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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Written by Derek Muller, Adam Becker and Jonny Hyman
Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jonny Hyman
Math City Animation by Another Angle 3D Visuals (www.anotherangle.ee)
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music and SFX by Jonny Hyman Additional Music from Epidemic Sound
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett
Associate Producers: Petr Lebedev and Emily Zhang

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For many people in the world, they get their water supplied to them through pipes in their houses or apartment. However, for the rest of the world not hooked up to centralized water, they get their water through either private or public wells. ‘

Wells are some of the most essential components to developing a sustainable society. They provide a clean and reliable supply of water for drinking, bathing, and irrigation, even in locations where water on the surface is scarce.

Wells are essentially just holes in the ground filled with water, but they have more complexities than meets the eye. Let’s take a closer look at how wells work.

All images and videos courtesy of the creative commons or used in accordance with fair use laws. For questions or concerns, please use the contact section on our channel

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Brittle Rille - Reunited by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
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Following the Spanish-American War, the United States foreign policy, under the influence of the Monroe Doctrine, intervened in several countries in Central America and the Caribbean. The United States Marine Corps was usually the military arm of these involvements as was the case in Cuba, Haiti and the Dominican Republic.

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» SOURCES
Bauduy, Jennifer, “The 1915 U.S. Invasion of Haiti: Examining a Treaty of Occupation” Social Education 79 (2015)

Castor, Suzy & Garafola, Lynn, “The American Occupation of Haiti (1915-34) and the Dominican Republic (1916-24)” The Massachusetts Review, Vol. 15, No. 1/2, Caliban (Winter - Spring, 1974)

Gilderhus, Mark T, The Second Century: U.S.-Latin American Relations Since 1889, (Wilmington, Delaware : Scholarly Resources Inc, 2000)

Johnson, Jeannie L. The Marines, Counterinsurgency, and Strategic Culture: Lessons Learned and Lost in America's Wars, (Washington D.C. : Georgetown University Press, 2018)

Langley, Lester D, The Banana Wars: United States Intervention in the Caribbean, 1898-1934, (Wilmington, Delaware : Scholarly Resources Inc, 2002)

Langley, Lester D, The United States and the Caribbean, 1900-1970, (Athens, Georgia : University of Georgia Press, 1980)

Perez, Louis A., Jr. Intervention, Revolution, and Politics in Cuba, 1913-1921, (Pittsburgh, Pennsylvania : University of Pittsburgh Press, 2009)

Posner, Walter H. “American Marines in Haiti, 1915-1922” The Americas, Vol. 20, No. 3 (Jan., 1964)

Schreadley, R. L. Intervention! : the Americans in Haiti, 1915-1934, (Charleston, South Carolina : Evening Post Books, 2017)

Yates, Lawrence A, “The US Military’s Experience in Stability Operations, 1789-2005”, Global War on Terrorism Occasional Paper 15, Title 1, Series 2, (2006)


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Syntropic farming is a new and ancient permaculture practice that can be implemented in any region, in any climate, in limitless ways – even in your own back yard. For over a decade the Lotz-Keegan family have been implementing permaculture practices to regenerate a degraded hillside into an abundant food forest of native and exotic trees that feed their family, their community, the wildlife, the soil, and their souls.

Combining the practices of syntropic agroforestry with the principles of permaculture and their own deeply thoughtful approach to land regeneration, food growing, and lifestyle, this family is partnering with nature to create a humming diversity on the land and a positive story about the role of humans in an eco-system.

We came away from our shoot with so much invaluable information about the why and how of syntropic farming as it’s practised at PermaDynamics. For this reason we’ve made the full interview with Klaus Lotz available on our website, and all 10 full-length interviews, some of which we couldn’t include in the film, available on our Patreon page. Also if you’re keen to dig deeper into this style of growing food and regenerating soil, check out PermaDynamics' own videos available on their Patreon page.

Get access to all 10 full-length interviews: https://happenfilms.com/patreon
Check out PermaDynamics on Patreon: https://patreon.com/PermaDynamicsNZ
The full interview with Klaus Lotz: https://happenfilms.com/film/k....laus-lotz-syntropic-


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** Find out more about Happen Films **
If you’re interested in supporting us to make more films, find us on Patreon: https://happenfilms.com/patreon

For more info about Happen Films, check out our website: https://happenfilms.com. We make short films and feature films, all with a permaculture, resilience, sustainability focus. Don’t forget to subscribe here on YouTube!

Find us on social media
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** Film credits **
Directed and written by Jordan Osmond & Antoinette Wilson
Produced by Antoinette Wilson
Cinematography and editing by Jordan Osmond
Story feedback and suggestions from Nick Tucker
Additional drone footage by Byron Birss (https://instagram.com/byron.in.new.zealand)
1990 photo by Malcolm Rands

** Thanks! **
To our wonderful supporters on Patreon, who helped make this film happen:
Kimberly Levesque, Matthew Zimmer, Rahul Banerjee, Jonathan Wise, Georjette Mercer, Mary Conlan, Kate Hall, V.J. Raghavan, Pierre Blom, Cicely Jette Stewart, Brett Davidson, Tony Schaufelberger, Namaste Foundation, Sankar Madhavan, Sue Campbell, Melissa Tripodi, Filip Zeman, Greg and Rachel Hart, Brian Newton, Susan Hunsberger, Kirti Patel, Kelly Milikins, Nathan Kitchen, Geoffrey Torkington, Alex Muir, Tiitus Laine, Rex and Jo, Jess O’Shea, Moana Kiff, William B. Everett, Ron Hastie, David, Lauren, Carolyn Gillum.

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Chapters
00:00 - Intro to Syntropic Farming
2:36 - 17-Year-Old Food Forest
7:48 - Market Garden and Orchard
12:20 - Native and Exotic Plants
14:45 - Annuals in the Food Forest
17:29 - Tropical Hothouse
19:17 - 3-Month-Old Food Forest

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Would you ditch the beauty industry for vegetable farming? Well that is exactly what one lady in Kiambu County did and has never looked back. Hope Wanjiru is one of the young farmers growing crops under the hydroponics system and together with her group, they have managed to secure contracts with large firms supplying them with lettuce and tomatoes every season. Denis Otieno has more on this week’s smart farm.






Citizen TV is Kenya's leading television station commanding an audience reach of over 60% and in its over 12 years of existence as a pioneer brand for the Royal Media Services (RMS), it has set footprints across the country leaving no region uncovered.

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https://www.obama.org/updates/....nigerian-leaders-end



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https://allafrica.com/stories/201703200933.html

https://www.voanews.com/usa/ob....ama-says-protectioni