Footnotes

1. The notion of effective theory is central to physics. A good example of an effective theory is hydrodynamics, which describes fluids in terms of a continuum. This is an approximation to the microscopic theory, which replaces the continuum by the discrete position of the constituent molecules of the fluid. For most questions, the effective theory is sufficiently precise, and offers a much handier description of the fluid.
2. Intuitively, surfaces of different geometry correspond to surfaces of different size and shape.
3. The objection “Why stop at 1-dimensional extended objects?” springs to mind immediately, and indeed, string theory has not stopped here. Higher dimensional objects, so-called D-branes (a play on membrane, where D denotes the spatial dimension of the object), also play an important role in the theory.
4. Denoting the genus as h and the string coupling constant as g_s, a contribution of a world-sheet of genus h is weighted by a factor (g_s)^h. In the weak coupling regime g_s < 1, this factor becomes smaller and smaller as the genus h increases.