We give two independent arguments why the classical membrane fields should be
loops. The first argument comes from how we may construct selfdual strings in
the M5 brane from a loop space version of the Nahm equations. The second
argument is that there appears to be no infinite set of finite-dimensional Lie
algebras (such as su(N) for any N) that satisfies the algebraic structure
of the membrane theory.Comment: 28 pages, various additional comment