[Guest]

As the description suggests, this is more a koan than a paradox - something to occupy your intuition rather than your rationalism. Does it have an "answer?" I suppose it does, but I think for most people it will challenge their rational answer. For this reason, I will not pose a question.

A man is walking in a world that is a perfectly flat infinite plane. He comes upon two lines scribed in the ground, parallel to one another. The first line stretches out in either direction as far as the eye can see, posted next to is is a sign with two arrows that reads "<-- Infinity -->" The second line starts at the center of a small inscribed circle or dot and stretches out in one direction as far as the eye can see, posted next to this line is a sign with one arrow that reads "Infinity -->"

The man decides, out loud, "I wish to walk towards infinity, but I am tired, and shall choose the second path, for it is only half as long, and if I get lost I can always return to the beginning."

[Guest]

the first could refer to positive AND negative infinity while the second only refers to positive infinity

[Guest]

I like to think about what would happen if the man can walk at an infinite velocity for an infinite amount of time.

[peace*out]

I like to think about what would happen if the man can walk at an infinite velocity for an infinite amount of time.

And yet what would happen if he lives forever? when would he reach the end?

[Guest]

The first would be infinity. It has no beginning and never ending. The second has a beginning so would not be infinity. So, walking the second path he wouldn't be walking on the infinite path he wishes to take. Plus he'd have to live that long. Think of a circle. Has no beginning and never ending. Then again no matter where he starts. He's just starting on either path. The second isn't infinate. Just choice of direction and doesn't mean infinate life for him. Either way it would be the beginning of a life long journey.

Edited March 11, 2010 by PhoenixFromTheFlames

[Guest]

And yet what would happen if he lives forever? when would he reach the end?

He wouldn't, which would be cool.

[Guest]

Think about it mathematically, what's : infinity/2. Of course you can't divide infinity by 2 or it would still be infinity anyway. So infinity is infinity regardless of whatever you do with it.

Edited April 12, 2010 by Eragon

[Guest]

The two lines present different thought exercises - different spiritual concepts. But the practicality of the physical situation is that they present three identical challenges. You stand at a point, and you choose a direction.

[Guest]

The first would be infinity. It has no beginning and never ending. The second has a beginning so would not be infinity. So, walking the second path he wouldn't be walking on the infinite path he wishes to take. Plus he'd have to live that long. Think of a circle. Has no beginning and never ending. Then again no matter where he starts. He's just starting on either path. The second isn't infinate. Just choice of direction and doesn't mean infinate life for him. Either way it would be the beginning of a life long journey.

but this worls is an infanite plane meaning it is flat and goes on forever...it cant be a sphere

[Guest]

Okay, I'll get technical with this. This place must be in a universe. If it's in a universe, then the universe is expanding (granite, it's expanding in a speed faster than light). The only way for the plane to be infinite, it would have to cross dimensions. If it crosses dimensions, then the plane is a plane no longer.

[Guest]

I'll also add this: by definition, an infinite line must extend in both directions, so the second line can't be an infinite line. Unless (I'll get technical again) the line has a negative refractive index.

[Guest]

If the man is tired, he should know there is no shorter path to infinite, weather positive, negative, or with a starting point.

[Guest]

i'd like to think the second line is the point in time and space where man stands in relation to infinity.

[Guest]

This is sort of like the "almost endless food" paradox. The man is wrong about the second line being half as long, but he's right about being able to return to the beginning.

[Guest]

not return to the beginning but where HE began

[Guest]

The second line is measuring infinity from a set point, where as the first measures infinity without a proper start. For all we know, maybe the first line ends. It doesn't really matter because the line just represents infinity to a certain extent. Even if the lines end at both sides, infinity goes on.

Or maybe infinity is the name of this large half donut shaped town, allowing you to follow either of the lines and still get there.

[Guest]

As the description suggests, this is more a koan than a paradox - something to occupy your intuition rather than your rationalism. Does it have an "answer?" I suppose it does, but I think for most people it will challenge their rational answer. For this reason, I will not pose a question.

A man is walking in a world that is a perfectly flat infinite plane. He comes upon two lines scribed in the ground, parallel to one another. The first line stretches out in either direction as far as the eye can see, posted next to is is a sign with two arrows that reads "<-- Infinity -->" The second line starts at the center of a small inscribed circle or dot and stretches out in one direction as far as the eye can see, posted next to this line is a sign with one arrow that reads "Infinity -->"

The man decides, out loud, "I wish to walk towards infinity, but I am tired, and shall choose the second path, for it is only half as long, and if I get lost I can always return to the beginning."

at maths there are the 2 axes x,y in the 2 dimensional word. now lets say that the man is athth epoint O(0,0) where the 2 axes cross each other. all directions leads to infinite where you call possitive infinite at the axe X of negative. the same goes for the axe Y so wherever he go when he diside to go back he will go to the point O(0,0) !

[Guest]

Think about it mathematically, what's : infinity/2. Of course you can't divide infinity by 2 or it would still be infinity anyway. So infinity is infinity regardless of whatever you do with it.

Not if you multiply it times 0

(Then again, Infinity is not a number, but rather, an idea, so you can't divide it by 2 anyway...)

But to talk about the koan...

The man is being foolish,

it really doesn't matter which way he goes,

after all,

his reasoning is both that he is tired, and he worries about getting lost,

he should rest...

seriously though,

he should know no one can walk towards Infinity (unless it's a place called Infinity)

so it doesn't matter which way he goes,

because he can never get lost,

I mean come on...

there are BIG ARROWS on the ground!

and to return to where he started,

hey, guess what,

he can just go back to the signs!

so,

in conclusion,

the man is a fool.

[bonanova]

The man decides, out loud, "I wish to walk towards infinity, but I am tired, and shall choose the second path, for it is only half as long, and if I get lost I can always return to the beginning."

The man is correct that if he gets lost he can always return to the beginning. But it is not correct to believe the second path is only half as long.

Suppose mile markers were placed on the two paths. The first would have markers at 0, +/-1, +/-2, +/3, ... +/-N, .... The second would have markers at 0, 1, 2, 3, ..., N, ....

For any finite distance N from his starting point, the first path would be twice as long: 2N miles as compared with N miles. But as N increases without bound,

lim_N->inf [N] = lim_N->inf [2N] = inf.

Similarly, there are the same "number" of even integers as integers. With infinite sets, the algebra of cardinality that holds for finite sets breaks down.

[voider]

The two lines are parallel. If he walks along the second line, it is implied that the first line would still be visible without having to walk between them.

Just for fun:

1) A straight line is an arc of a circle with infinite radius.

2) Starting at any point on the circumference of a circle, you can take either direction along it and eventually reach your starting point.

3) Therefore, if the man travels to the left (away from the second line) for an infinite period of time, he may eventually see the second line and even return to the starting point.