I'd like to write a performance-sensitive application in Python, so executing it under PyPy is a natural choice. However, a significant portion of my code depends on numpy, scipy, and scikit-learn. Would it be possible to embed a CPython instance within a running PyPy program in order to call array-oriented code? If not, what's the easiest way to make PyPy and CPython talk to each other?
No, you can't embed CPython inside PyPy AFAIK. You can, however, use distributed/parallel execution systems to make PyPy talk to CPython. Both execnet and Pyro mention this precise PyPy <-> CPython use case. Other packages from Python Wiki's Parallel Processing page are probably suitable too.
Also, as delnan mentions, there's a current discussion about PyPy developers' plan on implementing Numpy in PyPy (which doesn't include support for scipy, and scikit.learn so far).