Pv2 is right.
Half speed, and you'll get there.
Half distance, and it takes infinitely long.
This is because your steps are always the same length, that is, the are quantifiable distances. You are not a car.
Half speed, and you'll get there.
Half distance, and it takes infinitely long.
This is because your steps are always the same length, that is, the are quantifiable distances. You are not a car.
Guys I'm sorry I didn't mention you should consider your steps' speed and length, otherwise it wouldn't be too hard to assume you'd eventually get there. So Pv2 is right about that, having your speed decreased repeatedly but never reaching zero wouldn't stop you from reaching the goal.
So here's what blows my mind:
At each and every step you take, the average length and speed of your step is halved.
Noting that you can't reach zero by halving something.
Which proposes the point that, it might be possible not to reach a point even if you keep moving towards it. And I call that a paradox.
Also guys, don't consider a specific body type, walking speed or average step length for the person in question. The less specific you are when dealing with hypotheses like this, the better.
So here's what blows my mind:
At each and every step you take, the average length and speed of your step is halved.
Noting that you can't reach zero by halving something.
Which proposes the point that, it might be possible not to reach a point even if you keep moving towards it. And I call that a paradox.
Also guys, don't consider a specific body type, walking speed or average step length for the person in question. The less specific you are when dealing with hypotheses like this, the better.
Last edited by Sidvicious; Jun 17, 2013 at 09:22 PM.
Why didn't you say an object moves toward a point with an initial velocity, but every second its velocity is halved. Will the object ever reach the point?
Isn't that a much more generalised yet equivalent paradox?
Isn't that a much more generalised yet equivalent paradox?
That's a much simpler question, the answer would be Yes, it would reach the point, because by only halving its speed you wouldn't prevent it from moving forward. Plus, proposing a generic unspecified object doesn't tell you how fast it moves, or the nature of the movement. And even if you gave me that information, it would still be a constant movement.
The example of a person walking is different, because walking is divided in stages rather than a constant movement (you need to move one leg in order to move the other, and then start walking). We do know how our legs move, how far each foot moves, etc. It's a simple perspective we are all used to deal with, and, well, I think it's just more interesting than a generic body that's moving.
The example of a person walking is different, because walking is divided in stages rather than a constant movement (you need to move one leg in order to move the other, and then start walking). We do know how our legs move, how far each foot moves, etc. It's a simple perspective we are all used to deal with, and, well, I think it's just more interesting than a generic body that's moving.
An object moves a distance of x per step with a speed of y, with each successive distance x moved, it's speed y is halved, as is the distance of x.
Can the object ever reach a point at a given distance from its starting position?
Can the object ever reach a point at a given distance from its starting position?
Last edited by Fear; Jun 17, 2013 at 11:58 PM.
