An ancient Greek word (απειρων), pronounced "ah - PAY - rohn," usually translated 'unlimited' or 'boundless', perhaps incalculable. In the Pythagorean "table of the opposites" it appears thus:
limited        apeiron
one many
straight crooked
good bad
nodes freegel
(Unfortunately I don't have an authoritative source for that last pair.)

The Pythagoreans believed that, in the words of Aristotle, "the whole heaven is a harmony and a number" and this gives us a clue to what they thought about apeiron. The ancient Greek concepts of number and harmony were very much bound up in their concept of ratio, in Greek: logos. This has given us words to do with systematic attempts to understand the world: logic, rationality (the same metaphor filtered through Latin.) Apeiron, therefore, can be understood as standing in opposition to this Pythagorean good.

To see how the Pythagoreans might have understood the word, it helps to describe one of the Pythagorean struggles against apeiron. When Pythagoras invented his famous theorem about right-angled triangles, one of the immediate consequences was a demonstration of the existence of what we now call irrational numbers. The Greeks used the terms alogos (inexpressible) and arratos (without a ratio).

Remember, having no decimal point notation, they must conceive fractional parts as ratios between whole numbers. A simple proof shows that the dividend in the ratio for sqrt(2) (the length of the hypoteneuse for a right angled triangle with other sides equal to one, by Pythagoras' theorem) must be both odd and even. In other words, sqrt(2) cannot be exactly represented as a fraction. Even using the modern method, its representation would require an infinite decimal expansion: apeiron.

According to one story, the Pythagoreans took this so seriously that Hippasus, who wanted to go public with the information, was murdered at sea.

Apeiron can also be understood as chaotic, or infinitely complex - the Pythagoreans thought of a crumpled handkerchief as apeiron - and indeed there is a close relationship between the concepts of infinity and complexity.

One way of thinking of the task of defining larger and larger numbers is as the task of packing more and more complexity into a finite definition. But when it comes to the Absolute Infinite, somewhere along the line we give up the ghost.

To my mind, this Pythagorean denial of apeiron is reminiscent of a modern trend in philosophy, which I like to call physicalism. This holds that what is real is what can be treated of by physics. As physics is a formal discipline, this amounts to a denial of apeiron, the undelimited, the informal. This is not to say that physics is wrong, or even incomplete within its own domain, just that the philosophical use of a formalism such as physics as an ontological yardstick is undermined by the implied rejection of the reality of apeiron.

It's quite easy to place the opposing concept of limit, ratio, order, in our world: it's the regular way that stuff behaves when it moves about: Information, causality, natural law. Apeiron might seem harder to spot. But it seems we're immersed in the informal; it's just all the other stuff, the stuff that philosophers get blasted for ignoring! Emotion, values, consciousness, humour, the funny feelings you get when you're drifting off to sleep.. None of these are capable of a realistic treatment by latter-day Pythagoreans, because the anti-apeiron spectacles render them invisible. They must be reconstructed as regularities in behaviour, which, it seems, is precisely what they are not.

See also: Reflection principle.

A great shareware game for the Mac, released by Ambrosia Software in 1995. It was, for all intents and purposes, a Centipede clone, but it was damned addictive. For those of you who are unfamiliar with Centipede, it goes like this: you control a small mobile something (is it a ship? a scooter? a marital aid?) that zips around a mushroom field and shoots bullets that streak up the screen, unguided. Without power ups, you get one bullet onscreen at a time, so aim well. From the top of the screen, a centipede is winding his way down the mushrooms, descending one row and changing direction every time he bumps into one. Five bullets will destroy a 'shroom, one will destroy a segment of a centipede--or, more accurately, turn that segment into a mushroom. If you chop him in half, the rear half grows a head and continues autonomously, so chew him up from the front or the back. Once the centipede is gone, you progress to the next level. One bump from anything but a 'shroom, and you're dead, next life, restart the level.

To aid you in your quest, mushrooms would occasionally change color and offer power ups: 3x scoring, 5x scoring, 10x scoring, temporary invulnerability, extra life, and the coveted rapid fire. Enough points and you gain an extra life. With rapid fire you could clear practically every mushroom on the board. Occasionally, if you walked by my dorm room in 1995, you'd hear me shout "rock and roll!"--this meant I had grabbed rapid fire, and used it to secure a temporary invulnerability shroom and perhaps even a scoring multiplier. In this state, one could clear a level of mushrooms with impunity, as long as you left a few segments of centipede moving around.

The addiction to the game is in its fast and knee-jerk gameplay, but also in the little touches: the centipede-type critter appeared caricatured in several intermediary screenshots sitting on a Day Glo mushroom and smoking a hookah, a la Through the Looking Glass, and always had derisive laughter for you when your--ship? lawnmower? spider? laser?--got destroyed by the inevitable progress of longer and longer arthropods down your screen. Even if you could nail the centipede, the scorpion that popped in from the side and the... bugs that dropped from the top of the screen and ricocheted around would eventually nail you.

Apeiron is a Macintosh-only game that ranks as one of my absolute favorites. If you enjoyed the old Atari arcade games Centipede and Millipede, you're likely to find Apeiron downright addictive.

In this updated version of those old classics, you control a crystal shooter you use to blow away sneaker-wearing pentipedes, goggle-eyed fleas, grouchy scobsters, and flatulent geckos that zip down the mushroom patch, determined to do you in. The patch's landscape is altered by the occasional visit of a flying saucer. Game play is livened up by "yummies" such as psychedelic shrooms and bouncing gold coins that give you special powers such as machine-gun fire, guided shooting, an invulnerability shield, and additional lives (you get a maximum of eight shooters at any time).

The graphics and animation on this game are excellent and the sound effects are gleefully obnoxious. Game play is simple; use your mouse or trackball to move your shooter and press the button to fire (you can also use a keyboard or other input device). Everything you see on screen is worth shooting. There's nothing to get in between you and the pure arcade adrenaline that kicks in around Level 5 and doesn't let up until your last shooter shatters.

The first version of this game was developed in 1995 by Ambrosia Software's founder Andrew Welch and rapidly became a big hit for the fledgling company. Newer releases have addressed OS and hardware upgrades (the introduction of USB rendered the older version of the game unplayable due to system conflicts). The game's name comes from the Greek word for "countless", which refers to the number of enemies you'll face.

A very-playable shareware version of this game is available for tryout at

Game Cheats

The game can get tough, particularly after Level 12. But please note that if you use any of the cheats listed below (except pause) your score won't count towards the high score tally.

To abort the game because your boss is coming: Escape
To pause the game: Caps Lock

The game must be paused in order to apply the following cheat codes
  • SNAPPLE - locks in whatever "yummies" you've accumulated
  • PERNTS - adds points to your score.
  • NALA - give you the "sprinkly shield" of invulnerability
  • SQUISH - machine gun fire
  • USMC - adds 5000 to your bonus score
  • DJARUM - lets you pass through mushrooms
  • HECTOR - maxes out your lives to a total of eight
  • NICE BOX - give you guided shots
  • MORRISON - moves you ahead 12 levels

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