How to mentally visualise any square in terms of its colour and diagonals - Case study [Part 2]
This is part 2 and will make no sense whatsoever if you haven't referred to part 1 go here
Problem Statement: Which black 8th squares diagonally and anti-diagonally attack c4; what about the white first rank squares. Theorize and visualize about c4.
Prelude - Very important step: First picturize c4 from black position. c4 is when White's king's bishop (DS) is pushed twice. It is indeed a light square. If you are playing black, it should be to your centre-top/right and if you are playing white it should be to your centre-bottom/left. Think in terms of english opening, think in terms of Queen's gambit declined. Think in terms of Italian game. And if these terms make no sense to you, ignore them and just focus on the c4 square.
Anyways, now that we are given this square, what do we know from our calculations?
Step 1) It is one diagonal above the central diagonal. Diag factor +1
Step 2) It is light squared
Step 3) It is two diagonals below central anti-diagonal. AD factor -2 Visualize this hard!
Think about it again, you are dealing with the diagonal that is one diagonal towards the black edge (a8). You are dealing with the anti-diagonal that is two diagonals towards white edge. (a1) Recall this visuo-spatial fact about the diagonal in those steps that deal with diagonals. Recall this visuo-spatial fact about the Anti-diag in those steps that deal with anti-diagonals. Anyway, before you proceed - repeat the exercise you did in prelude again. Think about the c4 square in terms of these new facts.
Having done the above, let us mentally preview the board from black side. (mix these up - sometimes preview first from white, other times from black.)
Step 4: Diag attacks from black 8th rank to c4
What does a diagonal attack from black side look like? It basically looks like a SLASH from bottom left to top right. (It is the same for white too by the way). {Stop here and think about it for a few minutes if it doesn't make sense}
So let us compute what diagonal attacks is c4 subjected to from the black 8th rank. In a diagonal attack, we are interested in the difference between (rank)-(file). Here it was +1. But all black pieces are in 8th rank. Therefore, our desired square from where a diagonal attack on c4 can be launched is solved by the equation
- 8-file=1; solve for file.
- file = 7
- 7 denotes g.
- Hence a bishop g8 attacks c4.
Step back here and visualize the g8 square. It is a light square. It is one square to the right of h8. Originally the knight used to reside at g8. The castled king could also reside on g8. It is a light square. Notice h8 as dark square, notice f8 as a dark square also. Notice the fact that it is your c-bishop that travelled to g8.
More visualisation: Visualise the path from g8 to c4. Name each square between g8 and c4 and the squares that follow (b3 and a2).
Step 5: The anti-diag attack from black 8th rank to c4
Now that we have done the above, let us calculate which black squares can launch an anti-diagonal attack on c4. Is there any such square? Before that, what squares can launch an anti-diagonal attack on c4? A square that shares the same sum of digits.
c4 has 7 as sum of digits. Is there any such square on the 8th rank? No, that is a mathematical impossility. But, if that were possible, where would such a file have been? It should be the -2nd file or the file after a-rank (outside the board, a=1 so we are looking at (a-2) file).
Assuming that there is that imaginary square, where would the anti-diagonal attack enter the board from? from a6 {this is easy to calculate actually, a diag attack from (a-2)8 square enters the board from a(8-2) square}. So now visualize all the squares from a6 to c4 and beyond all the way to end of the board i.e. a6, b5, c4, d3, e2, f1).
Step 6: We are still enjoying black perspective, diag attacks from white 1st rank towards c4.
Remember, diag attacks are always from left bottom to top top or vice-versa. So a c square can be diagonally attacked from first rank squares that are b, a ... etc.
So what white squares at rank 1 can attack c4?
For diagonal we are interested in the difference between rank and file, and the difference is 1 here. Is there any such square on 1st rank such that difference between rank and file is one? It is a mathematically impossibility. But if it were possible, where would that attack be from? (a-1)1 square. That is one square to the (right of a) from black perspective. How would that attack enter the board? from a2 {this is easy to calculate actually, a anti-diag attack from (a-1)1 square enters the board from a(1+1) square} and it would descend as follows -> a2, b3, c4, d5 all the way until g8. Trace this path and undertand the fact that you have visited this path already.
Step 7: We are still enjoying black perspective, anti-diag attacks from white 1st rank towards c4.
Remember, anti-diag attacks are always from left top to right bottom or vice-versa.
A c square can be anti-diagonally attacked from the first rank squares like d, e, f, g, h etc.
Now lets talk about c4 square specifically. Anti-diagonal attack means that we have to look at sum of digits, which is 7. Is there any such square on first rank? Of course! the f1 square, the original location of white light square bishop. Notice how c4 enjoys the protection of f1. Can you think of any practical implications for this? Yes, this is one of the things that makes the queen's gambit possible! 1. d4, d5 2. c4 d5xc4 but this black pawn in c4 is under attack from the f1 bishop when the e2 pawn moves away. Okay, then lets go ahead towards the next step!
Step 8:
Now complete the whole picture. The light squared bishop at f1 travels to c4, on its way it meets e2 pawn and once it goes to c4 it looks back and sees a2 square is rear direction, and a6 is ahead. It is equally poised between both, not it takes a 90 degree turn and looks sternly upon the g8 square where the castled king shivers and f7 pawn shivers! Visualise this movement from every direction of the board, including top.
The italian game, the queen's gambit and everything else is made possible by this possibility of this motion!
Repeat all steps from step 4, again from white perspective. Go through everything, two-three more times. Do one square per day. We basically covered one diagonal and one anti-diagonal. Remember that there are a total of 30 diagonals and anti-diagonals.
Also, there are only sixty-four squares in a board. And hopefully, after two months - you will have covered every diagonal and anti-diagonal four times! You will not need (probably) to use this calculation method anymore!
To summarise:
1) Think of the square
2) Calculate Diag factor (file-rank)
3) Calculate anti-diag factor (file+rank-9)
4) Pick a side - black or white. Let us say you picked black
5) What diag attacks are possible from the eight rank on the square in question. (Since you picked black, we do this first). Travel through the diagonal.
6) What antidiag attacks are possible from the eight rank. Travel through the anti-diag
7) What diag attacks are possible from the first rank on the square in question.
8) What anti-diag attacks are possible from the first rank on the square in question.
When a diagonal attack or anti-diagonal attack is not possible from the first or eighth rank, picturize the square on the 'h' or the 'a' file where the attack can be said to originate from.
9) Complete the whole picture and travel through! While travelling its important that you start from the point of origin (edge of the board) and towards the square in question and then through it - rather than travelling from the square towards the edge of the board. I have found that travelling from the square itself is easier (and thus leads to a more passive approach).
Repeat 5-9 steps from the other colour's perspective.
