Imagine you're captured by hm... Who's a good capturer these days ? If we were in the 70s I'd have said the aliens, and the whole thing'd have then involved the threat of... you know, probing. Yeah, right there. You know where. Yeah.
In the 80s it'd have been perhaps the Soviets, or was that in the 60s ? And in the other 80s it'd have been the Berber slavers, of course.i But what is it by now ? I suppose it's the Americans, huh. Our previously very prosperous, very successful, muchly promising colonies in North America that we had such great hopes for meanwhile turned into... well... It's a sad thing to look upon, really. Like this upper middle class white kid that had straight As in high school, moved out to college on a full scholarship + stipend and then dropped out in junior year to do drugs and live in downtown Detroit.
But sad or not, it's what it is. So imagine you're captured by a troop of savage, lawless USisans from America. These lurid, immoral rogues give you one coin, and tell you that unless you manage to come up with a perfectly balanced random number generator they'll toss you into the endless burning pit of NSA. Which... you know, isn't really all that far off.
So what do you do ? How do you turn a coin that's potentially slanted, and who knows which way, into a tool of divine fairness ?
Suppose you can't measure its slant in any way, perhaps because the coin has a mechanism inside that alters it later on, or for whatever other reason. What do you do ?
I'ma give you a little space to think it through.
Ok, so did you come up with Newman's method or not ?
If not, here's how you do it : toss the coin twice. If it comes up both heads, or both tails (no matter which), report heads. If it comes up tails and heads (no matter in which order), report tails.
Basically, you're not measuring what the coin says, but how the coin differs from itself. This allows you to abstract the coin away from the entire process, and just deal with the quantum phenomena all randomness measures.
And now for the problem, because all this has been introduction : obviously a coin is a dice, with only two faces, conveniently labeled "heads" and "tails", which is ~==== 0 and 1.
What if we used the more general case of dice ? You know, the six faceted cube sort. How do you take six dice, which may be loaded in whichever way, and come up with actually fair dice throws ?
Ok, ok, I was cheating, you can't do this with two dice (you did notice that the original coin example used one not two, right ?). But anyway, so you get one die, how do you go about it ?———
- Oh, you didn't know about this ? Sure, your grandmother's mother got herself all wet in private thinking about how these Berber guys are capturing her ship and forcing their fingers, their thick rough nubbly stubbly fingers into all the womens' vaginas. To make sure there's no jewels hidden there, you see. Because the women of the other 80s walked around with rubies and emeralds shoved up their cunts all the damned time. Didn't you know ? [↩]