Say you are the room and are passed symbols on paper, like the suits of playing cards. You use a book (lookup table) to transform series of symbols into a new symbol, and pass it out of the room to the observer.

You get passed ♠ + ♣ and you return ♢. Do you have an understanding of the underlying concept? If so, reply and tell me what it is! But if you don't know what the underlying concept is, how could you argue that the person in the room does?