You're welcome, Robert. It was fun, since your questions and points are so good. Now for the next round:
1) I'm not sure what you mean when you say that it is logically possible for a computer to follow a program accurately. Computers certainly can follow programs accurately. But that's an empirical fact, not an analytic statement. I don't think we can ever guarantee that a computer will necessarily follow its program. It seems to me--I admit I might not have really understood your scenario--that it might be the computer that fails when connected to the Cassandra machine, rather than the other way around.
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As you will see in my paper, it is a generalized future-viewing machine that is put to the test, to see if it could act like a Cassandra machine, not a Cassandra machine.
Now, as I wrote in my previous response, I was taking what is strictly necessary for my argument to go through to extremes. Indeed, this argument could still work in a time before Alan Turing, when all they would have had to go on is logical possibility. I meant, then, that as long as there is no contradiction in the idea of a computer following a simple program and accurately controlling a robotic arm which operates properly, then the argument is solid. For a run of P-1, for instance, it is impossible for any kind of machine or omniscient being whatsoever to provide the computer with a definite x-value that will turn out to be correct with respect to the future position of the weight (during any run where the computer operates properly and the arm functions as designed), because x does not equal x 1 (in modulo 4). From this we know that the generalized future-viewing machine cannot be a Cassandra machine, i.e., it cannot be a future-viewing machine that can always supply definite and correct information about all future outcomes, in every circumstance. (The italicized words combine to mean that one must only determine whether it is possible for the computer and the arm to function properly, to see that the argument succeeds.)
2) You wrote that "all known optical systems can only receive information about past scenes" because "it always takes time for light from any scene to reach any lens". I took that to mean that we see the past rather than the future because the speed of light is finite. I'm guess I'm not sure now what you mean here.
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Yes, that is what I meant. Any finite speed of light would only allow us to see the past.
Now, if the speed of light were infinite, light would not come from the future. Arriving at a destination before leaving is not a matter of going faster. An infinite speed of light would allow us to see the present, no matter how far away the things we are looking at might be.
3) I'm not sure how information about the future from another point in spacetime can arrive faster than the speed of light. What am I missing?
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You might have meant information about a gamma ray burst while it is still in transit, say in 2015, but, in my last response, I was referring to viewer foreknowledge of its eventual detection on earth in, say, 2020. So, viewer foreknowledge received in 2014 of the 2020 detection event could be used in 2014 to deduce the burst's 2015 position.
4) My guess is that foreknowledge machines are not physically possible in our region of the universe. Especially if they depend on closed timelike curves to work. As far as I know, there's no evidence that such curves exist--Godel's spacetime is kind of a theoretical special case, right? And if a foreknowledge machine had to create and manipulate such curves to function--is there another way--I assume the amount of energy required would be literally astronomical.
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Who knows how they would work? The paper primarily offers logical observations to isolate the kind of useful machine that could exist, in principle. It leaves it up to others to eventually discover how to make one, if they happen to also be both physically possible and feasible.
(Continued in next post)