G4G8 -- 8th Biennial Gathering '4' (Martin) Gardner -- G4G8

Ritz-Carleton Hotel, 181 Peachtree Street, N.E., Atlanta, GA 30303 USA

Summary Note: Gathering '4' Gardner is an inter-disciplinary "stirring of the pot": a cross-disciplinary exposure to alternate viewpoints of similar problems -- and fresh view of old problems to spur revitalization.

Thursday, March 27th, 2008

8:15AM - 10:00AM

Drive from Champaign, IL to IND - Indianapolis

12:25pm CDT - 01:58pm EDT

Delta Flight 1221 from IND to ATL - Atlanta

2:45pm - 3:15PM

AtlantaLink shuttle van from ATL airport to Ritz-Carlton, Peachtree Street, Atlanta.

Rode with Prof. Claudio T. Silva of the Utah SCI Institute. Dr. Silva was traveling to the Program Committee meeting for the SIGGRAPH 2008 Conference.


Tohru Ogawaa, Interdisciplinary Institute of Science, Technology and Art of Tsukuba, Japan: A New Type of Transformation from 4D to 3D and Some 3D Designs

Professor Ogawa showed a particularly attractive R-P sliced torus model.

Amy Szczepanski Department of Mathematics, University of Tennessee at Knoxville Designing Patterns for Knitting Geometric Shapes Lite Project on-line

George Bohigian An Ancient Eye Test Using the Eight Stars of the Big Dipper

Al-Sufi, Arabian Astronomer ca. 800 AD (see WikiPedia entry) -- 5 arc-minutes ocular acuity equals 'E' of 20-20 line

Dick Esterle, Nobbly Wobbly, Eight Ways to Sunday and the Amazing Geometry Machine

Liberty Science Center, NYC; Bicycle-Wheel Cuboctahedron

Neil J. A. Sloane, AT&T Shannon Labs Eight Hateful Sequences

'667': The FAX number of the Beast.

Curling Numbers: XYYY...Y of the form XYk

The Traveling Salesman Problem on the Torus

Neil Sloane is the maintainer of The On-Line Encyclopedia of Integer Sequences

Alan Schoen, SIU Carbondale (Retired), "Five Platonic Polyhedral Puzzles"

24! ~= 6.02 x 1023

I had the opportunity, Saturday evening, to talk at some length with Alan Schoen. He was employed for some time at California Institute of the Arts. He took the position at SIU previously held by R. Buckminster Fuller.

Yossi Elran, Weizmann Institute of Science, Rechovot, Israel, A Graeco-Latin Search Game

Also: http://www.weizmann.ac.il/home/nyyossi

The links are a bit obscure, being in Hebrew...
Freetranslation.com doesn't do Hebrew.

Yossi Elran's presentation was on a superposition of two Greco-Roman games based on Magic Squares.

Harold Jacobs, Euclid in Color

From Edward Tufte's Visualizing Information

Jacobs has undertaken the task of digitally restoring Oliver Byrne's edition of Euclid's Elements in Adobe Illustrator.

Scott Aaronson, Massachusetts Institute of Technology Limits of Quantum Computers

Or, "What we won't be able to do with a computer we don't have."

Here, Scott Aaronson disproves Schor's 1994 Quantum Factoring Algorithm.

He began by invoking Stephen Wolfram's Principle of Computational Equivalence.

He mentioned an experiment I had not heard of, in which BuckyBalls exhibit wave-particle duality passing through a double-slit. I had previously only experienced this optically.

Other, interesting references with which I was not previously familiar:

Friday, March 28th, 2008

Michele Emmer, Dipartimento di Matematica, Uni-Roma, Italia, The Adventure of the Square

At 8:30AM, Professore Emmer could not be found, so we watched his 1987 film, "Flatlandia" on DVD -- his dramatization of the book, "Flatland", 1881 by Edwin A. Abbott.

Slavik Jablan, The Mathematical Institute, Serbia, Knot Theory - Some Open Problems

Knot Link -- Shadows, "Because we are all Flatlanders in a certain sense."

Hard Unlinks and Unknots

We know the isitopy operations, but not the order of their application.

Conway Tangle Notation

Knot-Link as a Sequence Generator

See also: Neil Sloan's Encyclopedia of Sequences

Robert Wainwright, New Rochelle, NY, Digital Challenges

Not the kind of digital challenges I was imagining. An integer game derived from Martin Gardner.

Base Digits (1,2,3,4) Arithmetic Operations -> Target(8)

Adrian Ocneanu, Pennsylvania State University, Mechanical Quaternion

OctaCube - 24-X Octahedra

To transform from 4D onto 3D,
Project onto a sphere, then open the sphere into a stereographic projection.

Rubick's Hypercube -- 2x2x2x2

4-D Sculpture -- Mechanical, gear-driven, Euler-angle differential-transmission.

Add 3 copies of Euler-angle differential-transmission -- in Hypercube configuration -> through Sphere-Mapping -> Stereographic Transform -> Mechanical Quaternion Machine.

Scott Morris, Amazing Eight

Empirically lucky penny -- tossed 44 pounds (20Kg) of pennies -- 50% land heads-up -- discard tails -- re-toss heads, repeat... one penny landed heads 18 times in a row.

Numerology of Eight

3/28/08 (G4G8) is the 88th day of the year.

Seven-Segment 8The seven-segment eight encompasses all other digits.

Beijing Olympics will open at 8:08 AM, 8/8/08

Chinese -- "ha" = prosperity

Thoth - God of Moon

8-fold way of Buddhism -- see also: Carlo Sequin

"Raise 8 and a star will appear."

Bruce Oberg, Sucker Punch Productions (video game company), Bellevue, WA, I H8 8

A rebuttal -- 0100 octal

October, 8th month (Julian), Scorpio, 8 legs, 8th sign

Dharma Wheel The Eight-Fold Way

Lee Algebra Group E-8

Hirokazu Iwasawa, Yokahama, Japan, Tricky Solutions for Integrals with Crazy, Lazy Eight

Definite Integral Puzzle Recreation

Improper Integrals, Gaussian, Fresnel Integrals

Raymond Smullyan, Magician-Philosopher, Elka Park, NY, Puzzles and Paradoxes

"Never tell all you know." -- Raymond Smullyan
"I've already told you more than I know" -- Jay Sloat, "Dinosaur" Production Software Supervisor

Smullyan is the Daily Puzzle columnist at PianoSociety.org.

The Barber who shaves everyone in town who doesn't shave himself -- proves that borbers don't exist.

"Only an idiot would believe this sentence!

Frans de Vreugd, Katwijk, Netherlands Puzzle locks from India

Kishar of Bombay hired as guide to locate Indian puzzle locks. Dr. Shah, pediatrician, architect of his own house. His puzzle lock collection -- over 500;

Karl Schaffer, De Anza College/Dr. Schaffer and Mr. Stern Dance Ensemble, Imaginary Dances

Quaternion of order Eight

Air on the Dirac Strings (see George Francis).

Karl Schaffer/Mr. Stern: "Imaginary Dances"

Rebecka: "Should Mathematicians Dance?"
Circle Dance Ensemble: "Everyone can dance!"

Ed Pegg, Jr, Wolfram Research, Inc., Champaign, IL, Meet the Attendees

Ed is wearing a Numb3rs T-Shirt


Michale Sklaar: "Thought is a subversive process."
ThoughtJuggler Events

George Hart: Brunelleschi Buono Blind Psychology Documentary

Saturday, March 29th, 2008

Rhonda Roland-Shearer, Art-Science Research Laboratory, How Marcel Duchamp, Dada jokester's original optical illusions and photo trickery put "ha ha" into the "aha!"

Stereo 3D without left-right eye image separation -- See Craig Hobbs

Duchamp's "Coat Rack"/"Hat Rack"s -- Photographic, Rational Cubism -- Absurd objects achieved through sequential photo-compositing.

Zdravko Zivkovic (Novi Sad, Serbia), Toby Gottfried and Kate Jones Tiling with Edge-Colored Octagons

Octagonal Edge-Matching Puzzle/Game -- DORIS (TheoDORa + ISadora)


Carolyn Yackel, Mercer University, (Knitting) Josephine's Hyperbolic Pants

Hyperbolic pants -- parameterized on the octagon:
                /              \
      outseam  /                \  outseam
              /    8-coloring    \
             o                    o
             |                    |
       cuff  |       on  the      |  cuff
             |                    |
             |                    |
             o    Double-Torus    o
              \                  /
      outseam  \                /  outseam
                \              /
Animate it! - SPD

With Sara-Marie Belcastro Josephine -- Sister of Joseph -- The Pants of many Colors

Stanley Eigen, NorthEastern University, The 2008 IG Nobel (Awards)

The Annals of Improbable Research

Jean Pederson, Santa Clara University, Stop Sign Theorems (on the Pascal Triangle)

"It works for a green parallelogram, will it work for a red parallelogram?"

Geometric proof of generalized Star-of-David Theorems

6, 8, 12 vertices; 2n = 10? (n=5)

Ken Knowlton, Budd Lake, NJ, Geometric Strategies for "Knowlton" Mosaic Tilings

"Do not associate Bell Labs with ASCII-Art Nude." (With Leon Harmon)
LATER (After New York Times article - 1970): "Be sure you mention Bell Labs."

I experienced the same contradiction at AT&T -- and in conversation with Lillian Schwartz.

Andrew Feuerstein in spools of thread.

Will Schwartz as NY Time Crossword.

I talked to Ken Knowlton after his talk, comparing notes on our respective times at AT&T Bell Labs. He left in 1982. I left in 1984.

Ken said: "Read my essays on-line and respond with e-mail."

Bill Cutler, A New Puzzle(-Solver) Program

Bill Cutler's program solved Stewart Coffin's Puzzle Challenge.

Algorithm: Exhaustive tree-search and classify solutions for design.

Archimedes' Square -- August, 2003 -- Vector Box-Fill algorithm.

Edi Nagata's 4-Arrow puzzle + Stewart Coffin -- Intended solutions do not follow a grid.

BoxPoly -- A general 2-D packing program.

Throw & Jiggle -- Q: Does the program catalog and avoid failed trials? A: No.

Roger Malina, Mathematics Made Flesh: Art, Scientific Simulation and a Life


C. P. Snow: "Two Cultures" (1959)

Eugene Wigner on the "Unreasonable Effectiveness" of Mathematics to model Nature.

LEONARDO Books: P. Fishwick: "Aesthetic Computing"

ISAST: F. Malina, Director, NASA/JPL;
F. le Lionnais, Mathematician; Oulipo ("Ouvroir de littératurepotentielle" -- "workshop of potential literature") -- (with Marcel Duchamp!)

60th anniversary: Cybernetic Serendipity

VIDA competition for artistic creativity in the field of Artificial Life, Telefonica foundation, (Espania), A-Life (Conway)

Sebastien Perez-Duarte, Frankfurt, Germany, Conformal Mappings and Photography

Tiled Spherical Views. 4π -> Sphere; Tileable projection.

Impossible lenses. Square or Hexagon, Triangle domains;

Use for CGI texture tiling

Ted Nelson, Filmmaker, Oxford Internet Institute, A New Agenda for Mathematics

Xerox-PARC Document proposal: Version-Control Extensions to Hypertext.

HyperChronicle -- Hyper-Thogonal Structured Web browser UI presentation.

Factories turn out rejects in centrally-planned societies. Therefore, central planning has no place in public education. (Education should not be public.) Alan Greenspan states this in The Age of Turbulence. Advance only comes through competition. Public Education has no motivation to compete.

In Central Planning, all curricula become political.

The Tri-Fold Brochure as an Artform: Welcoming, Initiative and Engaging.

Legitimation of Choosable Pathways.

Juggling Notation (presented yesterday)

Robert Bosch, Oberlin College, Recent Progress in Opt Art

Single-line (space-filling curve) shaded drawing -- Recursive solving the Traveling Salesman Problem.

Esher Tesselation in Fish.

Buddhist Endless Knot -- TSP on a torus?

Robert Fathauer, The Art of Fractal Knots

Fathauer's talk is posted as a link from Tessellations.com.

Knot Tessellation animations -- 2-D Photoshop -- not 3D

Dale Seymour, Teacher, Los Altos, CA, Introduction to Tessellations

Problem-solving in High School. (See Ted Nelson)

Escher Tessellations.

Jerzy (Jurek) Kocik, Southern Illinois University, Looking Through the Apollonian Window

"The HyperSkeptic does not believe skeptics."

Descartes Configuration

Leibnitz -> Apollonian Gasket

Integer-Valued Curvatures
Pythagorean triples - Triangles
Connecting circles

Vesica Piscis

Sequence Generators
Lens series Encyclopedia Sequences:

Tanya Khovanova, Massachusetts Institute of Technology, Number Gossip

OEIS Sequences

Barry Cipra, Northfield, MN, Sudokuniqueness

Intersection of a sphere with a cylinder -- what is the remaining volume?

V = (4/3)π3 -> 36π

Child with the Wart puzzle

Hermione Granger and the Seven Bottles problem


Glenn Iba, Lexington, MA, Explorations of Dynamic Tiling

3D Tetris implemented in LispWorks on MacOS -- Win32 -- Linux?

Like an inverse tiling solver

3-D extensions -- W x H x D

Sunday, March 30th, 2008

Mogens Larsen, Dept. of Maths, Univ. of Copenhagen, Denmark, Physical Mathematics (and Geometric Proofs)

Trisecting an angle

Cube-roots of Compass Numbers

Adam Atkinson, Applications of Vampires in Law and Medicine

Numb3rs, Mythbusters, Buffy, ...

Ultraviolet -- UK Vampire show.

Carlo Sequin, Department of Computer Science, University of California at Berkeley, Art and Math Behind and Beyong the Eight-fold Way

See: Helaman Ferguson -- Physicist's Elementary Particle Interactions.

Siddharta Gauntama (Buddha)

Klein's Quartic in 3D from 4D
Parameterized on the Poincaré Disk.

Helaman -- Petrie Paths on Klein's Quartic.

Jane Yen (1997), Yung Shon (2002), Programs for tiling genus 0,1;

Pushkar Joshi (2007) -- Lizard Tetrus

Polyhedral frame and smooth it -- like François Apéry's Optiverse via Ken Brakke's Evolver.

Four-Color Tiled Assembly in FDM.

Stewart Dickson Vedic Geometry and Tactile Mathematics