper

Anaximander had some curious ideas about the shape of the world. He believed the Earth to be a circular cylinder, with diameter exactly three times its height. We live on the top circular surface of this cylinder, which floats unsupported at the center of the universe, surrounded by the apeiron.

Anaxagoras, depicted in a fresco at the National University of Athens

The apeiron would later play a central role in the cosmology of Anaxagoras, a philosopher also born in Ionia in the late 6th century BC who is typically credited with bringing philosophy to Athens, where he lived during the early life of Socrates. As did Anaximander, Anaxagoras considered the apeiron to be the source of all else and seems to emphasize its infinite and eternal nature.

Anaxagoras … says that the principles are unlimited. He says that almost all of the homogeneous stuffs come to be and pass away in this way (just as fire and water do), viz., only by aggregating and dissociating; they are not generated or destroyed in any other sense, but persist eternally.

-Aristotle’s Metaphysics

Anaxagoras even described a remarkable mechanism for how the apeiron gave rise to the universe, namely that a powerful mind (nous) began rotating the apeiron so that pieces of it broke off to form other entities.

When nous began to move [things], there was separation off from the multitude that was being moved, and whatever nous moved, all this was dissociated; and as things were being moved and dissociated, the revolution made them dissociate much more.

-Fragment 13

Viewed in a certain light, there are striking resonances with our current scientific hypotheses regarding the Big Bang, that moment(?) when a point(?) of infinite(?) density exploded with infinite(?) energy and started in motion the series of events that led to everything else.

P.S. In modern times, Apeiron is perhaps most widely known as the title of two different video games: a currently-under-development fan-made reboot of Star Wars: Knights of the Old Republic and a 1995 remake of Centipede. As research for this post, I downloaded a trial version of the latter. It was aptly titled. The crude and too-small graphics, the aggressively irritating sound effects, and the awkward mechanics indeed made my one session seem endless, and I was relieved when the game abruptly stopped and I was given the message: “If you think we’re still going to let you play for free, I have to ask you, ‘What are you smoking?'” The experience brought to mind another quote from Anaxagoras, recorded in Cicero’s Tusculan Disputations and also used, in a different translation, as the epigraph to William Gass’s The Tunnel.

In truth the roads to the underworld are the same from anywhere.



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