Discover strange new universes that turn up at the core of Einstein’s General Relativity. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.

Special thanks to our Patreon supporters! Join the community to help us keep our videos free, forever:
https://ve42.co/PatreonDEB

If you’re looking for a molecular modeling kit, try Snatoms – a kit I invented where the atoms snap together magnetically – https://ve42.co/SnatomsV

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A massive thank you to Prof. Alex Kontorovich for all his help with this video.

A huge thank you to Prof. Geraint Lewis and Dr. Ashmeet Singh for helping us understand the applications of Non-Euclidean geometry in astronomy/cosmology.

Lastly, a big thank you to Dr. Henry Segerman and Dr. Rémi Coulon for helping us visualize what it’s like to be inside hyperbolic space and helping us understand hyperbolic geometry.

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Images:
Euclid via Science Museum Group - https://ve42.co/Euclid

Geodesy survey via ams - https://ve42.co/Geodesy

John Wheeler via NAS Online - https://ve42.co/Wheeler

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References:
Dunham, W. (1991). Journey through Genius: Great Theorems of Mathematics. John Wiley & Sons.

Bonola, R. (1955). Non-Euclidean geometry: A critical and historical study of its development. Courier Corporation.

Library of Congress. (n.d.). The Library of Congress. - https://ve42.co/LibofCongress

Euclid’s Elements, Wikipedia - https://ve42.co/Elements

The History of Non-Euclidean Geometry, Extra History via YouTube - https://ve42.co/ExtraHistory

We (could) live on a 4D Pringle - Physics for the Birds via YouTube - https://ve42.co/4DPringle

Parallel Postulate, Wikipedia - https://ve42.co/Parallel

Prékopa, A., & Molnár, E. (Eds.). (2006). Non-euclidean geometries: János Bolyai memorial volume (Vol. 581). Springer Science & Business Media.

St Andrews, University of. (n.d.). Bolyai. MacTutor History of Mathematics. - https://ve42.co/Bolyai

Bolyai, J. (1896). The Science Absolute of Space.. (Vol. 3). The Neomon.

Gauss, Wikipedia - https://ve42.co/Gauss

Singh, U. (2022). Gauss-Bolyai-Lobachevsky: The dawn of non-euclidean geometry. Medium. - https://ve42.co/CPNonEuclidean

Landvermessung, D. Z. (1929). Abhandlungen ueber Gauss' wissenschaftliche Taetigkeit auf den Gebieten der Geodaesie, Physik und Astronomie Bd. 11, Abt. - https://ve42.co/Landvermessung

Nikolai Lobachevsky, Wikipedia - https://ve42.co/Lobachevsky

Lobachevskiĭ, N. I. (1891). Geometrical researches on the theory of parallels. University of Texas.

A Problem with the Parallel Postulate, Numberphile via YouTube - https://ve42.co/NumberphileParallel

Riemann, B. (2016). On the hypotheses which lie at the bases of geometry. Birkhäuser. - https://ve42.co/Riemann

Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891-921. - https://ve42.co/Einstein1905

ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. - https://ve42.co/Einstein1905

Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background. - https://ve42.co/NANOGrav

Secrets of the Cosmic Microwave Background, PBS Spacetime via YouTube - https://ve42.co/PBSCMB

Wood, C. (2020). How Ancient Light Reveals the Universe's Contents. Quanta Magazine. - https://ve42.co/AncientLight

Collaboration (2014). Planck 2013 results. XVI. Cosmological parameters. A&A, 571, A16. - https://ve42.co/Planck2013

WMAP Science Team, NASA. (2014). Matter in the Universe. WMAP, NASA. - https://ve42.co/WMAP2014

What Is The Shape of Space, minutephysics via YouTube - https://ve42.co/SpaceShape

Shape of the universe, Wikipedia - https://ve42.co/UniverseShape

Crocheting Hyperbolic Planes: Daina Taimina by Ted, via YouTube - https://ve42.co/Hyperbolic

Hyperbolic Crochet model - https://ve42.co/Crochet

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Special thanks to our Patreon supporters:
Adam Foreman, Amadeo Bee, Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, Jesse Brandsoy, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Mario Bottion, Max Maladino, Meekay, meg noah, Michael Krugman, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures

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Directed by Casper Mebius
Written by Casper Mebius, Petr Lebedev, Emily Zhang, Derek Muller, and Alex Kontorovich
Edited by Jack Saxon
Animated by Fabio Albertelli, Ivy Tello, and Mike Radjabov
Illustrations by Jakub Misiek and Celia Bode
Filmed by Derek Muller
Produced by Casper Mebius, Derek Muller, and Han Evans

Additional video/photos supplied by Getty Images, Pond5, and by courtesy of: NASA, NASA's Goddard Space Flight Center, NASA Goddard Flight Lab/ CI Lab, NASA’s WMAP science teams, ESO, and ESA/Hubble.
Music from Epidemic Sound
Thumbnail by Ren Hurley

How do you make infinite choices? 👉 To try everything Brilliant has to offer for free for a full 30 days, visit http://brilliant.org/veritasium. You’ll also get 20% off an annual premium subscription.

Try Snatoms! A molecular modelling kit I invented where the atoms snap together.
https://ve42.co/SnatomsV

Sign up to the Veritasium newsletter for weekly science updates - https://ve42.co/Newsletter

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A huge thank you to Dr Asaf Karagila, Prof. Alex Kontorovich, Prof. Joel David Hamkins, Prof. Andrew Marks, Prof. Gabriel Goldberg and Prof. Elliot Glazer for their invaluable expertise and contributions to this video.

Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made - https://www.patreon.com/posts/patreon-behind-126443880?utm_medium=clipboard_copy&utm_source=copyLink&utm_campaign=postshare_creator&utm_content=join_link

▀▀▀
0:00 What comes after one?
2:42 Some infinities are bigger than others
6:17 The Well Ordering Principle
10:32 Zermelo And The Axiom Of Choice
17:22 Why is the axiom of choice controversial?
23:16 The Banach–Tarski Paradox
27:53 Obviously True, Obviously False
29:58 Your Proof Your Choice

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References:

Up and Atom - https://www.youtube.com/watch?v=X56zst79Xjg
Minutephysics - https://www.youtube.com/watch?v=A-QoutHCu4o
PBS Infinite Series - https://www.youtube.com/watch?v=hcRZadc5KpI&t=125s
Vsauce - https://www.youtube.com/watch?v=s86-Z-CbaHA&t=474s
Ernst Zermelo via Wikipedia - https://ve42.co/zermeloBio
Axiom of choice via Wikipedia - https://ve42.co/choiceAxiom
Georg Cantor via Wikipedia - https://ve42.co/cantorMath
Gregory H. Moore (2013). Consequences of the Axiom of Choice. Dover Publications - https://ve42.co/choiceBook
Georg Cantor (1874). On a property of the class of all real algebraic numbers. Journal für die Reine und Angewandte Mathematik - https://ve42.co/MeyerCantor1874
Heinz-Dieter Ebbinghaus (Dec 2012). Zermelo and the Heidelberg Congress 1904. Historia Mathematica - https://ve42.co/SciDirect1904
Herbert B. Enderton (1977). Elements of Set Theory. - https://ve42.co/SciDirectGCH

Additional References - https://ve42.co/AoCAdRefs

Images & Video:

Foundations of a general theory of sets by Georg Cantor via ViaLibri - https://ve42.co/grundlagen
Alfred Tarski by George Bergman via Wikimedia Commons - https://ve42.co/tarski
Alfred Tarski Offprint Group by Alfred Tarski via Bonhams - https://ve42.co/tarskipaper
La mission strasbourgeoise de Maurice Fréchet by Laurent Mazliak via Images des mathematiques - https://ve42.co/frechet
Kurt Gödel by Alfred Eisenstaedt via New Yorker - https://ve42.co/godel
Leopold Kronecker by Granger via Fine Art America - https://ve42.co/kronecker
Lashi Bandara (2006). Zermelo-Frankel Set Theory and Well Orderings. ResearchGate - https://ve42.co/zermelofrankel
Heidelberg, Germany 1936 by Wagner & Debes via Ward Maps - https://ve42.co/heidelberg
Pythagoras by J. Augustus Knapp via the marginalian - https://ve42.co/pythag
Paul Cohen by C. J. Mozzochi via C. J. Mozzochi - https://ve42.co/paulcohen
Instituto de Matemática Pura e Aplicada. Lecture 01: Introduction: a non-measurable set via Youtube - https://www.youtube.com/watch?v=llnNaRzuvd4&t=834s
Simons Foundation. Fields Medal: James Maynard. Youtube https://www.youtube.com/watch?v=un-z8kgOrV0&t=8s

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Special thanks to our Patreon supporters:
Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, HydrochloRick, Jon Jamison, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee


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Directed by Kaela Albert
Written by Kaela Albert and Emily Zhang
Edited by Jack Saxon and Luke Molloy
Assistant Edited by James Stuart
Animated by Fabio Albertelli, Andrew Neet, Alex Zepharin, Mike Radjabov, Emma Wright and Ivy Tello
Illustrations by Jakub Misiek, Maria Gusakovich, Cainejan Esperanza, Tommy A. Steven and Emma Wright
Additional research by Emilia Gyles, Gabe Bean, Geeta Thakur and Vincent Cheng
Produced by Kaela Albert, Casper Mebius, Derek Muller, Emily Zhang, Zoe Heron, Rob Beasley Spence, and Tori Brittain
Additional Editing by Luke Molloy and James Stuart

Thumbnail contributions by Ben Powell, Peter Sheppard and Ren Hurley

Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound

Electric cars are now ready to take over thanks to advances in battery technology and their inherent benefits: torque, handling, maintenance. This video was sponsored by BMW: https://www.bmwusa.com/

Full disclosure: I drive an #electric #car. I think electric cars are the future, not mainly because they're better for the environment (which they are if you drive the car for any reasonable length of time) but because they are just better cars. The have better torque and acceleration, better handling, they're more efficient, quieter, they don't smell, they're cheaper to run and best of all you never have to visit a gas station - this appeals to me. I never have to worry about being low on gas because every morning my car is charged and ready to go - just like my phone and laptop. And if you're worried about range, don't. Almost all trips can already be done in an electric car with modest battery pack. And fast chargers along the way make it possible to do longer road trips if necessary. You have to make rest stops anyway, just time them with the charging. And consider that battery tech is getting dramatically cheaper, smaller, lighter. All these reasons are why I see the #future of cars as electric.

Writing & Research
Derek Muller
Jonny Hyman
Matthew Shribman https://ve42.co/sciencebath

Editing, Animation, Audio, & Music:
Jonny Hyman

Camerawork:
Raquel Nuno
Jonny Hyman

1890s Music "National fantasie" by William Paris Chambers, archived in Library of Congress
#BMWUSA #NEXTGen #BMWPartner #ad

A song about Gravity set to the tune of John Mayer's Gravity.

Gravity is working with me
And Gravity, keeps me on the ground

All mass attracts all other mass
a force proportional to mass one and two
and inversely to the distance between them squared

Oh, gravity is working with me
and gravity, makes apples fall to ground

Oh twice the mass has twice the pull
but the force on each is still equal
It keeps the moon and the satellites
going round

Oh twice the mass has twice the pull
but the force on each is still equal
It keeps the moon and the satellites
going round

Oh gravity, the force that makes weight on me
Woah, gravity, now general relativity (how can that be?)

The force between us all is
The force between us all is
The force between us all is
Gravity between us all is
Gravity between us all is
Gravity between gravity between us all is

Microwave grape plasma: http://www.youtube.com/watch?v=RwTjsRt0Fzo
Northern Lights: http://www.youtube.com/watch?v=knwiWm4DpvQ
Nanodiamonds in candle flames: http://www.youtube.com/watch?v=KzOkuGQC3Rw
Relight Candle Trick: http://www.youtube.com/watch?v=1tXPVTIisl0

Is a flame really a plasma? Well it depends on your definition of plasma, but there are certainly ions in a flame, formed as molecules collide with each other at high speed, sometimes knocking electrons off of their atoms.

Special thanks to the Palais de la Decouverte for helping me perform this experiment. Using tens of thousands of volts on two metal plates, we created a strong electric field around the plasma. This pulled positive ions in one direction and negative ions in the other direction elongating the flame horizontally and causing it to flicker like a "papillon" (butterfly). Then we showed that much longer sparks can be made through the flame than through air since the ions increase the conductivity.

How much information is there in Spanish vs English, you vs the world? Check out Audible: http://bit.ly/AudibleVe
Huge thanks to all the amazing people who made this possible:
Christina Ochoa - Spanish https://twitter.com/christina_ochoa
Vanessa Hill - Filming https://www.youtube.com/braincraftvideo
Henry Reich - Filming, cameo http://youtube.com/minutephysics
Cara Santa Maria - Set design http://carasantamaria.com
Michael Stevens - cameo http://youtube.com/vsauce
Crystal Dilworth - consultation https://twitter.com/PolycrystalhD

Thanks also to MinutePhysics for wardrobe and lending the use of the amazing "Things to do when it's really cold outside" video: https://www.youtube.com/watch?v=j3Gs6tyiNX4

More on this theme to come in the main collaboration with Vsauce.

My hypothesis is that the algorithm, rather than viewer preference, drives views on the site. As the algorithm shifts, various YouTubers experience burnout (as what used to work no longer works) and right now click-through rate is the key metric. So clickable titles and thumbnails are the only way to get a lot of impressions and hence views - they are the only way to go viral. This leads me to wonder which audiences will become most prevalent on the site and if there will even be a place for educational content. In the long-term, hopefully YouTube is able to measure satisfaction through surveys and other metrics to ensure an optimal experience for everyone on the site.

Flipchart artwork by Maria Raykova
Filmed by Raquel Nuno
Thumbnail by Ignat Berbeci

A story is worth a thousand data points.
My second channel: http://bit.ly/2veritasium
More info on this topic: http://wke.lt/w/s/TzNC0

Check out 2Veritasium! https://ve42.co/2Ve
MinutePhysics has a great video on Milkman, vomiting levitator: http://dft.ba/-vomphysics
Jetpacking was awesome fun! Despite the fat lip I had a great time. I think knowing a bit about physics actually helps fly the jetpack. It works on the same principle as a rocket (Newton's 3rd law) but unlike the shuttle, you don't carry your own propellant with you. Instead, water is pumped out of the lake by the jetski at up to 60 litres a second. It is then fired out of the nozzles at around 15 m/s creating 1800 N of force, the equivalent of about 150 fire extinguishers. On me this can produce acceleration of about 1.5g's.

Music by Kevin McLeod (http://incompetech.com) Silly Fun, Also Sprach Zarathustra
Supported by Science Alert: http://on.fb.me/14ehuxA
Slow motion filming by Questacon: http://bit.ly/ZoWFGR

The Perseverance Rover and helicopter Ingenuity have landed safely on Mars. A few years back I got to visit NASA JPL to interview the scientists to find out their goals for the mission. I made this clip as a correspondent for Bill Nye Saves the World on Netflix.

Touring the Jet Propulsion Lab (JPL) in Pasadena was an awesome experience. I didn't think we were going to get into the control room but we got lucky. Some of the greatest moments in the history of space exploration have taken place there. They have a giant vacuum chamber where they can take the rover down to the atmospheric pressure on Mars (roughly .01x Earth's atmosphere) and test all of the devices to make sure there are no electrical discharges due to the reduced pressure. I also enjoyed seeing how the rocks will be cored and stored in tubes and deposited on the Martian surface awaiting pickup by the following mission.

Images courtesy of NASA.

Filmed by Raquel Nuno from 3:30 onwards.

Music: http://epidemicsound.com "Serene Story 2"

Why we can't seem to agree on what's true when it's easier than ever to check.
Videos like this are usually on 2Veritasium: http://bit.ly/2Veritasium
Support Veritasium on Patreon: http://bit.ly/VePatreon

This video was filmed at a meetup in Stockholm, Sweden on Dec. 9, 2016. Huge thanks to everyone who attended - I had a great time. Sorry to those of you I missed, especially Lund and Gothenburg.

Thanks to Patreon supporters (but this is a non-paid post):
Meshal Alshammari, Nathan Hansen, Bryan Baker, Donal Botkin, Tony Fadell, Saeed Alghamdi, Ron Neal

How the Black-Scholes/Merton equation made trillions of dollars. Go to https://www.eightsleep.com/veritasium and use the code Veritasium for $200 off your Pod Cover.

Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
https://ve42.co/PatreonDEB

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - https://ve42.co/SnatomsV

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A huge thank you to Prof. Andrew Lo (MIT) for speaking with us and helping with the script.

We would also like to thank the following:
Prof. Amanda Turner (University of Leeds)
Owen Maher (Electrify Video Partners)

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References:

The Man Who Solved the Market: How Jim Simons launched the quant revolution, Gregory Zuckerman. Penguin Publishing Group. - https://ve42.co/GZuckerman

The Physics of Finance: Predicting the Unpredictable: Can Science Beat the Market? James Owen Weatherall. Short Books. - https://ve42.co/FinancePhysics

The Statistical Mechanics of Financial Markets, J.Voigt. Springer. - https://ve42.co/Springer

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654. - https://ve42.co/BlackScholes

Cornell, B. (2020). Medallion fund: The ultimate counterexample?. The Journal of Portfolio Management, 46(4), 156-159. - https://ve42.co/Medallion

Images & Video:
Ed Thorp on The Tim Ferris Show - https://www.youtube.com/watch?v=CNvz91Jyzbg
Jim Simons on TED - https://www.youtube.com/watch?v=U5kIdtMJGc8
Jim Simons on Numberphile - https://www.youtube.com/watch?v=QNznD9hMEh0

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Special thanks to our Patreon supporters:
Adam Foreman, Anton Ragin, Balkrishna Heroor, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Diffbot, Evgeny Skvortsov, Garrett Mueller, Gnare, I.H., John H. Austin, Jr. ,john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures


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Directed by Will Wood and Derek Muller
Written by Will Wood, Emily Zhang, Petr Lebedev and Derek Muller
Camera operation by Raquel Nuno
Additional research by Gregor Čavlović
Edited by Jack Saxon and Trenton Oliver
Animated by Fabio Albertelli, Jakub Misiek, Ivy Tello, David Szakaly and Will Wood
Produced by Will Wood, Han Evans and Derek Muller

Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

If you ran evolution all over again, would you get humans? How repeatable is #evolution? This video is sponsored by @BountyBrand. #biology #science #QPU #HygieneBeginswithBounty #BountyPartner

Special thanks to Prof. Richard Lenski and team for showing me around the lab — it is an honor to be able to witness and document such a historic science experiment.
Thanks to Dr Zachary Blount for the help with research and setting up the competition time-lapse, Dr Nkrumah Grant for microscope images of the long-term line cells @NkrumahGrant
Devin Lake, Kate Bellgowan, and Dr. Minako Izutsu for being part of this video. Long Live the LTEE!

LTEE website — http://myxo.css.msu.edu/ecoli/index.html
Intro footage courtesy of the Kishony Lab — https://kishony.technion.ac.il
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References:
Lenski, R. E., & Travisano, M. (1994). Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations. Proceedings of the National Academy of Sciences, 91(15), 6808-6814. — https://ve42.co/Lenski1994

Lenski, R. E., Rose, M. R., Simpson, S. C., & Tadler, S. C. (1991). Long-term experimental evolution in Escherichia coli. I. Adaptation and divergence during 2,000 generations. The American Naturalist, 138(6), 1315-1341. — https://ve42.co/Lenski1991

Good, B. H., McDonald, M. J., Barrick, J. E., Lenski, R. E., & Desai, M. M. (2017). The dynamics of molecular evolution over 60,000 generations. Nature, 551(7678), 45-50. — https://ve42.co/Good2017

Blount, Z. D., Borland, C. Z., & Lenski, R. E. (2008). Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. Proceedings of the National Academy of Sciences, 105(23), 7899-7906. — https://ve42.co/Blount2008

Blount, Z. D., Lenski, R. E., & Losos, J. B. (2018). Contingency and determinism in evolution: Replaying life’s tape. Science, 362(6415). — https://ve42.co/Blount2018

Wiser, M. J., Ribeck, N., & Lenski, R. E. (2013). Long-term dynamics of adaptation in asexual populations. Science, 342(6164), 1364-1367. — https://ve42.co/Wiser2013

N, Scharping. (2019). How a 30-Year Experiment Has Fundamentally Changed Our View of How Evolution Works. Discover — https://ve42.co/Scharping

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Special thanks to Patreon supporters: Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Research and Writing by by Derek Muller, Petr Lebedev and Casey Rentz
Animation by Ivy Tello
Filmed by Derek Muller, Emily Zhang and Raquel Nuno
Edited by Derek Muller
Music by Jonny Hyman and from Epidemic Sound https://epidemicsound.com
Additional video supplied by Getty Images
Thumbnail image courtesy of the Kishony Lab
Produced by Casey Rentz
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Does light take all possible paths at the same time? 🌏 Get exclusive NordVPN deal here ➵ https://NordVPN.com/veritasium It’s risk free with Nord’s 30 day money-back guarantee!✌

A massive thank you to Dr. Andrew Mitchell for all his help and expertise. If you want to delve further into this topic then we highly recommend his lecture on Classical physics derived from quantum mechanics: https://www.youtube.com/watch?v=2iuLwWDYC4U&t=1s

We’re incredibly grateful to Prof. David Kaiser, Prof. Steven Strogatz, Prof. Geraint F. Lewis, Elba Alonso-Monsalve, Prof. Christopher S. Baird, Prof. Anthony Bloch, and Prof. Stephen Bartlett for their invaluable contributions to this video.

A special thanks to Mahesh Shenoy from FloatHeadPhysics for his help with this video. Check out his excellent intuitive video on the UV Catastrophe here (Sep 2024): https://www.youtube.com/watch?v=ALEDjjAVZSY

Sign up to the Veritasium newsletter for weekly science updates - https://ve42.co/Newsletter

▀▀▀
0:00 What path does light travel?
2:40 Black Body Radiation
6:47 How did Planck solve the ultraviolet catastrophe?
9:42 The Quantum of Action
13:25 De Broglie’s Hypothesis
15:16 The Double Slit Experiment
20:00 How Feynman Did Quantum Mechanics
25:01 Proof That Light Takes Every Path
31:16 The Theory of Everything

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Sign up to our Patreon to watch the Q&A for free: https://www.patreon.com/c/veritasium

Try Snatoms! A molecular modelling kit I invented where the atoms snap together.
https://ve42.co/SnatomsV

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References:
Armin Hermann (Nov 1974). The Genesis of Quantum Theory (1899-1913). - https://ve42.co/genquanttheor
Richard P. Feynman (1985). QED The Strange Theory of Light and Matter. - https://ve42.co/qed
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. - https://ve42.co/Bloch2018
Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. - https://ve42.co/LazyU
PBS Space Time. (Nov 2021) - https://www.youtube.com/watch?v=Q_CQDSlmboA
Sabine Hossenfelder. (May 2022) - https://www.youtube.com/watch?v=A0da8TEeaeE
Max Planck (1901). On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik - https://ve42.co/lawdistenergy
Paul Ehrenfest (1911). Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle?. Wiley Online Library - https://ve42.co/quantthermrad
Nils-Erik Bomark and Reidun Renstrøm (Aug 2023). The Ultraviolet myth. Proceedings of Science - https://ve42.co/uvmyth
Planck's law. In Wikipedia - https://ve42.co/planckslaw
PBS Space Time. (Jul 2017). - https://www.youtube.com/watch?v=vSFRN-ymfgE&t=10s
Einstein and The Photoelectric Effect. (Jan 2005) via APS News - https://ve42.co/einsteinphotoelec
Louis de Broglie (1924). On the Theory of Quanta. - https://ve42.co/theoryquanta
Larry Sorensen (2012). Path Integrals 1. University of Washington - https://ve42.co/pathintegrals
Feynman’s Method of “A Particle Exploring All Possible Paths”. (Mar 2018) via Pure Dhamma - https://ve42.co/allposspaths

Additional References - https://ve42.co/AdditionalReferences-PoLA2

Images & Video:
Nobistor Altona 1880 via NDR - https://ve42.co/streetlight
Edison incandescent lights by William J. Hammer via Wikimedia Commons - https://ve42.co/edinclights
The full expanded form of the Standard Model Lagrangian by Chen Ning Yang et al. via Wikipedia - https://ve42.co/stmodellang
Muon Ray. (2011). https://www.youtube.com/watch?v=-QUj2ZRUa7c
Muon Ray. (2011). https://www.youtube.com/watch?v=1C7abO7LtV0
Bohrs Atomic Model via EEEGUIDE.COM - https://ve42.co/bohrmodel

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Special thanks to our Patreon supporters:
Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, qiaohui wei, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee

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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver and Peter Nelson
Animated by Fabio Albertelli, Mike Radjabov, Ivy Tello, Andrew Neet and Emma Wright
Illustrations by Jakub Misiek, Tommy A. Steven and Cainejan Esperanza
Filmed by Derek Muller and Casper Mebius
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Strong, Geeta Thakur, Emilia Gyles, Zoe Heron, Emily Zhang and Tori Brittain

Thumbnail contributions by Ignat Berbeci, Ben Powell, Jakub Misiek, Ren Hurley, and Peter Sheppard

Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound

Spinning magnets near copper sheets create levitation!
Try Audible free for 30 days: http://bit.ly/AudibleVe
Special thanks to Hyperloop One for showing me around.

Thanks to Patreon supporters:
Nathan Hansen, Donal Botkin, Tony Fadell, Saeed Alghamdi, Zach Mueller, Ron Neal, Perry cl, Bryan Baker
Support Veritasium on Patreon: http://bit.ly/VePatreon

Filmed by Raquel Nuno, Edited by Trevor Carlee

Obviously this "quadcopter" is a demonstration device, showing how moving magnets over a conducting surface can generate levitation. It has not been optimized to minimize losses or be an efficient mode of transport. I still think it's pretty cool. I'm used to seeing light things levitated by induced currents but not a 100+ lb machine.

For more on Hyperloop One: https://hyperloop-one.com/

Do odd perfect numbers exist? Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.

Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
https://ve42.co/PatreonDEB

A massive thank you to Prof. Pace Nielsen for all his time and help with this video.

A big thank you to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and help.

To try GIMPS out yourself: https://ve42.co/GIMPS

These sources were particularly helpful:
Perfect numbers via MacTutor - https://ve42.co/MTPerfect
Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. - https://ve42.co/Cai2022
Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. - https://ve42.co/Dunham2022

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References:
https://www.youtube.com/watch?v=T0xKHwQH-4I&pp=ygUPcGVyZmVjdCBudW1iZXJz
https://www.youtube.com/watch?v=q8n15q1v4Xo&pp=ygUPcGVyZmVjdCBudW1iZXJz
Dickson, L. E. (1919). History of the Theory of Numbers.. (Vol. 1). Carnegie Institution of Washington.
Knill, O. (2007). The oldest open problem in mathematics. NEU Math Circle, December2. - https://ve42.co/Knill2007
Perfect number via Wikipedia - https://ve42.co/WikiPerfect
Introduction to Arithmetic via HalthiTrust - https://ve42.co/IntroArithmetic
Nicomachus of Gerasa via MacTutor - https://ve42.co/MTNicomachus
Sonja, B. (1988). The First Perfect Numbers and Three Types of Amicable Numbers in a Manuscript on Elementary Number Theory by Ibn Fellûs. Erdem, c. IV, 11. - https://ve42.co/Sonja1988
Ibn Fallus via Wikipedia - https://ve42.co/WikiFallus
Mersenne prime via Wikipedia - https://ve42.co/WikiMP
List of Known Mersenne Prime Numbers - https://ve42.co/ListOfMP
Marin Mersenne via MacTutor - https://ve42.co/MTMersenne
Leonhard Euler via Wikipedia - https://ve42.co/WikiEuler
Frank Nelson Cole via Wikipedia - https://ve42.co/WikiFNCole
GIMPS History via Mersenne.org - https://ve42.co/GIMPSHistory
EFF Cooperative Computing Awards via EFF - https://ve42.co/EFFAwards
Jonathan Pace via Primewiki - https://ve42.co/PWikiPace
Book with just one number sells out in Japan via BastillePost - https://ve42.co/PrimeBook
Predicted distribution of Mersenne primes via John D. Cook - https://ve42.co/JDCookMP
Euler’s Odd Perfect Numbers Theorem via Cantor's Paradise - https://ve42.co/EulerOPN
A Perfect (Math) Mystery via Medium - https://ve42.co/Machado2024
Brent, R. P., Cohen, G. L., & te Riele, H. J. (1991). Improved techniques for lower bounds for odd perfect numbers. Mathematics of Computation, 57(196), 857-868. - https://ve42.co/Brent1991
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. - https://ve42.co/Ochem2012
Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine - https://ve42.co/QuantaSpoofs
Descartes number via Wikipedia - https://ve42.co/WikiDescartesNumber
Andersen, N., Durham, S., Griffin, M. J., Hales, J., Jenkins, P., Keck, R., ... & Wu, D. (2022). Odd, spoof perfect factorizations. Journal of Number Theory, 234, 31-47. - https://ve42.co/Andersen2022
Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via OddPerfect.org - https://ve42.co/Heuristic

Images & Video:
Clip of Piergiorgio Odifreddi - https://www.youtube.com/watch?v=y0paHEA8-gA
Euclid’s Elements 1 via Claymath - https://ve42.co/CM1
Euclid’s Elements 2 via Claymath - https://ve42.co/CM2
Euclid’s Elements 3 via Claymath - https://ve42.co/CM3
Diophanti - https://ve42.co/Diophanti
Gauss book - https://ve42.co/GaussDis
Euler’s Archive 1 - https://ve42.co/Euler1
Euler’s Archive 2 - https://ve42.co/Euler2

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

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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Peter Nelson
Illustrated by Jakub Misiek
Animated by Fabio Albertelli, Ivy Tello, David Szakaly, Alondra Vitae, Alex Drakoulis, and Leigh Williamson
Filmed by Derek Muller, Raquel Nuno, and Peter Nelson
Additional research by Aaron Santos, Camilla Machado, and Gregor Čavlović
Produced by Casper Mebius, Gregor Čavlović, Han Evans, and Derek Muller

Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

How jumping spiders reveal an entire secret world of colors. Let BetterHelp connect you to a therapist who can support you - all from the comfort of your own home. Visit https://betterhelp.com/veritasium and enjoy a special discount on your first month.

A massive thank you to everyone at Day’s Edge Productions for making this documentary happen. Check them out at https://daysedge.com/.

You can watch the full-length documentary “Spider Vision: Decoding Color” on Curiosity Stream - coming soon.

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Special thanks to our Patreon supporters! Join the community to help us keep our videos free, forever: https://ve42.co/PatreonDE

Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Bruce, 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 - https://ve42.co/SnatomsV

Production by Day's Edge fully funded by National Science Foundation (Grant #IOS 1831767)

Featuring: Dr. Nathan Morehouse (University of Cincinnati); Olivia Harris (University of Cincinnati), Dr. Megan Porter (University of Hawaii); Dr. Lisa Taylor (University of Florida); Dr. Wayne Maddison (University of British Columbia); and Dr. Emma Alexander (Northwestern University)

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Directed by Neil Losin
Written by Neil Losin
Edited by Neil Losin, Andy Laub, and Alan Saunders
Animated by Root House Studio and David Hutchinson
Filmed by Neil Losin, Nate Dappen, Alex Wiles, Andy Laub, and Barend van der Watt
Produced by Day’s Edge Productions

Repurposed for YouTube by Derek Muller, Casper Mebius, Petr Lebedev, Peter Nelson, Trenton Oliver, Emily Zhang, Giovanna Utichi, Rob Beasley Spence, Emily Taylor, and Gregor Čavlović

Thumbnail contributions by Ren Hurley and Peter Sheppard

Video/photos supplied by Day’s Edge Productions and Storyblocks
Music by Adrian Younge, PBS, Epidemic Sound, and Jonny Hyman

This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. To make antivenom, you first need to collect venom from the world’s most deadly snakes.

Huge thanks to the Australian Reptile Park for having us over to film – special thanks to Zac Bower for milking all of these snakes for us and Caitlin Vine for organizing the shoot. Absolute legends. https://www.reptilepark.com.au

Huge thanks to Dr Timothy Jackson from the Australian Venom Research Unit for answering our questions, and fact checking the script. This video would not have been the same without you.

Thanks to Seqirus Australia for providing B-roll footage of the horses and the antivenom production.

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References:
Calmette, A. (1896). Le venin des serpents: Physiologie de l'envenimation, traitement des morsures venimeuses par le sérum des animaux vaccinés. Paris: Société d'éditions scientifiques.

Broad, A. J., Sutherland, S. K., & Coulter, A. R. (1979). The lethality in mice of dangerous Australian and other snake venom. Toxicon, 17(6), 661-664. – https://ve42.co/Broad79

WHO Expert Committee on Biological Standardization. (2016). WHO guidelines for the production, control and regulation of snake antivenom immunoglobulins. Geneve, Switzerland. – https://ve42.co/WHO2016

Calmette, A. (1896). The treatment of animals poisoned with snake venom by the injection of antivenomous serum. British medical journal, 2(1859), 399. – https://ve42.co/Calmette1896

Hawgood, B. J. (1999). Doctor Albert Calmette 1863–1933: founder of antivenomous serotherapy and of antituberculous BCG vaccination. Toxicon, 37(9), 1241-1258. – https://ve42.co/Hawgood99

Pucca, M. B., Cerni, F. A., Janke, R., Bermúdez-Méndez, E., Ledsgaard, L., Barbosa, J. E., & Laustsen, A. H. (2019). History of envenoming therapy and current perspectives. Frontiers in immunology, 1598. – https://ve42.co/Pucca19

Kang, T. S., Georgieva, D., Genov, N., Murakami, M. T., Sinha, M., Kumar, R. P., ... & Kini, R. M. (2011). Enzymatic toxins from snake venom: structural characterization and mechanism of catalysis. The FEBS journal, 278(23), 4544-4576. – https://ve42.co/Kang2011

Hawgood, B. J. (2007). Albert Calmette (1863–1933) and Camille Guerin (1872–1961): the C and G of BCG vaccine. Journal of medical biography, 15(3), 139-146. – https://ve42.co/Hawgood2007

Vonk, F. J., Admiraal, J. F., Jackson, K., Reshef, R., de Bakker, M. A., Vanderschoot, K., ... & Richardson, M. K. (2008). Evolutionary origin and development of snake fangs. Nature, 454(7204), 630-633. – https://ve42.co/vonk2008

Bochner, R. (2016). Paths to the discovery of antivenom serotherapy in France. Journal of Venomous Animals and Toxins including Tropical Diseases, 22. – https://ve42.co/Bochner2016

Young, B. A., Herzog, F., Friedel, P., Rammensee, S., Bausch, A., & van Hemmen, J. L. (2011). Tears of venom: hydrodynamics of reptilian envenomation. Physical review letters, 106(19), 198103. – https://ve42.co/Young2011

Madras Medical Journal, Volume Second, July-December 1870. Page 355

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Special thanks to Patreon supporters: Inconcision, Kelly Snook, TTST, Ross McCawley, Balkrishna Heroor, Chris LaClair, Avi Yashchin, John H. Austin, Jr., OnlineBookClub.org, Dmitry Kuzmichev, Matthew Gonzalez, Eric Sexton, john kiehl, Anton Ragin, Benedikt Heinen, Diffbot, Micah Mangione, MJP, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Michael Schneider, jim buckmaster, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Stephen Wilcox, Marinus Kuivenhoven, Clayton Greenwell, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Petr Lebedev and Derek Muller
Edited by Trenton Oliver
Filmed by Jason Tran and Petr Lebedev
Animation by Fabio Albertelli, Jakub Misiek, Ivy Tello and Mike Radjabov.
Molecule animation by Reciprocal Space – https://www.reciprocal.space
Additional video/photos supplied by Getty Image
B-roll supplied by Seqirus Australia
Music from Epidemic Sound and Jonny Hyman
Thumbnail by Ignat Berbeci
Produced by Derek Muller, Petr Lebedev, and Emily Zhang

I took a boat through 96 million black plastic balls on the Los Angeles reservoir to find out why they're there. The first time I heard about shade balls the claim was they reduce evaporation. But it turns out this isn't the reason they were introduced.

Huge thanks to LADWP for arranging this special tour for me. Next time let's put the GoPro on the submersible!

The balls are made of high density polyethylene (HDPE) which is less dense than water so they float on the surface of the reservoir even if they break apart. They are 10cm (4 inches) in diameter and contain about 210ml of water. So the main reason they are on the reservoir is to block sunlight from entering the water and triggering a chemical reaction that turns harmless bromide into carcinogenic bromate. This effect occurs with prolonged exposure to bromate so regulators insist that levels be kept below 10 microgram per liter on average over a 12 month period.

Special thanks to our Patreon supporters! Join this community to help us keep our videos free, forever:
https://ve42.co/PatreonDEB

Thanks to:
Las Virgenes Reservoir for footage of initial shade ball dump
Euro-Matic for bird into jet-engine footage

Researched and Produced by Casey Rentz

Animations by Maria Raykova

Music from http://epidemicsound.com "Colorful Animation 4" "Seaweed"

And from Kevin MacLeod "Marty Gots a Plan"

This is an educational video about the science of water quality.

How an SAT question became a mathematical paradox.