I was wondering whether it makes sense, yes.

I'm not sure your code tests that exactly. I mean, you specify that it runs infinitely fast, but the question you ask is just whether the last integer is even. There's no last integer.

Does this show that no matter how fast you go, counting integers takes an infinite amount of time? If so, that's interesting. It does quash the assumption that doing anything faster makes it take less time -- not true if the task is infinite.

Is this our conclusion?

In Thomson's lamp the end point is unknowable, but we know our end point already and we know our start point in Zeno's Paradox. So maybe a supertask is not the best way to think about this.

Maybe the concept of a supertask is what is being misplaced here. 0 is your starting point, now all I need is the end point, let's pick 1. Net change on a straight line is 1. — Jeremiah

So is it possible to count the rational numbers between them? No. And for the same reason it's impossible for any object to pass through all the $\frac{1}{2^n}$ points between 0m and 1m. That one can sum a geometric series doesn't say otherwise in either case.

Does this show that no matter how fast you go, counting integers takes an infinite amount of time — Srap Tasmaner

It shows that no matter how fast you go you can never finish.

Take the room crossing example, where I have to keep going to the half way point. If that is a supertask it should be impossible for me to cross the room, but I can prove empirically that I am able to cross the room, hence motion is not a supertask or supertasks are not impossible. Making the aspect, when considering motion, of being a supertask moot.

Who cares if I can count an infinite number of points or not, I don't need to I have calculus.

If that is a supertask it should be impossible for me to cross the room, but I can prove empirically that I am able to cross the room, hence motion is not a supertask or supertasks are not impossible. — Jeremiah

This is exactly what I said here. And given that completing a supertask is demonstrably impossible, it must be that motion isn't a supertask. But for motion to not be a supertask it must be that Zeno's premise that an object must pass through an infinite number of half-way points is false. Motion is possible only if it is discrete rather than continuous.

Who cares if I can count an infinite number of points or not, I don't need to I have calculus. — Jeremiah

An object moving through an infinite number of half-way points in succession is like counting the rational numbers between 0 and 1. If the latter is impossible then so is the former. Being able to sum a geometric series doesn't mean that we can count the rational numbers, and nor does it mean that an object can move through an infinite number of half-way points. Calculus can't solve Zeno's paradox.

Ya, I read your post the linked pages.

And given that completing a supertask is demonstrably impossible, it must be that motion isn't a supertask — Michael

It must mean motion is not a supertask OR supertasks are not impossible. At anyrate it is moot.

And given that completing a supertask is demonstrably impossible, it must be that motion isn't a supertask — Michael

It must mean motion is not a supertask OR supertasks are not impossible. — Jeremiah

Look at the first part of that sentence: given that completing a supertask is demonstrably impossible....

Maybe you should go back and read your own links.

Form one of your own links on Zeno's paradox.

Zeno's argument to reach the conclusion that either motion is not a supertask or not all supertasks are impossible.

Yes, and supertasks are impossible, therefore motion is not a supertask.

Hey man, I am just citing the reference you gave me, maybe next time don't use Wikipedia.

Are you being serious, or is this trolling?

Actually the conclusion in Wikipedia makes more sense than yours.

Let's try this another way:

P1. Zeno's paradox shows that either motion is not a supertask or supertasks are possible.
P2. Thomson's lamp shows that supertasks are not possible.
C. Therefore, motion is not a supertask.

I don't care about the supertask thing, I feel it is moot. We don't need it one way or another.
--

Now back on topic...

We already know that motion is possible and we know there are infinite parts between Achilles and the turtle. Whether you want to say those parts are continuous or discrete, that does not really matter, as you can't count them anyways, so they are effectively continuous and effectively infinite. We know Achilles can pass the turtle. This sounds like a job for calculus.

we know there are infinite parts — Jeremiah

Thing is, we don't know that space is infinitely divisible. Atomicity versus Infinite Divisibility is still up for debate in science, and things like Zeno's paradox suggest that there is a smallest possible division of space.

Currently, I believe, Planck lengths are theoretically the smallest possible distances.

It truly does not matter. Infinite is just another word for more than I can count. Which is why we use calculus.

How can it not matter? If space is only finitely divisible, it solves the paradox.

The paradox was solved by partial sums a long time ago.

Could a quantum computer not complete a supertask? Does this imply that the notion of discrete space is not required for motion, only that quantum reality prevails?

Infinite is just another word for more than I can count. — Jeremiah

No. Infinitesimal numbers are infinite not because it's more than what you can count in principle.

Infinitesimal infinite parts. There are more parts than I can count without approximating somehow or using calculus.

That is the different between a convergent series and a divergent series. We know the distance between Achilles and the turtle converges to a finite number, so you are kind of arguing a moot point. — Jeremiah

What laws of physics do Achilles and the turtle obey? What do these LAWS say will happen?

P1. Zeno's paradox shows that either motion is not a supertask or supertasks are possible.
P2. Thomson's lamp shows that supertasks are not possible.
C. Therefore, motion is not a supertask. — Michael

Does P2 show that all supertasks are impossible, or just a certain class of tasks?

Are we not labouring under the conflation that certain abstract attributes are the same thing as physical attributes that share the same name? Why should the abstract idea of infinity and its properties determine what can and what cannot happen in reality?

If the laws of physics tell us that Achilles will cross an uncountably infinite number of points in a finite time to catch the tortoise, then that is what he will do. Nothing physically infinite has occurred.

So,

1. What Achilles can and cannot do is not deducible from mathematics.

2. Stop confusing abstract infinity with physical infinity.

If the laws of physics tell us that Achilles will cross an uncountably infinite number of points in a finite time to catch the tortoise, then that is what he will do. — tom

This is ambiguous. By "laws of physics" are you referring to our models or the way things actually behave? If the latter then I would argue that, if Zeno's paradox is correct in calling into question the notion of infinite divisibility of movement, then things don't actually move in a continuous manner but in a discrete manner. If the former then I would argue that, if Zeno's paradox is correct in calling into question the notion of infinite divisibility of movement, then our models are faulty.

Mathematically, Zeno showed a finite number can be divided infinitely and there's no mathematical "atom" or Planck distance. That's fine. He showed that a line is not a collection of points (a popular view back in ancient Greece). Fine too.

Where it goes wrong, is to translate this mathematical argument into one about physical reality. Zeno wasn't arguing for a physical theory of motion or distance but was making points about mathematics by using an allegory, which shouldn't be taken literally. There isn't a paradox because mathematically he's correct.

For physical motion it's s = d/t and Zeno's formulas are simply the wrong ones to use.

As for discrete rather than continuous space, see quantum spacetime, loop quantum gravity, and string theory.

As for discrete rather than continuous space, see quantum spacetime, loop quantum gravity, and [url=]strign theory[/url]. — Michael

There is precisely zero evidence for a discrete space-time.

General Relativity is a theory of a continuous space-time, and Quantum Field Theory os a theory of continuous fields in a continuous space-time.

And, despite your claim, String Theory also takes place in a continuous space-time.