> Any computer program could be performed with pencil and paper, by getting a big file folder to simulate RAM, indexing it by numbers, and performing assembly instructions by hand with post-it notes as registers

Indeed. But surely if the purpose of the algorithm is something like "find whether this combination exists in a set of millions / billions of records within a tractable time" then it cannot possibly be done by hand in a tractable/practical way -- and it will fail this test?