How to mentally visualise any square in terms of its colour and diagonals [PART 1]

"My blind eyes now see what others cannot, that sometimes the hands of fate must be forced!" ~ Illidan 'Betrayer' Stormrage before playing a forcing move of chess

Importance of the ability to visualise board

Visualising the board clearly is the first step towards blindfold.

However, this doesn't mean that the ability to visualise is applicable only to those seekers.

Paraphrasing Daniel Rensch - anything that helps you visualize better, will improve your calculation abilities too, while improving board awareness, and reducing blunders.

Common-sense dictates that the more acquainted you are with your board, the more confident you will feel about your whole game.

Goal of the article

After you finish reading this article, you will be able to easily calculate the fact that g5 is a dark coloured square, that is located 2 diagonals below a1-h8 diagonal (from white perspective) and 3 diagonals above a8-h1 diagonal (from white perspective).

Introduction

Visualising the exact location and vicinity of a square is a useful skill and this has to ultimately happen through visuo-spatial intelligence alone. But this does not mean that we cannot take the help of mathematical-logical intelligence to facilitate the process.

So in this article, you will learn how to calculate the spatial and chromatic specifics of a square. With repeated practice, the author hopes that this calculation will translate to visualization.

Nomenclature

How do we name diagonals in an intuitive way? Did you know that a chessboard has a total of thirty diagonals! Fifteen of them are available to LS Bishops and the rest to DS.

Generalising it, a chessboard with n squares has 2n-1 diagnoals running from South-West to North-East and 2n-1 from North-West to South-East.

For practical purposes, let us call the former as diagonals and the latter as anti-diagonals. In the below picture the diagonals are represented by black lines and the anti-diagonals by red lines.

Further, since the chessboard has 15 diagonals and 15 anti-diagonals – let us call the ones running from the centre of the board as 0 and the ones above it as 1^st, 2^nd etc. and the ones below it as -1^st, -2^nd etc.

In the below pictures, the 0^th diagonal and anti-diagonal are represented by a black line, and the +ve and –ve diag and anti-diags are represented with brown and yellow lines respectively.

Note that the 0^th diagonal will be running from White queen side rook to black king side rook; and the 0^th anti-diagonal will run from Black queen side rook to white kingside rook. This sort of observation is important to translate your calculation into visualization.

So how do we determine the diagonal and anti-diagonal of a given square?

For example, how do we determine that b2 is on the 0^th diagonal and the 5^th anti-diagonal?

For both purposes let us translate the alphabet in the square to the corresponding number. Hence b2 will translate to 22, e4 will translate to 54, h8 as 88 etc.

Computing the diagonal

To compute the diagonal - let us find the difference between the 2^nd digit and the 1^st digit of the said number. In case of b2 it will be 2-2 = 0 and in case of e4 it will be -1.

Pay very careful attention to not only this number but also the sign

Of note is the fact that b2 will be on the 0^th diagonal (that is the diagonal that passes through the very centre from a1 to h8) and e4 will lie on the diagonal that is just below it!

Determining the colour of the diagonal and the square.

Also note that when this difference is even, the colour of the diagonal will be dark and when its odd, the colour of the diagonal will be light. Hence the 2^nd and -2^nd diagonal will be dark and 1^st and 5^th diagonal will be white.

Computing the anti-diagonal

For antidiagonal, simply add both the digits and subtract 9. Thus e4 and d5 will be on the central anti-diagonal. What about b2? B2 translates to 2+2 =4. Applying subtraction, 4-9 = -5.

Hence it must be on the fifth  anti-diagonal below the central diagonal.

Pay very careful attention to not only this number but also the sign

The colour of the anti-diagonal will be the same as the colour of the diagonal.

Practice Problem

Based on the above method what can we say about the square b6?

B translates to 2. Hence b6 = 26.

Since 6-2 Is 4. It lies on the 4^th diagonal upwards (from a white perspective) from the central diagonal, that is towards black side. Further, since this difference is even, the colour of the square, diag and anti-diag must all be dark.

Further, 2+6 = 8, subtracting 9 from it, we get -1. Hence it lies on the -1^st anti-diagonal. That is one anti-diagonal below the central anti-diagonal.

Don’t stop here. Bear these facts – that is the colour, diagonal and anti-diagonal in mind and mentally picture how/where this square would appear if you were playing black and white? Evaluate the vicinity, and vulnerabilities of this square.

Implications and mental calculations

What is the implication of b2 being on the 5th anti-diagonal? It means that is in the same anti-diagonal as c1, (Don't just compute {3+1-9} to arrive at this conclusion, rather visualise the fact that c1 is five squares to the left of h1 - from white perspective). C1 is the bishop square, hence b2 enjoys the anti-diagonal protection and attack of c1 bishop. In fact any square that adds up to 4 enjoys the anti-diagonal attack of c1.

Similarly what is the implication of any square whose digits add up to seven?  They enjoy the anti-diagonal attack and protection from f1 square. Hence a6 is anti-diagonally attacked by f1 square.

What is the implication  of a square whose digits have a difference of 2? You tell me :) They are naturally under the diagonal attack and protection of c1!

Now which square will be under the attack of c1 and g3? The f4 square! Because the sum of  digits is same as g3 - hence the anti-diagonal attack from g3, and difference of digts same as c1. Hence the diagonal attack from f4.

Picturise the above discussion completely and stretch these arguments AS MUCH AS YOU POSSIBLY can!

Practical application:

Before you go and read part 2 - it is highly recommended that you mentally travel through each diagonal and anti-diagonal at least once (but preferably a few times). Verbally name each square while you travel through the squares mentally. For example - diagonal 0 - dark coloured a1, b2, c3, d4, e5, f6, g7, h8, g7, f6, e5, d4, c3, b2, a1. If you are unable to do even this, take an empty board without co-ordinates and do the exercise visually.

Refer to case study here: http://www.chess.com/blog/TheDarkRookRises/how-to-mentally-visualise-any-square-in-terms-of-its-colour-and-diagonals---case-study

Feedback is not only welcome, but also appreciated!