surprise paradox

This is a classic paradox that goes something like this:

A man is to be sentenced to death, but due to the severity of his crime, the judge decrees that the man is to be hanged one morning next week and he is not to know the exact date of his hanging.

The man is safe in the knowledge that he cannot be hanged. Why? Well it is a proof by induction. Suppose Friday is the last day of the week. If the man is not hanged by Thursday then he will know he is going to be hanged on Friday. Therefore he cannot be hanged on Friday. What about Thursday? Well if the man hasn't been hanged by Wednesday then he knows he is going to be hung on Tursday (since Friday has already been ruled out by the above logic). This rules out Wednesday as well. Carrying on this logic you can rule out all the days as well.

And then once you've ruled out every day of the week, you're not expecting to get hung ever. You'll be really surprised when the warden comes into your cell Wednesday afternoon with a noose.

QED. This proof also holds true for the Pop Quiz Paradox.

I though of this today in Math class, so it's most likely wrong. /msg me or add a wu if you find a flaw in my logic.

The only problem is, once you are not expecting to be hanged, you realise that this is the exact time you will be hanged. Being thusly expectant, you will not be hanged, which means this is the exact time you will be hanged, etc.

Of course, the execution will then take place as it had been planned all along, but you will be so distracted by the above circular reasoning that you won't actually be expecting it.

However, with this in mind, you will be expecting it, thus stopping the execution, but also creating another layer of circular thought to be distracted by, allowing the execution to go ahead again.

Of course, you know this, and thus layer after layer of this pointless reasoning goes on and on into infinity, occupying so much of your mind that you get hanged anyway.

But! You realise this! (and so on...)