3 ms·
Just like all such problems the 'TV and the Radio' problem shares its root with the liars paradox. The root cause, of course, are self referention, determinism
by SCHiM 12y ago
Just like all such problems the 'TV and the Radio' problem shares its root with the liars paradox. The root cause, of course, are self referention, determinism and recursion.
The problem is the 'prediction loop', which has no clearly defined exit. There's no path that can be followed that will terminate it:
The demon understands every part of your brain, and knows that if it says that you're going to watch TV while you're determined to prove it wrong will make you listen to the radio instead. So it enters the next iteration of the loop. This cycle would continue for infinity, which is where we perceive a paradox.
There are several naive resolutions that come to my mind. Assuming that predicting the future takes some time, even if it's only a fraction of a second, will allow a way out. The Demon will simply enter the loop and exit it once the evening has passed and every possibility of 'predicting it' has vanished. Of course this could be considered cheating, it has never been established if the Demon's computations take time or not, but asking this question can be considered cheating as well, since it's probably impossible to have _only_ two possible things you could be doing. Which introduces the second solution.
The Demon is more intelligent than you are, and while you'd sworn to yourself that there were only two possible outcomes to this evening: doing the opposite of what the Demon predicts, the Demon sees beyond the 'two' possibilities and correctly predicts a third possibility that you didn't envision.
The last solution attacks the notion of free will, if the Demon can exactly predict the future than this implies that the universe is deterministic. So instead of having only two options, or a third invisible option, there is only one real option and the demon cannot be wrong or it cannot be right.
All of these 'solutions' either introduce a new or alter a previous assumption and are thus not really solutions to the question asked, as it stands I think the question is unanswerable and introducing new concepts and ideas is inevitable.
- tuxcanfly 12y ago>So instead of having only two options, or a third invisible option, there is only one real option and the demon cannot be wrong or it cannot be right. This third neither right nor wrong option reminds me of 'Mu' found in eastern philosophy and highlighted in Hofstadter's GEB and it forms another crucial part of self-reference and recursion as mentioned earlier in your comment.
- deleted 12y ago[deleted]
- jmount 12y agoOr even worse: one of the "cosmic censorship" hypothesis turns out to be correct. In such case if you ask the demon, you might not live to the next day (or if you form the intent to ask the demon, you may not make it even that far). Or the "Star Trek" solution to the paradox: the demons starts repeating error in a high pitched mechanical voice and smoke pours out.
- whoopdedo 12y agoThe problem I have with the proof is how it begs the question of free will. The definition of the Demon assumes a purely mechanical universe. Free will is not mechanical. A person with free will cannot be part of the universe that the Demon is able to observe. I'm not sure it's even applicable to the universe we live in because of random events. Is the randomness we observe a result of a mechanical process, or is it inherently unpredictable? If the later, that would make a Demon inherently impossible. It could be we just don't have enough information to decipher the things that appear random to us. Or is randomness what happens when you try to apply Laplace's Demon. As you say, a Demon needs to be able to predict its own predictions. When such a self-referential loop occurs, then any possible event is a "correct" prediction, and that's what happens.