No, even the Wikipedia article links two demonstrations of it. In fact the first time I heard of this effect was when my experiment did not work because I was observing the atom too often and thus I inadvertently triggering this effect.
Zeno's paradox
- Thread starter Kyriakos
- Start date
No, even the Wikipedia article links two demonstrations of it. In fact the first time I heard of this effect was when my experiment did not work because I was observing the atom too often and thus I inadvertently triggering this effect.
punkbass2000
Des An artiste
Cool.
Something I've frequently wondered about, though perhaps this is more philosophical than Scientific, but what, precisely, constitutes "observation"?
Something I've frequently wondered about, though perhaps this is more philosophical than Scientific, but what, precisely, constitutes "observation"?
That is one of Zeno's other paradoxes, the "arrow paradox". The point is that if you think space is continuous then you get the Achilles and the tortoise paradox and also the dichotomy paradox, with the result that it's impossible to move any distance because you must first cover an infinite number of distances; but if you think space is discreet then you get the arrow paradox, with the result that there is no motion at all, because at any given moment the supposedly moving thing is at rest. Either way, there is no motion. Whether Zeno intended these arguments to show that there really is no motion or whether he was trying to expose the absurdity of this kind of arguing is unknown.
I like to think that he meant more than just showing the absurdity, but i am not familiar enough with physics to know if his paradoxes are discussed at any serious level.
I gave a reflection on how i view this particular one in the first page of the thread.
That the arrow is immobile at any given moment is obvious; if time could freeze one would observe it. Perhaps Zeno was trying to make the point that, as i said earlier, the human mind views nature in a way which is not necessarily the entire view (in other respects i do know that physics discusses the limiting objectivity of the observer, but i am not sure if it involves something particular to the Zenoic paradoxes).
I gave a reflection on how i view this particular one in the first page of the thread.
That the arrow is immobile at any given moment is obvious; if time could freeze one would observe it. Perhaps Zeno was trying to make the point that, as i said earlier, the human mind views nature in a way which is not necessarily the entire view (in other respects i do know that physics discusses the limiting objectivity of the observer, but i am not sure if it involves something particular to the Zenoic paradoxes).
That's a very good question and there isn't a universal agreed upon definition of this. The easy answer is: Whenever I get (classical) information out of the system that let's me deduct the quantum state of what I am observing, in other words whenever I make a measurement of the state. However then the question arises what a measurement is and when the boundary from quantum to classical is crossed. Here there is another easy answer: When we go from few particles to many particles. But as the objects that we can do quantum physics with get larger and larger, the question where this boundary is gets more difficult. And maybe there isn't one and under the right conditions we could entangle cats after all. At the moment this is indeed a philosophical question and there are debates but no definitive answer.
In the experiment it is rather easy to define what an observation is, because I know I have made one, whenever my photon counter clicks or charge is accumulated on the CCD camera or any other measurement device registers something that can be traced back to whatever I just observed. These things give me a classical Yes or No and I can count that as an observation, even if I don't know what the definition of an observation actually is.
I'd like to think that Zeno's point wasn't that there's no movement, nor that arguing about such things is absurd, but instead that his contemporary maths isn't very good model for the real world. Greeks had lots of trouble with quite a few things: infinites, irrationals, and atoms vs. continuum, and some of those difficulties are hard to even imagine for a modern man.
Or perhaps it was pure sophistry.
Or perhaps it was pure sophistry.
punkbass2000
Des An artiste
Ah, thank you.
I had suspected it wouldn't be so easily definable per se, though the "I know when I've done it" argument holds much water in my view.
Elaborate please.
Whew. Not easily. I can recommend this book. He takes a great deal of time explaining the reasoning behind the major theories of super-small physics, and (I think) gives them all fair treatment.
A great deal of it is allowing us to shift our perspective, though. By analogy, until you realise that 'addition' is 'subtracting a negative', there're just some ideas that seem wacky and contra-intuition. So, he shows how specific things are 'the same', if viewed from a different angle.
I hate to say "read this book", but it's actually extremely interesting. It's a good buy, imo, and fun casual reading (if you like that sort of thing).
A great deal of it is allowing us to shift our perspective, though. By analogy, until you realise that 'addition' is 'subtracting a negative', there're just some ideas that seem wacky and contra-intuition. So, he shows how specific things are 'the same', if viewed from a different angle.
I hate to say "read this book", but it's actually extremely interesting. It's a good buy, imo, and fun casual reading (if you like that sort of thing).
r_rolo1
King of myself
Well, to be honest, we still have enough of issues with the infinity
And in spite of Zeno original paradox being solved, the actual idea that Zeno IMHO wanted to convey, our complete lack of understanding of what infinity is and what is there ( math friends, take this wording as poetical liberty ) is more or less in the same state it was in Zeno's days. If you want a example can give you 2 modified Zeno paradoxes:- A lamp is programmed to switch between on and off at 1-1/(2^n) of a minute from this moment. In other words, it starts on , goes off in half a minute, gets on in 3/4 or a minute, gets off in 7/8 ... Exactly a minute from now the lamp is on or off ?
- Two trains are going to the same station by the same track at the same speed coming from oposite sides and started moving at a constant speed from the same distance from the station at the same time. A pigeon decided to fly across the track between the fronts of the two trains back and forth and when they both get to the station ( aka crash on each other
) the pigeon is between the trains. From what spot in the track the pigeon started in back and forth trip ?
warpus
Sommerswerd asked me to change this
How about: Whenever you bounce a particle off the thing you're observing and it comes back to you with some information.
Great! I have been a bit unsatisfied with the solution to Zeno's paradox too, since they didn't IMO capture quite the spirit of the original paradox. That is because the paradoxes themselves didn't capture the spirit either. I have spent some minutes trying to come up with a similar paradox but not reached it, and here you gave it! If the paradox isn't invented by you, may I ask, where did you get it from?
The problem with original Zeno's paradox is that it confuses the atomic and continuous views of time, and it does it so stealthy that only few notices: First the time is infinitely divisible, but at the conclusion the intervals are thought of having equal lengths ("the arrow never reaches" <-> the time intervals have size bounded from below <-> atomism)*.
Your version is much better because contrasting time with {on, off} removes needless confusion, and it has no word "never" to slip in other view of time via back door.
*) Someone might complain about the first <->, but I'm trying to describe the thought process of the paradox more than giving proof of anything.
Well, to be honest, we still have enough of issues with the infinity
- A lamp is programmed to switch between on and off at 1-1/(2^n) of a minute from this moment. In other words, it starts on , goes off in half a minute, gets on in 3/4 or a minute, gets off in 7/8 ... Exactly a minute from now the lamp is on or off ?
Doesn't work because the lamp doesn't switch on and off infinitely fast. At some point the lamp needs to switch faster than the switch itself can operate.
And even without that problem, your question makes no sense. Exactly a minute from now is outside the scope of what you've programmed.
- Two trains are going to the same station by the same track at the same speed coming from oposite sides and started moving at a constant speed from the same distance from the station at the same time. A pigeon decided to fly across the track between the fronts of the two trains back and forth and when they both get to the station ( aka crash on each other
Huh?
ParadigmShifter
Random Nonsense Generator
The light switching on and off doesn't converge, so the question has no meaning.
EDIT: It's basically the same as asking whether the sequence 1, -1, 1, -1, 1, ... converges. It doesn't.
EDIT: It's basically the same as asking whether the sequence 1, -1, 1, -1, 1, ... converges. It doesn't.
The convergence doesn't matter, since the light stays on once switched on. The lack of convergence is the reason why this is paradox at all.
Also, I think the physical limitations of light switch are little off the target, since this isn't about the real world, but rather about our modeling of it.
Also, I think the physical limitations of light switch are little off the target, since this isn't about the real world, but rather about our modeling of it.
But asking what state it'll be in after 1 minute is meaningless, because that's outside what's programmed. It's programmed to change state infinitely many times in just under 1 minute. If it's able to change state infinitely quickly, then there's no paradox. If it takes a finite amount of time to change state, then there's no paradox either, because there will only be a finite number of state changes before the minute is up.
r_rolo1
King of myself
It makes the exact same sense as the original arrow or the turtle paradox. if you go that way , Zeno original paradoxes aren't paradoxes because there is the Planck distance and because of that you can't divide space infinitely ( OFC if you can't sum to infinity the arrow never gets to the target and the turtle never surpasses Aquiles
)Anyway, the objection you made about physical limitations is meaningless for the discussion. I could had arranged for switch in electron spins, polarization of a photon or even change between orbital states of a molecule at the same energy ...
It might be dificult to visualise , but it is the reverse of the arrow paradox.
Strange objection ... first because no one said that n could not be infinity
But anyway, I must ask, why would not be a paradox if the change could be instantaneous in your opinion? I just can't see it.@ParadigmShifter
OFC the series does not converge
That was the point of my argument: historically Zeno launched the paradoxes because he was disgusted with the speculation about infinity that was the rage in mathematics in his time. Zeno liked the notion of infinity as much as Einstein liked quantum mechanics a la Copenhagen and the paradoxes he launched were his version of Einstein EPR thought experiment. I was just trying to put more on the naked the core idea that Zeno wanted to convey ... that wasn't how to sum converging series @Atticus
I read those two versions in a scientific divulgation book that had a chapter dedicated to Zeno paradoxes and derivatives. If I remember the name I'll post it ( it was some time ago though
)
punkbass2000
Des An artiste
Regardless of the program, a minute will pass.
How? I dunno if you need to reword it, or what. You appear to want to work out the pigeon's starting position, knowing that it ends squashed between the two trains. Every starting position leads to the same end, you can only backtrack if you know the state of the system at some point before that final state. I don't see why that's paradoxical, or equivalent to the idea that the arrow never makes a tortoise kebab.
Strange objection ... first because no one said that n could not be infinity
This thing will change state infinitely many times in the next second. What state will it be in after one second? That's all the question boils down to, and there's nothing paradoxical about it. The answer's a simple 'don't know'. The original paradox is that something that does clearly happen, i.e. arrow hitting tortoise, apparently logically can't. But what's the paradox here? What's the thing that does happen, but apparently is impossible by logically analysing what's happening?
r_rolo1
King of myself
Well, if you want to be picky, the arrow never reaches it's target because of the Planck distance ... it will always be never closer of 1.616252(81)×10^-35 m of the target
And Aquiles will never reach the turtle because of the same reason ( they will have to go sideways at best ... good ol'Pauli exclusion principle disalows 2 diferent bodies composed of matter of occupying the same space as well ). So neither of the original Zeno paradoxes actually happens as well ...
