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drethelin comments on Open thread, 3-8 June 2014 - Less Wrong
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So as several people said, Omega is probably more within the realm of possibility than you give it credit for, but MORE IMPORTANTLY, Omega is definitely possible for non-humans. As David_Gerard said, the point of this thought exercise is for AI, not for humans. For an AI written by humans, we can know all of its code and predict the answers it will give to certain questions. This means that the AI needs to deal with us as if we are an Omega that can predict the future. For the purposes of AI, you need decision theories that can deal with entities having arbitrarily strong models of each other, recursively. And TDT is one way of trying to do that.
In general, predicting what code does can be as hard as executing the code. But I know that's been considered and I guess that gets into other areas.
Even if that's the case, when dealing with AI we more easily have the option of simulation. You can run a program over and over again, and see how it reacts to different inputs.