  We give new and simple proofs of some classical properties of hereditarily
indecomposable Banach spaces, including the result by W. T. Gowers and B.
Maurey that a hereditarily indecomposable Banach space cannot be isomorphic to
a proper subspace of itself. These proofs do not make use of spectral theory
and therefore, they work in real spaces as well as in complex spaces. We use
our method to prove some new results. For example, we give a quantitative
version of the latter result by Gowers and Maurey and deduce that Banach spaces
that are isometric to all of their subspaces should have an unconditional basis
with unconditional constant arbitrarily close to $1$. We also study the
homotopy relation between into isomorphisms in hereditarily indecomposable
spaces.
