  Exploiting singularities in Feynman integrals to get information about
scattering amplitudes has been particularly useful at one-loop in theories
where no triangles or bubbles appear. At higher loops the integrals possess
subtle singularities. In this paper we give these singularities a physical
interpretation and show how they turn tedious computations into purely
pictorial manipulations. We illustrate our methods with various examples from
the computation of four-particle amplitudes in N=4 super Yang-Mills and N=8
supergravity. Along the way we find clues towards an understanding i) of the
rung-rule as a consequence of infra-red singularities, ii) of the non rung-rule
integrals included in the basis as corrections to the rung-rule and iii) of the
coefficients - including signs - of these two types of contribution. The role
of corrections is to cancel unphysical singularities generically present in
rung-rule integrals. A further byproduct, coming from the fact such unphysical
singularities are located where conformal cross-ratios become unity, is the
possibility of understanding the dual conformal invariance ansatz for
constructing the basis of four-particle amplitudes in N=4 super Yang-Mills.
