Paul Andersen explains how populations eventually reach a carrying capacity in logistic growth. He begins with a brief discussion of population size ( N ), growth rate ( r ) and exponential growth. He then explains how density dependent limiting factors eventually decrease the growth rate until a population reaches a carrying capacity ( K ). A mathematical simulation of this process is included along with a brief discussion of r and K selected species.

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According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.
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David Tong is a professor of theoretical physics at Cambridge University, specialising in quantum field theory.

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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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Written by Derek Muller, Adam Becker and Jonny Hyman
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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.

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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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Farmers in Kenya are dealing with the challenges created by a changing climate by making the switch to ecological farming.

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Enjoy reasoning from Dr Aris Latham explaining why human beings should never smoke marijuana. He recommends people consume marijuana in alternate ways that are less harmful to the body:
Marijuana Tea
Marijuana Juice
Juicing Marijuana
Stop Smoking Marijuana

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