Archive for April, 2010

G4G9, Day 4: Lasers, Sculptures, and Balloon Polyhedra

This is the 5th post in a series of posts about Gathering For Gardner: 1 2 3 4

We woke up the next day, and soon realized that the first talk had already started, but only by around a minute. Luckily, the conference was in the hotel I was staying in, so I only arrived a few minutes late. The first talk was by Jean Pedersen, about the extended face planes of various polyhedra. The next few talks were rather interesting:  Zdravko Zivkovic introduced a puzzle called “MemorIQ” where you have to make various shapes out of octagonal pieces which are colored on the sides. The sides of the pieces touching must also be the same, so it is a bit of a challenge to make a square with the pieces. Al Seckel then did a talk on “The Nature of Belief”, talking about various ambiguous optical illusions which change completely when you add a simple line to them, as well as a music track reversed which originally sounds like gibberish, but when words are added, comes out very clear. Greg Federickson did a talk on “Symmetry vs. Economy in Dissections of Squares and Cubes”.  In it, he showed many demonstrations of  dissecting squares and cubes into many smaller squares and cubes, in very symmetrical ways and also in the minimum number of pieces. He also showed examples for hinged dissections, some of which were very ingenious, especially for the cubes.  Lastly, Robert Crease talked about his new book about some of the most important equations in mathematics and science.

After a short break, the 2nd session began. Pablos Holman stated out with a great talk about “Hackers and Invention” in which he demonstrated how to kill mosquitoes by shooting lasers, changed the voicemail sound on Al Seckel’s phone by spoofing his caller ID, displayed a robot that wheels up to people and shows them their passwords, and showed how to pick a lock very quickly using a filed-down key and a hammer. After this talk, I went out with Bill Gosper, who was going to show John Conway the Universal Game Of Life Computer which Calcyman had made computing Pi. Bill also showed Conway some other Game of Life patterns, such as the same universal computer computing the digits of the Golden Ratio, and a Python script for going to a particular step in a Life simulation faster than the normal algorithm, which he demonstrated by simulating a pattern to a googol-1 steps. Because of this, I was a bit late for the last talk of the day, the overview of the math sculptures that were to be made later that day at Tom Rodger’s house, which ranged from a button knot to a huge zonohedral pavilion.

I had a quick lunch (i.e, none) and boarded the bus that would be going to Tom’s house. On the way there, I tried to figure out some particularly hard puzzles which had little or no instructions, and also talked with some of the other attendees. When we arrived, they had a lot of Japanese-style lunches set out on a table for us to eat before building the various sculptures and seeing some of the things that were already set up. Some of the most interesting things there were a metal polyhedral-ish sculpture that George Hart was making, an impossible box that you could stand in, and a huge black hyperbola that towered over everything else.

After eating my lunch, I helped build the base for the zonohedral pavilion by soaping the pieces and then placing them into place on the supports. When that was done, they started on the roof of the pavillion, and I showed a few puzzles to other attendees, inlcuding a version of the Enigma puzzle as well as a “chopstick” puzzle using some of the left-over chopsticks from lunch.

Afterwards , I helped out on another sculpture, this time a metal sculpture of a three-dimensional Peano curve, which had to be put together using  near-identical pieces and screws. The pieces were very rusty, so my hands got very dirty. Eventually it was almost done and I wandered off somewhere else. Back near the house, Vi Hart had been showing people how to make various polyhedra out of  balloons, such as simple octahedra and cubes.

I went with Gareth Conway and Max to explore a section of the landscape which Max said was an entrance to a gold or a silver mine, and which was almost completely covered with leaves from the surrounding trees. At some point, Max said that we’ll get famous for discovering this gold mine, to which Gareth responded that he was already famous for that he knew 130 digits of pi. I promptly responded with all of the digits of Pi I knew (only 30), and Gareth corrected me when I added on a few extra digits. It’s good that Michael Keith, the author of a book entirely written in Pilish wasn’t there at that point, because then I’d have to listen to quite a lot of digits of Pi. Eventually, however, it turned out that the “gold mine” was actually just a well.

Meanwhile, the polyhedral balloon-making had gotten completely out of control:

I went back to the main area, where I saw that a lot of the sculptures had been finished, such as the Chinese Button Knot and George Hart’s sculpture. I got to talk with Clifford Pickover about various things, such as the non-paradox that 100% of all integers have a 9 in them, and about some of the artwork in The Math Book, Pickover’s new book. Nearby was Ivan Moscovich, whom I talked with as well about various puzzles, such as his Mirrorkal series of sliding block puzzles in which you have to make a certain image with the pieces, which have mirrors on them so that the first puzzle is figuring out what configuration the blocks should be in afterwards. Soon, nearly all of the sculptures had been finished except for the pavilion which was almost finished and it was getting dark.

We had quite a nice dinner, although the tables were full so I had to sit nearby, where Gosper was.  We talked for some time, and I mentioned a formula that can calculate Pi to 42 billion digits but then soon diverges. After the dinner, I went into Tom’s house which, as I have said before, is absolutely filled with puzzles. I played with a few puzzles, including  a 3-piece burr and a few Japanese puzzle boxes but then encountered a puzzle that fell apart and then was impossible to put back together. By that time, it was time to go back to the hotel. I boarded the bus in the back- right next to George Hart and a few other people who had made the sculptures at Tom’s house that day, who I talked with for the ride back.

It had been a great day, and there was only 1 day of the conference left.

G4G9, Day 3: Random(Blog), Crazy Detectives, and the Rubik’s Cube

This is the fourth post in a series of blog posts about Gathering For Gardner 9: 1 2 3

We started out the 3rd day by changing the hotel where we were from the Peachtrees to the Ritz-Carlton, where I missed the first talk, which was apparently about “The Odd One Out and Unrevealing Coin Weighings”

The very first talk that I saw, then, was by John Edmark about “Geometric Patterns of Change”. It was mostly about the sculptures that he has made, some based on the Fibonacci sequence and the Golden Angle, while others were on various spirals which could change direction by simply changing the angle at the top. Adrian Fisher also did a talk on that he was making Custom Designed Mazes, specifically hedge mazes for any people who had a castle somewhere and liked mazes. Last in the first session was a 15-minute talk by Ed Pegg, called “Meet the Attendees”, which was where he would bring up various attendees who weren’t doing talks and have them describe themselves in 20 seconds, as he would show a slide that he had made for them.  I thought that he would only bring up the attendees who wanted a slide in the presentation.

Turns out, I was wrong. He really had made 70 individual slides, one for each attendee who wasn’t giving a talk, including me.

I was around 5th, but because many of the attendees had decided not to come up, I was instead in 2nd place for a 20-second talk. Of course, I hadn’t expected this, and so I had around 30 seconds to figure out what I was going to say.  When my time came, I went up and gave a very short description of my website, this blog, and my Scratch Projects, somehow in less than the 20 second I had. Many other people came up and gave short descriptions of what they did, some seeming to go over 1 minute, but Ed’s talk still came in before the 15 minutes he had.

The next session started out with two Dr. Matrix (one of Martin Gardner’s characters, a numerologist) impersonators, Scot Morris and Bruce Oberg, talk about the number 9. Scot’s talk was about “Cosmic 9” which detailed how 9 lay at the center of the universe: He pointed out the methods of counting out nines, that 9 was a square number, and so on. Bruce Oberg’s talk was about “Nein to Nine”, in which he pointed out how bad 9 was. My favorite line in his talk: “First, I will show that 9 is lazy. What happened in 9 A.D.? (pause) ABSOLUTELY NOTHING!” After a few more talks, Stephen Wolfram did a talk on all the work he has been doing, such as Mathematica, Wolfram|Alpha, and A New Kind of Science, a rather large book weighing in at 1,200 pages.

We had a short lunch break, in which I skipped eating in order to buy a few puzzles, which included a combinatorial puzzle in which you have to rotate 3 controls in order to get 10 disks to line up, as well as an interesting packing set of polyhedra. After this, I went back downstairs for the 3rd session.

Steve Macknik and Susana Martinez-Conde started out with a talk on why we are fooled by magic. They pointed out that this was because of the magician’s skillful use of misdirection, and showed us a few videos on this effect, starting out with a card trick:

And then following up with a case of “Whodunit”, where there are 21 changes in the scene:

David Kaye also did a talk on how to perform magic for groups of  children, using a video as an example where he is dressed up as a clown and proceeds to do a trick with scarves, except that many things go wrong while he is doing the trick. Adam Rubin then did a talk on “Gravity Unmatched” which was a magic trick where a knife, attached to a string which goes over a pole and is tied to a pen, is falling towards him, yet it stops just before stabbing him. Kenichi Mura then did a talk on using Reulaux triangles for buckets in a chaos experiment.

There was a short break, in which I went to the Thinkfun exhibit showing nearly all of the games and puzzles that Thinkfun has made, from its first puzzles based on the Chinese Rings to the classic Pentominoes to the new Tipover. I talked with some of the creators, such as Bill Ritchie and Tanya Tompson, and said that many of their old puzzles were really neat, and that perhaps they should do sort of a “2nd edition” of some of them.

The last session of the day was themed around the Rubik’s Cube, and started out with Jerry Slocum doing a talk on the history of the Rubik’s Cube which was very interesting especially in the part where he talked about various Rubik’s Cube variants, such as the Void Cube or some of Bram Cohen and Oskar Van Deventer’s twisty puzzles. Lucas Garron followed up by talking about speedcubing and other types of Rubik’s cube. My favorite talk of the session, though, was Bram Cohen’s demonstration of the twisty puzzles that he has been making, in which the cubes can have very strange forms once twisted in certain ways (They no longer in any way resemble cubes) and also where the cube is distorted and so will not permit certain moves once twisted. Many of the cubes he and Oskar have invented can be seen at Oskar’s Youtube page:

Rik Van Grol, editor of Cubism For Fun, did a talk on “The Quest for God’s Algorithm”  which is the algorithm which solves the Rubik’s Cube in the minimum number of moves. He detailed on how the number has gone down from a high 60 to a lower bound of 20 and an upper bound of 22. (News Flash! Tomas Rokicki has found an algorithm which solves the Cube in 21 steps. Could this be God’s Algorithm?) Roice Nelson, creator of many wonderful programs, then did a talk on his program for displaying 3-d Rubik’s Cubes as 2-dimensional stereographic projections which you can rotate.  Julian and Corey then went up and gave a talk entitles “Fun with the Minsky Circle Algorithm”. It summarized nearly all of their research with the Minsky Circle Algorithm, which is supposed to make circles, but they managed to tweak the variables so that it makes crazy fractal-like structures. For some reason, the plots of the periods often have symmetry, often based around a central point:

Click to view full size

After the last session, we waited while the room in which the talks were held was being converted into a dinner/magic room. While we were waiting in line to get food, a person managed to find me and said “Stephen Wolfram wants to see you.” I was absolutely amazed by this, so I followed her to where, in fact, Stephen Wolfram was. I talked with him for a bit about various cellular automata and his book, and then went back in line to get food.

The magic show was amazing. It started out with Mark Mitton bringing Gareth Conway (he must be getting awfully tired of these magic shows) up to demonstrate an optical illusion with a rotating spiral. Then a dancer came up and performed an act in which she would produce seemingly endless flowers and cards from a single flower. Mark went back up for an act in which he would get a (very confused) audience member to perform a magic trick, without him speaking any words. A few other magicians came up for acts, and Gary Foshee presented a gift to Tom Rodgers. Lennart Green did an amazing card trick where he would blindfold himself, duct-tape his entire face,  cover it with aluminum foil, and then perform a magic trick, sometimes spilling cards, but performing the trick flawlessly. I was actually called up for a trick by Derek Hughes, in which he would perform a card trick in which supposedly, whatever answers I gave to his questions, he would show that I did not have free will by showing that I chose one particular card.

Apparently I do have free will, because I managed to somehow mess him up by not cutting the cards.

There were many other acts, and the show in general was great. In the above video, there’s a multicolored blob to the left, which was because the first act was of Caspar Schwabe blowing up a giant inflatable model of the 59th stellation of the icosahedron.

After the magic show, we went back upstairs and went to bed.

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.

G4G9, Day 1: Pencils, Optical Illusions, and Bar Bets

Continued from the previous post

The next day, Wednesday, was the first official day of Gathering For Gardner. The only session that day was the Bar Bets section, which was where the magicians and some mathematicians would show various tricks and trick bets which were mathematically related or interesting. However, the session was in the afternoon, so in the morning we had some time to do whatever we wanted to.

Julian Ziegler Hunts and his family had arrived overnight, so we got to have breakfast with them, in which he showed me some interesting Minsky Circle maps based on varying ξpsilon and zeta in the Minsky circle algorithm and plotting the period. After this, my mom and I, as well as the Zieglers and Gosper slept in until 11:00,at which point we decided to head back over to Tom Rodger’s house to play with puzzles while we waited for the session to begin.

As I have mentioned before, Tom has a huge collection of puzzles and sculptures. Since Julian had never been here before, and Tom was on a quick errand, I quickly gave him a tour of the house. Inside the puzzle rooms, Bill noticed that there were many impossible objects made by Gary Foshee, who makes sculptures where the puzzle is to determine how the object got into the current state, not to get it out. A classic example is of the “arrow through the coke bottle”:

Of course, Tom had many others, such as multiple coke bottles, strung together in impossible ways:

Later, Tom Rodgers came back from his errand and showed us some secret closets filled with puzzles. He placed out a few of his favorites on the table for us, and we attempted to solve all of them:

Many of the puzzles I knew the solution to, such as the nails puzzle and the ring puzzle, others I was able to solve, but the majority of them completely stumped me and everyone else. Akio Hizume showed us two interesting programs he wrote, called Real Number Music and Real Kekak System. They were both based on using the coefficients of the continued fraction of the number to generate music, and often made music which I think I’ve heard in some songs. At around 2:00 P.M., we went to the Ritz-Carlton for the before-conference meet.

There at the meet were lots of people who were going to G4G9, such as Lucas Garron, a speedcuber who has some very interesting modded cubes, such as one which transforms the edges to the corners and the corners to the edges, and is equivalent to a Shepard’s cube. There were many puzzles there, including Oskar’s Gears and a set of 9 3×3 paper-folding puzzles which varied from easy to AAUUGGHH! I also got to meet Sandro Del-Prete, one of my favorite optical illusion artists and talk to him about his optical illusions and what he was inspired by to make some of his drawings. He didn’t have perfect English, and my German is terrible, so my mom had to act as a translator at some parts. I was still able to understand what he was saying, even in German, though.

by Sandro Del-Prete

At around 6:30, we were led into an adjoining room for the Bar Bets session, in which various people demonstrated interesting and amazing magic tricks and bar bets. One person attempted unsucessfuly to drop a cork so that it would balance on its edge, another was successful at the same thing with matchboxes. The Great Jordini showed how to solve a certain puzzle by blowing on it, and I even got to solve a simple matchstick puzzle, shown below:

Get the dime out of the glass by moving only two matchsticks

Many of the tricks originated from Martin Gardner, such as a trick where a person moves a ring from a lower upperhand knot to a higher one. This went on until around 11:30, at which point we went back to our hotel and slept.

Naturally, I was excited for tomorrow.