Should we give up hope of ever proving nonrelativizing circuit lower
bounds for complexity classes we care about? Alternatively, should we
dismiss oracle results as merely formalizing the obvious? I'll advocate
a negative answer to both questions, and illustrate with some new
results:

* For every fixed k, PP does not have quantum circuits of size n^k, not
even with quantum advice.
* PP has linear-sized circuits relative to an oracle. This yields only
the second example of a nonrelativizing separation in complexity theory
(and the first example below NEXP), and resolves an open problem of
Fortnow.
* In the circuit learning algorithm of Bshouty et al., adaptive NP
queries are in some sense provably necessary.