20 November 2005

concept of infinitesimals...

The Dichotomy: There is no motion, because that which is moved must arrive at the middle before it arrives at the end, and so on ad infinitum.

The Achilles: The slower will never be overtaken by the quicker, for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must always be some distance ahead.

Zeno's Achilles & the Tortois

The Arrow: If everything is either at rest or moving when it occupies a space equal to itself, while the object moved is always in the instant, a moving arrow is unmoved.

The Stadium: Consider two rows of bodies, each composed of an equal number of bodies of equal size. They pass each other as they travel with equal velocity in opposite directions. Thus, half a time is equal to the whole time.


Zeno of Elea's "Paradoxes," in Aristotle, Physics VI:9, 239b15

...can no time and no space exist?

1 comment:

mike/ said...

But what can you expect froma race of of people who thought the stomach was a radiator??

Who is to say it is not a radiator? If we all agree it is a radiator, is it not a "radiator?"

can no time and NO space exist" you say.
yup!!. sure can.


If time and space can and cannot exist, what is the truth about it. Something either is or it isn't. How can it be both at the same time? They do not have on and off switches.