Interesting paradox!
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Saw a really interesting question on my brother's tutorial a few days back, and thought I should perhaps share it. I still don't have the answers to the questions though...
The following paradoxes are thought up by some thinker from ancient time. I think I can find the answer easily simply my googling his name, except that I forgot his name, and the name of the paradoxes thought up by him. In fact, I've forgotten the question in it's exact words...so I'll just try writting them down in my own words.
Paradox 1: Suppose two competitor, A and B, are getting ready for a race with each other. Competitor B's starting point is 100m ahead of competitor A. However, competitor A runs 10 times faster than competitor. Going by the logic of that thinker, it is theoretically impossible for competitor A to overtake competitor B. Why so?
Suppose the race starts. When competitor A has ran 100m (i.e. competitor B's starting point), competitor B would had ran 10m, since competitor B runs 10 times slower than competitor A (in another word, competitor B is 10m ahead of A). When competitor A runs a further 10m, competitor B would be 1m ahead of competitor A. When competitor A runs another 1m, competitor B would be 10cm ahead of competitor A.
As this goes on, we can see that while the distance between competitor B and competitor A shortens as time goes by, it's impossible for competitor A to catch up with and overtake competitor B, for theoretically, competitor B is always ahead of competitor A. However, we know from our practical experiences that this is not so.
How do you explain this?
Paradox 2: According to that thinker's logic, motion is impossible.
For us to move 100m, we must have moved 50m. For us to move 50m, we must have moved 25m. For us to move even 1cm, we must have moved at 0.5cm.
In another words, for us to move, we must have moved a shorter distance. Yet, moving even the shortest distance should be impossible without moving an even shorter distance. Hence, motion is impossible.
My answer for this would be that nothing is ever stationary. For us to make sense of this logic, we must deduce another logic: that every partical or physical substances that makes up this world is in constant motion. Since we are always in motion, we are never stationary. Since we are never stationary, there's no need for us to start a motion. Hence, motion is possible (for it is always happening).
Still, I believe there's a simpler answer for this. I await those who can come out with a satisfactory answer...by themself! -
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Since you so free can come my house help me scrub toilet?
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Your first 'Paradox' is not a paradox is an argument that from the beginning is biased against competitor A if you havent noticed.. i don't know why your calculations in distance decrease as you go.. as if you want to calculate the shortest distance between A and B.. (which is why i say its biased)
try counting A running 200m after the race starts and you'll see
Now for your second 'Paradox'
yes its true that we must move and even shorter distance before we cover a short distance and an even shorter distance to cover that previous even shorter distance ect. But what we'll get in the end is an infinite regress to find the shortest distance possible.. BUT it doesnt mean motion is impossible just because at the moment the shortest distance theoritically can be infinitely small..Originally posted by mahawarrior:In another words, for us to move, we must have moved a shorter distance. Yet, moving even the shortest distance should be impossible without moving an even shorter distance. Hence, motion is impossible.
besides... even if we can count the infinitely small distance possible, it already proves that something has already MOVED that infinitely small distance. therefore motion is possible
You've committed the fallacy of the stolen concept, eg. you are trying to prove there is no motion by using motion in your calculation lol -
Some bo liao greek Mathematican thought of this. I can't remember his name tho...
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what the fuk are you babbling about.
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2nd point very easily proved. we are constantly in motion, heart beating, blood flowing, earth rotating...
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yea 2nd pt easily proven. primary school teach us dat molecules are constantly vibrating/moving.
yay 20 posts no more 5 mins wait le.. -
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sound complicated to me...
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All dat reading..make me sleepy....
Yawn... -
http://en.wikipedia.org/wiki/Zeno%27s_paradoxes
It has all gotta do with sums of infinite series. With calculus, it's not impossible. -
you are saying that if we want to move 100 meters, we "must" move 50meters, "stop" then move 100meters.Originally posted by mahawarrior:Paradox 2: According to that thinker's logic, motion is impossible.
For us to move 100m, we must have moved 50m. For us to move 50m, we must have moved 25m. For us to move even 1cm, we must have moved at 0.5cm.
In another words, for us to move, we must have moved a shorter distance. Yet, moving even the shortest distance should be impossible without moving an even shorter distance. Hence, motion is impossible.
Who says we must "stop"? -
This is A classic case of what is known as Zeno's paradox.
It is quite well-known in mathematical circles.Sometimes they use the example of Archilles and the tortoise.
A similar problem would be to consider this - imagine you take a picture of an arrow in flight. It will appear to be at rest instantaneously. of course, if you string together an infinite number of Still pictures -you get movement!
The key to understanding this is that an infinite sum of infinitesimal quantities may give a real result.
You can look at, for example, the Study of hyperreal numbers. -
walau eh wad subject is this sia...
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and hence no self and wu wei m i rite?
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reminds me of this video.....
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ur 1st 1 so dumb..
look at it from another perspective..
A runs 200m...
paradox undone.. -
Problem is...both will never complete the race.