The beautiful math behind six degrees of separation. Sponsored by Incogni - use code veritasium at https://incogni.com/veritasium to get an exclusive 60% off.

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

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

To play around with the simulations in the video, you can follow these links:
Disease spreading - https://www.veritasium.com/simulation2
Preferential attachment - https://ve42.co/barabasiAlbertSim


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A huge thank you to:
Duncan Watts, for creating the small-world model that inspired this video and expanding on his further work; Steve Strogatz, for telling the story with such clarity & humour; Albert-László Barabási, for revealing the the inevitability and impact of hubs; Mark Buchanan, for his insightful takeaways that pulled it all together.

Check out Duncan Watts’ books here - https://www.amazon.com/Six-Deg....rees-Science-Connect
Check out Mark Buchanan’s book here - https://ve42.co/bookNexusWorlds

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Chapters:
0:00 What is six degrees of separation?
4:23 Network Shortcuts
7:11 The Strength of Weak Ties
8:20 Proving it’s a small world
10:39 How quickly can disease spread?
12:36 Strogatz goes viral
16:59 What is a network hub?
18:23 Preferential Attachment
23:38 The Prisoner’s Dilemma
28:22 Your behavior can change the world’s


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References can be found here - https://ve42.co/networksRefs

Image and video references can be found here - https://ve42.co/networksVisuals

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Special thanks to our Patreon supporters:
Alex Porter, Alexander Tamas, Anton Ragin, Anupam Banerjee, Gnare, Ibby Hadeed, Jon Jamison, Juan Benet, Lee Redden, Meekay, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Ubiquity Ventures, Adam Foreman, Albert Wenger, armedtoe, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, gpoly, Jeromy Johnson, KeyWestr, Kyi, Marinus Kuivenhoven, Matthias Wrobel, meg noah, Michael Bush, Michael Krugman, Robert Oliveira, Tj Steyn & wolfee

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Writers: James Moore, Casper Mebius & Derek Muller
Producer & Director: James Moore
Editors: Peter Nelson & Jack Saxon
Camera Operators: Derek Muller & Casper Mebius
Animators: Andrew Neet, Emma Wright, Fabio Albertelli & Ivy Tello
Illustrators: Jakub Misiek
Assistant Editor: James Stuart
Researchers: Callum Cuttle, Aakash Singh Bagga & Gabe Strong
Simulations: Callum Cuttle, Gabe Strong & Ivy Tello
Sound Designers: Pavle Peric & James Stuart
Thumbnail Designers: Abdallah Rabah, Ren Hurley & Ben Powell
Production Team: Josh Pitt, Nicola Griffiths & Rob Beasley Spence
Executive Producers: Derek Muller & Casper Mebius
Additional video/photos supplied by Getty Images, Storyblocks
Music from Epidemic Sound

This deceptively simple math problem has stumped mathematicians for almost 300 years! 👉 Head to https://hensonshaving.com/veritasium and enter code 'Veritasium' for 100 free blades with the purchase of a razor. Make sure to add both the razor and the blades to your cart for the code to take effect.

If you’re looking for a molecular modelling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - 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 Steven Strogatz, Alex Kontorovich, Harald Helfgott, Senia Sheydvasser, Jared Duker Lichtman, Roger Heath-Brown, Kevin Ford, Carl-Fredrik Nyberg Brodda, Kaneenika Sinha & Shehzad Hathi for their invaluable expertise and contributions to this video.

Look out for the upcoming @fern-tv video on the tragic life of Srinivasa Ramanujan! A huge thank you to Ruben Katschko, Mathias Hawk, Chris Varga, Elmer and David from fern for working with us!

The full interview with Steven Strogatz is out now, exclusive to Patreon! - https://www.patreon.com/c/veritasium

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0:00 What is Goldbach’s Conjecture?
4:33 Goldbach and Euler
7:03 The Prime Number Theorem
11:16 The Genius of Ramanujan
14:57 The Circle Method
27:31 Proving the Weak Goldbach Conjecture
32:40 Math vs Mao
36:06 Back to Chen Jingrun
37:15 How you can prove the Strong Goldbach Conjecture

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References:
References can be found here - https://ve42.co/GoldbachRefs

Images & Video:
Image and video references can be found here - https://ve42.co/GoldbachVisuals

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

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Writers: Casper Mebius & Derek Muller
Additional Writers: Darius Garewal, Callum Cuttle & Aakasha Bagga
Producer & Director: Casper Mebius
Editors: Jack Saxon & Peter Nelson
Camera Operators: Casper Mebius & Derek Muller
Animators: Fabio Albertelli, Emma Wright, Ivy Tello, Allama Nandii, Emma Foster, Mike Radjabov & Andrew Neet
Illustrators: Maria Gusakovich, Jakub Misiek & Caine Esperanza
Assistant Editor: James Stuart
Researchers: Darius Garewal, Geeta Thakur & Gabe Strong
Thumbnail Designers: Ren Hurley & Ben Powell
Production Team: Rob Beasley Spence, Tori Brittain, Casper Mebius & Gregor Čavlović
Advice & Feedback: Gregor Čavlović
Executive Producers: Derek Muller & Casper Mebius

Additional video/photos supplied by Getty Images, Pond5.
Music from Epidemic Sound

Tiny particles from distant galaxies have caused plane accidents, election interference and game glitches. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

This video was inspired by the RadioLab Podcast "Bit Flip" https://ve42.co/BF -- they're brilliant science storytellers.

A Huge thanks to Dr Leif Scheick, Calla Cofield and the JPL Media Relations Team.

Thanks to Col Chris Hadfield. Check out his book: https://chrishadfield.ca/books/

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References:
J. F. Ziegler, "Terrestrial cosmic rays," in IBM Journal of Research and Development, vol. 40, no. 1, pp. 19-39, Jan. 1996, doi: 10.1147/rd.401.0019. -- https://ve42.co/Ziegler1996

D. Binder, E. C. Smith and A. B. Holman, "Satellite Anomalies from Galactic Cosmic Rays," in IEEE Transactions on Nuclear Science, vol. 22, no. 6, pp. 2675-2680, Dec. 1975, doi: 10.1109/TNS.1975.4328188 https://ve42.co/Binder1975

Ziegler, J. F., & Lanford, W. A. (1979). Effect of cosmic rays on computer memories. Science, 206(4420), 776-788 https://ve42.co/Ziegler1979

Drury, L. O. C. (2012). Origin of cosmic rays. Astroparticle Physics, 39, 52-60. https://ve42.co/Drury2012

Hess, V. (2018). On the observations of the penetrating radiation during seven balloon flights. arXiv preprint arXiv:1808.02927. --https://ve42.co/Hess2018

Carlson, P., & De Angelis, A. (2011). Nationalism and internationalism in science: the case of the discovery of cosmic rays. The European Physical Journal H, 35(4), 309-329. -- https://ve42.co/Carlson2011

Höeffgen, S. K., Metzger, S., & Steffens, M. (2020). Investigating the effects of cosmic rays on space electronics. Frontiers in Physics, 8, 318. -- https://ve42.co/Hoeffgen2020

Edmonds, L. D., Barnes, C. E., & Scheick, L. Z. (2000). An introduction to space radiation effects on microelectronics. Jet Propulsion Laboratory, National Aeronautics and Space Administration. -- https://ve42.co/Edmonds2000

NASA Mars 2020 website covering the specifications of the Perseverance Rover https://ve42.co/RoverBrains

Australian Government Australian Transport Safety Bureau report on QF72 -- https://ve42.co/ASTBQantas

Australian Government Australian Transport Safety Bureau summary on QF72 --https://ve42.co/ASTBQantas2

Great Blog post about QF72 -- https://ve42.co/DempseyQantas

Michael Barr's report on the Toyota acceleration issue --https://ve42.co/Barr2015

NASA's Report on Toyota -- https://ve42.co/NASAToyota

T. C. May and M. H. Woods, "A New Physical Mechanism for Soft Errors in Dynamic Memories," 16th International Reliability Physics Symposium, 1978, pp. 33-40, doi: 10.1109/IRPS.1978.362815. --https://ve42.co/May1978

P. M. O'Neill and G. D. Badhwar, "Single event upsets for Space Shuttle flights of new general purpose computer memory devices," in IEEE Transactions on Nuclear Science, vol. 41, no. 5, pp. 1755-1764, Oct. 1994, doi: 10.1109/23.317386. -- https://ve42.co/ONeill1994

Wikipedia about radiation hardening -- https://ve42.co/RadHardening

Toward Monitoring Fault-Tolerant Embedded
Systems (Extended Abstract) -- https://ve42.co/Goodloe2009

Article about speed run -- https://ve42.co/BurttSpeedrun

Article about speed run -- https://ve42.co/BountySpeedrun

Article about redundant systems in spaceflight -- https://ve42.co/NASAComputers

Article about the PowerPC750 -- https://ve42.co/Wener-FlignerNASA

Fuglesang C, Narici L, Picozza P, Sannita WG. Phosphenes in low earth orbit: survey responses from 59 astronauts. Aviat Space Environ Med. 2006 Apr;77(4):449-52. PMID: 16676658. -- https://ve42.co/Fuglesang2006

Good article about Cosmic Rays causing flashes -- https://ve42.co/AtkinsonEye

Good article about radiation resistance -- https://ve42.co/RoverResistance

Special thanks to Patreon supporters: Paul Peijzel, Juan Benet, Ruslan Khroma, Richard Sundvall, Lee Redden, Sam Lutfi, MJP, Gnare, Nick DiCandilo, Dave Kircher, Edward Larsen, Burt Humburg, Blake Byers, Dumky, 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

Written by Derek Muller and Petr Lebedev
Animation by Ivy Tello, Mike Radjabov, Fabio Albertelli, Jakub Misiek and Charlie Davies
SFX by Shaun Clifford
Filmed by Derek Muller, Raquel Nuno, and Emily Zhang
Edited by Derek Muller and Petr Lebedev
SFX by Shaun Clifford
Additional video supplied by Getty Images
Rover Footage From NASA/JPL-Caltech
QF72 footage from the Smithsonian channel https://youtu.be/H3q5S9PCoJA
SM64 footage from https://ve42.co/pannenkoek2012
Music from Epidemic Sound
Produced by Derek Muller, Petr Lebedev and Emily Zhang

The Salton Sea is the largest body of water in California, home to the second most diverse group of birds in America and it exists by accident.
Another great video on the Salton Sea: https://youtu.be/otIU6Py4K_A
I used archive from this video.

Music by Kevin MacLeod, www.incompetech.com ‘Mirage’, ‘Hyperfun’, ‘Marty Gots a Plan’, ‘Past the Edge’

Dr Ken Libbrecht is the world expert on snowflakes, designer of custom snowflakes, snowflake consultant for the movie Frozen - his photos appear on postage stamps all over the world. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Thanks to Dr Ken Libbrecht for showing us how to grow designer snowflakes. Obviously, this video would not have been possible without his help and his expertise. His website is full of information about snowflakes http://snowcrystals.com. His new book is also available to purchase from here -- https://ve42.co/SnowCrystalsBook

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References:
Libbrecht, K. G. (2019). A Quantitative Physical Model of the Snow Crystal Morphology Diagram. arXiv preprint arXiv:1910.09067. -- https://ve42.co/Libbrecht2019

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Special thanks to Patreon supporters: Luis Felipe, Anton Ragin, Paul Peijzel, S S, Benedikt Heinen, Diffbot, Micah Mangione, Juan Benet, Ruslan Khroma, Richard Sundvall, Lee Redden, Sam Lutfi, MJP, Gnare, Nick DiCandilo, Dave Kircher, Edward Larsen, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Ruslan Khroma, Robert Blum, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Michael Krugman, Cy 'kkm' K'Nelson, Ron Neal

Written by Derek Muller
Filmed by Derek Muller, Raquel Nuno, Trenton Oliver and Emily Zhang
Edited by Trenton Oliver
Animations by Ivy Tello and Trenton Oliver
Additional video supplied by Getty Images
Music from Epidemic Sound
Produced by Derek Muller, Petr Lebedev and Emily Zhang

A UCLA Physics Professor bet me $10,000 that my video about going downwind faster than the wind was wrong. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

For more information about the Veritasium Science Communication Contest check out -- https://ve42.co/contest

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The wager agreement: https://ve42.co/wager

Prof. Kusenko's slides: https://ve42.co/Kusenko

My rebuttal: https://ve42.co/rebuttal
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Huge thanks to Xyla Foxlin for building the model cart, and making the instructions so accessible to the public. Check out Xyla's video -- https://youtu.be/VUgajGv4Aok

A massive thanks to Bill Nye, Neil DeGrasse Tyson, and Sean Carroll for witnessing the signing of the wager.

A huge thanks to Prof. Alexander Kusenko for being a man of honour -- it's a difficult thing to change your mind, especially in a public forum.

A huge thanks to Prof. Mark Drela for the interview and help making sure we got the physics right.

A massive thanks to Rick Cavallaro for making Blackbird, all your insights, analysis, data, and general help with these videos -- it was so fun to work with you on this crazy project -- check out Rick's channel https://ve42.co/Rick

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References
M. Drela. Dead-Downwind Faster Than The Wind (DDWFTTW)
Analysis (Jan 2009) -- https://ve42.co/Drela

2013 AAPT United States Physics Olympiad Semifinal Exam -- https://ve42.co/AAPT2013

Rick's treadmill footage -- https://ve42.co/Treadmill

Rick's multiple explanations of how Blackbird works -- https://ve42.co/DDWFTTW

Blackford, B. L. (1978). The physics of a push‐me pull‐you boat. American Journal of Physics, 46(10), 1004-1006. — https://ve42.co/Blackford1979

Ruina corrects errors in the above paper: http://ruina.tam.cornell.edu/r....esearch/topics/misce

Forum discussions -- https://ve42.co/forum Blog -- https://ve42.co/blog1 and retraction https://ve42.co/BlogRetraction

Bauer, A. B. (1969, April). Faster than the Wind. In First AIAA Symposium on Sailing. -- https://ve42.co/Bauer1969

Bauer's Obituary -- https://ve42.co/BauerObituary

Gaunaa, M., Øye, S., & Mikkelsen, R. F. (2009). Theory and design of flow driven vehicles using rotors for energy conversion. In EWEC 2009 Proceedings online EWEC

Md. Sadak Ali Khan, Syed Ali Sufiyan, Jibu Thomas George, Md. Nizamuddin Ahmed. Analysis of Down-Wind Propeller Vehicle. International Journal of Scientific and Research Publications, 3, 4. (April 2013) ISSN 2250-3153.

The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software]. https://www.manim.community/

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Special thanks to Patreon supporters: Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Bill Linder, 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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Written and Edited by Derek Muller
Animation by Mike Radjabov
Manim equations by Jonny Hyman
Filmed by Emily Zhang and Raquel Nuno
Music from Epidemic Sound https://epidemicsound.com and by Jonny Hyman
Additional video supplied by Getty Images
Produced by Emily Zhang, Petr Lebedev and Derek Muller

Avalanches are beautiful, majestic, and completely terrifying – this is a video all about the science of avalanches. Head to https://brilliant.org/veritasium to start your free 30-day trial, and get 20% off an annual premium subscription.

A massive thank you to everyone at Whistler Blackcomb for making this shoot happen – Dane Gergovich, David Iles, Alastair Collis, Erin Taylor, and everyone else on the ski patrol team. Thank you for keeping us safe!

A massive thank you to Bruce Tremper, Niko Schirmer, and Mark Smiley for their expertise and help with this video. We are truly grateful for your time and expertise.

Check out Niko's channel here -- it's easily some of the best skiing content on YouTube. https://www.youtube.com/@Nikolai_Schirmer

If you have any intention of going into the backcountry, you have to read Bruce’s book – Staying Alive in Avalanche Terrain. It’s the Bible for this stuff, and the book that inspired us to make this video.

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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, 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

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References:
Tremper, B. (2001). Staying Alive in Avalanche Terrain. Mountaineers Books. - https://ve42.co/Tremper2001
McClung, D. & Schaerer, P. (2006). The Avalanche Handbook. Mountaineers Books. - https://ve42.co/McClung2006
Hopfinger, E. J. (1983). Snow Avalanche Motion and Related Phenomena. Annual Review of Fluid Mechanics. - https://ve42.co/Hopfinger1983
Schweizer, J. et al. (2003). Snow avalanche formation. Reviews of Geophysics. - https://ve42.co/Schweizer2003
Schweizer, J. et al. (2008). Review of spatial variability of snowpack properties and its importance for avalanche formation. Cold Regions Science and Technology. - https://ve42.co/Schweizer2008
Jamieson, B. (2006). Formation of refrozen snowpack layers and their role in slab avalanche release. Reviews of Geophysics. - https://ve42.co/Jamieson2006
Schweizer, J. et al. (2016). Avalance release 101. International Snow Science Workshop Proceeding. - https://ve42.co/Schweizer2016
Schweizer, J. (2008). Snow avalanche formation and dynamics. Cold Regions Science and Technology. - https://ve42.co/Schweizer2008-2

Images & Video:
Skiing and snowboarding footage by Niko Schirmer - https://ve42.co/NikoYT
World's Biggest Avalanche (c)Thom Goddard/All Star Films Ltd 2015. Thank you to the Thom Goddard Channel for use - https://ve42.co/ThomGoddard
Newspaper clippings via Newspapers.com – https://ve42.co/Newspapers
Video of a snow slab avalanche via Trottet, B. et al. (2022). Transition from sub-Rayleigh anticrack to supershear crack propagation in snow avalanches. Nature Physics. - https://ve42.co/Trottet2022
Remote Triggered Avalanche via Henry’s Avalanche Talk - Remote Triggering of an Avalanche
WW1 images via Brugnara, Y. et al. (2016). December 1916: Deadly Wartime Weather. Geographica Bernensia - https://ve42.co/Brugnara2016
Major Avalanches via Geomorphological Hazards - https://ve42.co/MajorAvi
White Friday avalanche illustration via Avalanches WIllow - https://ve42.co/WhiteFriday
White Friday aftermath via Lost In History - https://ve42.co/AviGraves
Field mass on Marmolada via Austrian National Library - https://ve42.co/AviMass
Yungay disaster via NOAA - https://ve42.co/Yungay
Yungay aftermath via AMC Museum - https://ve42.co/YungayAMC
Bruce Tremper Image via utavy - https://ve42.co/BruceTPic
Snowpack via SnowStudies.org - https://ve42.co/SnowStudies
Snowpack via Avalanche.org - https://ve42.co/SnowPackAvi
Snow crystals via Reiweger, I. (2011). Failure of weak snow layers. ETH. - https://ve42.co/Reiweger2011

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Directed by Petr Lebedev
Written by Petr Lebedev and Derek Muller
Edited by Peter Nelson (Additional editing by James Horsley)
Animated by Jakub Misiek, Fabio Albertelli, Alex Zepherin, and Alex Drakoulis
Additional Research by Gregor Čavloviċ
Filmed by Petr Lebedev and Ryan Regehr
FPV Drone by Mitch Winton
Produced by Petr Lebedev, Derek Muller, Han Evans, Giovanna Utichi, Rob Beasley Spence, Emily Taylor and Gregor Čavloviċ

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

Why does shaken soda explode? Does ice melt first in fresh or salt water?
Thank you Squarespace for sponsoring this video. Go to https://squarespace.com to save 10% off your first purchase of a website or domain using code: VERITASIUM

This video features experiments that have been shown to me by science teachers over the years. Does ice melt fast in salt water or fresh water was an experiment introduced to me at the Utah Science Teachers' conference. The ring of metal over a chain demo came from a teachers event in Florida. The idea shaking a carbonated drink increases pressure came from an email.

Special thanks to Petr Lebedev for building the pressure gauge.

Links to literature are below:
Victims of the pop bottle, by Ted Willhoft. New Scientist, 21 August 1986 p.28

Carbonation speculation
The Physics Teacher 30, 173 (1992); https://doi.org/10.1119/1.2343501

Agitation solution
The Physics Teacher 30, 325 (1992); https://doi.org/10.1119/1.2343556

Filmed by Cristian Carretero, Jordan Schnabel, Jonny Hyman, and Raquel Nuno

Music from https://epidemicsound.com "Seaweed" "Quietly Tense" "Mind Shift" "Observations"

Starring: Christie Wykes as Chlorine, Carbon, and Sodium
Director of Photography: Sean McCallum
Gravity (John Mayer Cover) http://www.youtube.com/watch?v=u7KpH9_I2Dw
I'm Atoms (Jason Mraz Cover) http://www.youtube.com/watch?v=DBjZz0iQrzI
Electricity (Jet Cover) http://www.youtube.com/watch?v=cY-kiddvAg0
Experiments A Cappella http://www.youtube.com/watch?v=lRbI_vPyOnc

Bowling has been reinvented many times over the past seven thousand years but especially in the last 30. This is the fascinating physics of balls, oil, lane and pins. A portion of this video was sponsored by Salesforce. Go to https://salesforce.com/veritasium to learn more.

Huge thanks to Steve Kloempken and all of Storm Bowling for letting us visit and get a glimpse into the crazy world of bowling.
Huge thanks to legends Chris Barnes and Pete Weber for taking the time to bowl with us.
Huge thanks to Creative Electron for their help with getting the bowling balls X-rayed. Check out their work here: https://creativeelectron.com/
Thanks to Ron Hatfield and James Freeman for their help with research. Check out their great book, Bowling Beyond the Basics: https://ve42.co/HatfieldFreeman
Thanks to the United States Bowling Congress (USBC) and Professional Bowlers Association (PBA) for their help with accessing archival data and footage.
Special thanks to Rod Cross for physics consultation.
Thanks to Bill Guszczo for giving us the idea to make this video in the first place.

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References:
Freeman, James, and Ron Hatfield. Bowling beyond the Basics: What's Really Happening on the Lanes, and What You Can Do about It. BowlSmart, 2018. -- https://ve42.co/HatfieldFreeman
N. Stremmel, P. Ridenour and S. Sterbenz. “Identifying the Critical Factors That Contribute to Bowling Ball Motion on a Bowling Lane.” United States Bowling Congress, 2008. -- https://ve42.co/BallMotionASQ
USBC Equipment Specifications and Certification Team. “Ball Motion Study: Phase I and II Final Report.” United States Bowling Congress, 2008. -- https://ve42.co/USBCBallMotion
Brettingen, Patrick, and Nicki Mours. “USBC static weight limits remain relevant.” United States Bowling Congress, 2011. -- https://ve42.co/USBCStaticWeight
Article on lane oil origins -- https://ve42.co/OilOrigins
Luna, Richard. “Bruce Pluckhahn says there's a little bit of bowling…” United Press International Archives, 1984. -- https://ve42.co/BowlingHistory
Johnson, Brody D. “The Physics of Bowling: How good bowlers stay off the straight and narrow.” St. Louis University. -- https://ve42.co/JohnsonPhysicsPpt
Talamo, Jim. “The Physics of Bowling Balls.” -- https://ve42.co/TalamoPhysicsPpt
Thompson, Ted. “Breakdown and Carrydown - Then and Now.” Kegel. 2012. -- https://ve42.co/ThompsonKegel
Frohlich, Cliff. “What Makes Bowling Balls Hook?” American Journal of Physics, vol. 72, no. 9, 2004, pp. 1170–1177., https://doi.org/10.1119/1.1767099. -- https://ve42.co/FrohlichHook
Article on bowling’s ranking in participatory sports -- https://ve42.co/BowlingRank
Speranza, Dan, and Dave Nestor. “Initial Oil Absorption Results.” United States Bowling Congress, 2016. -- https://ve42.co/USBCOilAbsorption
D. Benner, N. Mours, and P. Ridenour. “Pin Carry Study: Bowl Expo 2009.” United States Bowling Congress, 2009. -- https://ve42.co/USBCPinCarry
Hopkins, D. C., and J. D. Patterson. “Bowling Frames: Paths of a Bowling Ball.” American Journal of Physics, vol. 45, no. 3, 1977, pp. 263–266., https://doi.org/10.1119/1.11005. -- https://ve42.co/HopkinsPath
Normani, Franco. “The Physics of Bowling.” Real World Physics Problems. -- https://ve42.co/NormaniPhysics
Horaczek, Stan. “The insides of pro bowling balls will make your head spin.” Popular Science, 2020. -- https://ve42.co/HoraczekSpin
House shot oil pattern -- https://ve42.co/HouseOil. Licensed under Creative Commons: By Attribution 4.0.

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Special thanks to Patreon supporters: Andrew, Diffbot, Micah Mangione, MJP, Gnare, Nick DiCandilo, Dave Kircher, Edward Larsen, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Mac Malkawi, Michael Schneider, Big Badaboom, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Clayton Greenwell, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller and Emily Zhang
Animations by Mike Radjabov and Ivy Tello
Filmed by Derek Muller, Trenton Oliver, and Emily Zhang
Edited by Trenton Oliver
SFX by Shaun Clifford
Additional video supplied by Getty Images
Music from Epidemic Sounds
Produced by Derek Muller, Petr Lebedev, and Emily Zhang

The single principle that underpins all of physics. Head to https://brilliant.org/veritasium 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: https://www.patreon.com/posts/....principle-of-1160428

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 https://ve42.co/PatreonDE

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 - https://ve42.co/SnatomsV

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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. - 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
3Blue1Brown. The Brachistochrone, with Steven Strogatz via Youtube - https://ve42.co/Brach3B1B
Vsauce. The Brachistochrone via Youtube - https://ve42.co/BrachV
PBS Space Time. Is ACTION The Most Fundamental Property in Physics? via Youtube - https://ve42.co/PBSAction

Full list of references: https://ve42.co/LeastActionRefs

Images & Video:
Voltaire. (1753). Diatribe du Docteur Akakia. - https://ve42.co/DiatribeAkakia
Philosophical Transactions cover. via Wikimedia Commons - https://ve42.co/PhilTransImage
Kids Fun Science. (Jun 28, 2017). Refraction of Light with a arrow experiment via Youtube - https://ve42.co/RefractionFunSci
Physics with Simon Poliakoff. Refraction demonstration with water and laser via Youtube - https://ve42.co/SimonPoliakoff
Mercury Transit Across Sun. via Nasa.gov - https://ve42.co/MercTransit


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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 Strong, Gregor Čavlović, and Geeta Thakur
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Strong, 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

Aerogels are the world's lightest (least dense) solids. They are also excellent thermal insulators and have been used in numerous Mars missions and the Stardust comet particle-return mission. The focus of this video is silica aerogels, though graphene aerogels are now technically the lightest.

At one point Dr. Steven Jones literally held the Guinness World Record for making the lightest aerogel and therefore lightest solid. If you're interested in learning more about aerogels, let me know in the comments as there is a potential trilogy in the works...

Huge thanks to Dr. Stephen Steiner and the crew at Aerogel Technologies. To find out more or buy your own aerogel sample, check out: http://www.aerogeltechnologies.com/

Thanks to Dr. Steven Jones and Dr. Mihail Petkov at NASA's Jet Propulsion Laboratory

And thanks to FLIR for loaning us the awesome high definition thermal camera. The footage is amazing! https://www.flir.com

Special thanks to Patreon supporters:
Donal Botkin, Michael Krugman, Ron Neal, Stan Presolski, Terrance Shepherd, Penward Rhyme and everyone who provided feedback on an early draft of this video.

Filming by Raquel Nuno
Animations by Maria Raykova
Drawings by Mariel Solsberg

Music From http://epidemicsound.com "Seaweed" "Swagger Stagger"

The best and worst predictions in science are both based on the same underlying physics
Check out the Great Courses Plus: http://ow.ly/cePe303oKDM
Support Veritasium on Patreon: http://bit.ly/VePatreon

Special thanks to:
Prof. Sean Carroll
Prof. Brian Schmidt
Prof. Stephen Bartlett
Prof. Geraint Lewis

More on this topic: http://wke.lt/w/s/XDkwi

Patreon supporters:
Bryan Baker, Donal Botkin, Tony Fadell, Jason Buster, Saeed Alghamdi, Nathan Hansen

Virtual particles are a way of talking about fields and their interactions as though particles are doing all the work. This is why there is some controversy around using the term 'virtual particles'. Some people think the term is useful, especially since in calculating with Feynman diagrams you draw all the particle interactions that are possible (and then do the calculations to get the right answer). While others feel this terminology is misleading because virtual particles don't behave like real particles and can't be observed.

Go to our sponsor https://betterhelp.com/veritasium to get matched with a professional therapist who will listen and help.

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Huge thanks to the Australian Reptile Park for having us over to film – special thanks to Jake Meney for showing us the spiders and Caitlin Vine for organizing the shoot. https://www.reptilepark.com.au

Huge thanks to Dr Timothy Jackson with his help and answering our questions.

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


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References:

Pineda, S. S., Sollod, B. L., Wilson, D., Darling, A., Sunagar, K., Undheim, E. A., ... & King, G. F. (2014). Diversification of a single ancestral gene into a successful toxin superfamily in highly venomous Australian funnel-web spiders. BMC genomics, 15(1), 1-16 - https://ve42.co/Pineda2014

Isbister, G. K., Gray, M. R., Balit, C. R., Raven, R. J., Stokes, B. J., Porges, K., ... & Fisher, M. M. (2005). Funnel-web spider bite: a systematic review of recorded clinical cases. Medical journal of Australia, 182(8), 407-411 - https://ve42.co/Isbister2005

Herzig, V., Sunagar, K., Wilson, D. T., Pineda, S. S., Israel, M. R., Dutertre, S., ... & Fry, B. G. (2020). Australian funnel-web spiders evolved human-lethal δ-hexatoxins for defense against vertebrate predators. Proceedings of the National Academy of Sciences, 117(40), 24920-24928 - https://ve42.co/Herzig2020

Nicholson, G. M., & Graudins, A. (2002). Spiders of medical importance in the Asia–Pacific: Atracotoxin, latrotoxin and related spider neurotoxins. Clinical and experimental pharmacology and physiology, 29(9), 785-794 - https://ve42.co/Nicholson2002

Fletcher, J. I., Chapman, B. E., Mackay, J. P., Howden, M. E., & King, G. F. (1997). The structure of versutoxin (δ-atracotoxin-Hv1) provides insights into the binding of site 3 neurotoxins to the voltage-gated sodium channel. Structure, 5(11), 1525-1535 - https://ve42.co/Fletcher1997

Australian Reptile Park. (2022). Snake and Spider First Aid - https://ve42.co/ARPFirstAid

The Australian Museum. (20 ). Spider facts - https://ve42.co/SpiderFacts


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Special thanks to our Patreon supporters:
Orlando Bassotto, Tj Steyn, meg noah, Bernard McGee, KeyWestr, Amadeo Bee, TTST, Balkrishna Heroor, John H. Austin, Jr., john kiehl, Anton Ragin, Benedikt Heinen, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Juan Benet, Ubiquity Ventures, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, and Sam Lutfi


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Written by Katie Barnshaw & Derek Muller
Edited by Trenton Oliver
Filmed by Petr Lebedev, Derek Muller and Jason Tran
Animation by Ivy Tello, Jakub Misiek and Fabio Albertelli
Neuron animation by Reciprocal Space – https://www.reciprocal.space
Additional video/photos supplied from Getty Images, Pond5
B-roll supplied by Seqirus Australia
Music from Epidemic Sound
Produced by Derek Muller, Petr Lebedev, Emily Zhang & Katie Barnshaw

This fungus lives on your scalp and may affect the genes you express.
Check out Head & Shoulders research on getting rid of dandruff: https://ve42.co/HS

Animation by Pindex: https://ve42.co/pindex

When I started this project, I wasn't sure what caused dandruff and I also didn't think much science would go into making a shampoo like Head & Shoulders. So what I learned really surprised me:

There are hundreds of scientists working on this shampoo. They run crazy-sounding experiments like hanging hair near Tokyo highways to understand how real-world environments deposit dirt on hair. They use sophisticated scientific techniques like electron microscopes, nuclear magnetic resonance and gene sequencing to study dandruff on the molecular level.

In fact they sequenced the entire genome of Malassezia globosa in 2002, one year after the human genome project. Their findings are published in international refereed journals. What they have found is that the Malassezia fungi create free fatty acids as byproducts of their digestion, which for some people create irritation and lead to hyper-proliferation of skin cells, flaking, histamines, inflammatory cytokines, and blood proteins reaching the surface of the skin. These findings indicate the unhealthiness of dandruff scalp and suggest a possible remedy - controlling the metabolism of the Malassezia fungi. This is achieved using different active ingredients in different products and different parts of the world, including zinc pyrithione, selenium sulfide, and piroctone olamine. With the reduction of irritants, the scalp actually expresses different genes, producing a signature more similar to a non-dandruff baseline scalp.

Music from Epidemic Sound: http://epidemicsound.com
Music also by Kevin MacLeod: http://incompetech.com

This is a video about how Japanese samurai swords, aka katanas, are made – from the gathering of the iron sand, to the smelting of the steel, to the forging of the blade. Head over to https://hensonshaving.com/veritasium and enter code 'Veritasium' for 100 free blades with the purchase of a razor. Make sure to add both the razor and the blades to your cart for the code to take effect.

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

CORRECTION: There's a typo at 18:20. The combination of Ferrite and Cementite is Pearlite, not Perlite. Thanks, @neophoys for pointing it out.

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A massive thank you to John McBride for making this entire project happen. This would not have been possible without John. Please check out his japan walking tours https://walkjapan.com/
Massive thanks to Craig Mod, Inoue-san, everyone in the Tanabe family, and Takanashi-san. Also a massive thank you to Kevin Cashen – https://cashenblades.com/

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References:
Tanii, H., Inazumi, T., & Terashima, K. (2014). Mineralogical study of iron sand with different metallurgical characteristic to smelting with use of Japanese classic iron-making furnace “Tatara”. ISIJ international, 54(5), 1044-1050.

Tate, M. (2005). History of Iron and Steel Making Technology in Japan Mainly on the smelting of iron sand by Tatara. Tetsu-to-Hagane, 91(1), 2-10.

Krauss, G. (1999). Martensite in steel: strength and structure. Materials science and engineering: A, 273, 40-57.

Krauss, G., & Marder, A. R. (1971). The morphology of martensite in iron alloys. Metallurgical Transactions, 2, 2343-2357.

Yalçın, Ü. (1999). Early iron metallurgy in Anatolia. Anatolian Studies, 49, 177-187.

Kapp, L., Kapp, H., & Yoshihara, Y. (1987). The craft of the Japanese sword. Kodansha International.

Matsumoto, C., Das, A. K., Ohba, T., Morito, S., Hayashi, T., & Takami, G. (2013). Characteristics of Japanese sword produced from tatara steel. Journal of Alloys and Compounds, 577, S673-S677.

Inoue, T. (2010). Tatara and the Japanese sword: the science and technology. Acta Mechanica, 214(1), 17-30.


Images & Video:

Great video from NHK – https://ve42.co/NHK



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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 Petr Lebedev
Written by Petr Lebedev and Derek Muller
Edited by Trenton Oliver and Jack Saxon
Animated by Fabio Albertelli, Jakub Misiek, David Szakaly
Filmed by Petr Lebedev and Lui Kimishima
Produced by Petr Lebedev, Derek Muller, Han Evans, Giovanna Utichi, Emily Taylor
Additional research by Gregor Čavlović
Thumbnail by Peter Sheppard


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

In a competitive world, tiny advantages can make all the difference. Get 10% off Snatoms with code 'giveluck' in the US: https://ve42.co/USA or International: https://snatoms.com
If you would like to receive Snatoms, submit the form here: https://ve42.co/getluck

Snatoms are also available on Amazon Prime in the US but with no discount code: https://ve42.co/Asnatoms

Huge thanks to Gene and Sam from Potato Jet for filming with me: https://ve42.co/potatojet

This video was inspired by and draws examples from the book "Success and Luck: Good Fortune and the Myth of Meritocracy" by Robert H. Frank

Special thanks to Patreon supporters (and to everyone who commented on an earlier version of this video):
Marc Forand, Robert Dickerson, Christian Stauffer, LoadTooSlow, Vincent, Lyvann Ferrusca, DALE HORNE, Alfred Wallace, Kevin Beavers, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Michael Krugman, Ron Neal, Donal Botkin

Animations by Ivy Tello

Apollo astronauts trained in nuclear bomb craters at the Nevada National Security Site. But why?Thanks Audible! Start listening with a 30-day trial and your first audiobook plus two Audible Originals free when you go to http://audible.com/veritasium or text veritasium to 500500

I found this story fascinating because in a way a nuclear bomb crater is more like a meteorite impact site than an impact site itself. Consider: Barringer Crater was claimed to be a meteorite impact site but geologists dismissed it as a volcanic formation. It was only after studying nuclear bomb craters and the minerals found there that geologists concluded the energy and pressures that created Barringer Crater were too high to be from volcanic activity and therefore must have formed from a meteorite impact.

Special Thanks to:
Nevada National Security Site
The National Atomic Testing Museum
Jonny Hyman and Verse: https://youtu.be/7bUUGzi-AAY
Active Galactic for footage of craters in Arizona: https://youtu.be/yhoooBpndog

Special thanks to Patreon supporters:
a human, Alfred Wallace, Arjun Chakroborty, Brent Stewart, Bryan Baker, Chris Vargas, Chuck Lauer Vose, Clip Tree, Coale Shifflett, Colin Bellmore, DALE HORNE, Daniel Milum, Donal Botkin, Eric Velazquez, Illya Nayshevsky, James Knight, James Wong, Jasper Xin, Joar Wandborg, Johnny, June Kang, Kevin Beavers, kkm, Leah Howard, Listen Money Matters, Lyvann Ferrusca, Manuel Zürcher, Mathias Göransson, Michael Bradley Wirz, Michael Krugman, Mohammed Al Sahaf, OddJosh, Philipp Volgger, Pindex, Roberto Rezende, Robin DeBank, Ron Neal, Sam Lutfi, Stan Presolski, Tige Thorman, Warrior8252

Filmed by Raquel Nuno
Story and Editing by Derek Muller and Jonny Hyman
Music and Animation by Jonny Hyman
Produced by Casey Rentz

The 100 Prisoners Riddle feels completely impossible even once you know the answer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Destin of Smarter Every Day (https://ve42.co/SED), Toby of Tibees (https://ve42.co/Tibees), and Jabril of Jabrils (https://ve42.co/Jabrils) for taking the time to think about this mind bending riddle.

Huge thanks to Luke West for building plots and for his help with the math.
Huge thanks to Dr. Eugene Curtin and Dr. Max Warshauer for their great article on the problem and taking the time to help us understand it: https://ve42.co/CurtinWarshauer
Thanks to Dr. John Baez for his help with finding alternate ways to do the calculations.
Thanks to Simon Pampena for his input and analysis.

Other 100 Prisoners Riddle videos:
minutephysics: https://www.youtube.com/watch?v=C5-I0bAuEUE
Vsauce2: https://www.youtube.com/watch?v=kOnEEeHZp94
Stand-up Maths: https://www.youtube.com/watch?v=a1DUUnhk3uE
TED-Ed: https://www.youtube.com/watch?v=vIdStMTgNl0

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References:
Original paper: Gál, A., & Miltersen, P.B. (2003). The Cell Probe Complexity of Succinct Data Structures. BRICS, Department of Computer Science, University of Aarhus. All rights reserved. – https://ve42.co/GalMiltersen
Winkler, P. (2006). Seven Puzzles You Think You Must Not Have Heard Correctly. – https://ve42.co/Winkler2006
The 100 Prisoners Problem – https://ve42.co/100PWiki
Golomb, S. & Gaal, P. (1998). On the Number of Permutations on n Objects with Greatest Cycle Length k. Advances in Applied Mathematics, 20(1), 98-107. – https://ve42.co/Golomb1998
Lamb, E. (2012). Puzzling Prisoners Presented to Promote North America's Only Museum of Math. Observations, Scientific American. – https://ve42.co/Lamb2012
Permutations – https://ve42.co/PermutationsWiki
Probability that a random permutation of n elements has a cycle of length k greater than n/2, Math SE. – https://ve42.co/BaezProbSE
Counting Cycle Structures in Sn, Math SE. – https://ve42.co/CountCyclesSE
What is the distribution of cycle lengths in derangements? In particular, expected longest cycle, Math SE. – https://ve42.co/JorikiSE
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1). – https://www.manim.community/

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Special thanks to Patreon supporters: RayJ Johnson, Brian Busbee, Jerome Barakos M.D., Amadeo Bee, Julian Lee, Inconcision, TTST, Balkrishna Heroor, Chris LaClair, Avi Yashchin, John H. Austin, Jr., OnlineBookClub.org, Matthew Gonzalez, Eric Sexton, john kiehl, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Timothy O’Brien, Mac Malkawi, Michael Schneider, jim buckmaster, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

▀▀▀
Written by Derek Muller and Emily Zhang
Filmed by Derek Muller and Petr Lebedev
Animation by Ivy Tello and Jesús Rascón
Edited by Trenton Oliver
Additional video/photos supplied by Getty Images
Music from Epidemic Sound and Jonny Hyman
Thumbnail by Ignat Berbeci
Produced by Derek Muller, Petr Lebedev, and Emily Zhang

Who on Earth is exposed to the most ionizing radiation?
Check out Audible: http://bit.ly/AudibleVe
I'm filming a documentary for TV about how Uranium and radioactivity have shaped the modern world. It will be broadcast in mid-2015, details to come. The filming took me to the most radioactive places on Earth (and some places, which surprisingly aren't as radioactive as you'd think). Chernobyl and Fukushima were incredible to see as they present post-apocalyptic landscapes. I also visited nuclear power plants, research reactors, Marie Curie's institute, Einstein's apartment, nuclear medicine areas of hospitals, uranium mines, nuclear bomb sites, and interviewed numerous experts.

Notes about measuring radiation:
Sieverts are a measure of 'effective dose' - that means they measure the biological impact of the energy transferred to tissues from radiation.

Obviously I owe a debt to the fantastic chart made by xkcd, which inspired my visual approach to this video.
https://xkcd.com/radiation/

DOSES MAY VARY
The level of radiation varies widely around the world depending mainly on altitude and geology (excluding nuclear accidents).

Estimates of particular doses also vary. All numbers reported in this video should be taken as order of magnitude only.

The most contentious claim may be that smokers receive the highest dose of ionizing radiation. This is not a whole body dose, but a dose to the lungs as specified in the video. References are here:
http://en.wikipedia.org/wiki/H....ealth_effects_of_tob
http://www.rmeswi.com/36.html

Special thanks to:
Physics Girl: https://www.youtube.com/physicswoman
MinutePhysics: https://www.youtube.com/minutephysics
Natalie Tran: https://www.youtube.com/communitychannel
Bionerd23: https://www.youtube.com/bionerd23
Nigel and Helen for feedback on earlier drafts of this video.

Music is "Stale Mate"

Einstein was wrong about black holes, what else? Use code veritasium at the link below to get an exclusive 60% off an annual Incogni plan: https://incogni.com/veritasium

A massive thank you to Prof. Geraint F. Lewis and Prof. Juan Maldacena for their expertise and help with this video.

A huge thank you to those who helped us understand this complicated topic: Dr. Suddhasattwa Brahma, Prof. Carlo Rovelli, Dr. Hal Haggard, Prof. Martin Bojowald, Dr. Francesca Vidotto, Prof. Andrew Hamilton, and Dr. Carl-Fredrik Nyberg Brodda.

A special thanks to Alessandro Roussel from ScienceClic for his spectacular simulations and feedback on the video. Check out his channel here: https://ve42.co/ScienceClic

An excellent book on this topic and an inspiration for this video: Cox, B., & Forshaw, J. (2023). Black holes: the key to understanding the universe.

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Join us on Patreon to watch an exclusive bonus video that expands on the topic of white holes https://ve42.co/PatreonDE

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 - https://ve42.co/SnatomsV

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References:
Thorne, K. (1995). Black Holes & Time Warps: Einstein's Outrageous Legacy.
Relativity Playlist by ScienceClic - https://ve42.co/SCPlaylist
Hamilton, A. J. S. (2021). General Relativity, Black Holes, and Cosmology - https://ve42.co/Hamilton2021
Black Hole Events by PBS Space Time - https://youtu.be/vNaEBbFbvcY?l....ist=PLsPUh22kYmNBl4h
Newton’s Letters via The Newton Project - https://ve42.co/NewtonMail
Einstein, A. (1915). Die feldgleichungen der gravitation. - https://ve42.co/Einstein1915
Why Time and Space Swap by ScienceClic - https://youtu.be/GQZ3R81iyE0
Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. - https://ve42.co/Schwarzschild1916
Wali, K. C. (1982). Chandrasekhar vs. Eddington—an unanticipated confrontation. - https://ve42.co/Wali1982
How to Build a Black Hole by PBS Space Time - https://www.youtube.com/watch?v=xx4562gesw0
Oppenheimer, J. R., & Volkoff, G. M. (1939). On massive neutron cores. - https://ve42.co/TOVLimit
Oppenheimer, J. R., & Snyder, H. (1939). On continued gravitational contraction. - https://ve42.co/Oppenheimer1939
Schwarzschild Geometry by Andrew Hamilton - https://ve42.co/SchwarzGeom
Why all world maps are wrong by Vox - https://www.youtube.com/watch?v=kIID5FDi2JQ
Hamilton, A. J., & Lisle, J. P. (2008). The river model of black holes. - https://ve42.co/HamiltonLisle2008
Mapping The Multiverse by PBS Space Time - https://www.youtube.com/watch?v=4v9A9hQUcBQ
Rotating black hole via Wikipedia - https://ve42.co/WikiRBH
Wormhole Travel by PBS Space Time - https://www.youtube.com/watch?v=ldVDM-v5uz0
Morris, M. S., & Thorne, K. S. (1988). Wormholes in spacetime and their use for interstellar travel. - https://ve42.co/MorrisThorne1988

Images & Video:
D3 Geo Projection Library by Mike Bostock https://ve42.co/d3geo
Interrupted Maps by Jason Davies https://ve42.co/DaviesMaps
Kazmierczak, J. et al. (2021). NASA’s NICER Tests Matter’s Limits. - https://ve42.co/NasaNICER
Bridgman, T. et al. (2024). M5.1 flare 'Double Whammy', at Active Regions 13559 and 13561. NASA SVS. - https://ve42.co/NasaFlare
Schnittman, J. et al. (2019). Black Hole Accretion Disk Visualization. - https://ve42.co/NasaAccrDisk
Wiessinger, S. et al. (2020). A Decade of Sun. NASA SVS. - https://ve42.co/NasaSunDecade
Skelly, C. et al. (2017). What is a Neutron Star? NASA SVS. - https://ve42.co/NasaNeutron
What would we see if we fell into a black hole by ScienceClic - https://youtu.be/4rTv9wvvat8
Earth texture - https://ve42.co/NASAEarth
First image of Sgr A* - https://ve42.co/EHT1
Image of M87 - https://ve42.co/EHT2
Polarized light image of Sgr A* - https://ve42.co/EHT3

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Directed by Casper Mebius
Written by Casper Mebius, Derek Muller and Will Wood
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Mike Radjabov, David Szakaly, Jonny Hyman, and Alessandro Roussel
Illustrated by Jakub Misiek
Filmed by Derek Muller
Additional research by Gregor Čavlović
Produced by Casper Mebius, Derek Muller, Will Wood, Giovanna Utichi, Rob Beasley Spence, Gregor Čavlović, and Emily Taylor

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