Seeing through the layers

Presentation by Kate Jones

at 2010 Double Festival of

Project Renaissance

Seeing through the layers

• Life is a puzzle, and certain principles of system viability apply to both. I will be using puzzle images to illustrate the coherence, integrity and beauty of the Universe and, by extension, of the human mind.

• Both the physical Universe and the individual mind evolve through emerging layers of combinations, from unity to complexity, from chaos to organization. Both are combinatorial.

Bears in DaVinci poses

Polyominoes sizes 1 through 5

Rhombic Pentominoes

Sextillions (the 35 hexominoes)

The 108 heptominoes

The 369 octominoes

All polyominoes 1 through 9

The polyiamonds 1 through 7

The 66 octiamonds

The polyhexes 1 through 5

The 82 hexahexes

Rombix Jr., octagon dissection

Countless patterns

Rombix – 16 sides

Rainbow Rombix – 24 sides

Roundominoes – circle forms

Super Roundominoes

Grand Roundominoes

ChooChooLoops – arc forms

Matching by color - squares

Matching by color - triangles

Matching colors - hexagons

Matching colors - rhombs

Matching colors - octagons

Matching colors - triangulated

Matching colors – “Boats”

Matching colors - dodecagons

Matching paths - squares

Matching paths - hexagons

Matching paths - octagons

Matching paths - pentarcs

Matching shapes - squares

Matching shapes – 4 elements

Matching shapes - triangles

Matching shapes - hexagons

Matching shapes - pentagons

Matching shapes – wavy fives

Fitting shapes – “Whirlspools”

Fitting shapes – “Tulips”

Fitting shapes – seven-fold

Colors plus shapes – “Cubits”

Colors/shapes – “Diamond Star”

Colors and shapes – “Q-Bix”

Colors/shapes – “Quintapaths”

Colors/shapes – “Hexdominoes”

Colors and shapes – “Intarsia”

Combinations without limit

Harmonic balance

A short philosophical excursion

• Intarsia's simplicity—just two kinds of tiles—illustrates dramatically the amazing capacity of life, the Universe, and everything to build to complexity from varying combinations of the most elementary particles. At the human level of just 32 pieces, you can manipulate them with your own hands and reorganize them at will.

• To calculate the total number of possible placements in the tray takes heroic mathematical calculations. An analysis by friends yielded a mind-boggling total of 10 to the 24th power. That's a 1 followed by 24 zeroes!

• One pair of tiles can join to form a hexagon. We can pair them 3 ways. In each pair a tile can be either side up, giving us 4 different combinations for each of the three pairings, or 12. But a hexagon can have 6 orientations, so we get 12 times 6, or 72, including rotational equivalents. And we're only at the first step.

• How many ways can all 32 tiles be paired? That's 32-factorial, or 32x31x30x29... It's nice to know we have so many options, so many choices with which to bring our vision into reality.

• Gene Roddenberry, the creator of Star Trek, had a great motto: IDIC — "Infinite diversity from infinite combinations." We rediscover the truth of that with every Intarsia arrangement. Even when the total of possibilities is beyond the range of our ability to encompass, we can glimpse it and play with it in beautiful ways. Our minds can touch the infinite and feel its echo in ourselves.

A poetic summation

• The Universe, Life and Everything in 153 syllables

• Illustrated by Intarsia designs from the singularity to human intelligence and beyond.

See the slide show,

“9 Fine Lines of Thought”.