The End of the Long Bond Era

Math's Fundamental Flaw

Veritasium

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. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

Genetic Drift

Amoeba Sisters

Discover what happens when random events meet allele frequencies: genetic drift! This Amoeba Sisters video also discusses the bottleneck and founder effect as well as contrasts genetic drift with natural selection. Table of Contents: 00:00 Intro 1:33 Defining Genetic Drift 1:43 Comparing Genetic Drift to Natural Selection 2:05 Bottleneck Effect 2:52 Founder Effect 3:34 Genetic Drift is a Mechanism for Evolution 3:39 Population Sizes and Genetic Drift We cover the basics in biology concepts at the secondary level. If you are looking to discover more about biology and go into depth beyond these basics, our recommended reference is the FREE, peer reviewed, open source OpenStax biology textbook: https://openstax.org/details/books/biology ----------------------------- Biology Video Playlist: https://www.youtube.com/playlist?list=PLwL0Myd7Dk1F0iQPGrjehze3eDpco1eVz The Amoeba Sisters videos demystify science with humor and relevance. The videos center on Pinky's certification and experience in teaching biology at the high school level. Amoeba Sisters videos only cover concepts that Pinky is certified to teach, and they focus on her specialty: secondary life science. Learn more about our videos here: https://www.amoebasisters.com/our-videos ⭐ Our Linktree: https://linktr.ee/amoebasisters 🗂️ Resources that complement our videos! Visit https://docs.google.com/spreadsheets/d/1b3kmAzFEjWgoMKCrkeNCKFYunWk04IuLY93jI4OY0gY/edit?usp=sharing ❤️ Support Us? https://www.amoebasisters.com/support-us Our Resources: Biology Playlist: https://www.youtube.com/playlist?list=PLwL0Myd7Dk1F0iQPGrjehze3eDpco1eVz GIFs: https://www.amoebasisters.com/gifs.html Handouts: https://www.amoebasisters.com/handouts.html Comics: https://www.amoebasisters.com/parameciumparlorcomics Unlectured Series: https://www.amoebasisters.com/unlectured Connect with us! Website: http://www.AmoebaSisters.com Twitter: http://www.twitter.com/AmoebaSisters Facebook: http://www.facebook.com/AmoebaSisters Tumblr: http://www.amoebasisters.tumblr.com Pinterest: http://www.pinterest.com/AmoebaSister­s Instagram: https://www.instagram.com/amoebasistersofficial/ Visit our Redbubble store at https://www.amoebasisters.com/store TIPS FOR VIEWING EDU YOUTUBE VIDEOS: Want to learn tips for viewing edu YouTube videos including changing the speed, language, viewing the transcript, etc? https://www.amoebasisters.com/pinkys-ed-tech-favorites/10-youtube-tips-from-an-edu-youtuber-duo MUSIC: Music in this video is listed free to use/no attribution required from the YouTube audio library https://www.youtube.com/audiolibrary/music?feature=blog COMMUNITY: We take pride in our AWESOME community, and we welcome feedback and discussion. However, please remember that this is an education channel. See YouTube's community guidelines and how YouTube handles comments that are reported by the community. We also reserve the right to remove comments. TRANSLATIONS: Thank you so much to our translators! Português - Érika Hotz A. Stein Hindi Subtitles: Alisha Aggarwal While we don't allow dubbing of our videos, we do gladly accept subtitle translations from our community. Some translated subtitles on our videos were translated by the community using YouTube's community-contributed subtitle feature. After the feature was discontinued by YouTube, we have another option for submitting translated subtitles here: https://www.amoebasisters.com/pinkys-ed-tech-favorites/community-contributed-subtitles We want to thank our amazing community for the generosity of their time in continuing to create translated subtitles. If you have a concern about community contributed contributions, please contact us.