There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in. 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. ▀▀▀ Huge thanks to Prof. Colin Adams for his excellent help guiding us through the world of knots. Many thanks to Prof. Doug Smith, Dorian Raymer, Prof. David Leigh, and Prof. Dorothy Buck for helping us understand applications of knot theory. Many thanks to Prof. Dan Silver & Prof. Jim Hoste for speaking with us about the history and tabulation of knots. If you want to learn more about knots and play with them yourself, check out: The amazing KnotPlot tool — https://knotplot.com/. Thanks to Rob Scharein for providing technical help as well! A table of knots and all their invariants — https://knotinfo.math.indiana.edu/ The Knot Atlas for general info on knots — http://katlas.org/wiki/Main_Page ▀▀▀ Knot Theory Video References – https://ve42.co/KnotTheoryRefs Images & Video: Alexander Cutting the Gordian Knot by Donato Creti via Fine Art America - https://ve42.co/GordianCut Indus Valley tablet via Quora - https://ve42.co/IndusValley Pages from the Book of Kells via National Trust of Scotland - https://ve42.co/BookOfKells Medieval Celtic designs from @thebookofkellsofficial via Instagram - https://ve42.co/KellsInsta Chinese knotwork by YWang9174 via Wikimedia Commons - https://ve42.co/Panchang Quipu cords by Pi3.124 via Wikimedia Commons - https://ve42.co/Quipu Borromeo heraldry via Terre Borromeo - https://ve42.co/Borromeo Birman/Jones letter via Celebratio Mathematica - https://ve42.co/JonesBirman Molecular trefoil knot by M stone via Wikimedia Commons - https://ve42.co/TrefoilMolecule X-ray structure of trefoil knot by Ll0103 via Wikimedia Commons - https://ve42.co/XrayTrefoil Bacteria animation from Your Body's Molecular Machines by Drew Berry via the Walter and Eliza Hall Institute of Medical Research - http://wehi.tv Topoisomerase and knots from Orlandini et al. Synergy of topoisomerase. PNAS, vol. 116, no. 17, 2019, pp. 8149–8154. – https://ve42.co/Orlandini2019 KnotProt 2.0: A database of proteins with knots and slipknots - https://ve42.co/Knotprot ▀▀▀ Special thanks to our Patreon supporters: Anton Ragin, Balkrishna Heroor, 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 ▀▀▀ Directed by Emily Zhang Written by Emily Zhang and Derek Muller Edited by Trenton Oliver Animated by Fabio Albertelli, Ivy Tello, Jakub Misiek, and Mike Radjabov Filmed by Derek Muller, Raquel Nuno, and Emily Zhang Produced by Emily Zhang and Derek Muller Thumbnail by Ignat Berbeci and Mike Radjabov Additional video/photos supplied by Getty Images and Pond5 Music from Epidemic Sound ... https://www.youtube.com/watch?v=8DBhTXM_Br4

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: Bruce Sherwood, Ruth Chabay, Aaron Titus, and Steve Spicklemore https://matterandinteractions.org VPython simulation: http://tinyurl.com/SurfaceCharge Richard Abbott from Caltech Electrical Engineering YouTubers: Electroboom: https://www.youtube.com/c/Electroboom Alpha Phoenix: https://www.youtube.com/c/AlphaPhoenixChannel eevblog: https://www.youtube.com/c/EevblogDave Ben Watson: https://www.youtube.com/channel/UCgZUVIEtBnnBpFWJuxl_E5g Big Clive: https://www.youtube.com/c/Bigclive Z Y: https://www.youtube.com/user/ZongyiYang Further analysis of the large circuit is available here: https://ve42.co/bigcircuit Special thanks to Dr Geraint Lewis for bringing up this question in the first place and discussing it with us. Check out his and Dr Chris Ferrie’s new book here: https://ve42.co/Universe2021 ▀▀▀ References: A great video about the Poynting vector by the Science Asylum: https://youtu.be/C7tQJ42nGno Sefton, I. M. (2002). Understanding electricity and circuits: What the text books don’t tell you. In Science Teachers’ Workshop. -- https://ve42.co/Sefton Feynman, R. P., Leighton, R. B., & Sands, M. (1965). The feynman lectures on physics; vol. Ii, chapter 27. American Journal of Physics, 33(9), 750-752. -- https://ve42.co/Feynman27 Hunt, B. J. (2005). The Maxwellians. Cornell University Press. Müller, R. (2012). A semiquantitative treatment of surface charges in DC circuits. American Journal of Physics, 80(9), 782-788. -- https://ve42.co/Muller2012 Galili, I., & Goihbarg, E. (2005). Energy transfer in electrical circuits: A qualitative account. American journal of physics, 73(2), 141-144. -- https://ve42.co/Galili2004 Deno, D. W. (1976). Transmission line fields. IEEE Transactions on Power Apparatus and Systems, 95(5), 1600-1611. -- https://ve42.co/Deno76 ▀▀▀ Special thanks to Patreon supporters: Inconcision, Kelly Snook, TTST, Ross McCawley, Balkrishna Heroor, Chris LaClair, Avi Yashchin, John H. Austin, Jr., OnlineBookClub.org, Dmitry Kuzmichev, Matthew Gonzalez, Eric Sexton, john kiehl, Anton Ragin, Diffbot, Micah Mangione, MJP, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Michael Schneider, jim buckmaster, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Stephen Wilcox, Marinus Kuivenhoven, Clayton Greenwell, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀ Written by Derek Muller Edited by Derek Muller Filmed by Trenton Oliver and Petr Lebedev Animation by Mike Radjabov and Ivy Tello Additional video/photos supplied by ... https://www.youtube.com/watch?v=oI_X2cMHNe0

Adhesives based on gecko skin can hold huge weights – without sticking to anything. Head to https://brilliant.org/Veritasium to start your free trial. The first 200 of you will get 20% off Brilliant’s annual premium subscription. ▀▀▀ Thanks to Dr. Mark Cutkosky, Tony Chen, Amar Hajj-Ahmad, and the rest of the Biomimetics and Dexterous Manipulation Lab at Stanford University for showing us the power of gecko adhesives. ▀▀▀ References: Russell, A. P., Stark, A. Y., & Higham, T. E. (2019). The integrative biology of gecko adhesion: historical review, current understanding, and grand challenges. Integrative and comparative biology, 59(1), 101-116. – https://ve42.co/Russell2019 Hajj-Ahmad, A., Suresh, S. A., and Cutkosky, M. R. (June 6, 2021). "Cutting to the Point: Directly Machined Metal Molds for Directional Gecko-Inspired Adhesives." ASME. J. Micro Nano-Manuf. doi: https://doi-org.stanford.idm.oclc.org/10.1115/1.4051406 Kerst, Capella F., "Gecko inspired adhesives : permanent practical manufacturing, new materials, and applications," PhD Thesis, Stanford Universisty, December 2020. Suresh, S.A. "Engineering Gecko-Inspired Adhesives." Ph.D. thesis, Stanford University, 2020. [Online]. Available: https://purl.stanford.edu/cp134gr3166. Suresh, S.A., Kerst, C.F., Cutkosky, M.R., Hawkes, E.W. "Spatially variant microstructured adhesive with one-way friction." Journal of the Royal Society Interface. 2019. doi: 10.1098/rsif.2018.0705 Glick, P., Suresh, S.A., Ruffatto III, D., Cutkosky, M.R., Tolley, M.T., and Parness, A. "A soft robotic gripper with gecko-inspired adhesive." Robotics and Automation Letters. 2018. doi:10.1109/LRA.2018.2792688. Christensen, D.L., Hawkes, E.W., Suresh, S.A., Ladenheim, K. and Cutkosky, M.R., "µTugs: Enabling Microrobots to Deliver Macro Forces with Controllable Adhesives," IEEE/ICRA 2015 (preprint). Hawkes, E. W., "Applying Dry Adhesives to the Real World," Ph.D. thesis, Stanford University, 2015. ▀▀▀ Special thanks to our Patreon supporters: Meg Noah, Bernard McGee, James Sanger, Elliot Miller, Brian Busbee, Jerome Barakos M.D., Amadeo Bee, TTST, Balkrishna Heroor, Chris LaClair, John H. Austin Jr., Eric Sexton, John Kiehl, Anton Ragin, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Mike Schneider, John Bauer, Jim Buckmaster, Juan Benet, Sunil Nagaraj, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi ▀▀▀ Written by Derek Muller & Petr Lebedev Edited by Trenton Oliver Animation by Ivy Tello Filmed by Derek Muller, Raquel Nuno & Albert Leung Additional video/photos supplied by Pond5 & Getty Images Music from Epidemic Sound Exec. Produced by Derek Muller, Petr Lebedev, and Emily Zhang ... https://www.youtube.com/watch?v=vS0TuIPoeBs

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/ ▀▀▀ 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 ... https://www.youtube.com/watch?v=AaZ_RSt0KP8