Definition: Parameter
A parameter of a physical system is any characteristic of the system which can be quantified mathematically.
NOTE
Parameters can be pretty arbitrary, but we are usually only interested in those which are useful for physical predictions and obey certain laws such as position, momentum, temperature, pressure, etc.
Example: Room Full of People physical system which consists of a room full of people. The average age of the people is a parameter of the system, since it can be quantified mathematically by a number.
Imagine a
Example: Cyclops Staring at a Wall
Consider a physical system consisting of a cyclops staring at a wall with its single eye. The direction from which it is looking at the wall is a parameter of the system, since it can be quantified by a vector.
Definition: Parameterisation
A parameterisation of a physical system is any set of parameters of the system which we choose to examine and consider relevant.
Example: Gas
A gas is often parameterised by its volume, pressure, temperature and number of molecules, but this is just one possibility. An alternative parameterisation could be its density, mass and total kinetic energy of its molecules.
Definition: Equivalent Parameterisations
Two parameterisations of a physical system are equivalent if it is possible to calculate the values of all parameters in the first from the values of all parameters in the second and vice versa.
EXAMPLE
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