[Thorn]

http://www.space.com/scienceastronomy/time_theory_030806.html

still trying to wrap my brain around this one...

[an0n]

The most famous paradox invented by Zeno, the Greek philosopher, is called "Achilles and the tortoise." A tortoise gets a 10-meter head start in a race against Achilles. Zeno says the tortoise can never be passed. His logic: When Achilles has run 10 meters, the tortoise will have moved a meter; Achilles goes another meter, and the tortoise crawls 10 more centimeters. The race continues in this ever-more boring and incremental fashion.

I fail to see how this is a paradox.

So he goes 10m and the turtle is at 11m.
He goes to 11m (another 1m) and the turtle is at 11.1m.
Then he goes to 12m (another 1m) and the turtle is at 11.2m.

Now I'm no mathematician, but I'm reasonably sure 12 is more than 11.2.

[Dark_4ce]

Its bollocks in my oppinion. I read it, and was kind of accepting it, but then after I read it more its just plain ridiculous. Its like he's saying "time doesen't flow, it just is. Thats why it flows, because I say it does, but not."

Anyway, he's entiteled to his own oppinion, but I doubt it will rattle the halls of sience. It might just create a small echo...

[Dark_4ce]

He doesent go another meter twice.

[an0n]

Originally posted by Dark_4ce
He doesent go another meter twice.

Why not?



And he's right. I've thought that time wasn't flowing for a helluva long time. I also realised that without a masters in Temporal Physics, no-one cares what you think.

If you have space as a 4-dimensional space with infinite incriments in the 4th dimension (infinitely divisible time) you end up with all the energy and matter in space duplicated an infinite number of times, once for each point in time. So you end up with not only infinite energy, but a whole universe full of it.

And, as has been rammed down our throats for the past 100 years or so, the energy of the universe is finite.

[Flipside]

It just goes to show that either Quantum and time and Space are far more complex than we thought, or scientists really are making this crap up as they go along


Flipside

[Dark_4ce]

Good point... Anyway, I won't really take any notice until it really rattles the halls of science. And of the Paradox:

The Turtle has a 10m head start.
Achilles goes 10m.
Turtle goes 11m.
Achilles goes to 11m.
Turtle goes to 11.1m
Achilles goes to 11.1m
The turtle goes to 11.11m

See what happens?

[kode]

Originally posted by Flipside
It just goes to show that either Quantum and time and Space are far more complex than we thought, or scientists really are making this crap up as they go along


Flipside

the latter.

[an0n]

Originally posted by Dark_4ce
Good point... Anyway, I won't really take any notice until it really rattles the halls of science. And of the Paradox:

The Turtle has a 10m head start.
Achilles goes 10m.
Turtle goes 11m.
Achilles goes to 11m.
Turtle goes to 11.1m
Achilles goes to 11.1m
The turtle goes to 11.11m

See what happens?

Achilles goes 100m, the turtle hits 20m.

See.

And I have a feeling this can all be solved with some integration.

[Dark_4ce]

I didn't say that Paradox symbolized reality. Yes, a person will most likely outrun a turtle everytime. And I think the paradox itself is pritty weak, as in a paradox that requires unlikely things to happen as a rule. But if you follow the rules the paradox "works". But reality never follows the rules anyway.

But I still won't believe the guy.

[an0n]

The fun part comes when you realise that if you travel 1m, then 0.5m, then 0.25m, not only will you get down to moving in distances measured in Planck lengths, but you can travel an infinite distance.

Say you try to get to 2m. Theoretically, eventually you'll get there.

[Flipside]

Yes, but in order to fractalise the distance travelled, you must also fractalise the time, plot it on a slope and you will see that you eventually have to make time stand still for the theory to be practical.

Flipside

[Sandwich]

Originally posted by an0n

I fail to see how this is a paradox.

So he goes 10m and the turtle is at 11m.
He goes to 11m (another 1m) and the turtle is at 11.1m.
Then he goes to 12m (another 1m) and the turtle is at 11.2m.

Now I'm no mathematician, but I'm reasonably sure 12 is more than 11.2.

The theoretical situation they give is a bad one to use for an example, because of the circumstances. Here, look:

Code: [Select]


A         T BCZ
|---------|-|||----


Achilles is at point A, the Tortise is at T. In the time Achilles moves from A to T, the Tortise moves from T to B. The Tortise's speed is one-tenth of Achilles' speed, right?

Now, allow Achilles to travel only as long as it takes him to traverse a meter, to point B... the Tortise will then have moved from B to B+(Z-B)/10, or one centimeter from point B (Z being one meter from B).

Here's the conundrum: if you continue to exponentially shorten the distances that they both travel, then neither of them will ever get to point Z, which is where Achilles would have passed the Tortise had they been allowed to travel at their own speeds unhindered.

There is a better way to concieve of this "paradox", mentioned right after the above situation in the article. If you are a certain distance from your destination, and you travel half that distance, and then half the remaining distance, and then half of that remaining distance, et cetera, et cetera, ad infinitum - you will draw infinitely closer to your destination, but never actually get there.

The article's original situation, with Achilles and the Tortise, simply adds another moving entity to the "travel-half-the-remaining-distance" equation, thereby supposedly making even more of a point. However,the difference is that in the first example, the moving elements are travelling at increasingly slower speeds, whereas the 2nd example is stating forthright "travel half the remaining distance".

If you really want a real-life example of the first situation, it's perfectly possible, however. All you need to do is simply calculate to an infinitely accurate position where Achilles would actually pass the Tortise (if they both moved at constant speeds), and then take all your measurements and observations only from the section before he passes the tortise. With infinitely accurate measuring devices, yes, you will find that the tortise will _never_ be passed by Achilles in that selected section of the "race".

It's a kinda stupid way to compare things, though - sort of like having a 747 and a {insert 1200cc motorcycle name here} race down a 50 meter/yard stretch. Of course the bike will win - it will even if it has to start 50 meters behind the jumbo jet - but if you widen your "horizons" and allow them to race a bit further, you'll find that the jumbo jet will easily pass that puny bike a few kilometers down the line.

[Thorn]

Originally posted by Sandwich
It's a kinda stupid way to compare things, though - sort of like having a 747 and a {insert 1200cc motorcycle name here} race down a 50 meter/yard stretch. Of course the bike will win - it will even if it has to start 50 meters behind the jumbo jet - but if you widen your "horizons" and allow them to race a bit further, you'll find that the jumbo jet will easily pass that puny bike a few kilometers down the line.

Or the bike will get sucked into the plane's engine and they'll both lose

[mikhael]

The important thing about Zeno's Paradox is NOT that Achilles can never catch the turtle. That's bollocks. Of course he can. Given the contemporary scientific understanding of the world, this could not happen. Thus paradox: observed reality directly contradicts logic based on scientific reasoning. Zeno was pointing out the disparity.

Now this guy, who could be right (though I personally doubt it) has said that time is not granular. It doesn't matter, however, if time is granular or not, because you can't deal with anything shorter than a planck-interval in time OR space. On a very real level, granularity is enforced by the quantum nature of reality.

Of course, a better rebuttal, I think, is to point out that this schmuck came out of nowhere and said, "Mr. Hawking, I'm afraid you're wrong about imaginary time." Though, again, its possible that Hawking could be wrong, its somewhat like spitting on Einstein's shoe and saying, "About this General Relativity thing, I think you're a nutter!"

[an0n]

I dispute the Theory of Relativity. And the 'special' one too.

It's all self-indulgent non-sense.

[diamondgeezer]

I just finished Universe In A Nutshell. The main thing I've come away with it the concept that Universe is as it is because we would not be here to see it if it were otherwise. As for time, I've stopped worrying about it and just decided that time is what one makes of it. 'Tis easier that way.

[Galemp]

Ah yes, Stephen Hawking.

As for the rest of you claiming modern physics is rubbish... remember, we can never truly know what the universe IS. The best we can do is come up with mathematical models that approximate why the universe behaves the way it does. Occasionally a new model provides us with a better, more accurate prediction and it becomes accepted.

[Kamikaze]

http://mathworld.wolfram.com/ZenosParadoxes.html

Zeno's paradoxes are, in the end, illogical.

[Stryke 9]

You know, it strikes me that temporal physics is the one field in which you can smoke half a ton of grass and get paid for it. Aside from maybe politics.

Anyway, maybe I missed the "revolutionary new theory", but did they even really explain it? "There are no instants"- is that it? And a bunch of poorly phrased semimoronic gibberish? Yeah, be a real long time before anyone gets their heads behind that, you lofty-thinking excerable writer you. In the meantime, sneer about how everyone can't figure you out. Why, you're like a modern-day James Joyce, only without the capacity to form a coherent thought acceptably when you actually need to! Asshole.