## Gathering For Gardner, Day 2: Fractals, Puzzles, and Magic

* Continued from a previous post… and the one before that…*

The next day was Thursday, marking the start of the talks, where various mathematicians, optical illusionists, computer programmers and magicians would give short 10-30 minute talks about various subjects. The talks started at 8:30, but we got there a bit early, so my mom dropped off my exchange gift (a puzzle where you have to put together 9 nonahedral shapes together to make a nonahedron), while I watched the start of the talks. The very first talk was by Erez Lieberman-Aiden, who talked about how the human genome might fold itself into spacefilling curves, rather than in a big tangle. The talk was supposed to be 30 minutes long, but he finished 3 minutes early, so (due to a rule/tradition that any speaker who finished before his time limit was given 1 dollar for each minute that he was under time) he received 3 dollars. Vladmir Bulatov did a talk on models of hyperbolic geometry, starting with Escher’s Circle Limits and moving on to computer models and animations. Jason Rosenhouse also did a talk on “The Monty Hall Problem, Revisited” in which he described various variations on the Monty Hall problem, such as a Monty who completely chooses random doors, and sometimes shows the car before he allows you to make a decision. Gary Foshee did a 1-minute talk on the Tuseday Birthday Problem, based on the original birthday problem, except that one of the children is born on a Tuesday.

Then there was a 20-minute break, in which I went up to the exhibit room to help and watch the exhibitors set up. Hans Schepker was setting up a large staircase which appeared to defy gravity, even though wires were attached to each of the cubes that made it up. He also made a type of flexagon based on seven tetrahedra taped along their edges in which the shape folded out progressively around the circle instead of all at once. John Edmark was also there, with many sculptures based on the Fibonacci sequence, the Golden Ratio, and the Golden Angle, such as a whirligig which, when spun one way, made a smooth spiral, and when spun the other way, made a shape that looked like a pine cone.

The next session started out with John Conway doing a talk on the Lexicode Theorem** Non-Theorem** Puzzle, which led to the system of Nimbers, in which 8+8=0, and where 8*11=9. Uri Levi was next, with a demonstration of a new puzzle he had found called the “Magnetic Tower of Hanoi” which normally needs 3^n moves to solve, but variations on it can have rather complicated formulas for the minimum moves required. Neil Sloane also announced that the OEIS was going into a wiki format, and Benjamin Chaffin did a talk on computing the curling number conjecture and the Recaman Sequence.

By then it was time for lunch, and I skipped lunch to have a look at the sales rooms, where various puzzle creators were selling their puzzles for various prices. The first booth that I recognized when I first came in was that of Pavel Curtis, creator of insanely hard puzzles, who was selling nearly all of the puzzles he had on his website. I also noticed that the people who made ZomeTool had set up a booth selling the product. Inside the other room was even more puzzles, including various combinatoric puzzles, mathematical books, puzzle boxes and suitcases, and much more. Sandro Del-Prete, who I had met before before the Bar Bets session, was there and my mom bought one of his books for me, provided that he would sign the book in German, and that I would have to read what he had written. Nearby was Clifford Pickover, one of my favorite writers of math and computer science books, who I talked with shortly and then – something that would only ever happen in Gathering For Gardner- Ivan Moscovich, another one of my favorite authors of math and puzzle books, turned out to be right beside us. Of course, I talked with him for a while, and then went back to the other room, where I noticed that Kadon Enterprises, makers of tons of polyomino-based puzzles, were there, and quickly solved one of their easier puzzles, a set of pentominoes which could be stacked to make 3D shapes. By that time I went back down for the next set of talks, as an hour had already passed.

The next set of talks started out with a set of puzzle fonts by Erik Demaine, where you have to solve a puzzle to even figure out what the letter was, and then repeat that for each letter in the text. Kenneth Brecher did a talk on ambiguous figures, in 2D and also in 3D, and proposed a problem about 4 or more perspectives of an ambiguous object that I quickly solved by placing the Rubin Vase on a type of striped disk which produces either 4 or 6 perspectives, depending on what you consider it to be. Clifford Pickover did a talk on the making of his newest book, called *The Math Book*, and Glen Whitney finished off the session with a talk on The Museum of Mathematics, which is to be built very soon. Another short break, and then the last session for the day began.

First, there was a 30-minute talk on “The Art of Throwing Up” which is not what you may think it is. It was actually about juggling, and by the end of the talk I could actually juggle three scarves without grabbing everywhere. Tomas Rokicki, one of the programmers of Golly and a searcher for God’s Number on the Rubik’s Cube, then did a talk on ‘Modern Life” which was about recent developments in Conway’s Game of Life patterns. David Spies introduced GamesCrafters, a service where you can play around 70 games against a perfect opponent, and Robert Bosch talked about using the Traveling Salesman Problem to generate artworks. Sandro Del-Prete also did a talk about some of his illusions, a few of which were animated. Alex Bellos, author of a new book, *Here’s Looking at Euclid ( Alex’s Adventures in Numberland *in Britain) talked about why they still use abacuses in Japan (those kids are scary fast), and Eve Torrence, lastly, gave an improvement to Lewis Carroll’s Condensation Method.

Afterwards, we went to the 50th floor of a nearby tower for a large dinner with other attendees of G4G9. After the dinner, we were led into one of a few rooms where we were shown a number of short magic shows. I was in the room with Gareth Conway and John Conway, who I talked with about the Game of Life (it was originally simulated on Go boards), the talk about Nimbers he gave, and the Century Sliding Block Puzzle, which he apparently found by modifying the L’Ane Rouge puzzle. The magic shows were great, and I noticed that for some reason, Gareth, my mom, and I were chosen very frequently. Some of my favorite acts were a trick by Victoria Skye, who had 3 cards which would correspond to any answer to one of the questions she asked you; A trick by Mark Mitton in which he would place a card on the table, stand on top of a chair in a corner, and the card would turn out to be whatever the person named; and nearly all of Lennart Green’s card tricks. I was especially amazed by a trick by John Railing in which he turned a pack of cards into a sheet of plexiglass. This was especially amazing to me because I was holding the pack of cards at the time, and my hand was small enough that I could see in from the outside, and I still couldn’t tell when the switch happened.

Afterwards, we went back to our hotel and went to sleep, amazed by what had happened today.