I was taught the moves of chess by my parents and some drunken guests at a holiday party we, my family, were hosting at our then home in Germany. I was super excited to learn the moves. I had anticipated this. I even picked up little facts about the pieces from my relentless inquisitiveness. I knew the Queen was a powerful piece. I knew you didn’t want to get her taken. I had also heard that the knight can jump over other pieces. O, and something about pawns moving two squares but only on their first move. “So after the first move I have to move my pawns one square at a time?” “Can I take what’s in front?”
I took the adults instructions easily. I especially remembered that all which governed the knight was that it had to move in an L-shape. Ever since the lady told me about the L-shape move I can’t get my mind off how I’m going to totally win because everybody thinks the Queen is the most powerful piece but I know it’s actually the knight. After all, an L-shape move allows Black to capture White’s king on move one! These fools.
It wasn’t until we were playing that my tipsy tutor noticed I hadn’t quite grasped the rules of the knight yet. The opening I moved a pawn two squares — because that’s obviously what an educated chess-piece-mover would do. I figured people must be forgetting that they can move two squares all the time because of the way that the pawn’s rules were presented to me. I remembered. I won’t forget chess-rule-tutor. I won’t let you down like that. My turn again I picked up my knight and confidently drew an L-shape from b8 to e1, removing my opponents king and brilliantly winning the game.
“O, sweetly, you can’t move him like that, it has to be an L-shape.”
“But it is an L-shape. I drew it for you because I thought you might say that. It’s really an L though I can draw it again for you if you want.”
“Umm, no, that’s not what I mean. The knight doesn’t move the way you think it does. When I said “L-shape” what I meant was...” She reached across the tiny table we were playing at and moved the knight for me. “...two over and one up.” Okay, I thought, all I have to do is remember that. And I did.
I carried that rule with me like a mantra. It stayed with me incubating throughout those dormant years between learning the moves and actually playing the game until I was 14, calculating my first chess position. “Two over, one up; two over one up; two over one up.” Most pieces were easy to visualize moving but the knight, the TOOU (“Two Over One Up”) piece, it was the hardest. It seemed to me that this must be intentional; it must be an imbalance I have to deal with. But that isn’t true.
The knight is not some yoke to hobble the chess players mind. The knight isn’t even a more complicated piece relative to the others. In fact, besides the King, the pawn is the most complicated given en passant, the two-move rule, promotion, capturing, and, finally, moving! The knight is simply poorly described, misunderstood. The L-shape description with the piece jumping is too much. It’s an awkward and vague description. For a while after beginning chess it wasn’t obvious to me that the knight’s moves are symmetrical. And it would seem I’m not the only one as even Grandmasters find themselves surprised by backward knight moves — perhaps indicating that some of them are also TOOU calculators.
The knight is like the bishop but it has a slope of 3/2 and moves one square at a time. We can think of all the pieces like this, being governed by a unique angle(s). This is by far the easiest way. And, I suspect that this is a lost point of view. I think that, in describing the concept of slope, TOOU was used. Somehow, people forgot how the pieces so simplistically relate to one another and all that was left was the TOOU.