trotoise and achilles

http://www.mathacademy.com/pr/prime/articles/zeno_tort/
Follow the link to one of the classic paradoxes.

Trotoise? This is indeed a puzzle.

Originally posted by XanthosNZ
Trotoise? This is indeed a puzzle.

You didn't know about the Trotoise? Its just a hare faster than a tortoise and so modifies the original puzzle.

Its easy.

You are spliting both the time and distance into infinate parts. Thuthey cancel each other out, and it only takes him a small time to reach the tourtoise.

Aristotle tackled Zeno's Paradox, I believe, along with trying to find a way to measure the area bounded by a curve, reducing the solution into smaller parts ad infinitum. It's sad that he was soooooooooo close to developing integral calculus before he was slain by a Roman soldier and the library at Alexandria was sacked and burned, destroying so much of his work. Imagine if calculus had been developed fully in 300 BC instead of the late 1600's. There's a "what if" question for you.

Originally posted by General Putzer
Aristotle tackled Zeno's Paradox, I believe, along with trying to find a way to measure the area bounded by a curve, reducing the solution into smaller parts ad infinitum. It's sad that he was soooooooooo close to developing integral calculus before he was slain by a Roman soldier and the library at Alexandria was sacked and burned, destroying so much ...[text shortened]... eveloped fully in 300 BC instead of the late 1600's. There's a "what if" question for you.

Indeed, gunpowder would have not been far behind and the knowledge of trajectories given by the new maths. It almost happened in china too, they were delving into infintesimals also.
And there were supposedly batteries in Iraq a few thousand years ago too. BTW, while we are on the subject of ancients, did you get the news about the huge pyramids discovered in Bosnia? 220 meters high, the locals always called them Pyramid hills, not realizing they actually WERE pyramids.

Originally posted by General Putzer
Aristotle tackled Zeno's Paradox, I believe, along with trying to find a way to measure the area bounded by a curve, reducing the solution into smaller parts ad infinitum. It's sad that he was soooooooooo close to developing integral calculus before he was slain by a Roman soldier and the library at Alexandria was sacked and burned, destroying so much ...[text shortened]... eveloped fully in 300 BC instead of the late 1600's. There's a "what if" question for you.

That would be Archimedes. Aristotle really did made attempts at explaining the paradox but not very succesful. Besides Xeno's "paradoxes" were aimed at showing the difficulties of giving rational explanation of movement. Thus he did try to decribe the four possible cases (discrete time&continous spaces, continous time&discrete space, discrete time & discrete space, continous time&continous space) and the logical inconsistencies that appear within each of them.

arghhhhh....yes, Archimedes, not Aristotle. Good catch.

I MEANT Archimedes

Boring paradox that's been posted here time and again 😴



Yo.

Originally posted by Bowmann
Boring paradox that's been posted here time and again 😴



Yo.

Yep, wonder when the next version will be out.