Zeno's Paradox

[Neapolitan Ice Cream]

Any moving object must reach halfway on a course before it reaches the end; and because there are an infinite number of halfway points, a moving object never reaches the end in a finite time.

Or to put it another way, when a rock is dropped, it must first achieve half the distance to the ground. Then half again. And again. And again. And since there are an infinite number of half-distances for the rock to go through, it must never hit the actual ground.

Mind boggling right?

 

[Genie+]

Took me a minute. Basically any increment can be split in half. I guess when you push that rock down hard enough to squeeze out the last quark from under, it has finally ‘landed’

 

[bcla]

Not really. It relies on the belief of the infinite - that distance can be divided up infinitely into half the original distance. The real universe has quantum states and convergence.

Here's a discussion on this saying that it's been solved.

https://www.forbes.com/sites/starts...esolves-zenos-famous-paradox/?sh=27f37bd33f8f

 

[PollyannaMom]

It is a cool theory if we're talking about points in space, but the minute the radius of the rock exceeds the distance from the center of the rock to the ground, the theory is moot. The rock has hit the ground.

 

[Neapolitan Ice Cream]

My instinctive solution lies with in TAN graph. It hits infinity at one point, but less than a boson more and you hit NEGATIVE infinity, then tapers down to nil, before repeating. So surely infinity can be broken, right?

 

[DisneyOma]

Any moving object must reach halfway on a course before it reaches the end; and because there are an infinite number of halfway points, a moving object never reaches the end in a finite time.

Or to put it another way, when a rock is dropped, it must first achieve half the distance to the ground. Then half again. And again. And again. And since there are an infinite number of half-distances for the rock to go through, it must never hit the actual ground.

Mind boggling right?

I think you should test it for us - want to jump off a building and see what happens?

 

[lovesmurfs]

Nope. I learned about this years ago from Firesign Theater's Everything You Know is Wrong (1974).

 

[LuvOrlando]

This is how Chemistry half life works. I imagine the solution, resolution, way to manage the idea is a little like Sartre's Being and Nothingness where the point is (as I understood it to be) two things can become extraordinarily close, but never one and the same so the rock can fall ever closer to the ground but will never actually be the ground.

 

[bcla]

Zeno was not a scientist, but a philosopher. Infinity is interesting as an idea, but it's really just an abstraction.

In the math and engineering exercises I've done, nothing ever reaches infinity, but just approaches infinity. It's "close enough" to converge on a certain value.