
Zeno states that for motion to occur, an object must change the position which it occupies.
He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible.
Any thoughts? I see at least one flaw!
Why not start by saying what flaw you think you have found?
Hm, hm, good question, I guess in my country/ culture you start with an open matter and discuss the comments before you state your point.
There are a Greek standard (some philosopher) ! That does it differently !? I have taken a course in the art a year ago... hehe I must check that up...
It was Aristoteles!
He did his statement directly after telling the story. Then was the arguing  narrowing down the "truth" in his statement.
Here we do the arguing efter the facts  then a statement emerges!
The difference it that Aristoteles wants to deliver, my culture wants to discuss and is more open.
Well, since I am pretty sure that there is no flaw then I'm puzzled.
The 'flaw' is simply that the scenario is a converging series  each time the tortoise moves a bit more it is 'homing in' on a value which it cannot go beyond.
It is like starting with 1, adding 1/2 then 1/4 then 1/8...etc. You can carry on adding forever but the number will never go past 2  2 is the 'limit' of the series. For the tortoise, the limit is the point where the arrow hits.
Zeno's paradox is much more subtle than this obvious interpretation.
It essentially tells us something about the nature of spacetime.
The first question it raises is  is there a smallest distance (a 'quantum' of distance) or can you keep on dividing distances forever? Tied in with this is the same question about time. Is there a quantum of time (smallest possible unit of time)? If there is a quantum of distance then there must be a quantum of time, or more accurately there must be a quantum of the thing which is made of distance and time  spacetime.
(This is a critical question in modern physics. Relativity says you can divide forever. Quantum physics says there must be a 'quantum').
Think about it this way  if there IS a quantum of distance/time then:
start with an object. Move the object 'forward' for the smallest possible time and it will travel distance d (where d is our quantum of distance). But surely before an object travels distance d then it must have travelled distance d/2, d/4 etc. So how can there by a quantum of distance?
In this universe there is time, the arrow's properties can change after any number of snapshots, it can move, break, get wet.
If there wasn't time wouldn't the snapshot show the arrow in every position during it's path of flight? (because there was no time during it's movement)
Plus the magical snapshots in Harry Potter's universe captures motion
If life were a snapshot by snapshot world then the arrow would never actually be moving per se but there is still a modifier of propulsion or physics behind the object which calculate where it will be in the next snapshot.
As far as having a flaw, I am not entirety sure as to whether or not there is a flaw as that type of thinking is not something I do much thinking or research into.
Indeed. If velocity = distance/time and t=0 then clearly we have a problem.
In physics we generally talk about position and momentum, rather than velocity, because this is a more useful measure  momentum contains information about future movement, whereas velocity does not.
In maths we would use Calculus to calculate velocity and distance as t approaches zero.
As Bikerman said, you would use calculus. The velocity is the time rate derivative of position. This means for each infinitesimally small amount of time, the object moves an infinitesimally small amount. If you reduce the time all the way down to exactly zero (something which is not really feasible in reality) the object would not move. If you take a picture of something which is moving, effectively reducing the time to 0, the object would not be moving in the picture. I really don't see all that much of a paradox here.
The tortoise moves a bit and the chaser (hare?) is homing in! when has that happened in "real" life?
Never existed, the hare is always winning ! In the long run ... Even heading for a limit that is not true in "real" life.
So the foundation of that idea has a flaw  in my eyes. That idea is based on the idea of "time". Or something you can have a snapshot at... you are just dividing distances forever in "real" life.
spinout wrote:  The tortoise moves a bit and the chaser (hare?) is homing in! when has that happened in "real" life?
Never existed, the hare is always winning ! In the long run ... Even heading for a limit that is not true in "real" life.  Yes, it is 'true' in real life, it is just an unusual way of looking at the problem.
Quote:  So the foundation of that idea has a flaw  in my eyes. That idea is based on the idea of "time". Or something you can have a snapshot at... you are just dividing distances forever in "real" life.  Indeed, but that is not a flaw, it is a technique. It would be the wrong technique to apply to this particular problem, but there is no essential flaw.
Hm, adding a thing called "spacestrawberryjam" and use that as a "technique" to a problem called "spacejam moves faster than light" ... That is not a flaw!
It this time idea is not working in reality  why bother to try to freeze something that not exists? Just try to specify a thing as the smallest in a "relatively" seems like a "flaw" to me. But I have another terminology of a "flaw"  so I buy that.
It DOES work in reality.
We can demonstrate this with a hypothetical example. I'll use nice round figures, rather than realistic ones, but the method is the same either way.
Worked example:Scenario: The tortoise is 100metres away. The tortoise travels at 0.1 metres per second. The arrow travels at 40 metres per second.
Calculate how long the arrow takes to reach the tortoise.
Workings:
Iteration 1 After 2.5 seconds the arrow has reached 100m. In that time the tortoise has moved 0.25 metres.
Total time to this point 2.5 seconds
Iteration 2 The arrow takes 0.00625 seconds to cover 0.25 metres, by which time the tortoise has moved 0.000625 metres.
Total time to this point 2.50625 seconds.
Now, we could carry on, and with each repeat (iteration) our answer will become more and more accurate, but it is obvious from just 2 iterations that the answer is around 2.51 seconds.
If you didn't know calculus (and the Ancient Greeks didn't), then this is a pretty good way of getting a reasonably accurate answer to the question.
Important! Iterate from the other point of view:
When did the arrow pass the tortoise!
You can iterate from this point of view in the same fashion of course.
So when did he pass??? AHA! there is no time (to freeze)  just a relative reality.
Then my thinking: Motion is only possible without time!!!
because the statement below that includes a weird thing called TIME makes motion impossible:
"if it cannot move in a single instant it cannot move in any instant, making any motion impossible. "
This is confused to the point of incomprehensible.
a) You can iterate from any point of view.
b) The arrow passes, or hits, the tortoise at a clearly defined point. How accurately you can measure this point depends on your instruments, and depends on whether time is quantised (ie whether there is a smallest possible 'unit' of time).
b) Saying 'there is no time to freeze' is an assertion, not a proof.
c) 'Motion is only possible without time' is absolutely about as wrong as you can be. Motion is defined in terms of time. Velocity = distance/time. Without time there is no motion.
a) yes, just a matter of relativeness. You never get to the defined point...
b1) No. In sweden we had a driverslicens question about when we should turn on our nightheadlight when passing a car from the opposite direction: The answer is "in the eyeblink"  not in the moment. That is actually very correct phrased since there isn't a clearly defined point.
b2) yes, I see your point of view.
c) Motion is wrongly defined in "time". Since if there was anyting called "time" then motion don't exist; "if it cannot move in a single instant it cannot move in any instant, making any motion impossible."
