Ant On A Rubber Rope Paradox

An ant is placed on one end of a rubber rope and he begins walking at about 5cm per second. As he’s walking, the rope gets stretched… and stretched… at a rate of 10cm per second. The rope is getting stretched faster and longer relative to the ant’s consistent walking pace.

Can the ant ever get to the end of the rope? Is he caught in an endless, impossible trek in which the end keeps getting further and further away?

This classic paradox has very real implications to how we understand our position in a rapidly-expanding universe.

*********** LINKS *************

The Create Unknown Podcast: https://bit.ly/2TKVDdc

What Is A Paradox?: https://youtu.be/kJzSzGbfc0k

Ant On A Rubber Rope Discussion:
https://bit.ly/2DYQ7it

Harmonic Series Proof on Khan Academy
https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-6/v/harmonic-series-divergent

Harmonic Series Proofs
http://scipp.ucsc.edu/~haber/archives/physics116A10/harmapa.pdf

Harmonic Series Proof
https://web.williams.edu/Mathematics/lg5/harmonic.pdf

***********

Written by Matthew Tabor, Michael Stevens and Kevin Lieber

Huge Thanks To Paula Lieber
https://www.etsy.com/shop/Craftality

Get Vsauce's favorite science and math toys delivered to your door!
https://www.curiositybox.com/

Twitter: https://twitter.com/VsauceTwo
Facebook: https://www.facebook.com/VsauceTwo

Hosted, Produced, And Edited by Kevin Lieber
Instagram: http://instagram.com/kevlieber
Twitter: https://twitter.com/kevinlieber
Website: http://kevinlieber.com

Research And Writing by Matthew Tabor
https://twitter.com/matthewktabor

Special Thanks Michael Stevens
https://www.youtube.com/user/Vsauce

VFX By Eric Langlay
https://www.youtube.com/c/ericlanglay

Select Music By Jake Chudnow: http://www.youtube.com/user/JakeChudnow

MY PODCAST -- THE CREATE UNKNOWN
https://www.youtube.com/thecreateunknown

Next episode

S01E342 - The Birthday Paradox