The word half is weird. Think about it, if I have a long rope, say 10 feet long, and want to cut it in half as many times as I can, what would be the length of that rope when I'm finished?
Sounds like one of those math problems you got in school that seemed easy and then ended up being a "What the #%!& is going on?" question. Because it is.
If I cut the 10 foot rope in half, I'll have two 5 foot ropes. If I cut one of them in half, well, I'll have two 2.5 foot ropes. If I cut one of those in half 10 more times, I'll have two 0.0024 foot ropes. That's about 0.03 inches or about 0.7 mm. That's about half the thickness of a dime. Pretty thin, but if you see where I'm going, theoretically you can cut that in half again and do so for infinity. In real life, well.. I would have stopped cutting that rope a while ago since it's quite difficult to cut a half inch rope, never mind one that's less than 0.1 inches.
Regardless of the fact that I can't cut a rope that small, it stands that it can be halved again, and again, and again. This is a paradox, in fact, it's one of Zeno's Paradox, specifically the Dichotomy paradox.
Let's look at this slightly differently.
If I am moving my hand toward a wall, it can be thought of as halving the distance from my hand to the wall over and over again until I touch the wall. But if we follow the logic that I can infinitely halve the distance of one object (my hand) to another (the wall), it means I should never actually touch the wall! But clearly, I am touching the wall.
Want another one?
This is the Arrow Paradox. Picture an arrow flying toward a target. The arrow travels in the air, we can see it and feel it (ouch.. if it hits you) but if we think about the arrow in an instant of time, which means that time doesn't move for that instant, the arrow isn't moving. It is essentially stuck in that one freeze-frame of time. This means it's not moving toward the target since no time is elapsing for it to move, and already occupies the space it is at, at that instant. So if no motion happens at the instant and time itself is made up of instants, we can only conclude that there is no motion at all. But the arrow moves, and hits the target. How?
Well, the whole point of a paradox is that there is no true explanation. It's a logic loophole.
Thanks for reading!
Sounds like one of those math problems you got in school that seemed easy and then ended up being a "What the #%!& is going on?" question. Because it is.
If I cut the 10 foot rope in half, I'll have two 5 foot ropes. If I cut one of them in half, well, I'll have two 2.5 foot ropes. If I cut one of those in half 10 more times, I'll have two 0.0024 foot ropes. That's about 0.03 inches or about 0.7 mm. That's about half the thickness of a dime. Pretty thin, but if you see where I'm going, theoretically you can cut that in half again and do so for infinity. In real life, well.. I would have stopped cutting that rope a while ago since it's quite difficult to cut a half inch rope, never mind one that's less than 0.1 inches.
Regardless of the fact that I can't cut a rope that small, it stands that it can be halved again, and again, and again. This is a paradox, in fact, it's one of Zeno's Paradox, specifically the Dichotomy paradox.
Let's look at this slightly differently.
If I am moving my hand toward a wall, it can be thought of as halving the distance from my hand to the wall over and over again until I touch the wall. But if we follow the logic that I can infinitely halve the distance of one object (my hand) to another (the wall), it means I should never actually touch the wall! But clearly, I am touching the wall.
Want another one?
This is the Arrow Paradox. Picture an arrow flying toward a target. The arrow travels in the air, we can see it and feel it (ouch.. if it hits you) but if we think about the arrow in an instant of time, which means that time doesn't move for that instant, the arrow isn't moving. It is essentially stuck in that one freeze-frame of time. This means it's not moving toward the target since no time is elapsing for it to move, and already occupies the space it is at, at that instant. So if no motion happens at the instant and time itself is made up of instants, we can only conclude that there is no motion at all. But the arrow moves, and hits the target. How?
Well, the whole point of a paradox is that there is no true explanation. It's a logic loophole.
Thanks for reading!
Comments
Post a Comment