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[Vengeful Donut]

Actually the solution to the Achilles paradox is to say either that you have a finite number of tasks that can be divided infinitely, so while you can divide them smaller an infinite number of times, at any stage in that division there is only a finite number of tasks, the other solution of course is to say that distance is discrete, rather than continuous.

You seem to be disagreeing with me, but nothing you wrote contradicts anything I wrote.
This is a sign of impending disaster for a conversation, so I'm ending my participation in it.

[Neruz]

Calculus is usually used to deal with infinitesimals, the Achilles paradox is all about infinitesimals. How would you not use Calculus to solve the paradox?

[Armok]

How can you not use a thermometer to cook your food? Both are about heat, after all.

[dragnar]

But you can use a thermometer to cook food, you just don't have to.

[Bricks]

How can you not use a thermometer to cook your food? Both are about heat, after all.

I just use Maxwell's demon to cook all my food.  And to keep my ice cream cold.

[Armok]

But you can use a thermometer to cook food, you just don't have to.

And you can use calculus to solve the paradox, but you can't do it with ONLY calculus, and the calculus will most likely be of only tangential help, just like the thermometer.

[Hummingbird]

Ahh sweet smell of derailment. Maybe we need a subforum: "philosophy n other cool stuff"
Back to offtopic: I don't really get the wrestling. Tried 100 times wrestling a cougar (or a tiger) with legendary wrestler, superdwarvenly strong and still can't break the joints unless I missed something

For some reason, you can't break joints of non-sentient creatures.  You can still strangle them, or grab their heads with a free hand and gouge their eyes out.  That's about all you can do, though.

[Neruz]

But you can use a thermometer to cook food, you just don't have to.

And you can use calculus to solve the paradox, but you can't do it with ONLY calculus, and the calculus will most likely be of only tangential help, just like the thermometer.

So if you're not going to use the primary tool for dealing with infinitesimals to solve a problem about infinitesimals, how are you going to solve it? And why gimp yourself like that?

[Armok]

Because it in't a problem with the infinitesimal, it's a problem with the human perception and understanding of the infinitesimals.

[Neruz]

Of course it's a problem with infinitesimals; being able to complete an infinite process is logically unsound without using infinitesimals.

[Armok]

Being able to complete an infinite process is logically unsound without using infinitesimals, but being able to complete an infinite process is not the real problem. The real problem is human minds finding the sulution unintuitive.

[Baughn]

Infinitesimals are fun and all, but I thought I should make one thing clear for the less mathematically inclined of you...

Basic calculus does not involve infinitesimals, and does not offer a solution to zeno's "paradox" either. If you state a case where achilles passes the tortoise at 1 second in terms of zeno's paradox, what you get is an infinite process that calculus will easily show has a limit of 1; however, calculus specifically disclaims any ability to show that the solution actually *is* one, or that it even exists.

That it in this case does exist has nothing to do with it; calculus shows you that you can get arbitrarily close to the limit, not that you can actually reach it. For that, you have to use other methods.

..such as not stating the problem in terms of zeno's paradox in the first case. Just because you can state a situation in terms that make it impossible to predict what will happen without using very advanced mathematics, doesn't mean you have to do that; I really don't see why people thinks the paradox is a paradox. Do it the obvious way, by dividing distance by relative speed.

[dragnar]

The paradox is unsolvable, but only based on the flawed logical axiom that preforming an infinite number of tasks in a finite period of time is impossible.
Remove this idea and the problem isn't even a true paradox anymore.

[Neruz]

The paradox is unsolvable, but only based on the flawed logical axiom that preforming an infinite number of tasks in a finite period of time is impossible.
Remove this idea and the problem isn't even a true paradox anymore.

Well no shit, the paradox of going back in time and killing one's own grandfather isn't a paradox if we remove the idea that you're going back in time and instead say you just moved to an alternate universe.

Being able to complete an infinite process is logically unsound without using infinitesimals, but being able to complete an infinite process is not the real problem. The real problem is human minds finding the sulution unintuitive.

The Achilles paradox is a variation on the dichotomy paradox, or "That which is in locomotion must arrive at the half-way stage before it arrives at the goal."


Basically stating that before you can go from one point to another, you must first reach the half-way stage between those two points. And before you can get to the half-way stage you need to reach the point half-way betwen your current point and the half-way point and so on, ad infinitum.

Ergo, the conclusion is that in order to go from one point to any other point, one must first pass through an infinite number of points between the two, thus in order for an object to move, it must complete an infinite process, which is, as i previously stated, logically unsound.

From this, Zeno concludes that all motion is an illusion, i conclude that we're missing something, or possibly that distance and time are in fact discrete (if the mathematics behind Planck lengths are correct, one could put forth an argument for time and distance being practically discrete at a Planck scale, as it's supposed to be impossible to measure anything smaller.)



Also, unrelated to the dichotomy paradox, but the Arrow paradox is actually solved by the addition of inertia.

[dragnar]

There are several possible explanations for the paradox, but the simplest one that fits all of the data, and therefore the one chosen by occam's razor, is that it is possible to complete an infinite number of tasks.

Zeno's conclusion is essentially that nothing we sense is real, which, while possible, is needlessly overcomplicated. Besides, if time and distance are illusions then there is no point in thinking about it, as the very process of thought is, therefore, an illusion.

Since this conclusion is unacceptable, another must be used, even if Zeno was correct science is devoted to producing more accurate, useful models of the universe, not "correctness".