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The single principle that underpins all of physics. Head to to start your free 30-day trial and get 20% off an annual premium subscription.

A massive thank you to Prof. Steven Strogatz for his expertise and enthusiasm. As an exclusive bonus for our Patreon members, we've posted a longer interview with Prof. Strogatz over there:

A huge thank you to Prof. Haithem Taha, Prof. Anthony Bloch, Dr. Carl-Fredrik Nyberg Brodda, Dr. Sarah Millholland, and Dr. Andrew Mitchell for all their help with finding the story and getting it right.

A special thanks to Dr. Aurèle Adam, Ron Haaksman, Marc Serra Peralta, and everyone at the Delft Makerspace for their help with preparing and performing experiments.

00:00 One rule that replaces all of physics
00:51 The problem of fastest descent
05:09 Fermat's principle
07:17 Bernoulli's solution
10:38 Maupertuis' principle
12:28 Maupertuis attacked and ridiculed
14:01 Euler & Lagrange to the rescue
17:22 The general approach to solving these problems
19:32 Writing the principle into its modern form
23:17 Why the principle works
27:08 Another way to do mechanics
30:19 A “spooky” breakthrough

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Join us on Patreon for early access videos and exclusive bonus content

Patrons: Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, I. H., John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Martin, Matthias Wrobel, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, Toni , TTST, Ubiquity Ventures, wolfee

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically -

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Key references:

A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The
Principle of Least Action: History and Physics. -
Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. -
3Blue1Brown. The Brachistochrone, with Steven Strogatz via Youtube -
Vsauce. The Brachistochrone via Youtube -
PBS Space Time. Is ACTION The Most Fundamental Property in Physics? via Youtube -

Full list of references:

Images & Video:
Voltaire. (1753). Diatribe du Docteur Akakia. -
Philosophical Transactions cover. via Wikimedia Commons -
Kids Fun Science. (Jun 28, 2017). Refraction of Light with a arrow experiment via Youtube -
Physics with Simon Poliakoff. Refraction demonstration with water and laser via Youtube -
Mercury Transit Across Sun. via Nasa.gov -


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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Mike Radjabov, Gregor Čavlović, Emma Wright, James Finnemore and David Szakaly
Illustrated by Jakub Misiek, Emma Wright, and Maria Gusakovich
Filmed by Derek Muller and Casper Mebius
Additional research by Gabe Bean, Gregor Čavlović, and Geeta Thakur
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Bean, Gregor Čavlović, and Tori Brittain
Thumbnail contributions by Jakub Misiek, Ren Hurley and Peter Sheppard
Additional video/photos supplied by Getty Images, Storyblocks, and NASA SVS
Music from Epidemic Sound

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