Uhh I need help

So I was studying chess endgames as usual from this one book I recently got as a reward in a chess tournament for 2nd place. (Analysing the Endgame by Jonathan Speelman).

And I came across page number 10 (pawns) and I couldn't understand the following diagram 7,8 and the paragraph for it.

Starting from, 'I have borrowed ideas... --- diagram 8. I have cut the previous paragraph as it's completed and understandable. I have only highlighted the ones that I do not understand.

Can anyone help me with understanding the following?

I don't get it either 😅 sorry

It's okay it's a book of I think hard endgames so yeah 👍

I learned that in this video, but it's in spanish... try with subtitles

https://youtu.be/_ZXLl0eqvZU?si=BzLvA8QPSR8hA45v

It's not easy to understand and You will almost never see it in your OTB games

Can you explain it? What is it exactly?

Uf... its a 90 min video

I asked chatgpt and this is his explanation:

In chess, conjugate squares (or corresponding squares) are an advanced strategic concept, particularly relevant in endgames involving king and pawn versus king scenarios. This technique is used to determine the opposition and the optimal move to either win or draw a position.

Conjugate squares are pairs of squares on the chessboard that are related in such a way that if one king occupies one of these squares, the opposing king must occupy the corresponding square to maintain balance in the position. The idea is that any move by one king to a conjugate square allows the other king to move to its corresponding conjugate square, thus preserving a favorable position.

This concept is crucial for understanding and handling endgames where opposition (direct, distant, or diagonal) plays a significant role. King and pawn versus king endgames are a classic example where conjugate squares are essential in determining whether a player can force a win or secure a draw.

This concept can be extended to more complex positions, but the essence is that understanding conjugate squares allows a player to better manage opposition situations and control the outcome of the endgame.

Okay so this information is useless and just calculation is better?

In a real game you don't have time to see this, so calculation or intuition are better

Opposition is a particular case of conjugate squares and it is important that you know that, and that you know that there are conjugate boxes. Maybe in a correspondence game, with a lot of time, you can waste your time

Is not useless, but... you won't use it

Oh I see, thanks!

The basic idea, yes, but not to see all the sqares, you need a lot of time

There is no human who can solve a corresponding squares puzzle with pure calculation. Even an engine has a chance to fail. There are way too many variations.

I get it. Thanks!

I mean I do know corresponding squares but I didn't get the 1, 2 3.... Part. Like, isn't that the whole point of this chapter? Zugzwang.

It's the exact opposite: once you've studied and integrated the concept for good, you kinda instant see the squares you need to see, cos you then "see it".

Their definition of zugzwang in this position is a win by opposition. The squares numbered 1, 2, 3, 4 are just there to show where to move your king (assuming you are white) if black moves their king to such square. For example, if black moved their king to g7 (4) you would move your king to c7 (4), then if Kg6 (3) Kc6 (3), then if Kg7 (4), Kd5 (4), etc...

So different people have different opinions. I get it. Thanks!