The world's roundest object helps solve the longest running problem in measurement -- how to define the kilogram.
Support Veritasium on Patreon: http://bit.ly/VePatreon

A kilogram isn't what it used to be. Literally. The original name for it was the 'grave', proposed in 1793 but it fell victim to the French Revolution like its creator, Lavoisier. So begins the tale of the most unusual SI unit. The kilogram is the only base unit with a prefix in its name, and the only one still defined by a physical artifact, the international prototype kilogram or IPK.

But the problem with this definition has long been apparent. The IPK doesn't seem to maintain its mass compared to 40 similar cylinders minted at the same time. The goal is therefore to eliminate the kilogram's dependence on a physical object. Two main approaches are being considered to achieve this end: the Avogadro Project and the Watt Balance.

The Avogadro project aims to redefine Avogadro's constant (currently defined by the kilogram -- the number of atoms in 12 g of carbon-12) and reverse the relationship so that the kilogram is precisely specified by Avogadro's constant. This method required creating the most perfect sphere on Earth. It is made out of a single crystal of silicon 28 atoms. By carefully measuring the diameter, the volume can be precisely specified. Since the atom spacing of silicon is well known, the number of atoms in a sphere can be accurately calculated. This allows for a very precise determination of Avogadro's constant.

Special thanks to Katie Green, Dr. David Farrant, the CSIRO, and the National Measurment Institute for their help. Thanks also to Nessy Hill for filming and reviewing earlier drafts of this video.

There is debate as to whether this is truly the roundest object ever created. The Gravity Probe-B rotors are also spherical with very low tolerances such that they may in fact be rounder.

Music by Kevin McLeod (incompetech.com) Decision, Danse Macabre, Scissors

Why do spikes form on ice cubes? Without them the world would be vastly different.
Awesome Jingle by Accent: http://bit.ly/AccentVe
Thanks to Prof. Stephen Morris from UofT: http://bit.ly/1GFANBE

Filmed in part by Martin Marek in Olomouc, Czech Republic

Time lapse of a growing ice spike by Lesley Hill, Russ Sampson and Edward Lozowski, with technical help by Kenny Lozowski.

Ice spike image by Dan and Lynn Wolaver: http://wolaver.org/log/09.11.29.htm

Concerned ice spike video by rocknut420: https://www.youtube.com/watch?v=GwM0we_t94c

Earth footage courtesy of NASA: https://www.youtube.com/watch?v=G4BPOEmugtM

Ice vase image by PgunnG: http://www.reddit.com/r/pics/c....omments/1voeqk/so_i_

Second ice vase image by A K Haart: http://akhaart.blogspot.com/20....15_01_01_archive.htm

Blimps and airships might be relics of the past, but could they help save the future? Head to https://www.odoo.com/r/veritasium to start building your own website for free.

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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Thank you to Eli Dourado for letting us explore the argument he describes in his article: https://ve42.co/Dourado

A huge thank you to Dan Grossman and Nick Allman for their time, help, and expertise.

Also a massive thank you to those who helped us understand the world of modern airships, and provided valuable feedback - Prof. Barry Prentice, Gennadiy Verba, Prof.
Christoph Pflaum, Heather Roszczyk, Dr. Casey Handmer, Richard Van Trueren, & Thibault Proux.

We are also grateful for the collaboration of the companies who are working hard to make this comeback happen - Atlas LTA, Buoyant Aircraft Systems International, Hybrid Air Vehicles, LTA Research, & Flying Whales.


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References:

How Airships Could Overcome a Century of Failure, Bloomberg Originals via YouTube - https://ve42.co/AirshipsCoF

Why the Airship May Be the Future of Air Travel, Undecided with Matt Ferrell via YouTube - https://ve42.co/FutureAirships

Airship, Wikipedia - https://ve42.co/AirshipWiki

Handmer, C. (2020). A quick note on airships. Casey Handmer’s Blog - https://ve42.co/Handmer2020

UNCTAD (2020). Review of Maritime Transport 2020 - https://ve42.co/RMT2020

National Transportation Research Center (2023). Freight Analysis Framework Version 5 (FAF5) - https://ve42.co/FAF5

Hybrid Air Vehicles (2023). HAV - https://ve42.co/HAV

LTA Research (2023). Lighter Than Air (LTA) Research - https://ve42.co/LTAResearch

OceanSkyCruises (2023). North Pole Expedition - OceanSkyCruises - https://ve42.co/NPExpedition

Flying Whales (2023). Flying Whales - https://ve42.co/FlyingWhales

Buoyant Aircraft Systems International (2023). BASI - https://ve42.co/BASI

Atlas LTA (2023). Atlas Electric Airships | Atlas LTA Airships - https://ve42.co/AtlasLTA

Prentice, B. (2021). Hydrogen gas-fuelled airships could spur development in remote communities. The Conversation - https://ve42.co/HydrogenAirships

Grossman, D. (2009). The Hindenburg Disaster. Airships - https://ve42.co/Hindenburg1

Hindenburg Disaster, Wikipedia - https://ve42.co/HindenburgWiki

What happened to the Hindenburg?, Jared Owen via Youtube - https://ve42.co/Owen2019

National Museum of the U.S. Navy. USS Akron (ZRS-4) - https://ve42.co/USSAkron

USS Akron, Wikipedia - https://ve42.co/USSAkronWiki


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Special thanks to our Patreon supporters:
Adam Foreman, Amadeo Bee, Anton Ragin, Balkrishna Heroor, Benedikt Heinen, 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, MaxPal, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures

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Written by Casper Mebius & Derek Muller
Directed by Casper Mebius
Edited by Jack Saxon
Filmed by Derek Muller, Jamie MacLeod, Han Evans, & Raquel Nuno
Animation by Mike Radjabov & Fabio Albertelli
Additional video/photos supplied by Getty Images, Pond5, & Envato Elements
Music from Epidemic Sound & Pond5
Produced by Casper Mebius, Derek Muller, & Han Evans


More footage & photos from:
Thermite Rail Welding video by dulevoz via YouTube - https://www.youtube.com/watch?v=rNjosF789X4

O’Rourke, T. (2016). Chronicle Covers: When the Hindenburg burst into flames. San Francisco Chronicle - https://ve42.co/Hindenburg2

Wind turbine blade transport video by DOLL Fahrzeugbau via YouTube - https://www.youtube.com/watch?v=5aPXuap0LZw

Wind turbine blade transport through mountains video by CGTN via Youtube - https://www.youtube.com/watch?v=9dtUrY8_1CM

Former Airship Hangar by Stefan Kühn - https://ve42.co/Aerium

Many videos on YouTube show water freezing almost instantaneously. This video shows you how to replicate the experiment and it explains how the phenomenon works. Molecular illustrations are courtesy of:
PhET Interactive Simulations
University of Colorado
http://phet.colorado.edu.

Mounting evidence suggests a lot of published research is false.
Check out Audible: http://bit.ly/AudibleVe
Support Veritasium on Patreon: http://bit.ly/VePatreon

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

More information on this topic: http://wke.lt/w/s/z0wmO

The Preregistration Challenge: https://cos.io/prereg/

Resources used in the making of this video:

Why Most Published Research Findings Are False:
http://journals.plos.org/plosm....edicine/article?id=1

Trouble at the Lab:
http://www.economist.com/news/....briefing/21588057-sc

Science isn't broken:
http://fivethirtyeight.com/fea....tures/science-isnt-b

Visual effects by Gustavo Rosa

There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers. 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.

If you're looking for a molecular modeling kit, try Snatoms - a kit I invented where the atoms snap together magnetically: https://snatoms.com

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References:

Koblitz, N. (2012). p-adic Numbers, p-adic Analysis, and Zeta-Functions (Vol. 58). Springer Science & Business Media.

Amazing intro to p-adic numbers here: https://youtu.be/3gyHKCDq1YA
Excellent series on p-adic numbers: https://youtu.be/VTtBDSWR1Ac
Great videos by James Tanton: @JamesTantonMath

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Special thanks to our Patreon supporters:
Emil Abu Milad, Tj Steyn, meg noah, Bernard McGee, KeyWestr, Amadeo Bee, TTST, Balkrishna Heroor, John H. Austin, Jr., john kiehl, Anton Ragin, 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, Sam Lutfi.

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Written by Derek Muller and Alex Kontorovich
Edited by Trenton Oliver
Animated by Mike Radjabov, Ivy Tello, Fabio Albertelli and Jakub Misiek
Filmed by Derek Muller
Additional video/photos supplied by Getty Images & Pond5
Music from Epidemic Sound & Jonny Hyman
Produced by Derek Muller, Petr Lebedev, & Emily Zhang

Concrete = cement + sand + gravel. Cement is the most important man-made material on Earth. Offset your carbon footprint on Wren: https://wren.co/veritasium . For the first 100 people who sign up, I will personally pay for the first month of your subscription!

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A huge thank you to Nevada Ready Mix for being willing to bury me in concrete, especially Elu Chavez and Mike Sherwood. https://www.nevadareadymix.com

And to Brandon Birchak of Six Foot Productions for providing the big fish bowl, safety equipment, planning and filming: https://www.sixfootcreations.com

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References:
Instant stone (just add water), Roots of Progress, https://rootsofprogress.org/in....stant-stone-just-add
https://rootsofprogress.org/cement-redux

Cement Chemistry and Sustainable Cementitious Materials
https://www.youtube.com/@cemen....tchemistryandsustain

Ahmad, S., Lawan, A., & Al-Osta, M. (2020). Effect of sugar dosage on setting time, microstructure and strength of Type I and Type V Portland cements. Case Studies in Construction Materials, 13, e00364. – https://ve42.co/Ahmad2020

Seymour, L. M., Maragh, J., Sabatini, P., Di Tommaso, M., Weaver, J. C., & Masic, A. (2023). Hot mixing: Mechanistic insights into the durability of ancient Roman concrete. Science advances, 9(1), eadd1602. -- https://ve42.co/Seymour2023

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Special thanks to our Patreon supporters:
Emil Abu Milad, Tj Steyn, meg noah, Bernard McGee, KeyWestr, Amadeo Bee, TTST, Balkrishna Heroor, John H. Austin, Jr., Eric Sexton, 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, Cy 'kkm' K'Nelson, Sam Lutfi.

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Written by Derek Muller
Edited by Trenton Oliver
Filmed by Raquel Nuno, Austin Bradley and Bryson
Animated by Ivy Tello & Mike Radjabov
Additional video/photos supplied by Getty Images & Pond5
Music from Epidemic Sound & Jonny Hyman: the Bill Wurtz inspired ‘Skyscrapers are made of sea shells’
Produced by Derek Muller, Petr Lebedev, & Emily Zhang

Increasing entropy is NOT the only process that's asymmetric in time.
Check out the book: http://WeHaveNoIdea.com
This video was co-written by Daniel Whiteson and Jorge Cham
You can also check out PhD Comics: http://phdcomics.com


Special thanks to Patreon supporters:
Tony Fadell, Donal Botkin, Michael Krugman, Jeff Straathof, Zach Mueller, Ron Neal, Nathan Hansen, Joshua Abenir

Support Veritasium on Patreon: http://ve42.co/patreon

Original paper on parity violation by the weak force by Lee and Yang:
http://www.physics.utah.edu/~b....elz/phys5110/PhysRev

More on B-meson oscillations and time reversal violation:
Physics World Article: http://ve42.co/TimeReversal
Original paper: https://arxiv.org/pdf/1410.1742.pdf
https://en.wikipedia.org/wiki/B_meson

Physics consultant: Prof. Stephen Bartlett

Studio filming by Raquel Nuno

When evolution favours a stable ratio of traits rather than one dominant trait.
Check out Audible: http://bit.ly/AudibleVe
Animation by The Lyosacks: https://www.youtube.com/TheLyosacks

Hosting Neil Degrasse Tyson, info and tickets: http://bit.ly/NDTandVe
Aug. 22 in Sydney
Aug. 23 in Canberra

Special thanks to Richard Dawkins

Filmed at Academia Film Olomouc with help from Martyn Marek

Music by Kevin MacLeod www.incompetech.com 'Marty Gots a Plan' 'Sing Along with Jim'

Even the GOAT Tom Brady can’t throw a perfect spiral. Here’s why. 🌏 Get exclusive NordVPN deal here ➵ https://NordVPN.com/veritasium It’s risk free with Nord’s 30 day money-back guarantee!✌

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 Tom Brady for coming and throwing some footballs with us and letting us analyse his throw. You can check out his channel here: https://www.youtube.com/@tombrady

Also thank you to Kevin Bonner and the team at Shadow Lion for helping make this happen!

A big thanks to Daniel Hare and Wilson for all their help collecting and analyzing the data.

A massive thank you to Prof. Philip Ansell, David Attig, Matt Brotnow, Sam Hince and Derrick Wiberg at the University of Illinois at Urbana-Champaign for all their work testing out footballs in their wind tunnel (more of that to come in our second video).

We’d also like to shout out Stewart Bible, Ryan Sayko and the rest of the team at Resolved Analytics for all their work on the CFD models - https://www.resolvedanalytics.com/

Thank you to Mike Lopez and Tom Bliss from the Football Data and Analytics at the NFL for sharing data and insights from across NFL history.

We’re incredibly grateful to Prof. Richard Price and Major Brett Gibbons for their invaluable contributions to this video.

Thank you to Prof. Chad Orzel, Prof. John Eric Goff, Dr Ainissa Ramirez, Prof. Tony Schmitz & Jonathan Ferguson for all their help on the project.

Also thanks to Chris Anstis for his help as a stand-in QB!

▀▀▀
0:00 How Tom Brady Throws a Football
2:51 Why do you spin a football to throw it?
5:36 How does rifling affect a projectile?
9:09 The Turnover Paradox
11:15 How fast can Tom Brady throw?
14:31 Analysing Brady’s Throw
16:38 Gyroscopic Procession
19:47 It’s impossible to throw straight
23:17 Outdoor vs Dome Stadiums
24:31 Why Tom Brady is the GOAT

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

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

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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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Producer & Director: Henry van Dyck
Writing: Henry van Dyck & Derek Muller
Editor: Trenton Oliver
Animators: Mike Radjabov & Fabio Albetelli
Illustrator: Jakub Misiek
Researchers: Emilia Gyles & Gabe Strong
Field Producer: Katy Savage
Camera Operators: John Nicholls, Trenton Oliver, Melkwych Pierre-Louis & Scott Wellington
Drone Operators: Nathan Taupez Scinto, Angelo Fiorini
Sound Recordist: Vlady Garcia
Production Assistant: Leah Jiji
Media Manager: Gabriel C. Rodriguez
Assistant Editor: James Stuart
Thumbnail Designers: Ren Hurley & Ben Powell
Production Team: Josh Pitt, Rob Beasley Spence, Tori Brittain & Barbara Abraul
Executive Producers: Derek Muller & Zoe Heron

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

The physics behind Kelvin's Thunderstorm explained. No, it is not a practical way of generating electricity, which is why we use turbines at hydro stations.

This video goes into more detail about the phenomenon demonstrated in this Hunger Games collab video: http://youtu.be/Rwa26CXG1fc

This video is about stuff: light bulbs, printers, phones and why they aren't better. Go to https://NordVPN.com/veritasium and use code VERITASIUM to get a 2-year plan plus 1 additional month with a huge discount. It’s risk free with Nord’s 30 day money-back guarantee!

References:
The Man in the White Suit — https://ve42.co/Suit

London, B. (1932). Ending the depression through planned obsolescence. — https://ve42.co/London32

Slade, G. (2009). Made to break: Technology and obsolescence in America. Harvard University Press — https://ve42.co/madetobreak

Krajewski, M. (2014). The great lightbulb conspiracy. IEEE spectrum, 51(10), 56-61. — https://ve42.co/Phoebus

Planet Money, The Phoebus Cartel - https://ve42.co/PMobs

The Light Bulb Conspiracy - https://youtu.be/e9xmn228HM0

Special thanks to Patreon supporters: Mac Malkawi, Oleksii Leonov, Michael Schneider, Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, 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
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Video supplied by Getty Images

Music by Jonny Hyman and from https://epidemicsound.com"Aquatic Planet", "Rhythm of Dreams", "Tread Lightly", "Unexpected Visitors", "Curved Mirrors" "Drunken Lullaby" "Fluorescent Lights"

Thumbnail by Raquel Nuno and Karri Denise

Scientists are being inspired by nature to design the next generation of security devices. Arrays of nanoscale holes create beautiful reflected colours that are almost impossible to forge. This video was supported by TechNyou - check out their series on logical fallacies: http://bit.ly/WBsD31

Soon these nanoscale security devices could replace holograms. They are many times more reflective than holograms, and although the structures are smaller scale, they are lower aspect ratio and therefore easy to manufacture in bulk.

The electron wiggle simulation is from PhET, the best physics simulations ever: http://phet.colorado.edu

Special thanks to Thomas from Copenhagen who showed me around the city including the science museum where he assisted with the soap bubble demonstration.

Clint Landrock is the Chief Technology Officer for Nanotech Securities: http://www.nanosecurity.ca

Music is "Firefly in a Fairytale" by Gareth Coker

What are these electric blue ponds in the middle of the Utah desert? And why do they keep changing color?

Join Derek Muller (Veritasium) as he looks into the weird, bizarre, and seemingly inexplicable images found on Google Earth to discover what on Earth they actually are. It’s a travel vlog, documentary, and science show wrapped into one. It’s Pindrop.

0:00 Intro
0:29 Electric Blue Ponds
2:13 Finding The Truth
5:47 Importance Of Potash
8:41 Potash From Rocks
14:04 Safer Ways To Mine
15:02 Droning
17:28 Potash The Savior

Bayes' theorem explained with examples and implications for life.
Check out Audible: http://ve42.co/audible
Support Veritasium on Patreon: http://ve42.co/patreon

I didn't say it explicitly in the video, but in my view the Bayesian trap is interpreting events that happen repeatedly as events that happen inevitably. They may be inevitable OR they may simply be the outcome of a series of steps, which likely depend on our behaviour. Yet our expectation of a certain outcome often leads us to behave just as we always have which only ensures that outcome. To escape the Bayesian trap, we must be willing to experiment.

Special thanks to Patreon supporters:
Tony Fadell, Jeff Straathof, Donal Botkin, Zach Mueller, Ron Neal, Nathan Hansen, Saeed Alghamdi

Useful references:
The Signal and the Noise, Nate Silver
The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, by Sharon Bertsch McGrayne

Bayes' theorem or rule (there are many different versions of the same concept) has fascinated me for a long time due to its uses both in mathematics and statistics, and to solve real world problems. Bayesian inference has been used to crack the Enigma Code and to filter spam email. Bayes has also been used to locate the wreckage from plane crashes deep beneath the sea.

Music from http://epidemicsound.com "Flourishing Views 3"

Are you heaviest at night before you go to bed and lightest in the morning? I tried to tease out the factors to figure out what really causes weight gain and loss during the day, and what causes daily weight fluctuations.

A launch mishap led to the best experimental confirmation of gravitational redshift. Get a free audiobook with a 30-day trial of Audible: http://audible.com/VERITASIUM or text VERITASIUM to 500500

Huge thanks to
Dr. Pacome Delva: https://ve42.co/pacome
Dr. Sven Herrmann: https://ve42.co/sven
Gravitational Redshift Test Using Eccentric Galileo Satellites: https://ve42.co/GRtest

Disclaimer: It is arguable what is THE best test of general relativity because there are different ways to test the theory. This is the best confirmation of gravitational redshift, which is one of the three original tests proposed by Einstein.

Special thanks to Patreon supporters:
Donal Botkin, James M Nicholson, Michael Krugman, Nathan Hansen, Ron Neal, Stan Presolski, Terrance Shepherd

Animations and editing by Alan Chamberlain

Music from http://epidemicsound.com "Subtle Substitutes 2" "A sound Foundation 1" "Cell Research 1" "Particle Attraction 1"

Corn flour blown through a funnel produces an excellent fireball. This both looks cool and demonstrates some interesting science. In any chemical reaction, the reactants must mix with each other significantly in order to increase the rate of reaction. Here we demonstrate that corn flour on a spoon burns slowly, but blown from a funnel, the reaction is dramatic and violent. This is because the surface area where the reaction can occur is greatly increased.

HD Slinky Slow-mo http://bit.ly/TRa4sE
How to make solid nitrogen http://bit.ly/RqPw8l
Levitating BBQ http://bit.ly/SWgOWh
Electric Flame http://bit.ly/Q3enCb

As always, if you are planning to recreate this experiment, make sure you have appropriate supervision and take necessary precautions.

A general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality. 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 Amir Alexander, Dr Alexander Kontorovich, Dr Chris Ferrie, and Dr Adam Becker for the helpful advice and feedback on the earlier versions of the script.

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References:
Some great videos about the cubic:

500 years of not teaching the cubic formula. -- https://youtu.be/N-KXStupwsc

Imaginary Numbers are Real -- https://youtu.be/T647CGsuOVU

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York. -- https://ve42.co/Dunham90

Toscano, F. (2020). The Secret Formula. Princeton University Press. -- https://ve42.co/Toscano2020

Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. -- https://ve42.co/Bochner63

Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. -- https://ve42.co/Murio21

Branson, W. Solving the cubic with Cardano, -- https://ve42.co/Branson2014

Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. -- https://ve42.co/Rothman

Vali Siadat, M., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. -- https://ve42.co/Siadat21

Merino, O. (2006). A short history of complex numbers. University of Rhode Island. -- https://ve42.co/Merino2006

Cardano, G (1545), Ars magna or The Rules of Algebra, Dover (published 1993), ISBN 0-486-67811-3

Bombelli, R (1579) L’Algebra https://ve42.co/Bombelli

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: 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, Pindex, Michael Krugman, Cy 'kkm' K'Nelson,Ron Neal

Executive Producer: Derek Muller
Writers: Derek Muller, Alex Kontorovich, Stephen Welch, Petr Lebedev
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jesús Rascón
SFX: Shaun Clifford
Camerapeople: Derek Muller, Emily Zhang
Editors: Derek Muller, Petr Lebedev
Producers: Derek Muller, Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Music from Epidemic Sound and Jonny Hyman

Common pitfalls of New Year's resolutions and how I plan to avoid them.
Thanks to Simone Giertz for sending me and Every Day Calendar!
Order here: https://everydaycalendar.co
Start listening with a 30-day trial and your first audiobook plus two Audible Originals free when you go to https://audible.com/veritasium or text veritasium to 500500.


Special thanks to Patreon Supporters:
Alfred Wallace, Arjun Chakroborty, Chuck Lauer Vose, Dale Horne, Jasper Xin, Joar Wandborg, Kevin Beavers, Leah Howard, Lyvann Ferrusca, Michael Krugman, Noel Braganza, Ron Neal, Tige Thorman