New Hubble pictures, YEC explanations just don't make sense.

Do the math. He overtakes the tortise.This is only a stumper in a world without calculus.

Right, but it takes less time each time. Christ, we solved this ages ago. Where the hell have you been?

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The faulty logic in Zeno's argument is the assumption that the sum of an infinite number of numbers is always infinite. While this seems intuitively logical, it is in fact wrong. For example, the infinite sum 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... is equal to 2. This type of series is known as a geometric series. A geometric series is a series that begins with one and then each successive term is found by multiplying the previous term by some fixed amount, say x. For the above series, x is equal to 1/2. Infinite geometric series' are known to converge (sum to a finite number) when the multiplicative factor x is less than one. Both the distance that Achilles travels and the time that elapses before he reaches the tortoise can be expressed as an infinite geometric series with x less than one. So, Achilles traverses an infinite number of "distance intervals" before catching the tortoise, but because the "distance intervals" are decreasing geometrically, the total distance that he traverses before catching the tortoise is not infinite. Similarly, it takes an infinite number of time intervals for Achilles to catch the tortoise, but the sum of these time intervals is a finite amount of time.

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From No webpage found at provided URL: http://www.deltalink.com/dodson/html/zeno.solution.html

No, it doesn't. Did you even read the explanation?Because it's a reducing series, it takes Achilles finite time to cover the infinite distance intervals. What the fuck are you talking about? The equation is simple. Follow this link and all is explained. No webpage found at provided URL: http://www.deltalink.com/dodson/downloads/zenomath.pdfIf you expect "vortex theory" to have legs than you're going to have to base it on more than your own ignorance of math.

...so? The turtle only travels a finite reducing distance in each time interval. Therefore the sum of the distance intervals, though there's an infinite number of them, is finite. So Achillies catches the turtle. And Zeno is wrong, which I have demonstrated. I don't assume that the race has an end - I proved it.

What does that have to do with anything?Since you're changing the subject, can I assume you've conceded the debate?

Mathematically, there's no such distance.In the quantum world we live in, that distance is the Plank length. You can't tell the difference between moving less than the Plank length and not moving at all.So which world are we talking about? In either one, Achillies catches the turtle. In fact he catches the turtle faster in the real world because eventually the turtle isn't moving at all.

Um, no. That's just you who can't comprehend infinity. The rest of us don't have that problem because infinity is a very well-defined concept mathematically. It's not incomprehensible, it's just undetectable. I have no difficutly comprehending a sub-Plank distance. Yeah. I see Achillies catch the turtle, just like math predicts.

Infinity isn't a number, dude. Therefore you won't find infinity as a part of any sequence of numbers.See what I mean about how hard it is for you to comprehend infinity? You don't even know enough to ask the right questions.

It's the concept represented by the fact that, given any number, there exists at least one larger number.

Of course. Assuming you're talking about a set of numbers that doesn't exclude the negatives.

If the universe is of infinite size, that question might not make sense.If the universe is not of infinite size, which I believe is true, then we just don't know what's outside of it. And how could we unless what's outside of the universe has an effect on what's inside it?

Sigh... nice try, but you know that's not what I agreed to. Thank you for deomstrating my point - that you have no idea what you're talking about.

How do you figure? If we know how fast light travels (we do) and we know how far those objects are (we do), then we know how long it took the light to arrive from those objects. In this case, billions of years.Sounds like we can begin to set the minimum age of the universe, anyway. Unless God is trying to trick us? I was unable to duplicate the results. Can you explain the discrepancy? According to physical law it must be. Unless you think God is trying to trick us?

I love your logic. The guys who, using their intellects, plumb the mysteries of the observable universe via logic and scientific methodology, without regard to dogma or politics, are sheep, but the people who believe only what a 2000-year-old book tells them to are not. Brilliant![This message has been edited by crashfrog, 03-12-2004]

I'm not sure that's possible thermodynamically. If the universe were of infinite duration in the past then in the present, there would be no energy avaliable for work.Since energy is clearly avaliable for work, the universe must be of finite duration in the past - that is, it had a beginning.