Motion

[Chesterton]

This is only a problem if we accept Zeno. There are theoretically an infinite number of infinitely small points between any given two points, but continuous motion would still be possible because they take a similarly infinitely small amount of time to traverse.

(Now it's working.)

What does infinitely small mean?

 

[variant]

(Now it's working.)

What does infinitely small mean?

It means lacking in dimension.

It means you can fit as many of them in-between the points as you can describe.

This is why Zeno says you can halve the distance over and over into infinity.

You can but the time it takes to traverse it is halved as well so F(t) still gets there.

 

[Chesterton]

It means lacking in dimension.

It means you can fit as many of them in-between the points as you can describe.

This is why Zeno says you can halve the distance over and over into infinity.

You can but the time it takes to traverse it is halved as well so F(t) still gets there.

If it lacks dimension, that means it can't be divided? So it would not be infinitely small, it would just be the smallest thing?

 

[variant]

If it lacks dimension, that means it can't be divided? So it would not be infinitely small, it would just be the smallest thing?

It means infinitely small you can always put a higher number for x in 1/x to describe the distance , but still Zeno's paradox doesn't work because there is a corresponding 1/t equally small and just as quickly traversed.

Since t will progress past the time when the arrow hits the target, then infinities of infinitely small time periods are indeed possible.

Zeno's paradox doesn't work to disprove continuous motion because the description of continuous motion merely requires descriptive infinities to exist.

Infinities are descriptive in set based calculus so Zeno can not use this as a reason for why motion must be discreet. The logical argument doesn't work.

 

[Chesterton]

It means infinitely small you can always put a higher number for x in 1/x to describe the distance , but still Zeno's paradox doesn't work because there is a corresponding 1/t equally small and just as quickly traversed.

Since t will progress past the time when the arrow hits the target, then infinities of infinitely small time periods are indeed possible.

Zeno's paradox doesn't work to disprove continuous motion because the description of continuous motion merely requires descriptive infinities to exist.

Infinities are descriptive in set based calculus so Zeno can not use this as a reason for why motion must be discreet. The logical argument doesn't work.

I know about Zeno and why it was wrong (sort of). But it seemed something was different in this discussion, or more likely I'm just confused. In school I would sit near the exit, so when the math teacher turned her back I would make a "discreet motion" out the door.

 

[variant]

I know about Zeno and why it was wrong (sort of). But it seemed something was different in this discussion, or more likely I'm just confused. In school I would sit near the exit, so when the math teacher turned her back I would make a "discreet motion" out the door.

The point is that Zeno is saying that we would need to describe an infinite series of events if motion were continuous and he takes this to mean motion is not continuous.

He is wrong because we CAN describe an infinite series of events logically because we can sum infinite series.

He may be correct that motion is discrete, but not because the description (math) of an infinite series reduces to the absurd.

Any attempt to use reasoning similar to Zeno is also going to be wrong though.

Attempts like this:

I'm just going by Resha's set-up from page one. He posits an infinite number of "points" between A and B. Obviously, point B can never be reached. Which raises the question "can any point be reached?" No, there could really be no motion.

This is textbook Zeno and is wrong for the same reason.

 

[Chesterton]

The point is that Zeno is saying that we would need to describe an infinite series of events if motion were continuous and he takes this to mean motion is not continuous.

He is wrong because we CAN describe an infinite series of events logically because we can sum infinite series.

He may be correct that motion is discrete, but not because the description (math) of an infinite series reduces to the absurd.

Any attempt to use reasoning similar to Zeno is also going to be wrong though.

Attempts like this:

This is textbook Zeno and is wrong for the same reason.

But that's just math. On paper you can always put a higher number for x in 1/x. We don't know if we can do that in reality.

 

[variant]

But that's just math. On paper you can always put a higher number for x in 1/x. We don't know if we can do that in reality.

Right we don't know. But, we also can't say it is impossible based off of the logic of Zeno's paradox as the paradox is criticizing continuous motion as contradictory math and logic (it is an argument that tries to logically reduce continuous motion to the absurd).

Since math can handle infinitely divisible continuous motion, then Zeno can't say that infinitely divisible continuous motion is incorrect because it is logically impossible.

 

[Chesterton]

Right we don't know. But, we also can't say it is impossible based off of the logic of Zeno's paradox as the paradox is criticizing continuous motion as contradictory math and logic (it is an argument that tries to logically reduce continuous motion to the absurd).

Since math can handle infinitely divisible continuous motion, then Zeno can't say that infinitely divisible continuous motion is incorrect because it is logically impossible.

Honestly I never took Zeno seriously. I'm convinced he was an extremely intelligent smart aleck, and I picture him with a big grin on his face when he thought his stuff up.

 

[variant]

Honestly I never took Zeno seriously. I'm convinced he was an extremely intelligent smart aleck, and I picture him with a big grin on his face when he thought his stuff up.

Well then, you shouldn't worry much about if an electron can cross an infinity of infinitely small points in space one by one.

That obviously isn't the right question.

 

[Resha Caner]

I'm just not buying your blinking out of existence for a bit idea as I don't think the electron ever ceases to exist.

It works if say, the electron exists as a moving field with an array of probability of existing as an electron at any given point.

That may be hard for you to conceptualize neatly but it doesn't mean it's not a better description of what is happening.

I can visualize it, and actually thought of that possibility. That's why I went to the pains of describing a point where we know the electron is not which discretely changes to a point where it could be (i.e. where the field now is).

 

[Resha Caner]

Honestly I never took Zeno seriously. I'm convinced he was an extremely intelligent smart aleck, and I picture him with a big grin on his face when he thought his stuff up.

Well, that's why I like Grimaldi's paper. Jumping to a mathematical explanation risks forcing one to take a Platonist position, and it may be that those who go that direction misconstrue what the paradox is about. They risk exactly what you're concluding - that it's just word games by a smart aleck.