Answer me this, you lovely people

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

That's precisely why time travel is impossible. I think.

EDIT: I have to be honest, I'm a little tipsy so I probably didn't understand it.

Even though you are dealing with an infinite number of points, you're still dealing with a finite amount of space. You're just dealing with smaller and smaller segments of space within that overall space.

Since the passage of time you've proposed is expressed as speed (amount of space covered per unit of time, or second), then you're sub-points don't enter into the equation at all. In the end, you're still dealing with the same amount of finite space you were dealing with at the beginning.

I obviously missed something.

Unless point 1 is constantly moving with you (making point 2 move with it), I don't understand the issue. One second is one second no matter how you slice it.scorch-62

[QUOTE="scorch-62"]Unless point 1 is constantly moving with you (making point 2 move with it), I don't understand the issue. One second is one second no matter how you slice it.Baconbits2004

[QUOTE="scorch-62"]Unless point 1 is constantly moving with you (making point 2 move with it), I don't understand the issue. One second is one second no matter how you slice it.Baconbits2004

In calculus, the sum of infinitely small quantities can in some cases add up to a finite number.

[QUOTE="Baconbits2004"][QUOTE="scorch-62"]Unless point 1 is constantly moving with you (making point 2 move with it), I don't understand the issue. One second is one second no matter how you slice it.scorch-62

Even though you are dealing with an infinite number of points, you're still dealing with a finite amount of space. You're just dealing with smaller and smaller segments of space within that overall space.

Since the passage of time you've proposed is expressed as speed (amount of space covered per unit of time, or second), then you're sub-points don't enter into the equation at all. In the end, you're still dealing with the same amount of finite space you were dealing with at the beginning.

mattbbpl

1) There aren't infinite splits between points in time.

2) There may be infinite splits. You just aren't "in that realm of infinity," so to speak. Like multiple universes. They may exist, but "you" may just be in this one.

The second sounded way better before I typed it out...

[QUOTE="mattbbpl"]

Even though you are dealing with an infinite number of points, you're still dealing with a finite amount of space. You're just dealing with smaller and smaller segments of space within that overall space.

Since the passage of time you've proposed is expressed as speed (amount of space covered per unit of time, or second), then you're sub-points don't enter into the equation at all. In the end, you're still dealing with the same amount of finite space you were dealing with at the beginning.

SolidSnake35

In calculus, the sum of infinitely small quantities can in some cases add up to a finite number.

spacesheikh

Sounds about right.. I can't get my head around it still, though. In my head I have an analogy of a passenger in a car... passing way points. Though they are extremely small, they are still successive. You must pass them all. You must pass them all in one second. But you surely cannot, for there an infinite number of them. You might fly past a zillion of them in 0.9 seconds... but there'd be another zillion to pass in the last 0.1 seconds you have left.SolidSnake35

[QUOTE="SolidSnake35"][QUOTE="mattbbpl"]

Even though you are dealing with an infinite number of points, you're still dealing with a finite amount of space. You're just dealing with smaller and smaller segments of space within that overall space.

Since the passage of time you've proposed is expressed as speed (amount of space covered per unit of time, or second), then you're sub-points don't enter into the equation at all. In the end, you're still dealing with the same amount of finite space you were dealing with at the beginning.

mikegtfc

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

[QUOTE="SolidSnake35"]Sounds about right.. I can't get my head around it still, though. In my head I have an analogy of a passenger in a car... passing way points. Though they are extremely small, they are still successive. You must pass them all. You must pass them all in one second. But you surely cannot, for there an infinite number of them. You might fly past a zillion of them in 0.9 seconds... but there'd be another zillion to pass in the last 0.1 seconds you have left.scorch-62

1) There aren't infinite splits between points in time.BranKetra

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

[QUOTE="scorch-62"][QUOTE="SolidSnake35"]Sounds about right.. I can't get my head around it still, though. In my head I have an analogy of a passenger in a car... passing way points. Though they are extremely small, they are still successive. You must pass them all. You must pass them all in one second. But you surely cannot, for there an infinite number of them. You might fly past a zillion of them in 0.9 seconds... but there'd be another zillion to pass in the last 0.1 seconds you have left.SolidSnake35

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

SolidSnake35

So if you count them all on the way by, what number do you get to?SolidSnake35

Is time also space? Forgive me if I am wrong, but how is one dealing with a finite amount of space when dealing with infinte about of time? I'm not trying to be a jerk, that just doesn't make sense to me... your traveling through time, not a distance of space...

lulz, I feel like messing with TC's state of mind right now.

Should we start out with the harmonic series?

Or how about Monty Hall's 3 door game?

[QUOTE="SolidSnake35"]

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

frostybanana

[QUOTE="frostybanana"][QUOTE="SolidSnake35"]

So I've been thinking to myself whilst studying and such... and I thought this. You might have to bear with me. I might be going insane. Anyway, take any timespan. There's point 1 and point 2, and it takes 1 second to reach point 2 from point 1. Now, smack another point (3) right in the middle of that timespan. It takes half a second to get from 1 to 3, and from 3 to 2. Smack another point (4) between 1 and 3... quarter of a second between 1 and 4, right?

Okay, so you get the idea. You can keep splitting the points in time. And the time it takes to pass from one point to another gets ever shorter. Now, you can do this ad infinium. So there's a teeny tiny time span between 1 and n. But don't forget, there are tiny timespans after this... which all add up to one second (1 second between points 1 and 2).

My question... there's an infinite number of smaller timespans between 1 and 2. If we travel through time, beginning at 1, and have to traverse each one to reach 2... how do we ever reach 2? Surely we cannot.. for then we would've reached the end of infinity. We would have travelled through an infinite number of timespans. Paradox. Explain where my logic is failing, please, before I implode.

spacesheikh

[QUOTE="BranKetra"]1) There aren't infinite splits between points in time.scorch-62

Ask Sheldon. He'll know ;)

Ask Sheldon. He'll know ;)

SicklySunStorm

[QUOTE="scorch-62"][QUOTE="SolidSnake35"]Sounds about right.. I can't get my head around it still, though. In my head I have an analogy of a passenger in a car... passing way points. Though they are extremely small, they are still successive. You must pass them all. You must pass them all in one second. But you surely cannot, for there an infinite number of them. You might fly past a zillion of them in 0.9 seconds... but there'd be another zillion to pass in the last 0.1 seconds you have left.SolidSnake35

In reality there isn't an "infinite" number of points, only in the concept of time we use there is.

I only clicked on this topic because I was called lovely. But now after reading, this whole thing just went right over my head.:?

Thats one of xeno's paradoxes, look it up.

Time travel is possible forwards, just not backwards. If you move fast enough, you move slower through time than everybody else. If you were to send a guy in a spaceship at the speed of light for like 5 years, he would come back to Earth and more than 5 years would have passed.

Theory of Relativity. Pretty crazy.

Xeno? Is that you?Theokhoth

Exactly what I was thinking. :lol:

It doesn't matter how many points you have to cross. As long as the distance is finite, the energy and time requirements will be finite. Even if you divide the path into an infinite number of points it doesn't matter - each point will simply take an infinitely small amount of time and energy to cross.