I drew more or less the same conclusion, i.e., that it is a proof by contradiction. I'd like to see a mathematical derivation of that point though. I think I see what he's saying about the Fourier transform, but not how to apply it to the earlier point.

<Perhaps a good place to go from here is to discuss what it really means to be "relativistically invariant". I used to think that it just means "conforming to special relativity"--you don't want your theory to run into contradictions when you have two observers on very fast moving rocket-ships, who can't agree on whether t1 came before t2.>

It's a little bit like a carpenter who wants to make a square table with 9 square feet of area. He will, if he's smart, have to solve this equation to learn how long the edges should be

x = √ 9

But if this carpenter is skilled at math he will notice that there are really two solutions to this equation

x = 3, x = -3

Our carpenter recognizes that the -3 solution is meaningless in the real word, so he discards that as an unwanted byproduct and only pays attention to the solution which is meaningful. And so it was with Dirac. His equations kept giving him these negative solutions, and he didn't like them. He told his colleagues that the equations imply the existence of "electrons with a positive charge", but that sounded as ludicrous to him as it did to his peers. So he went back to the chalkboard to try to find some way to make the negative solutions go away.

Imagine his surprise when the antiparticle was first confirmed, only a few years after his initial research.

Case in point: Vallejo can play an opening that has a published bust in MCO and still snooker Kramnik with it. Kramnik doesn't know the published bust, even though 1000s of club players have it memorized. Funny. (Kramnik vs Vallejo-Pons, 2005)>

Remember that brief discussion we had during a live game broadcast where I showed you a crazy line on the White side of a Najdorf? Check out this game:

Wang Hao vs Dao Thien Hai, 2008

<Marmot PFL: "If g6 was prepared than surely he would have analyzed this?">

Nigel Short, who was with us on that occasion, answered succinctly:

All preparation has to stop somewhere.
If you cannot analyse the whole thing to its end then you will stop when you feel comfortable and are sure that you can find the rest over the board. And sometimes remembering your preparation may be as hard as to discover it again in actual play.

That's true, and not only that, there are times when you want to review your preparation in your mind just to make sure that you know what's going on. It's the understanding of the position and not the ability to regurgitate moves that makes these guys GMs.

Recently I played a game at the local chess club and found myself in this position (I'm Black, it's my move.)

click for larger view

This was in my preparation, and my prepared move here was 9...Bd6--a fancy-pants sort of move that I've trapped a few people with in blitz games. My opponent sometimes thinks I've made a mistake so they snatch the bishop 10.hxg4 then I drop the bomb ...Qxg3!!, they invariably play 11.fxg3 and then I get to checkmate them with a lowly bishop 11...Bg3#. Very cute and funny little checkmate trap.

But OTB, I realized something that never came up in a blitz game. All the guy has to do is toss in Qa4+ as an intermezzo, and I'm down a queen for absolutely nothing. All those blitz "victories" were people getting checkmated in positions where they should have been taking my queen for free!!!

Luckily I saw the hole in my preparation and took a different approach. Whew! If I played my prepared move I would have been forced to resign almost instantly.