"Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there'."
- Mouseover text of http://xkcd.com/552/

The point of the clockwise spiral stairs is that it restricts right handed attackers going up the stairs, but not right handed defenders facing down them.

So while a left handed knight would have an attacking advantage they would have a disadvantage when defending instead.

You're missing the point. The USA may be able to say that they own the moon, and even get everyone on earth to agree to it, but without a permanent base on the moon, and a way to defend it, they can't enforce the claim.

Let's imagine that the whole of a small country, like France, is magically teleported to the moon. (With a protective air bubble, and the necessary resources to survive and defend it.)

The entire population of earth might still agree that the moon belongs to the USA, (as they could be coerced by military action and trade agreements), but the entire population of the moon would say the moon belonged to France - or the Moonians as they might call themselves - until the USA becomes motivated to put a competing presence there.

Flags are an effective means of designating territory on earth because they represent the nation whose power is backing up the claim. The flag on the moon is not backed up by the US Navy or Airforce, but instead with the knowledge that they last put three people there, for under a week, 41 years ago.

>> ^messenger:

I know that multiple balls hitting one side will cause multiple balls to be released from the other side, but momentum isn't measured by counting the incoming particles; it's measured by mass velocity, and that's all. One ball hitting with great speed usually releases one ball at great speed out the other side. Two balls with very low speed, even with less total momentum than the single fast-moving ball, will release two balls from the other side at the same low speed. It's something about the number of particles, not their momentum, that determines how many are ejected.

As you said momentum is mass*velocity, and force is mass*acceleration.

It's the mass of the particles entering that determines the mass of the particles leaving.
As the balls in a Newton's cradle all have equal mass it's tempting to restate that as the number of particles rather than the mass of the particles.
However if you designed a cradle to have four 1kg balls and one 2kg ball then swinging the 2kg ball would cause two 1kg balls to be displaced. (The same effect as taping or gluing two 1kg balls together.)

In a normal Newton's Cradle the acceleration, due to gravity, is constant.
The constant mass and constant acceleration cause the predictability, as the only energy lost is to air resistance and other negligibles such as sound or minimal compression of the balls on impact.

The forces introduced by the magnet scale inversely with distance, making the outcome a lot more unpredictable.

"Don't let notation get in the way of your understanding" - beautiful!