How Did Water Solve the 1800-Year-Old Talmudic Bankruptcy Problem?

Today we are solving an ancient bankruptcy puzzle from the Talmud using the principle of communicating vessels. A very nice visual way of making sense of an otherwise tricky problem. "Game theoretic analysis of a bankruptcy problem from the Talmud" by Robert J Aumann and Michael Maschler https://www.sciencedirect.com/science/article/pii/0022053185901024 " ‘Hydraulic’ rationing" by Marek M. Kaminski https://www.sciencedirect.com/science/article/pii/S0165489699000451 Also check out his book about his time as a political prisoner Games Prisoners Play: The Tragicomic Worlds of Polish Prison "Notes on the Bankruptcy Problem: an Application of Hydraulic Rationing" by Tamás Fleiner and Balázs Sziklai https://www.econstor.eu/bitstream/10419/108227/1/MTDP1123.pdf Robert Aumann with an anecdote of fair division from his childhood https://www.youtube.com/watch?v=rHDUMQfDkmQ Andrew Kepert contributed this nice geogebra app: https://www.geogebra.org/classic/bfkqsmbk I did not mention this but the three creditors are actually the three wives of the man who dies. The Talmud online: Hebrew and English https://www.sefaria.org/texts/Talmud Scanned pages in Hebrew http://e-daf.com Talmud references: The bankruptcy case: Ketubot 93a https://www.sefaria.org/Ketubot.93a.1?lang=bi (on e-daf Ketubot is spelled Kesuvos) Contested garment: Bava Metzia 2a https://www.sefaria.org/Bava_Metzia.2a.1?lang=bi The brother who dies childless case: Yevamot 38a https://www.sefaria.org/Yevamot.37b.1?lang=bi (on e-daf Yevamot is spelled Yevamos) A few of the images in this video are from the wiki page dedicated to the Talmud. There is something called the Water filling algorithm in information theory https://en.wikipedia.org/wiki/Water_filling_algorithm Music: "Here to fight" by Roman P. T-shirt: One of my own (I think) from a long time ago. Enjoy! Burkard