Apologies for posting so much in the June Open Threads. For some reason I'm getting many random ideas lately that don't merit a top-level post, but still lead to interesting discussions. Here's some more.

1. How to check that you aren't dreaming: make up a random number that's too large for you to factor in your head, factor it with a computer, then check the correctness by pen and paper. If the answer fits, now you know the computing hardware actually exists outside of you.

2. How to check that you aren't a brain in a vat: inflict some minor brain damage on yourself. If it influences your mind's workings as predicted by neurology, now you know your brain is physically here, not in a vat somewhere.

Of course, both those arguments fall apart if the deception equipment is "unusually clever" at deceiving you. In that case both questions are probably hopeless.