  Black hole complementarity, as originally formulated in the 1990's by
Preskill, 't Hooft, and myself is now being challenged by the
Almheiri-Marolf-Polchinski-Sully firewall argument. The AMPS argument relies on
an implicit assumption---the ``proximity postulate---which says that the
interior of a black hole must be constructed from degrees of freedom that are
physically near the black hole. The proximity postulate manifestly contradicts
the idea that interior information is redundant with information in Hawking
radiation, which is very far from the black hole. AMPS argue that a violation
of the proximity postulate would lead to a contradiction in a
thought-experiment in which Alice distills the Hawking radiation and brings a
bit back to the black hole. According to AMPS the only way to protect against
the contradiction is for a firewall to form at the Page time. But the
measurement that Alice must make, is of such a fine-grained nature that
carrying it out before the black hole evaporates may be impossible. Harlow and
Hayden have found evidence that the limits of quantum computation do in fact
prevent Alice from carrying out her experiment in less than exponential time.
If their conjecture is correct then black hole complementarity may be alive and
well.
  My aim here is to give an overview of the firewall argument, and its basis in
the proximity postulate; as well as the counterargument based on computational
complexity, as conjectured by Harlow and Hayden.
