Zeno's Paradox - PowerPoint PPT Presentation

Slide1 l.jpg
1 / 26

  • Uploaded on
  • Presentation posted in: Pets / Animals

Zeno's Paradox. The hare and the tortoise decide to race. Since I run twice as fast as you do, I will give you a half mile head start. Thanks! . ½ . ¼ . ½ . ¼ . The hare quickly reaches the turtle’s starting point – but in that same time The turtle moves ¼ mile ahead. ½ .

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Presentation

Zeno's Paradox

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Slide1 l.jpg

Zeno's Paradox

Slide2 l.jpg

The hare and the tortoise

decide to race

Slide3 l.jpg

Since I run twice as fast as you do, I will give you a half mile head start.


Slide4 l.jpg



Slide5 l.jpg



The hare quickly reaches the turtle’s

starting point – but in that same time

The turtle moves ¼ mile ahead.

Slide6 l.jpg



By the time the rabbit reaches the

turtle’s new position, the turtle

has had time to move ahead.

Slide7 l.jpg



No matter how quickly the hare

covers the distance between himself

and the turtle, the turtle uses that

time to move ahead.

Slide8 l.jpg



Can the hare ever catch the


Slide9 l.jpg

How can I ever catch the turtle. If it takes me 1 second to reach his current position, in that 1 second, he will have moved ahead again!

Slide10 l.jpg

This is a paradox because common sense tells us that eventually the much swifter hare must overtake the plodding tortoise!

Slide11 l.jpg

If the rabbit runs twice as fast as the turtle, then the rabbit runs 2 miles in the same time the turtle runs 1 mile.

1 mile

2 miles

How do we model time and space l.jpg


A unit of time( hour, minute, second ) or a unit of space(mile, foot, inch) can be divided in half, and then divided in half again, and again. Can we continue to break it into smaller and smaller pieces ad infinitum, or do we eventually reach some unit so small it can no longer be divided?

Twentieth century philosophers on zeno l.jpg


Slide14 l.jpg

“Zeno’s arguments in some form, have afforded grounds for almost all the theories of space and time and infinity which have been constructed from his day to our own.” B. Russell

Slide15 l.jpg

“The kernel of the paradoxes … lies in the fact that it is paradoxical to describe a finite time or distance as an infinite series of diminishing magnitudes.”E.TeHennepe

Slide16 l.jpg

“If I literally thought of a line as consisting of an assemblage of points of zero length and of an interval of time as the sum of moments without duration, paradox would then present itself.”P.W. Bridgman

Opposing models l.jpg

In classical physics, time and space are modeled as mathematically continuous - able to be subdivided into smaller and smaller pieces, ad infinitum.

Quantum theory posits a minimal unit of time - called a chronon - and a minimal unit of space- called a hodon . These units are discrete and indivisible.


Slide18 l.jpg

  • With the race between the turtle and the rabbit, Zeno argues against a model of space and time that allows units to be divided into smaller and smaller pieces to infinity.

  • Zeno has another paradox, called “the stadium” that argues against the existence of indivisible units of space and time!

Slide19 l.jpg

The paradox of the stadium is about soldiers marching in formation - turtles will play the rolls of soldiers.

Slide21 l.jpg

If the bottom two rows march in the directions indicated, will blue in row 2 pass yellow in row 3?

Slide22 l.jpg

If the motion is continuous, yes!

Slide23 l.jpg

Now, suppose the turtles are 1 hodon apart, and marching at a rate of 1 hodon per chronon. The 2 bottom rows move simultaneously. One instant they are here:

Slide24 l.jpg

The next instant, (one chronon later) they are here. At no point in time was the blue turtle in row 2 opposite the yellow turtle in row three. The red faced turtles do not pass!

Slide25 l.jpg

In one indivisible instant (chronon) , turtles move from top position to bottom position, and the red faced turtles do not pass!

Do both models lead to paradox l.jpg

Do both models lead to paradox?

  • Login