[Guest]

If I start at point a and walk to point b - (having to pass a 1/2 way point we will call c) then from that point c to point b- (having to pass a 1/2 point we will call d) then from that point d to point b (having to pass.....etc.)

Play this out to infinity - how can I ever arrive at point b?

Sorry about that!!!!

Edited September 7, 2008 by AAAsn888s

[Guest]

mm are your b and a mixed up?

if you mean that you are halving the final distance each time then neve, but i may be misundeerstanding your question

edit to say i'm rethinking the OP has been edited

Edited September 7, 2008 by Lost in space

[Guest]

turn around and go in the opposite direction

[Guest]

mm are your b and a mixed up?

if you mean that you are halving the final distance each time then neve, but i may be misundeerstanding your question

Yeah - kinda screwed up my first attempt -- try reading it again... I edited my error...

[Guest]

you get there - you are just passing halfway points as in mot stopping so you pass an infinite number of halfway points

distance i presume is not greater than normally acheivable, say 100 meters off the top of my head

[Guest]

I'm gonna go with LIS... Never

[Guest]

you get there - you are just passing halfway points as in mot stopping so you pass an infinite number of halfway points

distance i presume is not greater than normally acheivable, say 100 meters off the top of my head

How can I pass an infinite number of points?

[Guest]

I'm gonna go with LIS... Never

But I CAN walk from pt a to pt b

[Guest]

How can I pass an infinite number of points?

even if you are 0.000000000000000000000000000000000000000000000000000001 mm away, you can still halve it

[Guest]

How can I pass an infinite number of points?

As you go from a to b you are passing all the other points not actually visiting them

...(having to pass a 1/2 way point we will call c....

your op says you pass it

So imagine you have a journey over 100 km and you pass each half way point

but not stop, you passed 50 km ... 75 km... 87.5 km ..etc

Does not matter the length so long as it is humanly possible - the amount of halfway points are the same, but either way the journey is at a constant speed of 6 - 8 km per hour (depends if it is a fast or slow pace/contest

[Guest]

As LIS pointed out you passed the points, so you should get there if you just keep going

[Guest]

As LIS pointed out you passed the points, so you should get there if you just keep going

You are correct - you DO get there, but how - if you are passing an infinite number of 1/2 way points?

[Guest]

You are correct - you DO get there, but how - if you are passing an infinite number of 1/2 way points?

Asn8s - a >>>>>>>>>>>>>>>>>>>>b non stop, so time = t distance =d, speed = s d/s = t

[Prof. Templeton]

Time and space are not infinetly divisible.

[Guest]

Time and space are not infinetly divisible.

You are correct - hence the parardox (Zeno's Paradox)- - this can be shown mathematically as well:

"Suppose we take Zeno's Paradox at face value for the moment, and agree with him that before I can walk a mile I must first walk a half-mile. And before I can walk the remaining half-mile I must first cover half of it, that is, a quarter-mile, and then an eighth-mile, and then a sixteenth-mile, and then a thirty-secondth-mile, and so on. Well, suppose I could cover all these infinite number of small distances, how far should I have walked? One mile! In other words,

At first this may seem impossible: adding up an infinite number of positive distances should give an infinite distance for the sum. But it doesn't – in this case it gives a finite sum; indeed, all these distances add up to 1! A little reflection will reveal that this isn't so strange after all: if I can divide up a finite distance into an infinite number of small distances, then adding all those distances together should just give me back the finite distance I started with. (An infinite sum such as the one above is known in mathematics as an infinite series, and when such a sum adds up to a finite number we say that the series is summable.)

Now the resolution to Zeno's Paradox is easy. Obviously, it will take me some fixed time to cross half the distance to the other side of the room, say 2 seconds. How long will it take to cross half the remaining distance? Half as long – only 1 second. Covering half of the remaining distance (an eighth of the total) will take only half a second. And so one. And once I have covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 4 seconds, and here I am, on the other side of the room after all."

Copied from Prime Articles found on Mathacademy.com

[unreality]

There is a point when you step off, let's just say 1/64 left to go and land on the 0 left to go (the finish line), you have just stepped over the remainder of the infinite halfway points (ie, 1/128 and 1/256 and etc for the whole infinite series) in one step of the foot, since at some point the distance becomes so small that we step over it

But if this is more of a theoretical math problem of a point traveling along a line or something, rather than reality-based, it can indeed cross an infinite number of points in a finite number of time. In fact, in the first second of its travel, it's already passed an infinite number of points, same with the first millisecond, and nanosecond, etc

[Guest]

You are correct - hence the parardox (Zeno's Paradox)- - this can be shown mathematically as well:

"Suppose we take Zeno's Paradox at face value for the moment, and agree with him that before I can walk a mile I must first walk a half-mile. And before I can walk the remaining half-mile I must first cover half of it, that is, a quarter-mile, and then an eighth-mile, and then a sixteenth-mile, and then a thirty-secondth-mile, and so on. Well, suppose I could cover all these infinite number of small distances, how far should I have walked? One mile! In other words,

At first this may seem impossible: adding up an infinite number of positive distances should give an infinite distance for the sum. But it doesn't – in this case it gives a finite sum; indeed, all these distances add up to 1! A little reflection will reveal that this isn't so strange after all: if I can divide up a finite distance into an infinite number of small distances, then adding all those distances together should just give me back the finite distance I started with. (An infinite sum such as the one above is known in mathematics as an infinite series, and when such a sum adds up to a finite number we say that the series is summable.)

Now the resolution to Zeno's Paradox is easy. Obviously, it will take me some fixed time to cross half the distance to the other side of the room, say 2 seconds. How long will it take to cross half the remaining distance? Half as long – only 1 second. Covering half of the remaining distance (an eighth of the total) will take only half a second. And so one. And once I have covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 4 seconds, and here I am, on the other side of the room after all."

Copied from Prime Articles found on Mathacademy.com

When you sum a geometric series, depending on whether it is converging (as in the case of this puzzle), or it's diverging as would happen if you decided to, say run a marathon that is always 10% longer than the previous one you ran, you will either end up with a finite or an infinite sum.

As for someone's remark on space and time being finitely divisable, the physics departs from the math. Per physics, you can get as far as a subatomic particle (so you can get to approximately 1/(10-to-the-24) for each cubic meter of space), but per math, you can always divide that by any number larger than 1 to get even smaller.

[Guest]

This is a paradox, there isn't really a right answer if I can remember correctly. We must first realize that distance is a measurement that we invented to grasp the thought of moving in general. If I can remember the theorys correctly, they say that you must either...

+Assume that there is a finite amount. (i.e. nanometer) that we must stop at, consitering we can't measure infinity, or...

+Forget about measurements as a whole, and then infinity is not an issue.

The main point is that we can move, regardless of the theory proposed.

[Guest]

You are correct - hence the parardox (Zeno's Paradox)

When i read this riddle the first thing that popped into my head was Zeno's Paradox and im glad someone brought it up. Although what you posted was just an interpretation of the original Achilles and the Tortoise

[Guest]

I thought it was going to be something clever, like, 'until you get to the end of the alphabet'.

[Guest]

I thought it was going to be something clever, like, 'until you get to the end of the alphabet'.

then you use c1,d1,.. c2,d2.... infinite

[Guest]

If I start at point a and walk to point b - (having to pass a 1/2 way point we will call c) then from that point c to point b- (having to pass a 1/2 point we will call d) then from that point d to point b (having to pass.....etc.)

Play this out to infinity - how can I ever arrive at point b?

Sorry about that!!!!

The premise is non-sequitur. The fact that you pass through an infinite number of intermediate states between the origin and destination is irrelevant.

If one were to apply the logical steps of the OP in reverse order, one would conclude that it is impossible to move at all, and that the entire universe is completely static.

[Guest]

As you go from a to b you are passing all the other points not actually visiting them

your op says you pass it

So imagine you have a journey over 100 km and you pass each half way point

but not stop, you passed 50 km ... 75 km... 87.5 km ..etc

Does not matter the length so long as it is humanly possible - the amount of halfway points are the same, but either way the journey is at a constant speed of 6 - 8 km per hour (depends if it is a fast or slow pace/contest

This is a parodox!!!!!!

AHHHH

It messes with my head