Greetings,
Sort of like asking 'Why doesn't a game character know that it's a game character?'
Simply put, it all depends upon the game characters level of A.I. programming and preprogrammed knowledge. Do you program the characters level of A.I. around the programmed game world psychology and physics, or do you program it around our worlds psychology and physics? If you program an A.I. to simulate human's minds with human mental learning capabilities and then put it into a game world, then it would have the mental capabilities (the programming) needed to figure out that the game limits and game flaws are 'extremely bizarre puzzles that don't make much sense' for which the game characters would then dwell on and theorize on until they find a theory that best describes and explains it from their point of view - assuming that you (the programmer) don't intervene and give them 'special' knowledge of our world, which would then give them a basis of comparing their game world's psychology and physics to.
Plus, the amount of flaws and limits to the game world would depend upon the programmers knowledge, the programmers attention to detail, the limitations of the computer that the 'game' is programmed and running on, as well as each game character's level of A.I.
Also, just as games and programs go, when the cpu requires longer processing times (in your example of 10 minutes of real time processing = 1 minute of game time passage), the entire game lags and slows down effecting everything within the game simultaneously, so from the game character's points of view, they do not notice any time differences (sort of like when you are playing Diablo II and a lot of characters come into view, the entire game slows, characters and all). How game programmers reduce this lag time in real life in most 3D games is by making sacrifices - sacrifices in animation and graphics details, physics laws implemented, game world limitis, character's levels of a.i. and character capabilities.
If I myself had the necessary programming skills, psychology and physics understanding needed to create a game world that realistically and truly simulated both our world and the people in it, and the super duper computer needed to processes all of the necessary routines and functions fast enough for me to observe them in real time, and the time needed to write such a program, then yes, I would make it just out of curiosity (and entertainment).
Because of this, I would have to answer the original question 'Could we be living in a Matrix and just not know it?' as yes, I believe that it could be a possibility, however the memory and cpu processing requirements would be so extremely great that it is very unlikely that we are, simply because we (in this world) do not have the super duper computer needed to realistically simulate out world and everything in/on it in such fluidic detail for long lengths of time (long being longer than a few seconds), yet.
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'Only you can live your life, and only your life you must live'