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.