Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. 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 Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015

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Special thanks to Patreon supporters: 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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Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman
SFX & Music: Jonny Hyman
Camerapeople: Derek Muller, Raquel Nuno
Editors: Derek Muller
Producers: Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett

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If there’s a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes — this is important to know if you’re the manager of the Hilbert Hotel.

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References: Ewald, W., & Sieg, W. (2013). David Hilbert’s Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. — https://ve42.co/Ewald2013

Gamow, G. (1988). One, two, three–infinity: facts and speculations of science. Courier Corporation. — https://ve42.co/Gamow1947

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Special thanks to Patreon supporters: 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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Animation by JD Pounds and Jonny Hyman
Thumbnail by Ivy Tello
Music by Jonny Hyman and from Epidemic Sound and E’s Jammy Jams (Hotel Lavish – Radio Nights, Steps in Time – Golden Age Radio, What Now – Golden Age Radio, Book Bag – E’s Jammy Jams, Arabian Sand – E’s Jammy Jams, Firefly in a Fairytale – Gareth Coker)
Written By Derek Muller and Alex Kontorovich
Sound Design by Jonny Hyman

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This robot has applications to archaeology, space exploration, and search and rescue — with a simple elegant design inspired by a plant. Sign up to Morning Brew for free today: https://ve42.co/mb

Make your own Vine Robot! — https://www.vinerobots.org
Special thanks to A/Prof. Elliot Hawkes, Nicholas Naclerio, Margaret Coad, David Haggerty for appearing in this video and showing off your amazing robots. For more info on vine (and other types of) robots check out https://ve42.co/HawkesLab, and https://ve42.co/CHARM

Research at UCSB supported in part by the National Science Foundation grant 1944816, by an Early Career Faculty grant from NASA’s Space Technology Research Grants Program, and by the Packard Foundation.

B-roll footage of robots from the supplementary materials of (Hawkes et al., 2017) https://ve42.co/VineVideos, and from Stanford University https://ve42.co/StanfordVideo

Additional info on the intubation vine robot here: https://www.wardenchem.com/vine

References: Hawkes, E. W., Blumenschein, L. H., Greer, J. D., & Okamura, A. M. (2017). A soft robot that navigates its environment through growth. Science Robotics, 2(8). — https://ve42.co/Hawkes2017

N. D. Naclerio, A. Karsai, M. Murray-Cooper, Y. Ozkan-Aydin, E. Aydin, D. I. Goldman, E. W. Hawkes, Controlling subterranean forces enables a fast, steerable, burrowing soft robot. Sci. Robot. 6, eabe2922 (2021).
https://robotics.sciencemag.org/content/6/55/eabe2922

Coad, M. M., Blumenschein, L. H., Cutler, S., Zepeda, J. A. R., Naclerio, N. D., El-Hussieny, H., … & Okamura, A. M. (2019). Vine robots: Design, teleoperation, and deployment for navigation and exploration. IEEE Robotics & Automation Magazine, 27(3), 120-132. — https://ve42.co/Coad2019

Blumenschein, L. H., Coad, M. M., Haggerty, D. A., Okamura, A. M., & Hawkes, E. W. (2020). Design, modeling, control, and application of everting vine robots. Frontiers in Robotics and AI, 7. — https://ve42.co/Blumenschein2020

Haggerty, D. A., Naclerio, N. D., & Hawkes, E. W. (2019, November). Characterizing environmental interactions for soft growing robots. In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 3335-3342). IEEE. — https://ve42.co/Haggerty2019

Naclerio, N. D., Hubicki, C. M., Aydin, Y. O., Goldman, D. I., & Hawkes, E. W. (2018, October). Soft robotic burrowing device with tip-extension and granular fluidization. In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 5918-5923). IEEE. — https://ve42.co/Naclerio19

Special thanks to Patreon supporters: 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

Edited by Trenton Oliver
Animation by Ivy Tello
Filmed by Derek Muller
Thumbnail by Ignat Berbeci
Music by Jonny Hyman and from Epidemic Sound https://epidemicsound.com

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

For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Happy Pi Day!

References:
Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media — https://ve42.co/Arndt2001

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley — https://ve42.co/Dunham1990

Borwein, J. M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In From Alexandria, Through Baghdad (pp. 531-561). Springer, Berlin, Heidelberg — https://ve42.co/Borwein2012

Special thanks to Alex Kontorovich, Professor of Mathematics at Rutgers University, and Distinguished Visiting Professor for the Public Dissemination of Mathematics National Museum of Mathematics MoMath for being part of this Pi Day video.

Special thanks to Patreon supporters: 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 Alex Kontorovich
Animation by Ivy Tello
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music by Jonny Hyman and Petr Lebedev

Additional Music from https://epidemicsound.com “Particle Emission”, “Into the Forest”, “Stavselet”, “Face of the Earth”, “Firefly in a Fairytale”

Thumbnail by Gianmarco Malandra and Karri Denise

Robots of the future may be softer, squishier and bendier than robots today. This could make them ideal for space exploration. Check out http://kiwico.com/Veritasium50 for 50% off your first month of any subscription!

On Thursday February 18th, 2021 the NASA Perseverance Rover will land on Mars. It is a wonderful robot, made out of steel and wire — but will future robots look like Perseverance? There is an emerging field of research on “soft robots”, where the machines are flexible. These soft robots have many advantages over traditional robots — they’re safer, lighter, more flexible and can change their shape and size.

NASA is investigating the use of soft robots for space missions. For future visits to Enceladus or Europa, a lander could cut a hole in the ice and then insert a compliant robot through the hole. This robot could then grow and change shape on the other side.

References:
N. S. Usevitch, Z. M. Hammond, M. Schwager, A. M. Okamura, E. W. Hawkes, S. Follmer, An untethered isoperimetric soft robot. Sci. Robot. 4,
https://ve42.co/Hammond2020 — paper about the truss robot

https://ve42.co/Usevitch2020 — press release and video about the truss robot

Electronics-free pneumatic circuits for controlling soft-legged robots
Dylan Drotman1, Saurabh Jadhav, David Sharp, Christian Chan, Michael T. Tolley Sci. Robot. 6, eaay2627 (2021)
https://ve42.co/Drotman — paper about the turtle robot

Special thanks to Patreon supporters:
Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, Robert, fanime96, Marc Forand, Juan Benet, Ruslan Khroma, Robert Blum, Grace O’Maille KRON x Arc iOS, 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, Bryan Baker

Video supplied by Getty Images

Thanks to Zachary Hammond for showing me the soft truss robot
Filmed by Derek Muller
Edited and GFX by Trenton Oliver
Animation by Ivy Tello
Music by Jonny Hyman
Thumbnail by Ignat Berbeci, Dan Meyer

I got the chance to interview Bill Gates so I asked him: Will Covid-19 be the last pandemic? How does he deal with misinformation and conspiracy theories? And what is the next disaster? The Foundation Letter is here: https://ve42.co/BG21

Special thanks to Patreon supporters:
Ludovic Robillard, jim buckmaster, Robert, fanime96, Marc Forand, Juan Benet, Robert Blum, Grace O’Maille KRON x Arc iOS, 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

Thanks to Petr Lebedev for the thumbnail, early edits and Jonny Hyman for feedback

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

Physics students learn the speed of light, c, is the same for all inertial observers but no one has ever actually measured it in one direction. Thanks to Kiwico for sponsoring this video. For 50% off your first month of any crate, go to https://kiwico.com/veritasium50

Huge thanks to Destin from Smarter Every Day for always being open and willing to engage in new ideas. If you haven’t subscribed already, what are you waiting for: https://ve42.co/SED

For an overview of the one-way speed of light check out the wiki page: https://ve42.co/wiki1way

The script was written in consultation with subject matter experts:
Prof. Geraint Lewis, University of Sydney https://ve42.co/gfl
Prof. Emeritus Allen Janis, University of Pittsburgh
Prof. Clifford M. Will, University of Florida https://ve42.co/cmw
The stuff that’s correct is theirs. Any errors are mine.

References:
Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891-921.
(English) https://ve42.co/E1905 (German) https://ve42.co/G1905

Greaves, E. D., Rodríguez, A. M., & Ruiz-Camacho, J. (2009). A one-way speed of light experiment. American Journal of Physics, 77(10), 894-896. https://ve42.co/Greaves09

Response to Greaves et al. paper — https://arxiv.org/abs/0911.3616
Finkelstein, J. (2009). One-way speed of light?. arXiv, arXiv-0911.

The Philosophy of Space and Time – Reichenbach, H. (2012). Courier Corporation.

Anderson, R., Vetharaniam, I., & Stedman, G. E. (1998). Conventionality of synchronisation, gauge dependence and test theories of relativity. Physics reports, 295(3-4), 93-180. https://ve42.co/Anderson98

A review article about simultaneity — Janis, Allen, “Conventionality of Simultaneity”, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.) https://ve42.co/janis

Will, C. M. (1992). Clock synchronization and isotropy of the one-way speed of light. Physical Review D, 45(2), 403. https://ve42.co/Will92

Zhang, Y. Z. (1995). Test theories of special relativity. General Relativity and Gravitation, 27(5), 475-493. https://ve42.co/Zhang95

Mansouri, R., & Sexl, R. U. (1977). A test theory of special relativity: I. Simultaneity and clock synchronization. General relativity and Gravitation, 8(7), 497-513. https://ve42.co/Sexl

Research and writing by Derek Muller and Petr Lebedev
Animations by Ivy Tello
VFX, music, and space animations by Jonny Hyman
Filmed by Raquel Nuno

Special thanks for reviewing earlier drafts of this video to:
Dominic Walliman, Domain of Science: https://ve42.co/DoS
Henry Reich, Minutephysics: https://ve42.co/MP
My Patreon supporters

Additional music from https://epidemicsound.com “Observations 2”

As the universe expands, #expanding #space is said to “stretch” photons. But if it stretches photons, does it also stretch molecules, galaxies and you? A portion of this video was sponsored by Salesforce. Go to https://salesforce.com/veritasium to learn more.

Special thanks to Geraint Lewis – this video was based on his paper “On the relativity of redshifts”
https://arxiv.org/abs/1605.08634
Check out his YouTube channel: https://ve42.co/gfl and books: https://ve42.co/GFLbooks

References:
Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis
https://arxiv.org/abs/0707.0380

Editing and VFX by Trenton Oliver
Thumbnail by Ignat Berbeci

Music from https://epidemicsound.com

#SMB #smallbiz #startups #SalesforceEssentials