Infinity x Zeno's paradoxes

I'm helping bringing the topics here and this is very nice.

How do you think infinity will deal with Zeno's paradoxes?

1. Dichotomy paradox:

Before an object can travel a given distance d, it must travel a distance d/2. In order to travel d/2, it must travel d/4, etc. Since this sequence goes on forever, it therefore appears that the distance d cannot be travelled.

Shocked

The resolution of the paradox awaited calculus and the proof that infinite geometric series such as sum_(i=1)^(infty)(1/2)^i=1 can converge, so that the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances.



2. Achilles and the tortoise paradox:

A fleet-of-foot Achilles is unable to catch a plodding tortoise which has been given a head start, since during the time it takes Achilles to catch up to a given position, the tortoise has moved forward some distance. But this is obviously fallacious since Achilles will clearly pass the tortoise! The resolution is similar to that of the dichotomy paradox.


3. Arrow paradox: An arrow in flight has an instantaneous position at a given instant of time. At that instant, however, it is indistinguishable from a motionless arrow in the same position, so how is the motion of the arrow perceived?


4. Stade paradox: A paradox arising from the assumption that space and time can be divided only by a definite amount.

The dichotomy paradox leads to the following mathematical joke. A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t=10, d/4 at t=20, d/8 at t=30, and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.

Gotta love this Universe....

hehe yes, it's quite fun. About q2, I'm not sure the puzzle is about time at all. It is about completing an actually infinite set of tasks whether in a finite time or in an infinite time. Suppose Achilles has infinite time at his disposal. How would that help?
Nor do I think the puzzle is just about space. Forget about motion for the moment. Suppose you have a finite line segment. Bisect it, then bisect that bisection and so on. Suppose that our initial line segment is composed of an actual infinity of line segments. I don't think there is a problem about how those sub segments add up to, or compose, the initial finite segment. In fact, here I think the 'calculus solution' in terms of the limit of a convergent infinite series works. A finite line segment can have infinitely many proper sub segments.

These paradoxes arise from due to our current Mathematics allowing the presence of infinite.
The same paradox occur simply by counting from 1 to 1.000001 or less.
Mathematics, Physics and all Sciences are just model to interpret and compreend the real life. These models have been continuosly updated through time and still are.
The closest we ever got from understanding the Universe with a Man made model was with Einstein and his unfinished "Theory of All".

The answers to paradoxes are very simple, they are mere exceptions wich occur from the fact that the theory behind does not fully describe reality as it is.

Thats what I think at least.