Any operation requires a duration of time in order to occur. Therefore in a finite amount of time that sequence of operations would not be completed. A supertask is logically impossible. — Metaphysician Undercover
And I believe atomic electron transition is a known example of discrete motion in nature. — Michael
If you are thinking of discrete quantum states of electrons in an atom, that is not an obvious example of discrete motion (except in a generalized sense of "motion" as "change"). — SophistiCat
Why not? The electron's position is a value in its quantum state. — Michael
This is why I find the use of the aforementioned geometric series to address the paradox to be nothing more than trickery. It assumes from the start that it takes a finite amount of time to travel some finite distance (e.g. 10 seconds to reach the half way point), and then extrapolates from there. But obviously if your reasoning assumes that it takes 20 seconds to get from A to B (which you have done if you've also assumed a constant speed), then you're going to conclude that it takes a finite amount of time to get from A to B. — Michael
So instead of halving the unit of time for each successive half way point, why not double the unit of time for the previous half way point (e.g. by defining a new unit of time for each successive half-way point and considering that to be the unit that is used to measure the time spent)? The logic is the same, but the maths doesn't work out the way the "solution" wants it to.
E.g. when considering 0 - 0.5m, define the time as 1 unit. But then when considering 0.5m to 0.75m, define that time as 1 unit and so the time from 0 - 0.5m is 2 units, and so on. What's the sum then? — Michael
Now I don't understand what you are doing here. A unit of time is set out, determined, by some physical activity. You cannot just randomly change your unit of time, so that the same activity which takes 1 unit of time will later take 2 units of time, and then 4, etc.. What kind of measurement of time is that? — Metaphysician Undercover
It might be indivisible at a certain scale, but it's not indivisible at every scale — Michael
Even if we are to assume an operation which requires a zero duration of time, — Metaphysician Undercover
There is no half at any scale. — Rich
There is no such thing as zero duration. If there was, then the flow of duration (time) would have to stop and then what. Stop for how long? How does it restart? Duration (real time) is continuous and heterogeneous. It never stops and cannot be seen as stopping. Scientific time (clock time) is just a movement in space (not real time) that is symbolic and is used to approximately establish simultaneity. This is something different and shouldn't be given ontological significance. Doing so leads to all kinds of paradoxes such as those associated with Zeno's and Relativity's. — Rich
Sure there is. If the object is to travel 10 meters then it passes the half-way point after 5 meters. And this is true even if we're not measuring it. — Michael
There is a half way point between the start of a 100m line and the end, and this is true even if we don't plot it, which is why I don't understand aletheist's and apokrisis' objection at the start. — Michael
We do not have to treat every halfway point as a discrete step in the motion from the start of that 100-m line to its end. We can traverse the one full interval (100 m) without individually traversing infinitely many half intervals (50 m, 25 m, 12.5 m, etc.). — aletheist
Space and time must be thought of in a different way as not being divisible. An object doesn't travel half-way. It moves from here to there in one indivisible motion. There is no half in a continuously flowing and changing space. — Rich
We do not have to treat every halfway point as a discrete step in the motion from the start of that 100-m line to its end. We can traverse the one full interval (100 m) without individually traversing infinitely many half intervals (50 m, 25 m, 12.5 m, etc.). — aletheist
As above, I don't get this. You do travel half the way before you reach the end. That's just a fact that's entailed by continuous motion. — Michael
But I didn't move half-way. I moved from here to there. In retrospect to may try to figure out what half-way might have been and you may be approximately correct with your measurements, but my motion was one motion as you viewed it and add I experienced it - the two being totally different.
To understand experiences one must understand from the point of consciousness, not via some mathematical symbol or equation. Observe what you see. — Rich
I don't get this. You do pass the half-way point (after 50m). And you do pass the quarter way point (after 25m). And so on, ad infinitum. — Michael
Yes, you pass each of those arbitrarily identified "points"; but each instance of doing so is not a separate, discrete step in the continuous motion of traversing the entire 100-m line. — aletheist
The issue is attempting to find a half-way point when there isn't any. The problem begins with attempting to use a symbolic, 1/2, in a continuous flowing and changing motion. Can you find anything called half-way in the universe? No. Only when you start trying to symbolically attempting to dissect in memory does such things begin to emerge. I don't actually experience 1/2. I label n it as such for practical reasons sometimes after the motion is accomplished.
It order to relieve oneself of mathematical symbolism of life experiences, one must stop and observe what one is experiencing. I run from here to there. I don't run half-way. This is a very important observation to make. No one runs half-way. — Rich
It doesn't matter if you don't consider the movement to be in separate, discrete steps. — Michael
It has nothing to do with how I consider it. The movement does not actually consist of an infinite series of separate, discrete steps. It is simply a single, continuous motion from the start of the 100-m line to its end. This is what I mean when I say that the line itself does not actually consist of infinitely many separate, discrete points; it is simply a single, continuous line. — aletheist
you can try your best to represent life experiences using symbols, but try as you might 1 does not in any way describe the experience of going from a bed to a bathroom. — Rich
It stills has to pass through an infinite series of separate, discrete points. — Michael
Only if all of those points actually exist, which is precisely what I deny. The line does not consist of separate, discrete points; it can only be modeled as having separate, discrete points.
Your claim, as I understand it, is that the line does consist of infinitely many separate, discrete points, and thus can only be modeled (or "considered') as continuous. This seems to be our basic disagreement. — aletheist
Of course the points actually exist. There actually is a half way point between the start and the end of a 100m line. There actually is a quarter way point. And so on. Are you denying this? — Michael
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