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Saturday, July 23, 2011

7 paradoxes we bet you can’t solve-7 nghịch lý, chúng tôi cược bạn không thể giải được.

Paradoxes are rather loosely defined, but can be said to be a true statement that defies intuition. Some have solutions, some don’t. Here are 7 paradoxes we bet you can’t solve.

1. Free will

Image source - Wikipedia

If God is omnipotent and knows what we will do before he created us, how can we have free will?

ANSWER: This paradox is explained by God being outside of time–he knows the future just like he knows the past and the present. Just as the past does not interfere with our free will, neither does the future.

2. Crocodile Dilemma

Image source - Wikipedia

A crocodile steals a son from his father, and promises to return the child if the father can correctly guess what the crocodile will do. What happens if the father guesses that the child will not be returned to him?

ANSWER: There is no solution. If the crocodile keeps the child, he violates his rule, as the father predicted correctly. If the crocodile returns the child, he still violates his rule as the father’s prediction was wrong.

3. Grandfather paradox

Image source - zastavki.com

A man goes back in time, and kills his grandfather before the grandmother can meet his grandmother. This means that one of the man’s parents will not have been born, and the man in turn, will not have been born. This would mean that he could not have traveled back in time after all, which means the grandfather would still be alive, and the traveler would have been conceived allowing him to travel back in time and kill his grandfather.

ANSWER: The moment the time traveler changes something in the past, a parallel universe splits. This is supported by quantum mechanics.

4. Paradox of the heap

Image source - Wikipedia

There are 1,000,000 grains of sand in a heap. If we remove one grain, it is still a heap. If we remove another grain, if it still a heap. If we continue removing one grain at a time, when we’re left with one grain, is that still a heap?

ANSWER: Set a fixed boundary. If we said 10,000 grains of sand made a heap, then anything below it would not be a heap. Yet, it seems unreasonable to distinguish between 9,999 and 10,001 grains of sand. The solution can therefore be altered to say there is a fixed boundary, but they are not necessarily knowable.

5. Omnipotence paradox

Image source - Wikipedia

Can God create something so heavy He cannot lift it? If he can create something so heavy he can’t lift, then his lack of strength means he is not omnipotent. If he can’t create something so heavy he can’t lift, than he is not omnipotent.

ANSWER: The most common response is that as God is omnipotent, “can not lift” does not make sense. Other answers include the question being a contradiction, like a “square circle”.

6. Epimenides paradox

Image source - Wikipedia

Epimenides, in a poem wrote: “The Cretans, always liars, evil beasts, idle bellies!” However, Epimenides himself was a Cretan. If Epimenides is a Cretan and a liar, then his statement, “The Cretans, always liars” is a lie. This means all Cretans are truthful, then Epimenides’ statement is the truth. The paradox will infinitely regress.

ANSWER: If Epimenides knew of at least one Cretan (other than himself) who is not a liar, his statement is a lie (because he asserts all) even though it correctly describes the speaker as a liar.

7. Unstoppable force paradox

Image source - motivatedphotos.com

What happens when an unstoppable force meets an unmovable object? If the force moves the object, then it is not unmovable. If the force doesn’t, the force is not unstoppable.

ANSWER: This situation can never happen, as if there is an unstoppable force, there couldn’t be an unmovable object and vice versa. More interestingly, there can never be an unmovable object. An unmovable object would have to have infinite inertia, and therefore infinite mass. Infinite mass cannot exist in our finite universe, therefore an unmovable object cannot exist.

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