Perhaps we can use principles from the field of System Dynamics
to model the situation on the chessboard and use the insight we gain from that model to assess how promising the
position is for either side.
We might begin by determining the important relationships among
the pieces on the board and the constraints that exist which are likely to prevent our pieces from becoming fully engaged
in the game.
p.3-4"By applying physical laws to a specific system, it may be
possible to develop a mathematical model that describes the dynamics of the system. Such a model may include unknown parameters,
which must then be evaluated through actual tests. Sometimes, however, the physical laws governing the behavior of a system
are not completely defined, and formulating a mathematical model may be impossible. If so, an experimental modeling process
can be used. In this process, the system is subjected to a set of known inputs, and its outputs are measured. Then a mathematical
model is derived from the input-output relationships obtained.
Simplicity of mathematical model versus accuracy of results of analysis. [section title] In attempting
to build a mathematical model, a compromise must be made between the simplicity of the model and the accuracy of the results
of the analysis. It is important to note that the results obtained from the analysis are valid only to the extent that the
model approximates a given physical system.
In determining a reasonably simplified model, we must decide which physical variables
and relationships are negligible and which are crucial to the accuracy of the model... Whether any particular features are
important may be obvious in some cases, but may, in other instances, require physical insight and intuition. Experience is
an important factor in this connection.
Usually, in solving a new problem, it is desirable first to build a simplified
model to obtain a general idea about the solution. Afterward, a more detailed mathematical model can be built and used for
a more complete analysis."
A chess piece exerts a force that can be felt at a distance. We should think about a way we
can model this and use the model to accurately predict how effective each piece is in the game.
p.55"Force can be defined as the cause which tends to produce a change in motion of a body
on which it acts. To move a body, force must be applied to it. Two types of forces are capable of acting on a body: contact
forces and field forces. Contact forces are those which come into direct contact with a body, whereas field forces,
such as gravitational force and magnetic force, act on a body, but do not come in contact with it."
We might think of the chess pieces as having potential energy. This means that the piece
has the potential to do work, or the potential to restrict enemy pieces from doing work. This energy is derived from the piece's
position on the board and the relationships among the other pieces.
p.73"In a general way, energy can be defined as the capacity or ability to do work. Energy
is found in many different forms and can be converted from one form into another... A system is said to possess energy when
it can do work... The energy that a body possesses because of its position is called potential energy... Potential
energy is the work done by an external force."
Our evaluation function might consider the relationships among the various pieces and their ability
to accomplish objectives. We would need to come up with an accurate way to model this. Here is one approach.
p.109"A block diagram of a dynamic system is a pictorial representation of the functions performed
by each component of the system... Such a diagram depicts the interrelationships that exist among the various components...
In general, the functional operation of a system can be visualized more readily by examining a block diagram than by examining
the physical system itself. A block diagram contains information concerning dynamic behavior"
Perhaps we can set up a control loop where we use the 'goodness' of the pieces to steer our
search efforts. The feedback we use would be the estimated ability of the pieces to accomplish objectives and a general assessment
of how promising the position is for either side. If our positional estimates are fairly accurate, we can also decide to stop
searching certain lines if it is determined that the position is not promising. We would need to analyze to a certain search
depth in order to protect against possibility of a tactical combination.
p.492"A system that maintains a prescribed relationship between the output and the reference input
by comparing them and using the difference as a means of control is called a feedback control system or simply a
control system."
