Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: Thorn on August 14, 2003, 04:12:49 pm
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http://www.space.com/scienceastronomy/time_theory_030806.html
still trying to wrap my brain around this one...
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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.
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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...
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He doesent go another meter twice.
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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.
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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
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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?
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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.
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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.
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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. :D
But I still won't believe the guy. :D
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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.
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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
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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:
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. ;)
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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 :D
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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!"
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I dispute the Theory of Relativity. And the 'special' one too.
It's all self-indulgent non-sense.
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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.
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Ah yes, Stephen Hawking. :nod:
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.
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http://mathworld.wolfram.com/ZenosParadoxes.html
Zeno's paradoxes are, in the end, illogical.
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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.
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Meh, time. All the important stuff happens outside it, anyway. :p
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It should be noted that a lot of the "science" the Greeks came up with was, like Zeno's paradox, pure garbage. In that era actual physical experimentation was considered gauche. The idea was that, since nature is based on logic, you should be able figure it out by just sitting around thinking up theories.
This didn't do too much damage to theology and philosophy, but it saddled the physical sciences with all sorts of crap that lives on in our cultural consciousness to this day.
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I'm surprised people still hold Zeno's "paradox" as one, anyway. I mean, it's compound density in measurements. Nothing particularly mysterious there, we've known about it forever. Hell, half of, whatsisname, Calculus or Algebra (slept through both) involves asymptotic exponentials and the like anyway.
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But alas, this guys theory, although he claims it solves alot of paradoxes, fails to solve the most important one. "Which one came first? The chicken or the egg?" ;)
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Since Time is toroidal, both simultaneously came first, last, and in the middle. And, by the same token, never existed in the first place. There is no chicken.
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Whoah... Never thought of it that way... :blah:
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If my biology teacher is right, the egg.
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If you think about it, is there really any difference between time running straight forward, time branching off infinitely, or time not actually existing at all to a person who is observing it within that theory?
In situation 1, which has a single, unbroken temporal reality, the person would observe time moving forward, and he would be correct.
In situation 2, with the fractal temporal reality, it would appear to the observer that time was moving forward, since he would have no way to observe the other realities.
And in situation 3, in which time does not really exist, and in which each moment is its own separate universe, the person would still believe that time was going forward.
Since we lack any way of viewing alternate temporal realities, we cannot prove the way time flows any better than the Greeks could.
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Originally posted by ZylonBane
It should be noted that a lot of the "science" the Greeks came up with was, like Zeno's paradox, pure garbage. In that era actual physical experimentation was considered gauche. The idea was that, since nature is based on logic, you should be able figure it out by just sitting around thinking up theories.
I always wondered about that, but never heard it said so succinctly. Though you're right, I think that generally people don't give the Greeks enough credit for the intelligence they had back then (even if their physical sciences came out ridiculous). Gives an illusionary sense of human progress, I think.
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Originally posted by Stryke 9
I'm surprised people still hold Zeno's "paradox" as one, anyway.
I'm afraid I must now disabuse you of the notion that most people have a working knowledge of the mathematics required to disprove Zeno's paradox.
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That Zeno situation is phrased in a way that makes it seem like a paradox but it is actually quite obvious where the seeming inconsistency comes from. Not only is the distance travelled by Achilles and the tortoise cut into a tenth every time you record their progress, but so is the time taken for each increment to occur. So as both the time taken and the distance travelled by the two go to zero, we get a 0/0 style limit which can of course be a finite quantity.
We can say that Achilles is at position 10T from the starting point while the tortoise is at T+10, but T is actually a function of a different variable, say U, something like T = 10/9 (1 - 10-U), where U takes integer values. They will obviously meet at T = 10/9; the value of U for which this occurs is ¥ but that's perfectly okay, since U is just an independent variable being used to place increments in the time and does not denote the elapsed time itself. As I said, the confusion comes from the way the problem is worded since most people tend to think that T itself is the independent variable.
What exactly is that guy's idea though? That article does not say much about the actual theory... :p
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Originally posted by Thorn
http://www.space.com/scienceastronomy/time_theory_030806.html
still trying to wrap my brain around this one...
Well it has been determined through experiments that time is not broken into a planck intreval.
If time cannot be measured by quanta, then via Occam's razor the simplest solution to the answer is that there is nothing to have the quanta of. In essence, time does not exist.
Since we think with a dialogue based on time, (biochemical patterns in the brain are effected by stimuli) it is natural to assume that previous information or future information within the universe exists.
I do not believe that Lynd himself is a 'genius' but he is a good excuse to allow for physicists who want to challenge traditional assumptions to have a field day. Something that is difficult to due because of the nature of science. Moreso, even "enlightened scientists" have a hard problem working beyond human nature.
Anyway, there is an odd correlation between Zeno's paradox and the way that light operates as a constant, don't you think? :p
Just as space and time as one object allows for a solution to Zeno's paradox, there is certainly something missing from relativity ;)
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Originally posted by CP5670
That Zeno situation is phrased in a way that makes it seem like a paradox but it is actually quite obvious where the seeming inconsistency comes from. Not only is the distance travelled by Achilles and the tortoise cut into a tenth every time you record their progress, but so is the time taken for each increment to occur. So as both the time taken and the distance travelled by the two go to zero, we get a 0/0 style limit which can of course be a finite quantity.
We can say that Achilles is at position 10T from the starting point while the tortoise is at T+10, but T is actually a function of a different variable, say U, something like T = 10/9 (1 - 10-U), where U takes integer values. They will obviously meet at T = 10/9; the value of U for which this occurs is ¥ but that's perfectly okay, since U is just an independent variable being used to place increments in the time and does not denote the elapsed time itself. As I said, the confusion comes from the way the problem is worded since most people tend to think that T itself is the independent variable.
What exactly is that guy's idea though? That article does not say much about the actual theory... :p
Huh - just what I said, only in Equationish instead of English! :p
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Well... If time does not exist... Then you can't measure speed. Because speed is the time it took to go a specific distance right? So, according to the theory, I'll just go outside and drive about 240km/h on a 40 road, and explain to the cops, that will finally shoot my wheels out, that according to the new laws of physics, I wasn't going any speed, because there is no time. As well as that I wasn't there cause there is no today. So I can safely say that I was at home at the time of overspeeding... :hopping:
Or....:wtf:
*brain shuts down.*
...:blah:
*drool*