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

Four

2006

42" Wide x 26" Tall Quadriptych
(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