Free parameters are those variables in a physical model or mathematical equation that can be freely altered. These parameters are not constrained by other variables or parameters and can be independently adjusted. In experimental design, free parameters are the variables that can be changed to influence the outcome.

For example, in a dice-rolling experiment, the number of sides on the die is a free parameter because you can choose to use a die with any number of sides. This choice can affect the outcome of the experiment, so it is considered a free parameter.

In more complex scientific experiments, there may be many different free parameters that can be changed, such as the magnitude of a force, the mass of an object, or the value of a charge. These are free parameters because they can be independently altered without affecting other variables.

The concept of free parameters is essential in many scientific and engineering fields because they allow researchers to modify certain aspects of an experiment or model in order to better understand or predict phenomena. By adjusting free parameters, researchers can explore different possibilities and find the most suitable solution or explanation.

In summary, free parameters are variables that can be independently adjusted without being constrained by other variables or parameters. They play a critical role in scientific research and experimental design, allowing us to modify and optimize results.

For example, if we add a constraint to a parameter:

$$ w_{25,j}=w_{9,j} $$

Then, these two parameters actually count as one parameter.

To avoid exhaustive attacks, the description of constraints should also be considered as part of the parameter count.