Let’s start with some examples to understand what paradoxes are. We won’t be discussing about the examples I illustrated. We’ll just discuss about the UNEXPECTED HANGING paradox.
What if you have a heap of sand in your hand, and you take one grain out of it, it’ll still be called a heap of sand, right? Now remove another grain of sand. Still a heap?
Keep removing grain by grain until you reach a point when only one grain of sand is left in your hand. Now would you call it a heap? At what point did the heap of sand ceased to be a “heap”!?
This is called Sorites paradox.
If I say, “This sentence is false”, is it true or is it false?
If the line “This sentence is false”, is true, then according to the statement I made, the sentence, “This sentence is false” should be false. But if the sentence is false, then “This sentence is false” is truly false i.e. it is actually true.
There within lies the paradox, the liar’s paradox.
The Unexpected Hanging!
This paradox will twist your mind in the simplest most complex way possible.
The judge tells a prisoner that he’ll be executed at “noon”, someday between Monday and Friday (Monday and Friday included). And the day will not be told to the prisoner, so that he’ll be surprised on the day of his hanging.
1. Between Monday and Friday
2. Surprise (Prisoner should not know the day of his hanging)
Now, let’s go into the mind of the prisoner.
“If I am not executed on Thursday, there is only one day i.e. Friday left for my execution. This then means that I’ll be hanged on Friday. But then I know the day of my execution, that means I’ll not be surprised. Therefore I cannot be hanged on Friday.
Now, there are only 4 days left, i.e. till Thursday. By following the same logic, I cannot be hanged on Thursday as well, and then Wednesday too, then Tuesday and then Monday.
Therefore, I cannot be executed as this will lead to the breaking of one or both of the promises of the Judge”
The Judge hangs him on Wednesday. Why?
First answer : Because, why not? For all we know he was surprised like never before!
Second answer : The deductions of the prisoner started from the last day, taking into the account the assumption that he is not executed till Thursday. On Friday, the promise will break, but that is only if he is not hanged until Thursday. Note that he could only rule out the possibility of Friday if he is not hanged till Thursday. If he’s hanged between any day from Monday to Thursday, he cannot make predictions about Friday.
Next thing he considered was hanging on Thursday, while ruling out Friday. He cannot rule out Friday, if he is considering the possibility that he’ll be hanged on Thursday.
This is a little difficult to understand, but when you get it, it is actually quite interesting.
Judge knew that he had to give the punishment before or on Thursday, or else his promises would break.
Therefore he hanged him on Wednesday.
What do you think?