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http://en.wikipedia.org/wiki/Digital_physics (It's been years since I read that article; I'm going to read it again...)
I read that too as soon as I saw thomblake's reply. I'm a newcomer here, and I hadn't heard of this view of physics before so it was very informative (though the quality of the wiki article isn't that high, citation wise). I've also been talking to a physicist/philosopher about this (he's been saying a lot of the same things you have) and he gave me the impression that if there's a consensus view in physics, it's that time is continuous...but that this is an open question.
Is this computationalist view of physics popular here, or rather, is it more popular ...