A little more practcally, a phase space is any imaginary space, plotting measurements of a few

phemonena pertinent to a particular physical or mathematical

system.

If you were showing the states of a pendulum, for example, you might choose a two-dimensional phase space so that you could plot the pendulum's horizontal

position versus its

speed at any one given point in time.

You might even throw

time in to your phase space to get three dimensions (although time with one other dimension is usually called a

time series rather than a phase space), but you would definitely *not* add a dimension to plot the pendulum's vertical position, since that doesn't give you any new information.

One well-known phase space is the

Hertzsprung-Russell Diagram used by

astronomers to plot the

luminosity of a star (as evidenced by its

absolute magnitude) against its

temperature (as derived from the star's

color).

If you pick the right phenomena to include as dimensions in your phase space, when you plot your observations, patterns will emerge to tell you something about your system.

This happened in the early 1960s when

Edward Lorenz reduced complicated equations about

convection to

differential equations in three dimensions. When he plotted his observations in the phase space those dimensions represented, he got the famous

strange attractor which bears his name.