The argument isn’t about the sum but that the task is shown to be a hypertask. Zeno doesn’t claim that the time intervals don’t fit.
If I have code like:
distance=0
goal=100
while (distance<goal):
distance+=(goal-distance)/2.0
return distance
it doesn’t terminate until it runs into floating point imprecision. In the limit of actually accurate floats it doesn’t terminate. This doesnt have that much to do what I am doing with the numbers. Either the decomposition of the moving task is unfair, time doesn’t perfectly divide or moving is impossible. Refractoring the loop out of it would be cheating. The general case of having recursion which doesn’t bottom out will leave your machine in a livelock. Thus if you have a highly recursive function that doesn’t livelock, you know it bottoms out.
In using the alternative analysis you are implying logic about running and keeping inertia. The way the movement is specified ight not be compatible. If I have kids in the backseat of a car and they keep asking “are we there yet?” it is not the case that they keep asking it and I answering it after we have arrived.
The argument can also be understood as commenting on the claim that if you have a process which on every step moves forward in time and never backward in time if you take sufficiently many/infinite steps you will neccessary cover all of time. This is false as we can provide a process that constantly moves forward but doesn’t cover all of time. There is some slight of concept in that “never” is ambigious in respect to coordinate time vs step time.
You can take the tortoise location graph and the runner location graph and make a line that bounces between them when the runner is checking their position (draw horizontal line where he check where the tortoise is, draw a vertical line to wait until the runner reaches that point). This line doesn’t terminate and it doesn’t cross the crossing point of the runners. And this line doesn’t cover all of coordinate time despite moving in time and never backing up. Letting you run the process longer and longer won’t help you.
I don’t think you addressed the actual points but dedistracted yourself fromj some surrounding technicalities.
The argument isn’t about the sum but that the task is shown to be a hypertask. Zeno doesn’t claim that the time intervals don’t fit.
If I have code like:
distance=0
goal=100
while (distance<goal):
distance+=(goal-distance)/2.0
return distance
it doesn’t terminate until it runs into floating point imprecision. In the limit of actually accurate floats it doesn’t terminate. This doesnt have that much to do what I am doing with the numbers. Either the decomposition of the moving task is unfair, time doesn’t perfectly divide or moving is impossible. Refractoring the loop out of it would be cheating. The general case of having recursion which doesn’t bottom out will leave your machine in a livelock. Thus if you have a highly recursive function that doesn’t livelock, you know it bottoms out.
In using the alternative analysis you are implying logic about running and keeping inertia. The way the movement is specified ight not be compatible. If I have kids in the backseat of a car and they keep asking “are we there yet?” it is not the case that they keep asking it and I answering it after we have arrived.
The argument can also be understood as commenting on the claim that if you have a process which on every step moves forward in time and never backward in time if you take sufficiently many/infinite steps you will neccessary cover all of time. This is false as we can provide a process that constantly moves forward but doesn’t cover all of time. There is some slight of concept in that “never” is ambigious in respect to coordinate time vs step time.
You can take the tortoise location graph and the runner location graph and make a line that bounces between them when the runner is checking their position (draw horizontal line where he check where the tortoise is, draw a vertical line to wait until the runner reaches that point). This line doesn’t terminate and it doesn’t cross the crossing point of the runners. And this line doesn’t cover all of coordinate time despite moving in time and never backing up. Letting you run the process longer and longer won’t help you.
I don’t think you addressed the actual points but dedistracted yourself fromj some surrounding technicalities.