Zeno (of Elea)

I am a big fan of Zeno, so I decided to make a thread regarding him.

He is most famous, as you may already know, for his paradoxes, and especially his argument against motion.
As far as I know, he is YET to be proved wrong. His arguments can be calculated, but not fully explained.

Here are short versions of his paradoxes -

1) Dychotomy Motion is impossible since "that which is in locomotion must arrive at the half-way stage before it arrives at the goal.

Example -

An object moves from point A to point B.
To get to point B the object must first reach the midpoint B1 between points A and B. However before this can be done the object must reach the midpoint B2 between points A and B1. Likewise before it can do this, it must reach the midpoint B3 between points A and B2, and so on. Therefore it is impossible to move through an unlimited number of points in a limited amount of time.

2) Arrow Flying arrow is motionless "If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.

Example -

An arrow is flying continuously forward during a certain time interval. Take any instant in that time interval. It is impossible that the arrow is moving during that instant because an instant has a duration of zero, and the arrow cannot be in two different places at the same time. Therefore, at every instant the arrow is motionless, hence the arrow is motionless throughout the entire interval.

Courtesy of Wiki

3) The Achilles Achilleas could never outrun Tortoise:

Example -

The running Achilles can never catch a crawling tortoise ahead of him because he must first reach where the tortoise started. However, when he reaches there, the tortoise has moved ahead, and Achilles must now run to the new position, which by the time he reaches the tortoise has moved ahead, etc. Hence the tortoise will always be ahead.

Thoughts? Anyone else likes Zeno? Anyone doesn't?

Pretty paradox. One might assume there is a smallest possible distance though, for which there is no midway point. Obviously that can hardly be proven. Motion might not exist for other reasons as well though. Anyways, I am not generally familiar with him or his philosophies generally though.

I thought his arguments were disproved/explained by calculus.

Originally posted by Bardock42
Pretty paradox. One might assume there is a smallest possible distance though, for which there is no midway point. Obviously that can hardly be proven. Motion might not exist for other reasons as well though. Anyways, I am not generally familiar with him or his philosophies generally though.

You are correct. We are able to move because at the smallest level there is no midpoint.

See Quantum foam.

http://www.ldolphin.org/qfoam.html

Zeno's paradoxes, while thought-provoking, are basically mathematical abstractions which fail when applied to the real world. This is because they assume reality has the quality of infinite division.

For example: never reaching a destination because you'll just keep reaching infinitely smaller half-way points. Other than this being demonstrably not true (otherwise, how could I type this response), even if I had the power to move at subatomic distances, eventually I would reach (as Shak pointed out) the quantum scale. At this point, I either make the final quantum leap to my destination (we've plum run outta half-way points on this scale), or I don't.

The arrow never moving: an instant is an infinitely small division of time...which as far as we know, does not exist, at least not in the classical world where the arrow exists (space and time are inseparable due to the lightspeed limit). Therefore, during that smallest interval of time (Planck time), the arrow does cover distance. Now, there are some interesting physics theories which postulate Time is an illusion, but that's another story, and it still wouldn't violate the quantum aspect of reality.

Basically, Zeno was able to put forth his paradoxes cuz he was not aware of quantum mechanics. It would be interesting to have seen his thoughts on that.

Zeno's paradoxes, while thought-provoking, are basically mathematical abstractions which fail when applied to the real world.

btw I hate math

You thought you might be unable to move?

Yeah sorta......Though mentally I'm invincible.

Mentally you're seriously unspectacular. Copyright Morrissey, 1987 (or so).

Originally posted by Victor Von Doom
Mentally you're seriously unspectacular. Copyright Morrissey, 1987 (or so).

1988...which might be implied in the "or so". Still useful. Very useful.

Originally posted by Victor Von Doom
Mentally you're seriously unspectacular. Copyright Morrissey, 1987 (or so).

Originally posted by debbiejo
What? A mind is transcendent of the body......It can move... 🙄

...what?

In physics actually there is a limit to distance. A smallest distance possible, it is called Planck´s distance.

I think these paradoxes happen when we try to apply our physical real-world intuition to mathematical concepts, but we need to remember that math is not physics. In physics we must always discriminate which mathmatical concepts have physical sense and which do not.