In physics and mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate (the polar coordinate angle), so the circle is 1-dimensional even though it exists in the 2-dimensional plane. High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics. Ie: these are abstract spaces, independent of the actual space we live in. The state-space of quantum mechanics is an infinite-dimensional function space. Some physical theories are also by nature high-dimensional, such as the 4-dimensional general relativity and higher-dimensional string theories.