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.

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.

Curling Numbers: XYYY...Y of the form XY^{k}

The Traveling Salesman Problem on the Torus

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

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.

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.

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

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:

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

Example:

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

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.

Numerology of Eight

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

The 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."

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

Dharma Wheel The Eight-Fold Way

Lee Algebra Group E-8

Improper Integrals, Gaussian, Fresnel Integrals

"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!

Air on the Dirac Strings (see George Francis).

Karl Schaffer/Mr. Stern: "Imaginary Dances"

Rebecka: "Should Mathematicians Dance?"

Circle Dance Ensemble: "Everyone can dance!"

Michale Sklaar: "Thought is a subversive process."

ThoughtJuggler.com

ThoughtJuggler Events

George Hart: Brunelleschi Buono Blind Psychology Documentary

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

waist o------------o / \ outseam / \ outseam / 8-coloring \ o o | | cuff | on the | cuff | | | | o Double-Torus o \ / outseam \ / outseam \ / o------------o waistAnimate it! - SPD

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

Geometric proof of generalized Star-of-David Theorems

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

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."

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.

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 ("**Ou**vroir de **li**ttÃ©rature**po**tentielle"
-- "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)

Impossible lenses. Square or Hexagon, Triangle domains;

Use for CGI texture tiling

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)

Esher Tesselation in Fish.

Buddhist Endless Knot -- TSP on a torus?

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

Escher Tessellations.

Descartes Configuration

Leibnitz -> Apollonian Gasket

Integer-Valued Curvatures

Pythagorean triples - Triangles

Connecting circles

Vesica Piscis

Sequence Generators

Lens series
Encyclopedia Sequences:

- # A011922
- # A064170
- # A00644
- # A032

V = (4/3)π^{3} -> 36π

Child with the Wart puzzle

Hermione Granger and the Seven Bottles problem

"Sudokubiquitous"!

Like an inverse tiling solver

3-D extensions -- W x H x D

Cube-roots of Compass Numbers

Ultraviolet -- UK Vampire show.

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.