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<   No. 882   2005-06-26   >

Comic #882

1 Death 1: BETTER DEATH BENEFITS! {as Charity Collector Guy walks along picket line}
2 Death of Insanely Overpowered Fireballs: {to Charity Collector Guy} STOP, MORTAL SCAB. WE WON'T LET YOU CROSS THE PICKET LINE.
3 Charity Collector Guy: You do realise you're a finite number of Deaths, and this is an infinite featureless plane? I can just walk around you.
4 Death of Insanely Overpowered Fireballs: CURSE EUCLID. CHOKING ON A DODGY KEBAB WAS TOO GOOD FOR HIM.

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Euclid was a Greek mathematician who laid the foundation stones for the formal study of geometry. He proposed a series of "self-evident" postulates governing how points and lines and angles and stuff behave, and from there derived a lot of the geometrical theorems we still rely on today.

Kebabs are Greek or Turkish food items made by rolling hot sliced meat and salad items in pita bread. I'm not sure if they had been invented in Euclid's time, but anachronism is the least of this comic's concerns. (Technically this is döner kebabs; there's also shish kebabs, where the meat is strung on a skewer, but most people talking about "kebabs" mean döner kebabs.)

I received a lot of feedback about this annotation. If you're currently thinking "But I've never heard of döner kebabs; everyone I know means shish kebabs when they say 'kebab'!", please stop and think if you and everyone you know qualifies as "most people". I know that in the USA and Canada people usually mean shish kebabs. But North America does not constitute "most people"...
2014-08-23 Rerun commentary: I dont want to get into that again. Let's just say "kebab" means different things to different people and leave it at that.

What's perhaps more surprising is that nobody has ever mentioned the "self-evident" bit about Euclid's geometrical postulates. One of his postulates concerned the behaviour of parallel and non-parallel lines. He expressed it as follows (as phrased in Wikipedia):

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Euclid figured this was obvious, given what else he knew about geometry, but try as he might he could never prove it using other obvious geometrical properties.

There was a very good reason for this. And that is because it is not true. At least not in general.

You can define a geometry in which Euclid's parallel postulate is true, and this turns out to be the sort of geometry which we are most familiar with, corresponding to high school geometry and all the usual properties we know about. This sort of geometry is called Euclidean geometry.

But we can also define a self-consistent geometry in which the two straight lines mentioned above, if extended indefinitely, do not meet anywhere. And what's more, we can also define another, different, but equally self-consistent geometry in which the two straight lines mentioned above, if extended indefinitely, meet on both sides of the intersecting line segment. These two different types of geometry are called non-Euclidean geometry, and each one is just as valid as Euclidean geometry.

I've mentioned these briefly a couple of times before. Maybe one day I should write something a bit more detailed about them.

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