#Simone Borcherding

[justforbooks]

John Horton Conway: the world’s most charismatic mathematician known for the Game of Life whose inventions ranged from the surreal numbers to the Doomsday Rule

John Horton Conway, who has died aged 82 after contracting Covid-19, was one of the most prolific and charismatic British mathematicians of the 20th century. He was active in many branches of mathematics, including group theory, coding theory, knot theory, geometry, number theory and quadratic forms, as well as in recreational mathematics.

An iconoclastic academic, he held court for over half a century in mathematics departments worldwide, notably at Cambridge and Princeton universities. Although he thought it one of his lesser accomplishments, John is best known for his late 1960s invention of the Game of Life. It is an “organic life” simulation carried out on a square grid of cells, each of which is alive or dead according to how many living neighbours it has. Despite the simplicity of John’s defining rules, it turned out that anything that can be algorithmically computed can be done so within the zero-player Game of Life. While John’s approach was done with pen and paper, the game was a catalyst for computer programmers in the 70s and is now viewed as a watershed development in the field of cellular automata.

John, together with Elwyn Berlekamp and Richard Guy, is credited with co-founding the field of combinatorial game theory. That is the mathematical analysis of games such as noughts and crosses, draughts, chess and Go, as well as a wealth of original games that John and assorted collaborators devised over the decades, such as Phutball (short for Philosopher’s Football), a two-person board game played on a grid using one white stone (the ball) and numerous black stones (representing men), Hackenbush, and Sprouts. This led to a joint book, Winning Ways for Your Mathematical Plays (1982).

In the early 70s, John came up with the definitive refinement of what is now known as the Monster Group. Groups arise from the study of symmetry of objects in mathematics and in nature. For instance, the group of symmetries of an equilateral triangle has six things in it: three rotations and three flips. There are standard “atomic building blocks” of all finite groups of symmetries, which are well understood, and 26 strange additional ones, called sporadic groups, of which the Monster Group, predicted independently by two mathematicians, Bernd Fischer and Bob Griess, is the largest. In 1973 Griess finally constructed the Monster itself, and John then came up with a simpler construction. This group has 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 symmetries in it. That is vast beyond comprehension, and about 1,000 times the current estimate for the number of atoms in the Earth.

A few years later, John went further. Along with his former PhD student Simon Norton, he came up with the Monstrous Moonshine conjecture, connecting group theory with the seemingly unrelated study of modular forms. Another of John’s former students, Richard Borcherds, got a Fields medal (one of the two highest honours in mathematics) in 1998 for his successful proof of the conjecture.

John often said that his proudest invention was the surreal numbers, a unifying number system that he conceived in the late 60s, which encompassed ordinary numbers as well as those that are infinitely small or large. He was also particularly pleased with the free will theorem in quantum mechanics from early in the current century, which he formulated with Simon Kochen. In his own words, it says that “if experimenters have free will, then so do elementary particles”.

John was a prodigious mental calculator too. He delighted in being challenged to shout out the day of the week for any randomly chosen date in history, which he could do using his own so-called Doomsday Rule; his methods were adapted and streamlined from Lewis Carroll’s 1887 algorithm. He attributed his success in so many different arenas to his habit of always working simultaneously on several unrelated problems: he might be stuck on most of them but suddenly have an idea leading to a breakthrough on another one.

While many of John’s creations were the products of his own fertile mind, he thrived on collaboration. His best known book, the Atlas of Finite Groups (1985), was co-authored by Norton, Robert Curtis, Richard Parker and Robert Wilson. Around 1976, he helped Roger Penrose refine the analysis of what we now know as Penrose tiles, and he came up with the catchy terms kite and dart for the two basic shapes from which they are made.

John left his mark on the groundbreaking book series The Art of Computer Programming. The computer scientist and author of that work, Donald Knuth, who also wrote a book about Conway’s surreal numbers, said: “Although John was a pure mathematician, he covered so many bases that I’ve cited him more than 25 times (so far) for different contributions to The Art of Computer Programming.”

The American writer Martin Gardner helped to popularise much of John’s output in his Scientific American columns, going back to the late 50s. A decade ago, John worked with the editor Peter Renz on updated versions of some of Gardner’s books of collected columns, again contributing fresh results of significance, including a new proof of Morley’s theorem about triangles. “Anyone who has sat with John has been touched, changed for ever,” said Renz. “He had a way of refining things to their purest forms.”

Born in Liverpool, John was the son of Agnes (nee Boyce) and Cyril Horton Conway. His father was a chemistry lab technician at the Liverpool Institute high school for boys, which John, and later Paul McCartney and George Harrison of the Beatles, attended. He then went to Gonville and Caius College, Cambridge, gaining his BA in 1959. A PhD (1964) followed, under Harold Davenport.

He became an assistant lecturer at Cambridge, later rising to be professor of mathematics. In 1987 he took up the position of John von Neumann professor of applied and computational mathematics at Princeton University, New Jersey.

While he was reportedly shy as a young man, over time John developed a disarming charm and an extrovert Pied Piper persona. He earned a reputation for delivering one brilliant lecture after another, and his classes at both Cambridge and Princeton were invariably oversubscribed. His infectious enthusiasm turned on generations of young people to the joy of research mathematics.

His biographer, Siobhan Roberts, dubbed him “the world’s most lovable egomaniac”, adding, “He is Archimedes, Mick Jagger, Salvador Dalí and Richard Feynman, all rolled into one.”

John was elected FRS, a fellow of the Royal Society, in 1981 – following which he told people he was now officially a Filthy Rotten Swine – and was the first recipient of the London Mathematical Society’s Pólya prize in 1987. He was awarded the Nemmers prize in mathematics (1998), the Leroy P Steele prize for mathematical exposition (2000), and the Joseph Priestley award (2001-02), and received honorary doctorates from the University of Liverpool (2001) and Jacobs University, Bremen (2015). He retired in 2013, when he became emeritus professor at Princeton.

In a 2014 video for the online channel Numberphile, John discussed getting over his feelings of inadequacy in his 20s, facing mortality in his 70s, and his lingering mathematical wish to really understand why the extraordinarily large Monster Group exists.

His first two marriages, to Eileen Howe and Larissa Queen, ended in divorce. He is survived by his third wife, Diana (nee Cutsogeorge), whom he married in 2001, and their son, Gareth; four daughters, Susie, Rosie, Ellie and Annie, from his first marriage; two sons, Alex and Oliver, from his second marriage; three grandchildren; and six great-grandchildren.

• John Horton Conway, mathematician, born 26 December 1937; died 11 April 2020

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[bigyack-com]

John Horton Conway, a ‘Magical Genius’ in Math, Dies at 82

Dr. Conway’s mother, a great reader, especially of Dickens, had worked from age 11. Family lore has it that she boasted about finding her son at age of 4 reciting the powers of two. At 18, in 1956, John left home for the University of Cambridge, where he earned his Ph.D. His adviser, Harold Davenport, a number theorist, once said that when he would give Dr. Conway a problem to solve, “he would return with a very good solution to another problem.”As a student, Dr. Conway cultivated his acknowledged lifelong preference for being lazy, playing games and doing no work. He could be easily distracted by what he called “nerdish delights.” He once went on a flexagon binge, courtesy of Mr. Gardner, who described flexagons as “polygons, folded from straight or crooked strips of paper, which have the fascinating property of changing their faces when they are flexed.”He built a water-powered computer, which he called Winnie (Water Initiated Nonchalantly Numerical Integrating Engine). He read and annotated H.S.M. Coxeter’s edition of W.W. Rouse Ball’s classic work, “Mathematical Recreations and Essays” and wrote Coxeter a lengthy letter that started a lifelong friendship between these two classical geometers.Hired at Cambridge as an assistant lecturer, Dr. Conway gained a reputation for his high jinks (not to mention his disheveled appearance). Lecturing on symmetry and the Platonic solids, he might bring in a turnip as a prop, carving it one slice at a time into, say, an icosahedron, with its 20 triangular faces, eating the scraps as he went. “He was by far the most charismatic lecturer in the faculty,” his Cambridge colleague Peter Swinnerton-Dyer once said.Dr. Conway invented a profusion of games — like Phutball (short for Philosopher’s Football, which is a little like checkers on a Go board) and collected them in the book “Winning Ways for Your Mathematical Plays,” in collaboration with Elywn Berlekamp and Richard Guy.All the gaming was supported by a loyal following of graduate students, among them Simon Norton, with whom Dr. Conway published the Monstrous Moonshine conjecture, investigating an elusive symmetry group that lives in 196,883 dimensions. (His Ph.D. student Richard Borcherds received the prestigious Fields Medal in 1998 for his proof of the conjecture.) Read the full article

[jeremiahingham]

Best of YouTube: Brown; color is weird | You can support this channel on Patreon! Link below This video discusses the color brown. Seriously. That Aging Wheels playlist: https://www.youtube.com/playlist?list=PLmBDJoIaNRGiK2BgCwz2ALDnNanKBSOgO And, of course, the Weird World in RGB for those of you who I couldn’t manage to summon a card for: https://www.youtube.com/watch?v=uYbdx4I7STg How about some other, more different links? Technology Connextras (the second channel that stuff goes on sometimes): https://www.youtube.com/channel/UClRwC5Vc8HrB6vGx6Ti-lhA Technology Connections on Twitter: https://twitter.com/TechConnectify The TC Subreddit https://ift.tt/2Sk14PE You can support this channel on Patreon! Thanks to contributions from viewers like you, Technology Connections can continue being as weird and unpredictable as it is. If you’d like to join the cool people who bring these totally rad videos to you (I’m hip and with it!), you can find out how at the link below. Thank you for your consideration! https://ift.tt/2CskvOK And thank you to the following patrons! Jorge Caballero, Kyle Messner, Mainstream, Matthew Schwartz, gs, ashka, Mr. Yan, Matthias Feist, RedR0ze, adan c, Thomas Fuchs, Alan Holland, Philipp Doppelhofer, Dan Boulden, Simon Hookham, Phiroze Dalal, Benn Bocinski, Devin Rosenthal, Avalon Hamakei, Ray Hardman, G Cowell, Dan Coulson, Mike Berman, Kevin Hamilton, Jack Manning, Chase Tarson, Christopher D'Arpa, Marshall Kurtz, Hurf Durr, shaun morris, David Bell, Miguel Gonzalez, Ed Giardina, Bryce Ontiveros, Kenneth A Cusson, Johnathan Reale, Charles Corbin, Simon Arrow, Brett Walton, Martin Schröder, lakewalk3r, Hayden McAfee, Dan Maku, Mark Injerd, Paul Demers, Stephen P Wilshaw, Vladi Ivanov, Michael Sandler, Jacob Harrington, Gustav Toth, Pete Iacono, Perl the Raven, Clay, Jason Letchworth, Benjamin Deming, Thorbjörn Meyer, Eben, M1GEO, Alan Shieh, Christopher Whyte, Michael Kaegler, Chrno, Taylor Smith, Colin Macdonald, Shlomi Borovitz, Krispin Miller, Jan Borcherding, Matthew Castellana, Finn, Sean Anderson, David, Duncan Mulholland, Chaz Serir, Jason Downs, Joe Snaza, Lincoln Cole, Deviant Ollam, Dillan Weems, Eldrin_22, Mitch SuperKnot, Andrew Bogard, Cameron McCormick, Craig Guy, Brandon Ryan, Keith Hemenway, Travis Geiselbrecht, Andrew Eslick, Pedro Brito, Ryan Milke, AARGH!, Marko, splateagle, Ada Cohen, MaikSan, Timothy Miller, Jim Renney, Steve Lafferty, Joseph Mayfield, Noah Dobson, William Astle, Zufalligeule, Joe King, John Plasket, Don Eitner, Adam Belebczuk, Matt, Karol Koziol, Matt Lawrence, Matthew Krajnak, James Fuhrman, Erik Welander, Mark Majewicz, Logan Shelts, Ryan Dean, Arcanox, Matt Beard, Chad L, Sebastian Mellor, Will Palmer, Steets, Matt, Joel Jauregui, James Alexander, Joon Shin, Joseph Weiss, Ben Slater, Calvin Walton, Jesse Crawford, Justin Tokke, Ryan Morash, Matt Towers, digit777, Tee Jay, Delliardo, Eidorian, MsWhit, Jeremy Price, Lydia Saunders, Henry Fitzgerald, Nishith Thakkar, Samuel Colburn, Raphael Wichary, Pykrete_O.Sages, HailSaturn, Evan Langlais, Andyface, Hugo Melchers, ShirleyNeko, R Fisher, Brian Stilson, ColdRamen77, Cameron Lane, Sam Atkinson, PanicOpticon, Don Riesbeck, Craig Engbrecht, Marco Menendez, Nils Schneider, Rob Tapp, Sebastian Muñoz, Andrew Bedia, John Sanchez, Kenneth Dahle, Patrick Wolfensberger, datajerk, Jimmie Rodgers, Dukey, Biff McKeldin, Sam Farrelly, AFylH9X9ZZGKbxF, Martin Porcheron, Justin Baros, Stephen Turner, kara mccabe, Denzil Wilson, Thomas Daede, Jiri van Bergen, Craig Matthews, Travis Estell, David (chipgw), Patrick McCart, H.D. Gregg, Ariel Valenzuela, Cape, Julian Kaagman, Mauri Virtanen, PseudsPie, Mark Wingerd, Antonio Juarez, Tobi, Wesley Reynolds, Tyler King, Splendid Gecko, Anicast, Steven Salerno, Kevin Tangney, Nicolae Berbece, Andrew Sebastian, Daniel A.A. Pelsmaeker, Joar Wandborg, Walter Huf, Chester Plemany, Keith, Allen Singer, Chris Gardner, Skylar Strickland, Nick Daniels, Robert Loewen, Michael Dragone, Diego Egido, Malcolm Slater, Devin Wright, Mark Provan, Zarko Kuvalja, Ivar Hosteng, Kevin Ragsdale, Karsten Müller-Bier, Ron Painter, WALLE1Doctor1Who, Joe Turner, Shaun Faloon, Andrew Collings, Robin Monks, EndoliteMatrix, Ragnar Jensen, Neale Genereux, Alexander Swaim, Aaron Hile, Austin Nunn, WishMakers, Kevin Chevalier, Declan M Martin, Michael Butkiewicz, Andrew Crawley, Eric Laska, OG-Biebs, Nathaniel Thompson, Paul Giroux, Daniel Ziegler, Chris Hodapp, Wearwolf, Greg Morin, Scott Hutcheson, Ted Kern, Ellen Murray, Paul John Sandoval, Tony Cook, Ben Cook-Feltz, Jim Burgan, dim85, Sam Lentz, AkeBjorn, Lane Robert, MPc, Daniel Prows, Christopher Lucas, Marcin Żyła, Scott McCarthy, Michael Thomas, Zach Flauaus, Vincent Larson, Bryan Boettcher, paustin, Ian Baltutis, Lucy, Tytyty, MetricConversion, AwkwardHuggs, Lex Sketch, john lombard

[photographynewpress]

September 2015. A new South African online magazine was launched on September 1st. Frank Ellis of Hotel Magazine wants ‘....to re-kindle some of the awe, some of the tactile joy of print, in digital format’. For their launch we shot a photo-essay on the inhabitants of Oude Molen Village in Cape Town.

The full article can be viewed here http://hotelmag.co.za/articles/life/oude_molen.html

[haydenphippsphotography]

MEMENTOS FROM A CITY VILLAGE / Hotel Magazine.

In political speak Oude Molen is a socio-economic development. In layman’s terms it’s known as a hybrid eco village. What is often forgotten is that Oude Molen is a place that people call home.

All the buildings form part of a defunct psychiatric hospital that was once for non-white patients and cared for prior to our country's liberation in 1994. After that the patients got relocated to a better facility a little way off, and so this part of the medical complex known as Valkenberg became a white elephant, deteriorating to rubble and squalor at the hands of looters and vandalism.

In 1997 a man called Gary Glass along with a man named Hudson McComb took on this public space, mobilising local communities around the property to convert and restore this forgotten, derelict, vandalised and somewhat spooky place into a thriving, public social enterprise.

The full article can be viewed here http://hotelmag.co.za/articles/life/oude_molen.html