## 07 September 2010

### Datura

Size: 34” Wide x 55” Tall

Medium: Oil on Canvas

Date: JUL 2010

No Longer Availabl

The structure, symmetry and growth patterns of plants often follow the “laws” of nature which are defined by the Fibonacci series of numbers. If you measure the distance between leaves on a plant, you'll find the phi relationship which is approached by taking the ratio of two adjacent Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55...) and if you count the number of petals on a flower, you’ll frequently, although not always, find Fibonacci hiding there as well...

Datura and Cannas have a single blossom

Only a few plants have just 2

Clover leaves, Ivy, Poison Ivy are all 3-leaved

Malva sylvestris, Goldenstar, Vinca, Blueheart & Geranium all have 5 petals

Coreopsis has 5 petals

Pine Cones have 5 / 8 rows of spirals going in opposite directions

Daisies have 13, 21, or 34 petals, depending on the variety

Sunflowers have a spiral seed pattern of 55 / 34 rows going in opposite directions

Datura, beautiful but poisonous, is shown over a Golden Section Diagram

### Homage to Fibonacci

Size: 34” wide x 55” tall

Medium: Oil on Canvas

Date: 2010

No Longer Available

I am fascinated by the proportions and natural growth patterns of nature. The physical structure and proportions of plants correlate to those of humans, animals and insects. The rhythms and patterns in nature resonate with a frequency that, like a tuning fork, sets the tone for all living creatures.

This painting honors Fibonacci, the greatest mathematician of the middle ages. Leonardo of Pisa (1170-1240), known as Fibonacci (son of Bonaccio), wrote Liber Abaci (literally, Book of Calculation) which introduced Western Europeans to the ten-digit Hindi -Arabic numerals, the concept of zero as a number, and the ‘place-value’ method of calculating that we use today, as well as a fascinating sequence of numbers that we now call the Fibonacci Series.

The Fibonacci Series, closely related to the Divine Proportion (aka Golden Section), is observed in phylotaxis, the study of the ordered position of leaves on a stem. This phenomenon occurs from the dynamics of plant growth which creates the spirals that can be seen in sunflowers, pine cones, and twining vines. It is referred to as a ‘law of nature’.

The number of petals found on a flower is quite often one of the Fibonacci numbers, especially 3-5-8-13-21-34-55 and 89-petaled flowers. Daisies commonly have either 21 or 34 petals. The arrangement of the florets (which turn into seeds) of Sunflowers is a spiral, with 55 spiraling out in one direction and 89 spiraling out in the other direction (or 21/34 or 34/55). These are logarithmic or equiangular spirals.

Starting with the number 1, add it to the number before it. Continue adding each number to the one before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610… When you divide each successive pair of Fibonacci Numbers (3:2, 5:3, 8:5), you get a ratio.

The farther along the series you calculate the ratio, the closer and closer you get to a very specific irrational number, 1.618…, called phi, which is prevalent in the natural world. Phi is also known as the Divine Proportion or the Golden Section.

The number sequence and the Hindu-Arabic place-value method of calculating were well known to ancient Indian mathematicians who applied it to the metrical sciences (prosody, the study of rhythm in music and poetry). To give them credit, their names can be found in the upper portion of the painting (Pingala, 200 BC; Virahanka, 6th Century; Gopala and Hemachandra 12th Century).

This painting is on a board that has Golden Section proportions (Fibonacci Numbers 34 & 55). Zinnias, Devil’s Walking Stick in foreground

## 12 July 2010

### One Squared, aka Homage to the Weed

Title: One Squared, Homage to the Weed

Size: 34" Wide x 55" Tall

Medium: Oil on Canvas

Date: JUL 2010

No Longer Available

We have this bizarre concept that we're individuals. We think of ourselves as separate. See the man? He's like the number 1....alone, singular, even vertical and narrow....and they both hide themselves. The man (or statue) turns his back as if rejecting the rest of this overgrown world.

The Weed, on the other hand, stakes its claim to this handful of dirt. A lowly weed, but straight and bold...certain of its place, understanding of its oneness in a way the man cannot...the oneness of pure consciousness. Without thought. It has no concept of separateness and so is closer to what is real than all our thoughts added together.

Plants frequently --- not always --- follow the Fibonacci series of numbers in their growth patterns and in their symmetry. If you count the number of leaves on a plant, you'll find the Fibonacci numbers...1 - canna blossom, 2 - a pair of opposite leaves, 3 - a clover leaf, 5 - the pentagon shape in an apple core...or 55 seeds going in one direction & 89 seeds going in the opposite direction in a sunflower.

I call this painting ONE SQUARED because...well, you can't really turn a one into a square, but I already painted ONE painting called ONE....so, in contemplating calling it One, II, ONE TWO, ONE SECOND or ...well...ONE SQUARED came into my consciousness. ONE times ONE is always ONE. To square it is as insignificant as adding zeros.....as insignificant as a WEED.

This particular weed is Vicia grandiflora, commonly known as Vetch.

Available through Brunner Gallery at www.brunnergallery.com

## 30 April 2010

### 1.618

Title: 1.618...

Medium: Oil on Canvas

Size: 34" Wide x 55" Tall

Completed: APR 2009

## 22 October 2009

### Homage to Pythagoras

Painting Title: Homage to Pythagoras

Size: 34" wide x 55" tall

Medium: Acrylic on Board

2006

**No Longer Available**

Pythagoras (569-475 BC) was a Greek philosopher who made important discoveries in mathematics, astronomy and music theory. He is best known for the mathematical theorem named for him. The Pythagorean Theorem, written ALGEBRAICALLY, is

It is depicted VISUALLY as the central motif, with the word PROOF alongside it. The Babylonians knew about this theorem1000 years earlier, but Pythagoras proved it.

He, or rather one of his followers, also proved that irrational numbers exist, as shown in the mathematical proof in the upper portion of the painting. Phi, written

is found in the relationships between the sides, the edges and the vertices of the Platonic Solids, and was considered by the Pythagoreans to be so significant that they were sworn to secrecy on the subject. When Hippasus of Metapontum (who is credited with discovering the dodecahedron) divulged the secret of the existence of the irrational, he was thrown in the river and drowned. Phi, expressed to about 20,000 places is printed to the surface in the painting.

Pythagoras discovered the mathematics in music. By dividing a string into sections, so lengths have the ratios of 2:1, 3:2, 4:3, or 5:4 (octave, fifth, fourth, third), harmonic tunes result. He was quoted as having said, "There is geometry in the humming of the strings". In music theory, the diatonic scale, depicted on the left side of the theorem proof, is a 7-note musical scale with the pattern repeating at the octave (diatonic is translated by Greek, meaning literally "progressing through tones").

Pythagoreans discovered the dodecahedron, the fifth regular/Platonic solid. Actually, Neolithic people of Scotland 2000 BC knew about these shapes, as evidenced by the stone carvings they left behind. However, the Pythagoreans were enamored and studied these shapes.

If you fit any regular solid just inside a sphere, all the vertices touch the inside of the sphere. If you fit a sphere just inside any regular solid, it touches all the faces of that regular solid.

The Pythagoreans believed that the universe consisted of a central, spherical earth surrounded by one of the five regular solids, in turn surrounded by a crystalline sphere surrounded by another regular solid, and so on until five spheres surrounded the earth, each circumscribed about a regular solid. The planets and the stars were attached and, as they rotated, created musical harmonies. The Pythagoreans believed most people couldn’t hear this "harmony of the spheres" because they had grown accustomed to it from birth, but that Pythagoras alone could hear it.

The space is broken up into a Golden Section Proportion. Click here to go to the Museum of the Golden Ratio

## 21 October 2009

### Homage to Napier

Medium: Interactive Mixed Media

Size: 64" Wide x 57.75" Tall

Number Columns 4" x 48" each

Year Completed: 2006

No Longer Available

John Napier (NAY-peer) (1550-1617) was a Scottish mathematician. He is responsible for the development of Logarithms. He spent twenty years on his theories and in 1614 published them in a book Mirifici Logarithmorum canonis descriptio (A Description of the Wonderful Law of Logarithms).

This piece is based on an abacus, called "Napier's Bones", that was developed by John Napier. It was a system for calculating products and quotients of numbers. It was used until the mid 1800's and is considered a precursor to the calculator & thus the computer.

This is an interactive piece. Each "stick" comes out and can be moved into any slot to line up the numerals necessary to make up the number you want to multiply or divide.

Instructions for use: Go to http://en.wikipedia.org/wiki/Napier

In November, 2008, I taught a MATH / ART workshop to High School students in Tupelo, MS...the Art students did paintings based on "math" or "numbers" & the Math students created this Napier's Bones work of art:

Labels:
abacus,
calculator,
logarithms,
mathematician,
Napier

## 20 October 2009

### INFINITY

### Prime

Labels:
Euler,
Fermat,
Ferrier,
Fibonacci,
Gauss,
Genocchi,
Mersenne,
Prime,
Prime Numbers,
Riemann,
Riemann's Landscape,
Zeta Function

### Homage to Euclid

2006 Installation - Brunner Gallery

Wall Panel 33.75" Tall x 101.75" Wide Framed

(21" x 89" Inside)

Platonic Solids Varied Sizes

No Longer Available

Euclid was a Greek mathematician who lived in Alexandria, Egypt around 325-265 BC. He is called "the father of Geometry" and is most famous for his 13 books known as The Elements. He is credited with the PROOF of the 5 polyhedra also known as the Platonic Solids, even though these shapes were known for centuries (the oldest CARVINGS are from Scotland around 1500 BC, carved by NEOLITHIC man), long before there was any math to prove anything.

This installation consists of a large Mahogany Panel which has images, routed into the surface, of each of the 5 Platonic Solids circumscribed within a circle. They are, from left, the Tetrahedron, Octahedron, Heptahedron, Icosahedron and Dodecahedron, thus named for the number of sides on each shape (4, 8, 6, 20, 10). And, YES, I realize they're "out of order". I'll happily show you my Creative License which gives me permission!

In front of the panel are the 5 Platonic Solids in 3-d form. They are made of mdf & painted black with a lacquer finish. Imagine blowing up a balloon such that a perfect sphere surrounded each of these objects... each of the vertices would touch the balloon.

I want to give credit to my son, Rodney Tassistro-Drennen. Together, we figured out the angles (the dihedral angle for the dodecahedron was a killer). Rodney engineered all these pieces using the design software program he uses for cabinets, and who cut out all the parts, built the frame & glued together the Platonic Shapes. Without him, this piece would still be just an image in my head.

## 30 September 2009

### Zero

**Painting Title: Zero**

Size: 34" wide x 55" tall

Medium: Acrylic on Board

This painting is on a board that has Golden Section Dimensions.

The Space is broken up into the Golden Section Proportions.

No longer available

Zero has two uses…both important, but distinctly different from each other.

One use is as an empty place indicator in our place-value number system. For instance, in the number 102, the zero is used simply to put the 1 and 2 in the correct "place". When the place-value use of zero was introduced, a simple dot was used…note the diamond-shaped dot…the ancient Hindu form called the ‘bindu’.

Secondly, the zero is used as a number itself, meaning "none", "empty" or "nothing". Indians used the Glyph "0" as early as 640 BC. Fibonacci, the Italian mathematician who introduced the Hindu-Arabic number system to Europe around 1200, called it a "sign" rather than a number. His name for zero was "Zefiro"---from the Semitic sifr, which meant "empty".

In this painting, the most prominent figure is of the Glyph (symbol) we westerners use for the number zero. The glyphs in the upper right and left corners are ancient Sanskrit. Other words which mean zero are in the painting: nul, null, nol, nula, cipher, etc. Meden agan ……Greek for "nothing in excess"…the wise words of the Greek oracle at Delphi.

At the bottom right, the Greek Gnothi Seauton, means Know Thyself…it is the motto over the entrance to the temple of Apollo at Delphi.

Bottom left: In Quantum Physics, everything is in flux, a world of constant movement, a world of endless possibilities, so I have Zero’s in all sizes and shapes moving through that space…vibrating, swimming in the Akashic Field…ready to spring forth and become…what? A quantity…zero for now, but prepared to manifest. The Zero was, conceptually, the most difficult of all these paintings because as soon as a single mark was made, there was one, a mark…the only real Zero painting would have to be blank. Pulling Zero out of that blankness, manifesting it into solid form, through focus and intention tells a story of Quantum Physics.

One use is as an empty place indicator in our place-value number system. For instance, in the number 102, the zero is used simply to put the 1 and 2 in the correct "place". When the place-value use of zero was introduced, a simple dot was used…note the diamond-shaped dot…the ancient Hindu form called the ‘bindu’.

Secondly, the zero is used as a number itself, meaning "none", "empty" or "nothing". Indians used the Glyph "0" as early as 640 BC. Fibonacci, the Italian mathematician who introduced the Hindu-Arabic number system to Europe around 1200, called it a "sign" rather than a number. His name for zero was "Zefiro"---from the Semitic sifr, which meant "empty".

In this painting, the most prominent figure is of the Glyph (symbol) we westerners use for the number zero. The glyphs in the upper right and left corners are ancient Sanskrit. Other words which mean zero are in the painting: nul, null, nol, nula, cipher, etc. Meden agan ……Greek for "nothing in excess"…the wise words of the Greek oracle at Delphi.

At the bottom right, the Greek Gnothi Seauton, means Know Thyself…it is the motto over the entrance to the temple of Apollo at Delphi.

Bottom left: In Quantum Physics, everything is in flux, a world of constant movement, a world of endless possibilities, so I have Zero’s in all sizes and shapes moving through that space…vibrating, swimming in the Akashic Field…ready to spring forth and become…what? A quantity…zero for now, but prepared to manifest. The Zero was, conceptually, the most difficult of all these paintings because as soon as a single mark was made, there was one, a mark…the only real Zero painting would have to be blank. Pulling Zero out of that blankness, manifesting it into solid form, through focus and intention tells a story of Quantum Physics.

Labels:
0,
bindu,
connections,
Empty,
Golden Section,
Null,
physics,
potentiality,
quantum physics,
Void,
Zefiro,
Zero

## 31 July 2008

## 30 July 2008

### SEVENTEEN

Oil on Canvas

34" Wide x 55" Tall

2007

Available through Marion Drennen

There are 17 symetrical patterns, referred to as "wallpaper" patterns, from which all patterns are made. The Mathematician Gauss proved that the 17-gon (a polygon with 17 sides) is the largest polygon that can be created with a ruler and a compass. "Pattern" in different languages: Dutch: knippatroon, patroon Finnish: kaava French: schéma, prototype, pattern, ouvrer Hungarian: minta, séma, példa, motívum Italian: esemplare, campione di merce Latin: exemplum, exemplar Russian: образцовый Spanish: muestra, muestra, pauta, modalidad, patrón Swedish: förebild, mönster, model African: patroon, skema Japanese: ruikei, shihyou, moyou, gara, genkei, gikei, egara Norwegian: mønster Sanskrit: प्रतिमान transliteration: pratimaana आदर्श aadarza निदर्श nidarza Arabic:

**أسلوب**Portugese: teste padrão “Seventeen” in different languages: African: sewentien Danish: sytten Dutch: zeventien Finnish: seitsemäntoista French: dix-sept, dix sept Hungarian: tizenhét Italian: diciassette, diciasette Japanese: juunana, juushichi, sevunti-n Norwegian: sytten Portuguese: dezessete, dazassete Russian: семнадцать Spanish: diecisiete Swahili: kumi na saba Swedish: sjuttonde Arabic:

**سفنتين**Greek: δεκαεπτά Chinese transliteration: shi qi Sanskrit: सप्तदश transliteration: saptadaza

### ALEPH NAUGHT

2007

21"w x 34"t

Oil on Board

Available through Marion Drennen

Aleph is the first letter of the Hebrew alphabet. George Cantor used it as the symbol for his set theory of different sizes of infinity...hard to wrap your brain around, but Aleph Naught is the smallest infinity.

## 25 February 2008

### TEN

Size: 34"w X 55"t

Medium: Oil on Canvas

Date Completed: 2007

Date Completed: 2007

Available through FlyCoopStudios, Asheville, North Carolina

In Nov, 2008, I taught a workshop in Tupelo, MS for high school Art & Math students. Here's a photo of one of the Art Students working on his Number (10) / Math Concept Painting.

HMMMM.....Art students warming up to Math.....to see Math students warming up to Art, see the photo at my Napier's Bones entry.

## 23 October 2007

### Number is the Within of All Things

Size: 13" x 13"

Media: Mixed Media on Wood with Clay Sculpture, Acrylic Paint

Date Completed: 2006

Number is found everywhere, at every level; it IS the "within" of all things (as Pythagoras said).

Available through Marion Drennen

## 30 December 2006

### One

Size: 36" Wide x 60" Tall

Medium: Acrylic on Canvas

2007

**No Longer Available**

The most basic of all glyphs is the vertical line, originally a tally mark depicting a single unit. Since it also has connotations of God, a single vertical mark --- centered, bold and white --- was used as the first/original mark on this painting.

The sensuous Sanskrit glyph for one that overlays the white, vertical ONE mark means refined, consecrated and sanctified. Sanskrit (4,000 years + writing system), considered the "high, classical" Indian language, is used in religious and scientific applications, much as the romantic languages consider Latin to be classical and use it for religious and scientific applications. Sanskrit is the liturgical language of Hinduism, Buddhism, and Jainism.

The Sanskrit word for one, (pronounced eka), in the upper left, has been filled with Sanskrit text, which is translated as:

*All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards ONE another in a spirit of brotherhood.*

This is Article ONE of the United Nations’ Universal Declaration of Human Rights

Other interesting facts:

- ONE is the only digit that, when pronounced in English, has the same number of syllables as its valueIn all monotheistic cultures, ONE is identified with God.
- ONE has an interesting double meaning: first/smallest and most whole/complete.
- ONE is also the:
- First odd number (and the smallest positive odd number)
- First ordinal number (FIRST, PRIMARY, PRINCIPAL, INITIAL, BEGINNING)
- Lowest cardinal number

*has two cardinal values:

SMALLEST, MOST BASIC UNIT (one, unit, unity, solo, single, mono, uni-)

WHOLE, COMPLETE, TOTALITY (we are one---with the universe, nature - Atomic Number for Hydrogen
- Aries is the first astrological sign of the Zodiac
- Ancient Greece: 1 was not a number, only a unit. Two was considered the first proper number.
- ONE is the square of ONE, and also the cube of ONE.

## 29 December 2006

### Two

Painting Title: Two

2007

42" w x 34" t Diptych (each piece is 21" x 34")

Acrylic on Board

To evoke a sense of the number 2, this piece was painted on 2 panels. The 21" width and 34" height are in the Fibonacci Series of numbers, making their relationship approximating the Golden Ratio…the space is then divided into that relationship. The lower portion has strips of space that are broken down into Fibonacci Series dimensions also. The 2 large black dots were the Glyph used by the Mayans to depict the number 2. It is important to retain a sense of humor when dealing with all this, so included in this painting is this bit of silliness which reads: tea for two, couples, dos equis which is pretty good beer…2 sides to every story, 2 sides of the bed which actually has four, as well as 2 halves in a whole, 2 ends to every length, and humans have 2 legs, 2 arms, 2 eyes, 2 ears, 2 nostrils, 2 breasts. The 2 of Clubs is the lowest card in the deck. If you wear a tu-tu, you might dance a pas de deux. 2 wings on a bird. 2 tusks on an elephant. A 2 is necessary for the concept of opposites. It’s the first even number. Words for the number 2 in different languages used throughout the painting: Ancient Greek: duo Anglo-Saxon: twegen Aramaic: tareyn Armenian: erku Avestan: bae Baltic: dy, dyj Breton: diou Chinese: er Danish: to Dutch: twee English: two, distich, deuce, double,doubleton, due, duo, pair, twain, yoke, binary, brace, couple, couplet, duad, dyad, span, twosome French: dau German: zweni Old High German: zwene Gothic: twai, twa Hebrew: bet Italian: deux Indian: dvi, ashvin, yamala, Yugala, netra, bahu, Yama, qulphau, paksha Japanese: ni, putatu Korean: tul Latin/Roman: dos Lithuanian: du, dvi Oscan: duo, duae Old Erse: dau Old Icelandic: tveir Old Saxon: twene Polish: dwa Romanian: do Russian: dvau, dva, dvi Church Slavonic: duva, duve Sanskrit: dvau, dva, dvi Scots Gaelic: dwy, dau Spanish: doi, dos Swedish: tva Thai: song Tokharian A: ta Tokharian B: wu, we Welsh: dow

### Three

Size: Triptych 36" wide x 33" tall

(each piece is 12" wide x 33" tall)

Medium: Mixed Media on Wood

2007

Available through Marion Drennen

Ancient Tally Sticks and Clay Tablets that were used for accounting were the inspiration for this piece. Some glyphs are copies of ancient hieroglyphs that were actually used, some I made up.

Tally sticks were used in the same way we use a tally mark now, to count up to 4, then make a mark across it to signify 5 and so on…because the human eye cannot perceive of more than 4 at one time (see "Five").

When tallies were kept on a piece of wood, it was split in half, with one half kept by the seller and one half kept by the purchaser…to prevent either side from changing the quantities.

(each piece is 12" wide x 33" tall)

Medium: Mixed Media on Wood

2007

Available through Marion Drennen

Ancient Tally Sticks and Clay Tablets that were used for accounting were the inspiration for this piece. Some glyphs are copies of ancient hieroglyphs that were actually used, some I made up.

Tally sticks were used in the same way we use a tally mark now, to count up to 4, then make a mark across it to signify 5 and so on…because the human eye cannot perceive of more than 4 at one time (see "Five").

When tallies were kept on a piece of wood, it was split in half, with one half kept by the seller and one half kept by the purchaser…to prevent either side from changing the quantities.

There’s a famous painting by J. M. William Turner titled

Charles Dickens said, "…

*The Burning of The Houses of Lords and Commons*. It depicts an 1834 fire in London that was started accidentally because they decided to burn all the old tally sticks.Charles Dickens said, "…

*it took until 1826 to get these sticks abolished. In 1834 ... there was a considerable accumulation of them. ... What was to be done with such worn-out worm-eaten, rotten old bits of wood? The sticks were housed in Westminster, and it would naturally occur to any intelligent person that nothing could be easier than to allow them to be carried away for firewood by the miserable people who lived in that neighborhood. However [the sticks were no longer] useful and official routine required that they never should be, and so the order went out that they should be privately and confidentially burned. It came to pass that they were burned in a stove in the House of Lords. The stove, over-gorged with these preposterous sticks, set fire to the paneling; the paneling set fire to the House of Commons; the two houses [of government] were reduced to ashes; architects were called in to build others; and we are now in the second million of the cost thereof."*
Labels:
3,
counting,
Number,
tally,
tally mark,
tally sticks,
Three

## 28 December 2006

### Four

2006

42" Wide x 26" Tall Quadriptych

(each piece is 21" wide x 13" tall)

(each piece is 21" wide x 13" tall)

Acrylic on Board

**No Longer Available**

Four panels make up the Number 4 painting. In the center is a square (4 sides) with one of the Arabic Glyphs for "4". There are 4 Noble Truths in Buddhism: in this piece, I see these 4 truths in the panels:

**Upper Left: Suffering Exists**(I see all the words and glyphs for the # 4 as being the constant chatter in our heads…the absence of quiet space)

**Upper Right: Suffering Arises from Attachment to Desires**(the 4-sided pyramid is an "object" and so represents materialism)

**Lower Left: Suffering Ceases when Attachment to Desire Ceases**(more quiet space, holy Readings/ teachings, and the allowing-in of the "bubbles" from the 4th panel…)

**Lower Right: Freedom from Suffering is Possible**(I see the "bubbles" as the sheer potentiality of Quantum Physics, where the space is filled with and surrounded by the # 4, but they move freely, even moving up into the material-based panel above)

None of the panels is just one thing…each has the elements of the others:

*In the **upper left panel**is a large Indian Glyph for "4", with Arabic, Ancient Greek and Mayan

*In the

***upper right panel**, an Ancient Greek Glyph, the 4-sided pyramid, and the Babylonian "4" Glyph**The lower right panel**has a square with a hill shape in it, the Chinese Glyph for "4". The writing: The number 4 is a quantity. It represents "the first born thing" because it is the "…product of the procreative process" multiplication. 2 x 2=4. A four-leaf clover. There are 4 directions in the geographical coordinate system. Four beasts of the Apocalypse, Connect 4, 4 Wheel Drive, The Final 4, Mah Jong: Chinese game of 4 winds, Square Dancing: Hands 4, 4 Star Generals, Hotels and Restaurants, Degas’ 4 Dancers, As a form, 4 is a square and represents materialization. F. D. Roosevelt’s 4 Freedoms: speech, worship, want, and fear. Dogs are our 4-legged friends . The 4 preferences: Extroversion/Introversion, Sensing/ Intuition, Thinking/Feeling, Judging/Perceiving. 4-year College Degree Program, 4 Dimensions: Breadth, Width, Length, Time

**In the square in the lower left panel**, the writing: The four elements> air, water, fire, earth At Seder> 4 cups of wine, ask 4 questions, read about 4 sons The 4th utterance of redemption Aristotle’s 4 causes: Material, Formal, Efficient, and Final 4 – a Rational Number The 4 Evangelists: Matthew, Mark, Luke and John 4 Letter Words are Bad

**Words for "Four" in different languages used in this painting**: Sanskrit: catvaras, catasras, catvari, catur Avestan: cathwaro Tokharian A: stwar Tokharian B: stwer Armenian: corkh Ancient Greek: tettares, tessares, tetores t Oscan: pettier, petora Latin: quattwor Italian: Quattro Spanish: cuatro French: quatre Romanian: patru Old Erse: cethir, cethoir Breton: pevar Welsh: pedwar Scots Gaelic: peswar Gothic: fidwor Old Icelandic: fjorer Swedish: fyra Old Saxon: fiuwar Anglo Saxon: foewer English: four Old High German: vier German: vier Church Slavonic: cetyre Russian: cetyre Czech: ctyri Polish: cztery Lithuanian: keturi

Labels:
4,
Four,
potentiality,
quantum connections,
quantum physics,
tetrahedron

### Five

Size: 36" x 36"Medium: Acrylic on Canvas

2006

No Longer Available

No Longer Available

The central motif is a tally. From pre-historic time, through all ages and even today, this is man’s most basic method of keeping a record of a number. By making a mark for each one thing counted, and by making a different mark for every fifth, this universal symbol speaks of our connectedness to all mankind, across the globe and throughout time.

The human brain cannot comprehend a quantity of more than 4 without the need to count. If one were to glance up at the sky and see 4 birds flying by, it would be easy to know, instantly, there were 4 birds. If 5 birds were in that group and you only had a glance, you wouldn’t know how many were there because you’d need enough time to count them…1-2-3-4-5. That’s why all tally marks have something different happen at each fifth mark…to make it clear there was ONE MORE than FOUR without the need to count.

In the background is the Pentagon, the five-sided shape so important to the Pythagoreans.

All the words and glyphs in the background are the names and numerals for "5" in various languages; some of them are: fimf, fil, peti, pis, pump, pesi, cenci, piat, penti, pente, pan, chica, luna, and penkwe. Note the hand, which has 5 digits.

## 27 December 2006

### Six

2006

34" Wide x 55" Tall

Acrylic on Board

Acrylic on Board

**No Longer Available**

This painting is on a board that has Golden Section Dimensions. The Space is broken up into the Golden Section Proportions.

The lower section is filled with numbers (Phi up to 20,000)that are printed onto the board (archival ink).

"Meia duzia," literally translated from Portuguese, means "half dozen."

The black bar with a dot over it is the Mayan glyph for the number Six.

In the upper right corner, two triangles represent 6.

The central motif is a circle with 6 circles around it.

**If this is about 6, why are there 7 circles?**BECAUSE: If you take a circle of any given size and surround it by 6 more circles of the same size, EXACTLY 6 will fit around it, all touching.

Other interesting things about 6, some of which still shows through in the painting, but most of which was painted over:

*6 is the smallest perfect number (a number whose divisors add up to itself 1+2+3=6).

*6 cubed = 3 cubed + 4 cubed + 5 cubed.

*There are 6 strings on a standard guitar.

*Words that mean six: sextet, sestet, sextuplet, hexad, VI, sixer

*Carbon is # 6 on the Elemental Scale

*The honeycomb made by bees has six sides and exactly six of the six-sided shapes (a hexagon) fits around one.

Click here to go to the Museum of the Golden Ratio .

Click here to go to the Museum of the Golden Ratio .

Labels:
6,
Golden Section,
Mayan,
Phi,
Six,
The Golden Ratio

### Seven

Size: 48" Wide x 36" Tall

Medium: Acrylic on Canvas

**No Longer Available**

Every glyph, word and symbol in this painting means 7, in one language or another.

The graceful backward-S’s are Sanskrit. The 2 vertical lines and the 5-petaled flower are 7 in one of the African languages.

The square (4 sides) with the triangle (3 sides) = 7.

What may appear to be crosses is the Chinese glyph for 7.

7 = The Canopy of Heaven. Seven rhymes with heaven. (And the numeral 7, when flipped over, makes an "L" which rhymes with hell.)

7 is the Holy Number.

7 days in the week, 7 phases of the moon, 7 graces, 7 deadly sins, 7 senses, 7 virtues, 7 precious things of the Buddhists, 7 sacraments, 7 wonders of the world, 7 visible planets, the 7 year itch, the 7 hills of Rome, Snow White and the 7 dwarves.

7 is a prime number

73 is a prime number

739 is a prime number

7393 is a prime number

73939 is a prime number

739391 is a prime number

7393913 is a prime number

73939133 is a prime number

A square piece of paper cannot be folded in half more than 7 times.

The opposite sides of a die cube always add up to 7.

Synonyms for 7 in India: horses, mountains, the sages, the vowels, the 7 oceans, the island-continents, and the idea of "wind" can evoke the # 7.

**Words for 7 in lots of different languages**: sapta, hapta, sipta, spat, schichi, nana, nanatsu, bay, sibun, ewhtn, hepta, septem, siete, sept, shapte, secht, saith, seiz, sfkh, zeven, siau, sju, seven, siben, sieben, sedmi, siedem, septyni, zayin, schevet, schabbat

Labels:
7,
Sanskrit,
seven,
the holiest number

## 26 December 2006

### Eight

2007

Size: 52" Wide x 26" Tall

(Eight Pieces: each piece is 13" x 13")

Medium: Acrylic on Board

Available through Marion Drennen

Size: 52" Wide x 26" Tall

(Eight Pieces: each piece is 13" x 13")

Medium: Acrylic on Board

Available through Marion Drennen

Since the painting is about the # 8, there are 8 small panels. Many of the glyphs, words and symbols in this painting mean 8, in one language or another.

8 = 5 + 1 + 2 and 512 = 8 Eight pints make a gallon.

Eight looks the same when turned upside down (in our written language).

Eight legs on a spider

An Eight is a racing boat with 8 oars. Its crew is also called an eight

Eight people on a tug-of-war team.

Large cars have eight cylinders.

According the Indian mythology, the Earth is supported on the backs of eight white elephants (the only animal that has 4 knees…in case I left that off the # 4 description).

Octopus has 8 arms (or are they legs?)

**Top Row – Left to Right**: An Octagon with the symbol for Uranus (the 8th planet out from the sun); a chess board has 8 rows across and 8 rows front to back; the 3 yellow glyphs are Tibetan for 8. The yellow octagon has the number 8 in various fonts and the tops of 8 fingers.**Bottom Row – Left to Right**: The Octave and the 8-pointed star; eight spelled out on a panel filled with a variety of (language) glyphs; Words that mean 8 (octad, octet, octonary, ogdoad, octuplet, het, and a variety of pronunciations such as the Japanese yatu and tattsu) above a tile pattern using octahedrons, , 2; and an octahedron (an 8-sided polyhedron) in deep perspective with the house-shape created from the linear drawing of the Japanese glyph for 8.8 = 5 + 1 + 2 and 512 = 8 Eight pints make a gallon.

Eight looks the same when turned upside down (in our written language).

Eight legs on a spider

An Eight is a racing boat with 8 oars. Its crew is also called an eight

Eight people on a tug-of-war team.

Large cars have eight cylinders.

According the Indian mythology, the Earth is supported on the backs of eight white elephants (the only animal that has 4 knees…in case I left that off the # 4 description).

Octopus has 8 arms (or are they legs?)

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1 234 x 8 + 4 = 9 876

12 345 x 8 + 5 = 98 765

1213 456 x 8 + 6 = 987 654

1 234 567 x 8 + 7 = 9,876 543

12 345 678 x 8 + 8 = 98 785 432

123 456 789 x 8 + 9 = 987 654 321

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1 234 x 8 + 4 = 9 876

12 345 x 8 + 5 = 98 765

1213 456 x 8 + 6 = 987 654

1 234 567 x 8 + 7 = 9,876 543

12 345 678 x 8 + 8 = 98 785 432

123 456 789 x 8 + 9 = 987 654 321

Labels:
8,
8-sided Star,
Eight,
Octave

### Nine

Nine

34" Wide x 55" Tall

In order to evoke the # 9, nine cats are stretched out around a spiral created using the Golden Section. The board is built to Golden Section dimensions, broken down into smaller and smaller parts:

34" Wide x 55" Tall

Acrylic on Board

**No Longer Available**

In order to evoke the # 9, nine cats are stretched out around a spiral created using the Golden Section. The board is built to Golden Section dimensions, broken down into smaller and smaller parts:

34" x 55" board

34" x 34" square at the bottom

21 x 34" top section

21" x 21" top right square

13" x 21" top left section

13" x 13" top left square

8" x 13" section beneath that with

8" x 8" square and to the right of that,

5" x 8" section with

5" x 5" square and then

3" x 5" section with

3" x 3" square and

2" x 3" section with

(2) 1" x 1" squares

34" x 34" square at the bottom

21 x 34" top section

21" x 21" top right square

13" x 21" top left section

13" x 13" top left square

8" x 13" section beneath that with

8" x 8" square and to the right of that,

5" x 8" section with

5" x 5" square and then

3" x 5" section with

3" x 3" square and

2" x 3" section with

(2) 1" x 1" squares

These numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55 are Fibonacci numbers, a sequence of numbers whose successive ratios approach the Golden Ratio, as they approach infinity. (The Golden Ratio, is an irrational number --- one that goes on to infinity without ever repeating itself.) For instance, take the 2 and the 3 in the Fibonacci series 3/2 = 1.5; 5/3 = 1.67; 8/5 = 1.6; 13/8 = 1.63; 21/13 = 1.62, etc.

This golden ratio measures the fraction of a turn between successive leaves on the stalk of a plant: 1/2 for elm and linden, 1/3 for beech and hazel, 2/5 for oak and apple, 3/8 for poplar and rose, 5/13 for willow and almond, etc.

Words and Glyphs for the Number 9 are woven throughout the piece, with repetitions used to evoke the sense of patterns.

Click here to go to the Museum of the Golden Ratio .

Click here to go to the Museum of the Golden Ratio .

Labels:
9,
9 Lives,
Cats,
Golden Ratio,
Golden Section,
logarithmic spiral,
Nine,
Phi,
spiral

## 23 December 2006

### Big Tally

2006

Size: 36" Wide x 60" Tall

Medium: Acrylic on Canvas

Big Tally was based on ancient accounting methods. Pre-historic man made notches on bones. In Mesopotamia, 10,000 years ago, the Sumerians developed the first system of abstract numerical representation.

The Mesopotamian cuneiform writing system developed (5,000 years later) from this ancient clay token accounting system. In the 4th millennium B.C., the Mesopotamian accountants began enclosing tokens in clay envelopes (bullae) and impressing the tokens on the outside to indicate the contents.

Later, a pointed stylus was used to incise pictures of tokens in clay tablets instead of impressing the actual tokens. The stylus impressed a wedge shaped mark. (The Latin word cuneus means wedge, thus the name cuneiform.)

In the early token system, the concept of number was not distinct from the concept of the type of item counted. (ie: Ovals were used to represent jars of oil. Jars of oil could only be counted using these ovals.) Gradually, modifications to this accounting system led to an increasingly abstract form of counting.

It wasn’t until about 3,100 B.C. that the first numerals were invented.

To pay homage to those ancient accountants, Big Tally floats in a world of glyphs and marks that allude to quantities, objects, and the recording of information. It is not intended to be an actual depiction of a clay tablet or bulla, only an artist’s interpretation.

Labels:
cuneiform,
glyphs,
heiroglyphics,
Number,
numbers,
tally,
tally sticks

## 22 December 2006

### Artist's Statement

I used to dance. There’s something exquisite about losing yourself in movement. Sometimes, when I’m painting, I’ll start to dance, especially if I’m listening to Reggae or Zydeco. I almost always paint to music.
Being an idea person, an avid reader and researcher, my paintings manifest from contemplations on a variety of subjects --- Mathematics, The Golden Ratio, Quantum Physics, and Spiritual Matters. I glimpse connections and begin to draw thumbnail sketches around the edges of my notes. The internal dialogue is about the concept, then words gradually disappear and visual elements expand until only sketches are coming off the end of the pencil. Later, within the painting, words may reappear.
I’ll have an entire body of work "idea", with dozens of sketches as potential paintings, but nothing set in stone, nothing certain. All the thumbnails represent a chaotic assortment of ideas, as if each one were a different perspective on the issue, full of the potential to explain it, but just a fragment. Only if a cluster of fragments is seen together, in a full body of work, can they explain the total concept, as if they were pottery shards that must be glued together in order to see the whole vessel.
It reminds me of Quantum Physics which tells us that we are not solid, that we move and vibrate and are filled with the potential to manifest. We need only focus on our desire in order to make it real…solid. So that is how I approach the paintings. I focus on the desire to express the idea. I think about the idea…not the painting. I allow the painting to manifest itself.
After working with the Golden Ratio for several years, I now have custom painting surfaces made that allow me to paint within that format. It sets the stage. It is the architecture, the structure on which I begin to build. I break up the space and then insert my one or two shapes, the initial idea, and then the dance begins.
Getting lost in the painting process is the goal. It is the meditation, the prayer. It is timeless. There are no words. It is pure experience. And that experience is a joyful one.
I sometimes have a tendency to tighten up in my work, to make it more accurate, precise, literal, but I recognize that as a state of distrust. I remind myself that the viewer (and the painter) CAN be trusted to figure it out. Allowing the mystery, the nuance, just the glimpse of the idea to exist in a more painterly realm makes the painting richer and more seductive. With that as my intention, the focus on giving up the inherent struggle between tight and painterly, I have recognized the duality within myself and allowed it to be. And so I paint the way I must. And I do the dance.
Layer after layer of paint, I build up the surface, scraping/carving/writing, building it up like memory and digging into it in a search for the patterns and rhythms of Universal understanding. From subtle mark-making to deep cuts, glyphs/symbols, visual information--- anything I can use that will add depth---of spirit, of knowledge, of understanding, a sense of connectivity. We go back and forth, the painting and I, until the dance is complete.

Labels:
art,
artists,
manifesting,
mathematics,
Phi,
physics,
quantum connections,
quantum physics,
Spirit,
The Golden Ratio

### Quantum Connections Statement

This body of work was conceived as a dialogue about the inter-connectedness of all things. The single thread that weaves through every aspect of our existence is NUMBER, so the focus here has been on the concept of number, numbering, counting, the history of numbers, as well as the words and glyphs (symbols) that represent numbers.
The earliest marks made by man were notches, a single notch representing a single unit. Long before we had a concept of numbers, before there were any written languages, humans felt the need to QUANTIFY. And the first Quantity was ONE and the first symbol used was a single notch.
In every writing system, the second, third and fourth marks were two, three and then four vertical notches. Only after “4” did it become necessary to use a symbol, because the Human Brain is incapable of perceiving a quantity of more than 4 without counting. (ie, at a glance, we can perceive 4, but when we see 5 or more, we must count 1,2,3,4,5…)
That leap to the abstract concept of NUMBER opened the door to the development of mathematics, geometry, and science, all with the ultimate purpose of understanding our Universe. Ironically, in our pursuit of understanding our physical world, in the hope of understanding reality, we have come closer and closer to the understanding that nothing is real, as in solid, that reality is relative.
Our five senses tell us that we are solid. Quantum Physics tells us we are not. We are in a constant state of flux, moving, vibrating, filled with worlds of potentiality. We can affect the behavior of sub-atomic parts by merely focusing on them! How can this be? How can we get comfortable with the idea that we exist in multiple places at once?
To the Pythagoreans, facing the reality of an irrational number was so terrifying that they were sworn to secrecy, lest the entire world lose all faith in God, because as they all knew God created a rational world.
Only by going through the unknown, through what doesn’t make sense, grappling with the inconceivable, can we ever hope to glimpse reality. Number is purely abstract. It isn’t physical. It is how we measure, qualify, quantify, describe and explain, but it doesn’t EXIST. That duality, the existence/non existence of it, changes when we focus on Number as it relates to another…as a ratio, as a product, as a sum…that makes it real to us. Makes it come to life.
So, if we are all moving around like mad at our most elemental level, behaving like waves (with an interference pattern, which essentially means that we exist in multiple places at once), then we aren’t really solid. And, since what is real about Numbers is the relationship, then WE only become solid when we observe ourselves and real when we perceive ourselves in relation to others…ie, acknowledge our connectedness. In shifting our consciousness from Separate to Connected, we create balance and harmony in our lives.

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