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.
A similar method was used by Solaris protagonist to check if he isn't hallucinating.
Ouch! I read Solaris long ago. It seems the idea stuck in my head and I forgot its origin. And it does make much more sense if you substitute "hallucinating" for "dreaming".
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