Saturday October 17 to Friday October 23, 2020
– 21 Free Online Events for All Curious Minds –
Presentations at noon, 4:00 pm, and 8:00 pm EDT
Thank you to the hundreds of people who participated remotely.
We plan is to share the presentations on the G4G YouTube channel after post-production. Stay tuned.
Each October, people gather around the world, in small and large groups, for Celebration of Mind events. These celebrate the legacy of Martin Gardner (1914-2010), a prolific non-fiction writer who turned on several generations to the joys of mathematics and rational thinking. His interests were very broad, and included the works of Lewis Carroll, close-up magic, and philosophy.
This year is the 10th anniversary of Celebration of Mind! Gathering 4 Gardner is hosting a virtual Celebration of Mind and we are inviting everyone who loves Alice in Wonderland, brainteasers, puzzles, the math of fiber arts, paper fun, skepticism, and magic of all types to join us. This week-long event includes videos, live presentations and Q&A sessions for the curious of all ages.
Anyone who wishes to help us in our efforts to expand the G4G community is welcome to nominate themselves or others at this link.
Upcoming Presentations Include:
Steve Butler honoring the memory of Ron Graham with a juggling video, speedcuber Sydney Weaver explaining some of the math behind twisty puzzles, George Hart demonstrating how to make the “Taj Mahal” of little libraries (based on a polar zonohedron), Delicia Kamins speaking about fractal geometries, and Scott Kim demonstrating musical illusions. Carolyn Yackel will explain how shibori dyeing is informed by John Conway’s take on orbifolds, and magician Joe M. Turner will dazzle with dice.
There is a session on the documentary film Eddy’s World, which tells the story of Eddy Goldfarb, a 98-year-old working toy inventor, best known for the iconic Yakity Yak Teeth and other classic toys. This will include a live interview with Eddy himself.
Jim Gardner will present on what it was like growing up with Martin as his dad. Jeanette Shakalli will present on toothpick puzzles (Martin loved those!). On the last day, Bud Brown will recall some fun mathematics associated with Elwyn Berlekamp, John Conway and Richard Guy. The week will include something for everyone and we hope you will join us!
(All times are EDT – click a date to see the presentation descriptions)
Noon | “How Orbifolds Inform Shibori Dyeing” (15 mins) by Carolyn Yackel
Shibori indigo dyeing is a recent trend in home crafting that takes advantage of a traditional Japanese art form. The itajime variant involves carefully folding the material to be dyed and then applying clamped blocks to act as a dye resist before submersing the material in the dye. This talk settles the question of which wallpaper pattern types can be attained through itajime shibori by looking at the corresponding orbifolds. Explanations will be given so that viewers should not need to know the definitions of shibori, wallpaper pattern, or orbifold in order to understand the gist of the talk.
Carolyn Yackel is a professor of mathematics and a mathematical fiber artist at Mercer University. She delights in all sorts of patterns that arise both visually and through recreational mathematics. She enthusiastically explains mathematics to herself and to others. Her favorite methods for doing so arise from the interplay of abstract algebra and fiber arts. Her edited volumes include Making Mathematics with Needlework (2007), Crafting by Concepts (2011), and Figuring Fibers (2018). Much of Carolyn’s work is devoted to involving others in mathematical endeavors through teaching, editing, co-organizing the Knitting Circle at the Joint Mathematics Meetings, organizing conference sessions, and leading committees of the MAA, such as the Committee for the Teaching of Undergraduate Mathematics. She was the program chair and main papers editor for the Bridges Conference in 2020.
4:00 pm | “Toothpick Puzzles” (30 mins) by Jeanette Shakalli
Martin Gardner loved all kinds of mathematical puzzles. In this interactive presentation that is accessible for kids and adults alike, we will explore some fun puzzles that involve toothpicks. Come join us to discover the beauty and richness of mathematics while we immerse ourselves in the joy of play.
Dr. Shakalli is a Panamanian mathematician who loves to share her passion for mathematics with the general public. She is the Executive Director of the Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT), a private non-profit Foundation whose mission is to promote the study of mathematics in the Republic of Panama. She is the International Mathematical Union (IMU)’s Committee for Women in Mathematics (CWM) Ambassador for Panama. Dr. Shakalli has organized more than 50 math outreach events in the Republic of Panama, including Math Carnivals, MathsJams, Julia Robinson Mathematics Festivals, Celebrations of Mind and Origami Workshops, as well as more than 100 virtual events for FUNDAPROMAT on recreational mathematics.
8:00 pm | “Math and Juggling” (35 mins) by Steve Butler
Juggling can be described by the series of throws that you make. This is known as siteswap. We discuss a “string theory” approach to showing that the number of balls involved in a pattern is the average of these throws, and then look at how to take a collection of throws whose average is a whole number and form a pattern with that number of balls. This is connected to the work of Ron Graham who was both a mathematician and a former president of the International Jugglers Association. Anyone who has had algebra will follow along (no high-level math requirements).
Steve Butler is currently the Barbara J. Janson Professor of Mathematics at Iowa State University. He is an award-winning teacher and has made much of his teaching materials available online (calc1.org, calc2.org, calc3.org). He has also published over 70 research articles with topics including card shuffling, origami, hat guessing games, circle packing, and, of course, juggling. More information can be found at SteveButler.org.
Noon | “Musical Illusions” (5 mins) by Scott Kim
Ever heard a sound that keeps going up in pitch, but comes back to where it started? It’s called a Shepard tone, and it was invented by psychologist Roger Shepard in the 1960s. Filmmaker Christopher Nolan recently used this effect for the soundtrack of his movie Dunkirk, to create an endless sense of rising tension. The original Shepard tone was generated by computer, but I will show you how to play it on the piano. And I’ll show you how to hum and whistle two voices of the canon Frere Jacques at the same time.
4:00 pm | “Mini-Mathematical-Universes” (30 mins) by Gord Hamilton
Mini-Mathematical-Universes are the best way to teach the scientific method. When you come to this presentation you will be playing the game collaboratively with everyone else. Poke around like scientists trying to discover the laws of the Mini-Mathematical-Universe you find yourselves in. Mini-Mathematical-Universes were inspired by Robert Abbott’s Eleusis (Mathematical Games column, June 1959) and Sid Sackson’s Patterns II (Mathematical Games column, November 1969).
Gordon Hamilton is the director of MathPickle.com and the designer of board games like Santorini. He ZOOM-streams original puzzles every weekday on “PuzzleTime with MathPickle” which is fully supported by the Julia Robinson Mathematics Festival. He lives in Calgary, Canada.
8:00 pm | “Mathematics in Motion: Mathematical Themes in Dance and Choreography” (20 mins) by Laurel Lawson, Lindsay Giedle, Laura Briggs. Hosted by Catherine Messina.
Abstract: Mathematics in Motion began as a collective of artists and mathematicians doing experiments to connect their respective crafts. Their research produced many fun ways for the public to engage with mathematics through movement-based improvisations and choreography. Mathematics in Motion continues to use the arts to innovate in science and mathematics communication through new partnerships with the arts and community organizations through our Kristel Rose Tedesco Grant, named after one of our founders. Today, we have our three residency recipients showing you the work they have put together.
Laurel Lawson is a dance artist with Full Radius Dance and Kinetic Light. Her choreography weaves athletic partnering with the detail of physically integrated dance. Lindsay Giedl is a UGA alumni, teacher and choreographer in the Atlanta area, whose work explores social dialogue with improvisational contemporary movement. Laura Briggs is an Emory University alumni whose detailed work explores the queer, trans, and southern experience. All three are using different topics of mathematics to create performance work for live or in-camera performances.
Noon | “Flood Control: The Pandemic and Science Denial” by Robert Crease
Martin Gardner was one of the leading practitioners of something that we need more than ever: skepticism. What would Martin have said about responses to the current pandemic in the US? How would he have understood and discussed the reactions to it of US politicians, scientific institutions, and the public? I imagine that he might begin by saying that the COVID-19 virus is the 21st century Flood – which nearly wiped out the human species but whose silver lining is that it teaches lessons about preparing for disasters.
Robert P. Crease is a Professor in the Department of Philosophy at Stony Brook University (PhD Columbia University 1987). For the past 20 years he has written a column, “Critical Point,” on the historical and philosophical dimensions of science for the international science magazine Physics World. His most recent book is The Workshop and the World: What Ten Thinkers Can Teach Us about Science and Authority.
4:00 pm | “Believe It, Then Don’t” by Jim Propp
Question: Why do mathematicians often belabor the obvious, sometimes to the point of struggling to doubt things that they actually believe are true? Answer: Because sometimes things that are obvious turn out to be false, and because when we question our beliefs and then fight our way back to those beliefs, the tools we force ourselves to develop can be applied to the study of things that are neither obviously true nor obviously false (which includes most things). I’ll illustrate this with the problem of packing disks into rectangles. Clearly you can’t pack more than four disks of diameter 1 into a 2-by-2 square; it’s obvious, right? But what about packing disks of diameter 1 into a 2-by-4 rectangle? Or a 2-by-6? Or …
Jim Propp is a math professor at UMass Lowell (home page: http://jamespropp.org). His research interests include combinatorics, probability, dynamical systems, and games. His monthly essays about mathematics appear at his “Mathematical Enchantments” website (http://mathenchant.wordpress.com) and he spends too much time tweeting under the name @JimPropp. When not doubting obvious truths or proving unobvious ones, he enjoys exploring ridiculous propositions, such as “The dinosaurs were killed by a reversal of Earth’s gravitational field”, “Solar eclipses account for the evolution of human intelligence”, and “Pi equals 3”, and making videos about them.
8:00 pm | “Cut and Fold a Spinner” by Diana Davis
You’ve heard of origami, folding paper, but how about kirigami, cutting and folding paper? We’ll cut and fold a piece of paper so that it spins when you open and close it, which is really surprising when you first see it work (click here for a video). We’ll also discuss the design principles behind creating them in different shapes. Materials needed: a piece of cardstock or other thick paper, scissors, and a pencil or pen. This activity will take 15 minutes to do, plus 15 minutes to troubleshoot participants’ creations to make them work smoothly.
Diana Davis completed her Ph.D. at Brown University in 2013 under the direction of Richard Schwartz. She currently teaches at Phillips Exeter Academy. While a graduate student, she won an international award for the video she created to explain her PhD thesis result using colors and dance, which “went viral” in the mathematical community. Davis is also an educational innovator, creating and teaching problem-centered, discussion-based math courses of all levels, and studying their pedagogical effectiveness. Outside of research and teaching, she enjoys long-distance running, recreational sailing, traveling, and thinking about how to build community and create a sustainable world.
Noon | “Counter Productivity in Minimalist Origami” by Jeannine Mosely
In minimalist origami, the folder is limited to a small number of folds (typically 4 or fewer) to achieve a desired result. Origami paper that is colored on one side and white on the other can be used to create contrast between regions that “paint” the desired image. I have used this technique to represent each letter of the Roman alphabet using only 4 folds. In typographic design, regions of paper surrounded by ink, like the interior of the letter “O”, are called counters. Producing multiple counters with a small number of folds can be challenging. In this talk, I address the computational complexity of how many counters C it is possible to produce with F folds. We demonstrate a method where the number of counters C=Ω(F²).
Jeannine Mosely is widely known for her work as an origami artist. She is best known for her modular origami designs, especially her work using business cards. She has organized several crowd-sourced origami projects built from tens of thousands of business cards involving hundreds of volunteers for each project. She is also known for her minimalist origami designs, curved crease models, and her invention of “or-egg-ami” models made from egg cartons. She works as a software engineer for Akamai Technologies, where she writes software to monitor and control the flow of data on the internet. She holds a Ph.D. in EECS from the Massachusetts Institute of Technology.
4:00 pm | “Eddy’s World” by Eddy and Lyn Goldfarb
Eddy’s World tells the story of Eddy Goldfarb, a 98, year-old working toy inventor, best known for the iconic Yakity Yak Teeth and nearly 800 classic toys. He designed his first toys while on submarine duty during WWII, launching his 80-year career as an independent toy inventor. These days, Eddy still prototypes new toys in his garage machine shop, creates translucent lithophane portraits on his 3D printer, and writes 100-word stories. Optimistic and curious, Eddy is an endearing storyteller who brings us into his world of inventions and ideas. Eddy’s World is a Jury Award winner for “Best Short Documentary” at the Raw Science Film Festival, and was awarded “Best Short Documentary” at the Port Townsend Film Festival.
Eddy Goldfarb was born in 1921 in Chicago, Illinois — the son of Jewish immigrants from Poland and Romania. From the time he was a young child, he was interested in how things work and he always wanted to be an independent inventor. He excelled in math and science, but when his father died young, Eddy had to work to support his family, and abandoned his dream of going to college to study physics. When Pearl Harbor was bombed, Eddy enlisted in the Navy and studied radar. It was on the Batfish Submarine that he first decided to become an independent toy inventor. In 1949, he sold his first toy, the Yakity Yak Teeth, and since then, has invented more than 800 toys and holds close to 300 patents. In 2003, Eddy was inducted in the Toy Industry Hall of Fame, and in 2010, received the TAGIE (Toy and Game Innovation) Lifetime Achievement Award.
Lyn Goldfarb is an Academy Award-nominated documentary filmmaker with more than 19 documentaries on PBS and major cable, as well as short films for museums, exhibitions and non-profits. She is also Eddy Goldfarb’s daughter.
8:00 pm | “The Rubik’s Cube and Math” by Sydney Weaver
In this year’s Celebration of Mind, Sydney will dive deep into the math behind the Rubik’s Cube. She will explore how the subgroups of a cube work and interact with one another, the parity issues that lie behind the cube, and how to understand them, and touch on the function of commutators and conjugates.
Sydney Weaver is a 9-time gold medalist professional speed cuber with a passion for recreational mathematics and twisty puzzles. Sydney has been speedcubing and exploring twisty puzzles for over 8 years and was the first female to achieve many things in the speedcubing community such as being the first female in the world to solve a 6×6 cube blindfolded. In recent years, Sydney has turned her passion of speedcubing into a medium to teach math to kids and adults alike in a fun, relatable way. She travels internationally to math festivals and conferences to facilitate activities on the Rubik’s Cube as well as provide engaging lectures about the Rubik’s Cube. Some of these places include Australia, Europe, and Central America as well as several notable US Universities including Berkeley and Stanford. In her free time, Sydney enjoys gardening, solving ciphers, and playing video games.
Noon | “Down the Rabbit Hole with Flexagons” by Ann Schwartz
Flexagons have been around for decades—but beware! There are many more flexagons than the ones folded by Arthur Stone back in 1939. And once you start exploring and folding up new ones there’s no turning back. I should know. Here I’ll tell the story of how the first hexaflexagon was discovered and show one that has been made into a puzzle featuring the accomplishments of the multi-faceted Martin Gardner. I’ll then demonstrate some of the many new flexagons that have been discovered and their marvelous characteristics and complexities, including my favorite: flexagons that can lurk inside another one, like Russian nesting dolls.
Ann Schwartz has discovered more than a dozen triangle-based flexagons, some of which she has presented at the biennial Gatherings for Gardner from 2006 to the present. In 2015 she was the guest speaker at the Recreational Math, Puzzles and Games Conference at the Davidson Institute of Science Education, the Weizmann Institute of Science, in Rehovot, Israel. In 2018 she presented a flexagon at the 7OSME in Oxford, UK. She also has given flexagon workshops at the Museum of Mathematics in New York, including at its 2017 and 2019 MOVES. In 2019 she led the Neil Shore Flexagon Workshop with fellow flexagon experts Dr. Yossi Elran and Scott Sherman at the Davidson Institute. For more information about flexagons, feel free to email her firstname.lastname@example.org.
4:00 pm | “The Whimsical and Serious Side of Martin Gardner” by James Gardner
Jim Gardner, the eldest son of Martin Gardner, will share some favorite memories and anecdotes. Anticipate seeing some family photos, and hearing interesting stories that reveal Martin Gardner’s approach to work and life.
Jim Gardner manages the intellectual property of Martin Gardner’s Estate, where he focuses on keeping alive the legacy of Martin Gardner’s ideas and writing. He is a retired Professor Emeritus (University of Oklahoma) and specializes in Universal Design for Learning — with attention to instructional/assistive technologies for students with disabilities and learners at-risk for school failure.
8:00 pm | “Dice Dice Baby!” by Joe M. Turner
Joe M. Turner, usually found with a pack of cards in his hand, veers into somewhat less-traveled territory with this collection of interesting magic tricks and puzzles using dice. Some material is drawn from Gardner; some routines come from other sources. While some of it is mathematical, some of the content may require other assorted forms of sneakiness, all of which will be explained as needed. Attendees should bring three or four standard dice with them in order to follow along with the procedures. A downloadable PDF can be found here; it will be helpful to print it in advance as the diagrams will help during the interactive session.
Atlanta magician and mentalist Joe M. Turner is a three-time Greater Atlanta Magician of the Year whose twenty-year career in magic and corporate speaking has taken him to six continents. He has appeared at the Hollywood Magic Castle, Monday Night Magic in New York, the Chicago Magic Lounge, and the London Palladium. He has lectured on magic around the world and served as the 2015-2016 International President of the International Brotherhood of Magicians. His virtual magic show, launched on April 3, was recommended in the New York Times. Web: turnermagic.com
Noon | “Algorithmic Puzzles and Martin Gardner” by Dana Richards
The vast majority of mathematical puzzles ask for the existence of a solution. It is merely an exercise when the method is known and it is more of a puzzle when the method is not clear. An algorithmic puzzle takes this further by only asking for the method itself or a property of the method. It is in this sense that much of computer science is puzzle-solving. We discuss the theory behind this in the context of material taken from Martin Gardner’s Scientific American column. The answer to the following puzzle will be given: There are five pirates dividing up 100 gold coins. Pirates are strictly ordered by seniority, are very logical and wish to live. The rule pirates use to divide gold is: (1) the most senior pirate suggests a division, (2) all pirates vote on it, (3) if at least half vote for it then it is done, otherwise the senior pirate is killed and the process starts over. What happens?
Dana Richards is an associate professor of Computer Science at George Mason University. His research is on theoretical and algorithmic topics. He has been a friend of Martin Gardner for nearly four decades and has edited Gardner’s book “The Colossal Book of Short Puzzles and Problems”.
4:00 pm | “Little Zonohedral Library” by George Hart
I’ll show how a simple geometric process of extending v’s into parallelograms can be used to design a wide variety of physically constructable structures. The results are beautiful generalizations of zonohedra, a class of polyhedra based on parallel-sided faces. As a practical example, a “Little Library” is made out of laser-cut wood.
George Hart is a sculptor and applied mathematician who demonstrates how mathematics is cool and creative in ways you might not have expected. Whether he is slicing a bagel into two linked halves or leading hundreds of participants in an intricate geometric sculpture barn raising, he always finds original ways to share the beauty of mathematical thinking. Recently retired from Stony Brook University, he holds a B.S. in Math and a Ph.D. in EECS from MIT. His research explores innovative ways to use computer technology in the design and fabrication of his artwork, which is exhibited widely around the world. Hart co-founded the Museum of Mathematics in NYC and developed its initial set of hands-on exhibits.
8:00 pm | “Math Court – Alice in Königsberg” by Evans Harrell with Mathematics in Motion
Join Mathematics in Motion and students in Georgia Tech’s Club Math for Math Court! This skit recounts one of the foundation stories of mathematics, the puzzle of the Seven Bridges of Königsberg, solved by Euler in 1726. Except that it all takes place in a mad courtroom, and you are the jury!
Evans Harrell, who wrote Alice in Königsberg, is Professor Emeritus of Mathematics at Georgia Tech, where for many years he served as Associate Dean for Research in the College of Sciences. He does research in mathematical physics and geometric analysis, and he has brought mathematics and science to the public arena with the Atlanta Science Festival, Science in Vivo, the Julia Robinson Mathematics Festival, and educational institutions at all levels.
Noon | “Philosophy of Fractals” by Delicia Kamens
We know that fractals are nature’s pattern makers. Fractals are in fact everywhere we look: tree bark, snowflakes, mountain ranges, cloud, rivers, seashells, all the way up to the shape of galaxies. Beyond nature, however, human beings are fractal thinkers. We depend on fractal algorithms for financial analysis and to resize an image on a computer. Merrin Parkers, Alice Kelly and may others express its beauty in art. Modern movies would not be as elaborately realistic with fractal generation of landscapes, bodies of water or even the movement of leaves and hair – if you’ve seen Tron, Transformers, Star Trek or Stars Wars, you’ve enjoyed fractal generated worlds. Since Benoit Mandelbrot’s discovery of fractal geometry, we can’t seem to stop fractal-ing. This short talk bring out the pervasiveness of fractals in life, experience and even philosophy.
Delícia Kamins is fourth-year doctoral student in the Philosophy department at Stony Brook University. Her research focuses on whether philosophical treatments of “motion” – specifically as described by Aristotle, Kant, Hegel and Whitehead – might inform epistemological conundrums within quantum mechanics.
4:00 pm | “Puzzles and Wonders from Elwyn and Richard and Martin and John” by Bud Brown
This talk will be about some or all of these: Tic Tac Toe, Hat Puzzles, Blocks on a rug, Sequences, Dots and Boxes, Counting on your Fingers, How 16 times 16 equals 24, some evidence that there aren’t nearly enough Small Numbers, and a new kind of cipher that gave jobs to millions of worthy number theorists. There are sixty-four words in this abstract.
Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and LSU, and taught at Virginia Tech for 48 years, retiring in 2017 as Alumni Distinguished Professor of Mathematics. His research is in number theory, combinatorics, and expository mathematics – but one of his coauthors was a sociologist. A frequent contributor to the MAA journals, he sometimes impersonates Alex Trebek at the spring meetings of the MD-DC-VA section of the MAA. Bud and Art Benjamin co-edited “Biscuits of Number Theory,” a 2009 MAA publication that is an assortment of articles on number theory that are not too big, easily digested, and make you hungry for more. In May 2020 the AMS published Bud’s “The Unity of Combinatorics” coauthored with the incomparable Richard Guy. This was Richard’s last work. We all miss him.
The number of words in this biosketch is a perfect square.
4:00 pm Wed, Oct 28 (rescheduled) | “All you need is paper! – Puzzles for lockdown with nothing more than some regular sheets of paper” by Yossi Elran
It’s amazing how much math you can do with nothing but a sheet of paper. Just grab a few sheets of paper from your printer, and join me! I’ll challenge you to fold maximum-area geometric shapes, solve some intriguing puzzles, make some impossible objects and get you thinking out of the box — all with just a single sheet of paper! Here are some paper puzzles for you.
Yossi Elran is an Israeli popular math author and speaker, and director of the Innovation Center at the Davidson Institute of Science Education, the educational arm of the Weizmann Institute of Science. Over 70,000 people all over the world have enjoyed his popular recreational math Massive Open Online Courses on Future Learn. He is the co-author of the “Paper Puzzle Book” together with origami artist Ilan Garibi and mechanical puzzler David Goodman. He holds a Ph. D. in theoretical chemistry and has done post-doctoral research in the field of quantum mechanics at the Weizmann Institute and the University of Toronto.
3:00 pm | Auction Fundraiser Preview hosted by Bob Hearn
In mid-November, G4G will be hosting an online fundraising initiative and we’d love to have you participate! Through an online auction, we will showcase the great work and diverse talents of the G4G community and provide opportunities to get your hands on one-of-a-kind puzzles, books, services, experiences, and more.
The Zoom Auction Preview will feature a few special G4G-style presentations, it will provide more details on how the auction will work, and will showcase a selection of auction items. You won’t want to miss this sneak peek at the wide-ranging list of exciting and exclusive items!
To Whet Your Appetite:
Kate Jones as contributed a wonderful word puzzle, to print and play, here, Mark Burstein has a great video about Alice, and Sydney Weaver has one about parity and twisty puzzles. Mariano Tomatis made an Italian video “bill fold” tribute to Martin here (turn on English subtitles) .