By the way, if 1 - 2micrometer contains infinite distance inbetween, then we also consist of infinities, which means that the infinites would cancel out anyway and thus motion is possible.
Ray - just because we have infinite points between any two points on our body does not solve the problem. It is the finitude of time that was the original problem - not the infitude of points on my body.
TF
Howdy Sire,
Long time no see.
It is hardly unintentional.
I never buy a newspaper.I never drink coffee.I like the idea of brown stains on newspapers though.It is about all they are fit for.
Did I say motion was impossible.That's not like me.
I'm all motion.Zeno is word play.Nothing in it.
spendius.
Quote:Ray - just because we have infinite points between any two points on our body does not solve the problem. It is the finitude of time that was the original problem - not the infitude of points on my body.
I don't quite understand. If infinity cancels out, then we would be dealing with finite whole numbers, and since space is distance between any two objects measured relative to the two bodies, it is logical for us to be able to reach it since we know how fast we can move, in which case we could solve for motion.
I think, to an amateur like me, this is fairly simple.
If we take Zeno's hypothesis and divide the distance up into an infinite number of infinitely small points, then we must also do the same with the time it takes to traverse that distance. This means we end up with points of time, or in other words time with no length, which to my mind equates to frozen instances. In other words, we represent each point of the distance as an instance of the objects motion, containing vectors for velocity, direction etc., but no actual motion can take place in a point in time.
Therfore, when time is suspended as a point, there can be no motion since motion is velocity in a direction for a time, but when these are joined up into a continuum then time passes and motion is possible.
A bit like watching a movie really. Frames per second...
Armalite raises an interesting issue about time which points to the falacy of the argument.
(Mathematical recap of several posts)
motion(velocity) = distance/time
velocity = 50miles/2hours
25mph=50miles/2hours
We can divide this equation by an infinite number of other numbers and always have motion.
(25mph)/x=(50miles/2hours)/x
It is impossible to solve for x where the equation is no longer true or motion doesn't exist. (0 would not be a division of the distance and therefore outside Zeno's argument.)
If we assume motion can not exist then either time or distance must not exist. (Since no number solves the above equation.)
Since we assumed that distance does exist and can be divided infinite times then the only possible way that motion can not exist is if time does not exist.
The reverse assumption can be used to prove that distance doesn't exist but only time does.
parados
Very good point there.
In fact, Zeno's aporia can easily be clarified with elementary maths. Prime umbers are infinite. But the class of prime numbers is finite, because that class is not a prime number and countains only prime numbers.
The infinite division of the stadium has nothing to do with the fact the stadium is finite. Number 1 is finite but can be divided to the infinite.
But I think that Zeno had other things in mind. His problem was not motion. According to Parmenides, his teacher, the being is not multiple or divisible. In fact, Zeno would refuse the reality of time or distance and the possibility of division.
