Tree of motifs

After an unexpected twist, we all of a sudden have a tree of motifs to hang our knowledge on in stead of a coatrack. At the moment, I have stumbled on three motifs. One of the things we have to do, is hanging the coat hooks we already discovered on their rightful place in the tree of motifs.

But first, let's see if we can discover what the rationale is behind the motifs.

Rationale behind the geometry motif
Geometry is everything that concerns the lines of attack. Theoretically is should be possible to have a tactic with no straight line of attack whatsoever. Yet that is highly unlikely though. Usually, a combination exists of more tactical themes. One theme, take for instance a knight fork, can be without a straight line of attack, but 3 or 4 themes combined cannot. Because 4 of the 5 duplo attacks consist totally of themes with straight lines (pin, skewer, roentgen, discovered attack), while a lot of the double attacks are based on a straight line of attack either. So if you combine, say, three or more tactical themes, there always will be a straight line of attack involved. So it make sense to investigate the straight lines of attack whenever you encounter a position. The importance of the line of attack can be judged by its "readiness". How many quiet moves are needed to get to the position where the attacker attacks the target(s) along the line. We must make a distinction here between quiet moves that lose a tempo, and forcing moves that maintain the initiative. The readiness of the line of attack is not negatively influenced by forcing moves that get the line of attack ready for use. If you need quiet moves to get the line ready, the line of attack is probably not interesting enough to consider. Geometry is about the line of attack.

Rationale behind encirclement
Which pieces are the logical targets? Which pieces are close to be outnumbered? It is related to pure value, calculated value, the numbers of attackers and the number of defenders and their values. We must develop an easy to use universal system here to get the most juicy targets in view. I don't know much about mister Laskers view about encirclement, but he says: "Where there is superior force at  a given point and immobility within the defenders ranks a combination should be present".
Encirclement is about juiciness of the target.

Rationale behind function
If a piece has a function, it has obligations. Obligations limit the mobility of a piece. It can only move as long is it fulfills its duty. There are three typical methods to exploit a piece with a function:

• Harass the piece and make use of the fact that it no longer can fulfill its duty
• Make use of the limited mobility of the piece by trapping it
• When a piece is overloaded with obligations you make use of the fact that he can fulfill only one duty at the time.

 These three motifs should put you on track of any combination.
Let's see how it works in practice.

Diagram 1. Black to move

2rr2k1/pb2qppp/1p3n2/3p4/1b6/1PBQPN2/P3RPPP/2R2BK1 b - - 0 1
[solution]

Geometry
Lines of attack:
c8 - c1 already attacking
e7 - e1 already attacking
a6 - f1 can be ready in one move while preserving the initiative (Ba6)

Encircling
c4 is under attack

Function
Rc1 defends c3
Qd3 defends c3
Qd3 defends against the invasion at a6

All these motifs can be recognized in the position without any recognition of the tactical themes beforehand. It tells you that the queen has two duties it can't fulfill both. This means that bishop c3 = BAD. Only now you start for looking for the tactical themes to exploit it.