Zeno's paradoxes:
The most famous of Zeno's arguments is the Achilles:
'The slower when running will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must necessarily always be some distance ahead.'
This is usually put in the context of a race between Achilles and the Tortoise. Achilles gives the Tortoise a head start 10 m ,for ex, since he runs at 10 m/s and the Tortoise moves at only 1 ms-1. Then by the time Achilles has reached the point where the Tortoise started (T0 = 10 m), the slow but steady individual will have moved on 1 m to T1 = 11 m. When Achilles reaches T1, the labouring Tortoise will have moved on 0.1 m (to T2 = 11.1 m). When Achilles reaches T2, the Tortoise will still be ahead by 0.01 m, and so on. Each time Achilles reaches the point where the Tortoise was, the cunning reptile will always have moved a little way ahead.
This seems very peculiar. We know that Achilles should pass the Tortoise after 1.11 seconds when they have both run just over 11 m, so Achilles will win any race longer than 11.11m. But why in Zeno's argument does it seem that Achilles will never catch the tortoise?
THE BOOTSTRAP PARADOX:
The Bootstrap Paradox is a paradox of time travel that questions how something that is taken from the future and placed in the past could ever come into being in the first place. It’s a common trope used by science fiction writers and has inspired plotlines in everything fromDoctor Who to the Bill and Ted movies
examples—by Professor David Toomey of the University of Massachusetts and used in his book The New Time Travellers—involves an author and his manuscript.
Imagine that a time traveller buys a copy of Hamlet from a bookstore, travels back in time to Elizabethan London, and hands the book to Shakespeare, who then copies it out and claims it as his own work. Over the centuries that follow, Hamlet is reprinted and reproduced countless times until finally a copy of it ends up back in the same original bookstore, where the time traveller finds it, buys it, and takes it back to Shakespeare. Who, then, wrote Hamlet?
THE CARD PARADOX:
This one is realy easy
the second statement is true
the first statement is false
GRANDFATHER PARADOX:
Basically, the Grandfather paradox conveys the idea of a self-correcting universe and/or fixed points in time. Even if you were able to go back in time and, I don’t know, shoot your Grandpa in the head before he ever meets your Grandma (jeez, you must really hate that guy, huh?), your Grandfather would turn out to be an early sperm donor or something, who would still manage even posthumously to impregnate your Grandmother, because you would have to exist in order to have shot him in the head in the first place. So you might be able to fudge a few temporal details here and there, but no matter what you do, the end result stays the same.
EX: This one perfectly demonstrates the aforementioned Novikov self-consistency principle. The basic idea is that, no matter how hard you try, you can’t go back in time and kill your grandfather, because if you did, your mother or father would never have been born, which means that you would never have been born, which means you couldn’t have gone back in time and killed your grandfather, which means that you didn’t go back in time and kill your grandfather, because you can’t go back in time and kill your grandfather, because if you did, you wouldn’t be born, which you obviously have already been born because if you were never born then you couldn’t have gone back in time and tried (and failed) to kill your grandfather in the first place.
THE FLETCHER’S PARADOX
Imagine a fletcher (i.e. an arrow-maker) has fired one of his arrows into the air. For the arrow to be considered to be moving, it has to be continually repositioning itself from the place where it is now to any place where it currently isn’t. The Fletcher’s Paradox, however, states that throughout its trajectory the arrow is actually not moving at all. At any given instant of no real duration (in other words, a snapshot in time) during its flight, the arrow cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, the arrow must be stationary. But because all time is comprised entirely of instants—in every one of which the arrow must also be stationary—then the arrow must in fact be stationary the entire time. Except, of course, it isn’t....
Let’s Kill Hitler Paradox:
Similar to the Grandfather Paradox which paradoxically prevents your own birth, the Killing Hitler paradox erases your own reason for going back in time to kill him. Furthermore, while killing Grandpa might have a limited “butterfly effect”, killing Hitler would have far-reaching consequences for everyone in the world, even if only for the fact you studied him in school. The paradox itself arises from the idea that if you were successful, then there would be no reason to time travel in the first place. If you killed Hitler then none of his actions would trickle down through history and cause you to want to make the attempt.
By far the best treatment for this notion occurred in an a Twilight Zone episode called Cradle of Darkness that sums up the difficulties involved in trying to change history, with another being an episode of Dr Who called ‘Let’s Kill Hitler’.
Predestination Paradox:
A Predestination paradox occurs when the actions of a person traveling back in time ultimately causes the event he is trying to prevent to occur. He then becomes trapped inside a ‘temporal causality loop’ in which Event 1 in the past influences Event 2 (time travel to the past) which then causes Event 1 to occur, with this circular loop of events thus ensuring that history is not altered by the time traveler’s journey to the past. In other words, any attempts to stop something from happening in the past will simply lead to the cause itself, instead of stopping it. This paradox suggests that things are always destined to turn out the same way, and that whatever has happened must happen. Sound complicated? Imagine that your lover dies in a hit-and-run car accident, and you travel back in time to save her from her fate, only to find that on your way to the accident you are the one who accidentally runs her over.
Therefore, you cannot change the past and furthermore, anyone attempting to do so may literally find themselves trapped within a repeating loop of time. One way of dealing with this type of paradox is to assume that the version of events experienced are already built into a self-consistent version of reality, and that a time traveler trying to alter the past will only end up fulfilling his role in creating history, not altering it.
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