  We examine an interesting set of recent proposals describing a `wormhole
paradigm' for black holes. These proposals require that in some effective
variables, semiclassical low-energy dynamics emerges at the horizon. We prove
the `effective small corrections theorem' to show that such an effective
horizon behavior is not compatible with the requirement that the black hole
radiate like a piece of coal as seen from outside. This theorem thus
concretizes the fact that the proposals within the wormhole paradigm require
some nonlocality linking the hole and its distant radiation. We try to
illustrate various proposals for nonlocality by making simple bit models to
encode the nonlocal effects. In each case, we find either nonunitarity of
evolution in the black hole interior or a nonlocal Hamiltonian interaction
between the hole and infinity; such an interaction is not present for burning
coal. We examine recent arguments about the Page curve and observe that the
quantity that is argued to follow the Page curve of a normal body is not the
entanglement entropy but a different quantity. It has been suggested that this
replacement of the quantity to be computed arises from the possibility of
topology change in gravity which can generate replica wormholes. We examine the
role of topology change in quantum gravity but do not find any source of
connections between different replica copies in the path integral for the
R\'{e}nyi entropy. We also contrast the wormhole paradigm with the fuzzball
paradigm, where the fuzzball does radiate like a piece of coal. Just as in the
case of a piece of coal, the fuzzball does not have low-energy semiclassical
dynamics at its surface at energies $E\sim T$ (effective dynamics at energies
$E\gg T$ is possible under the conjecture of fuzzball complementarity, but
these $E\gg T$ modes have no relevance to the Page curve or the information
paradox).
