Date: April 17, 2006

From: Stewart Dickson

Re: Trip Report: 7th Gathering for Gardner
Atlanta, Georgia, March 16-19

The biennial Gathering for (Martin) Gardner has been held six times before. It is an invitation-only event. I do not know specifically how I was invited, other than by reputation or association (although not in the very recent past.)

The meeting had very much a "Conference"-like format. Martin Gardner, himself was not in attendance. He is over ninety years old, lives in Oklahoma and does not get out much.

The meeting was attended by two "camps" - mathematicians and "puzzlers". Also in attendance were several magicians. The following are my notes.

I arrived at the Conference Hotel Wednesday night at around 11:00PM. Thursday morning, I set up my exhibit.

The Gathering for Gardner was very much like traveling back in time. Many of the people there I had met at the Conference on the Study of Polyhedra at Smith College in 1984, and at Nathaniel Friedman's Art & Mathematics Conferences in 1992-1993.

The evening events were quite nice -

Thursday, March 16, 2006

Morning Sessions - 9AM - 12:30PM (includes a 20-minute break)

Adrian Ocneanu presented Mathematica movies of 3-D Skeletons of 4-topes, including a sculpture in stainless steel at the McAllister Building in which the Department of Mathematics is located at Penn State University.

o Louis Kauffman "Hard Unknots and Collapsing Tangles"

o Harold Jacobs "Martin Gardner in the Classroom"

Harold Jacobs teaches mathematics at Grant High School in the San Fernando Valley, Los Angeles County, CA. Mr. Jacobs presented some techniques he uses in the classroom, which he learned from Martin Gardner's columns.

o Dick Hess "Solving Coin-Weighing Problems"

There is a class of problems in which the goal is to identify counterfeit coins by weight - knowing that their weight is the only difference from genuine coins.

o Bathsheba Grossman "A Classification of the Point Groups in 3-Space by Intrinsic Merit"
I first met Sheba Grossman at Nat Friedman's Art & Mathematics Conference at SUNY Albany in 1993. I seem to run into her at SIGGRAPH and other conferences as well. She got a Bachelor's Degree in Mathematics and a Masters in Fine Art. She got in on the Internet boom early and is financially independent. She lives in Santa Cruz, CA.

Sheba's presentation made arguments on the aesthetic principles of the visual design she uses in her sculpture based on the three-dimensional symmetry groups.

o Istvan Lenart "Properties of a Binary Operation, Based on Spherical Geometry"

o Saul Griffith "Folding any 3D Object"

Self-assembling/Self-Replicating, Binary-Encoded cellular structures. A means of programming mechanical cells to self-assemble into a given shape. This is really quite clever - definitely geared toward nanotechnology.

o Byron Rubin "Seeing Molecules and Making Molecular Sculpture"
In the early 1970's Byron Rubin invented a machine for bending the sequence of bond angles along the backbone trace of a protein - known as "Byron's Bender". He soon attempted the same technique using stainless steel exhaust pipe and a bending machine used at a muffler shop. He now sells "portrait" sculpture of a bio-tech company's prize, patented molecule - from PDB models (Protein Data Bank).

Caspar Schwabe "The Ingredible Inversion"
I first met Caspar Schwabe at Nat Friedman's Art & Mathematics Conferences in 1992-1993. He was the son of an owner of a toy shop in Switzerland. He is now a visiting professor at the Kurashiki University of Science and the Arts in Okayama, Japan.

Thursday Evening

Tom Rodgers's Japanese house -
NY April 3, 2004

"And is the house itself not a source of wonder? Just outside is a Japanese rock garden and waterfall, landscaped by Takeo Uesugi using boulders from Tennessee; nearby, a humidity-controlled garage houses a collection of more than 1,200 dictionaries from before 1800."

And, of course, his puzzle collection...

Friday, March 17, 2006

Morning Sessions - 8:30AM - 12PM (includes a 20-minute break)

8:30 AM John Conway, Professor of Mathematics, Princeton University "Seven Mathematical Wonders" I first saw John Horton Conway speak at Nat Friedman's Art & Mathematics Conferences at SUNY Albany in 1993. Conway invented the "Game of Life" (October 1970) Stephen Wolfram's "A New Kind of Science" Is based on observations made in the process of enumerating all the possible cellular automata.

At G4G7, Conway spoke on a collection of short topics he put together since the Gathering began Thursday morning.

The Fano Plane (discussed later by Ed Pegg, Jr.) - the embedding of K7, the smallest projective space - has the property that all its Hamiltonian Circuits are knots.

o Yossi Elran Retrolife

Given a desired result of on-state squares on a grid that follows Game-of-Life rules, what should the initial on-state squares be?

The following were a rhapsody and rebuttal on the number seven, itself - the theme of the conference:

o Scot Morris Cosmic Seven

o Robert Sandfield Anti-Seven

o Istvan Orosz ...nothing but confusion? Anamorphoses with double meaning

Afternoon Sessions - 1:30PM - 5PM (includes a 20-minute break)

o George W. Hart "Orderly Tangles Revisited"

I met George Hart at Nat Friedman's Art & Mathematics Conferences in 1992-1993 and at an Art & Mathematics conference in Maubeuge, Northern France in 2000.

o Ed Pegg Jr The Fano Plane <>

o Janusz Kapusta "The NEW York Times, the NEW Geometrical Shape, a NEW Golden Construction"

Janusz Kapusta has created many editorial illustrations for the New York Times.
He has discovered and patented a new Golden-Mean construction and decomposition of the cube, which has many interesting and useful properties.

o Chaim Goodman-Strauss "Symmetry Fun"
I met Chaim Goodman-Strauss at Nat Friedman's Art & Mathematics Conferences in 1992-1993.

Friday Evening

Buffet dinner at the Georgia Aquarium
Entertainment was hosted by a husband-and-wife magician team from Las Vegas - the show included The Slinky Juggler.

Saturday, March 18, 2006

Morning Sessions - 8:30AM - 12PM (includes a 20-minute break)

Presenter Presentation Title

8:30 AM Roger Penrose

(30 min) (TBA)

Roger Penrose spoke on the Fano Plane as a multiplication table for the octonians (8-dimensional complex numbers), a topic he had just finished up on the plane --

A member of the audience asked a question on Quantum Coherence, referring to "The Emperor's New Mind" (1990 Oxford University Press

While reading "The Emperor's New Mind" in 1996, it occurred to me that what is missing from his Quantum Computational Graviton Model of neural functioning is the hologrammic physical the brain must have, as proved by Bela Julesz in his invention of and experiments using Random Dot Stereograms.

His answer to my question on this connection indicated that Dr. Penrose is not aware of Julesz' work. It seems to me that Penrose' idea of quantum neural coherence in the brain must be the same as Julesz notion of hologrammic phase coherence.

o Ed Pegg Jr Meet the Attendees II

o Peter Winkler (30 min) Puzzles You Think You Must Not Have Heard Correctly

o Dennis Shasha Unsolved Puzzle Variants

o Doug McKenna The Peano Quartet

o Rebecca G. Wahl The Perfect Configuration

o Ron Resch (30 min) Resch Egg-streme Tiling: Tiling Chicken Eggs, Kinematic Hierarchical Tiling, and Kinematic Heptagons

I remember the documentation of Ron Resch's "Ukrain Easter Egg" in LEONARDO

o Karl Schaffer Mathematics, Rhythm, and Dance, with Particular Attention to the Number Seven

Afternoon Sessions - 1:30PM - 6:30PM (includes a 20-minute break)

o Naoaki Takashima Seven is the Number of Colors of Rainbow in Japan

o Michael Longuet-Higgins Seven from the Sea -- Theoretical Biology

o Haruo Hosoya (20 min) Cactus Skeletons Carrying Lucas Number 7

o Daina Taimina (Latvia) Mysteries of hyperbolic plane
Daina made the original endeavor to crochet models of hyperbolic space.

o Eleanor Schwartz Braided polyhedra
I'm pretty sure I heard Eleanor Schwartz speak at the 1984 Conference on Polyhedra.

o Sarah-Marie Belcastro, (Xavier University) Carolyn Yackel Knitting and Crocheting Orientable Surfaces
More challenging problems in knitting and crocheting - Euler colorings of the torus.

o Ann Schwartz The Hexa-dodeca-flexagon

o Mick Guy Origami

o Jeannine Mosely o Robert J. Lang New Developments in Origami

o Jean Pedersen (30 min) Systematic Paper-Folding and a Related Number-Theoretical Conjecture Theorem Dodeca-Icosa pattern fold.

I'm pretty sure I heard Jean Pederson was an organizer of the 1984 Conference on Polyhedra.

o Thomas C. Hull (30 min) Folding regular heptagons

Hull presented an origami construction of the regular heptagon. The regular heptagon cannot be constructed with a compass and straight-edge. Hull was able to prove that the origami construction actually reduces the error with each successive fold.

o Thomas Banchoff The 4th Dimension in Art

I met Tom Banchoff again. The last time I saw him was at the Conference on Polyhedra at Smith College in 1984. I corresponded with him for a while after the conference. In 1987, when I was moving from Chicago to Los Angeles, Banchoff was telling me about David Hoffman and James Hoffman's new minimal surfaces. By 1990, I had constructed 3D models of them using stereolithography. I think I can credit Banchoff with getting me started in all of this.

Banchoff's account of his meetings with Salvadore Dali were astounding! I had not previously known about these.

o Tony Robbin (30 min) Picasso's Cubism is Really Hypercubism

Tony Robbin gave a talk on the influence of the 4th dimension on the cubists, particularly on Picasso. I have recently found an astonishing article on Marcel Duchamp's interest in the 4th dimension: Which seems to strengthen the connection between Duchamp's work and my recent "Botty Shelly": I hope that some sort of scholarly collaboration grows out of this.

Sunday, March 19, 2006

Morning Sessions - 8:30AM - 12PM (includes a 20-minute break)

o Chris K. Palmer Spiral Tilings with S-curves and C-curves ~ Using Combinatorics to Augment Tradition

o Emrehan Halici PuzzleUp the Web Portal -- a weekly puzzle competition

o George Miller 3D Printing comes of age George Miller owns his own rapid prototyping machine -- a Stratasys Dimension. He does his CAD modeling in SolidWorks. He specializes in taking 3D puzzle ideas from prototype to product.

o Jay Kappraff (30 min) Why God Reserved Day Seven for Himself: A Parable of Harmonic Law

This work came out of that of an ethnomusicologist on the musical scales of ancient Sumeria.

I have seen Kappraff speak at a previous meeting at which I also presented - back in the early 1990's.

o Erez Lieberman Evolution on Graphs

This work was first published in Lieberman, E., Hauert, Ch. & Nowak, M. (2005) Evolutionary Dynamics on Graphs. Nature 433, 312-316.

See also: Cellular Automata in the Hyperbolic Plane - a possible demonstration that P=NP

o Eric Harshbarger (30 min) A Study of 7x7 Word Squares

Squares tiled by the standard Scrabble letter set, which spell words either horizontally, vertically or both, using the standard Scrabble dictionary.

I have used images of Eric Harshbarger's Lego sculptures in my presentations on sculpture using Rapid Prototyping.

o Barry Cipra SeVenn, EleVenn, and Beyond

Barry Cipra is a mathematics writer. He was editor of "What's New in the Mathematical Sciences" (American Mathematical Society). He used my images of computer-generated sculptures for his article on Andrew Wiles' 1993 proof of Fermat's Last Theorem.

His talk at G4G7 was on a survey of Venn Diagrams of prime numbers of sets:
# [Ci03] Barry Cipra, Diagram masters cry 'Venn-i, Vidi, Vici', Science, 299 (January 2003) 651.
# [Ci04] Barry Cipra, Venn Meets Boole in Symmetric Proof, SIAM News, 37 no. 1 (January/February 2004).