New random rant (about symmetry)

I was thinking about a universe which was symmetric about a plane (across space 3D) and without quantum randomness (ie. the future is uniquely determined by the state of each particle now).

Imagine a person near the plane, staring at himself from the other side of the universe, although with exactly the same laws. He cannot go over, because any part of him cannot possibly cross over without hitting its counterpart.

A simplistic "solution" might be to agree with himself on the other side to both stick out their right hand across the plane of symmetry. This would have worked, if in his part of the universe, right had not been left (dang!).

It would appear that this symmetry can never be broken, just like a mirror, so I wondered a few things:

1) Is it really true that this symmetry cannot be broken?
2) How do we know that the mirrors we see on the wall are not planes of symmetry in the universe (assuming the daily notions of laws of physics)?

For question 2, I realised a rather trivial solution. A key difference between a mirror and a possible plane of symmetry is basically the property about a normal mirror that it is breakable. Planes of symmetry cannot break apart just like that.

For question 1, it would appear that the relation between electricity and magnets provides a solution, because reversing both magnetic field and electric field does not reverse direction, and hence both forces can be in the same direction, but is that really true? o.O I have no idea.

More whats.

Well, after the chaos of the previous visit's events, I decided to chance another trip to the H > P club. And sure enough, the management had the players running rings round them so fast they were like Saturn. In an ingenious twist of plot writing, the players had formed cliques with other players who preferred certain openings, and even the bouncers of the management took part in the squabble. I found out the following:

0. An individual may be in any number of cliques, and be a bouncer or a player, it matters not which for the below conditions.
1. All the bouncers alone formed the clique of the Sicilian O'Kelly. "And we are all good chessplayers who know better!" they rallied.
2. All the players alone vehemently insisted the Benko Gambit was better. "And we are all poor chessplayers!" they yelled somewhat ironically.
3. Each individual had a favourite opponent, and an opponent he most despised (not the same person; they're not that insane.)
4. Given any clique, all individuals whose favourite sparring partner/opponent/punchbag was on the clique, formed their own clique.
5. Ditto of 4, just replace "favourite" with "most despised".
6. Given any 2 cliques, there was at least one individual (let's call him Sad) whose favourite opponent thought Sad was on one clique, and whose most depised opponent thought Sad was on the other clique.

Well, this wouldn't do. Amidst the rat-tat-tat of Alekhine's Gun and the table-turning (sacrifices) that formed part of a huge brawl, I talked to the manager (wisely taking no part in this, hiding under a hedgehog.)

Me: "Are all your bouncers sane?!"
Manager: "Yes, at least they're supposed to be! What the heck is going on!"
Me: "Interesting! Do you know, there's at least one person who deserves to be thrown out of this establishment?"
Manager: "You think!?!!"


The Frighteningly Mad Professor Edalpo: Well, this is a rather queer parable. But indeed, the narrator was absolutely right; can you prove that there was some individual who shouldn't be there in that stead? Remember, all bouncers are supposed to be sane, while any poor chessplayers should not be allowed in.

What

I believe separately in all the following statements:

- Sane people have true beliefs.

- Insane people have false beliefs.

- Questions are asked only by questioners, who may be sane or insane.

- Type A questioners ask questions that they believe the answer to which must be true. Type B, false.

- Questioners may be sane or insane.

- Everyone utters what they believe is true.

Well then. Hello. So, I believe you know that I am insane? I'd have to be to be posting here, after all. So, to alleviate the boredom spent in the land of the mushroom clouds, here is a nice little set of questions, adapted from a little book of such.

So I took a little stroll to the H > P chess club down the street, where they had a couple of sane and insane players. Some were good players, some poor players. The good players believed the value of H > P, the poor ones believed H =< P. Due to the name of the chess club, it was obvious that the management would kick out the dissenters, but they were doing a lousy job of it! Can you spot all the infidels/heretics/cannon-lovers from the following interactions? [The management, represented by M, are all sane type As.]

M: You seem to be a good player.

Turtler: Thanks, but I believe I'm quite poor at this, really. Do bings move like queens?

M: *facepalms* [To M's opponent, Sacr] Is that why you're losing?

Sacr: I'll be kippered, 'tis so! Aren't you a smart one, laddie! I must be 'orrible at chess to not pick that up!

Turtler [To M]: You're saying bings don't move like queens?

M: *sigh* Am I the type who could lie about that? Now, if you're not convinced, ask him.

C. King: Do you believe I am the type who could ask you if you're insane?

Turtler: He's talking like a nutcase.

M: Tell it to him, CK. Just leave me out of this madhouse. *walks away*

C. King: You're a rather poor player to get into this position.

Turtler: For a good player, you're thoroughly insane. I'm winning!

Sacr [To Turtler]: Who're you to judge, madman?

*fight* *All 3 were thrown out for rowdiness*

The Frighteningly Sane Doctor Tarrfether: So, is everyone a good player? Or were there poor players? Am I the type who could ask you these questions? Am I sane? Are you? Is the writer of this post? [All can be answered.]