GALLERY 17 – Vipers and Bees

ARTWORK by Murray Hersch Young.

  1. THE REPTILIAN SIX
  2. THE REPTILIAN FOUR
  3. REPTILIAN REPETITION
  4. REPTILIAN DUPLICATION
  5. AMAZON ADVENTURE
  6. AT INFINITY
  7. HEXTING
  8. THE MATHEMATICS OF RACISM / BLACK LIVES MATTER
  9. THE EXISTENCE SET – UNREALITY, UNCERTAINTY, REALITY
  10. POLITICAL MUSIC
  11. HARRY POTTER AND . . .

Some of these works contain rep-tiles, irrep-tiles and infin-tiles. A REP-TILE (Replicating Tile) is a shape which can be subdivided into smaller shapes each of which is identical in shape to the large shape. All the smaller shapes in a rep-tile are the same size. If one subdivides a shape into smaller shapes each of which is identical in shape to the original but those smaller shapes are different sizes, then you have an IRREP-TILE. A rep-tile in which each of the smaller shapes also has an infinite perimeter is called an INFIN-TILE.

1. THE REPTILIAN SIX. September 15, 2020. 45.7 cm by 61 cm

This is a set of six large equilateral triangles each of which consists of a set of three rep-tiles. You can see how each of the six large equilateral triangles can also be subdivided into thirty-six small equilateral triangles. Since each of the small equilateral triangles can itself be subdivided into the same triple rep-tile set as each large equilateral triangle, that tells us that each of the largest rep-tiles can also be subdivided into thirty-six smaller replications of itself.

2. THE REPTILIAN FOUR. September 5, 2020. 45.7 by 61 cm

The main large equilateral triangle consists of four smaller equilateral triangles each of which contains three identical rep-tiles. In this case each of those rep-tiles can in turn be subdivided into nine smaller replications of itself all the same size. At the top, on the left and right, are two Sierpinski triangles, named after Waclaw Sierpinski. A Sierpinski triangle can be subdivided into smaller and smaller replications of itself and if you subdivide it an infinite number of times theoretically the entire large triangle gets filled in. Since all the smaller and smaller triangles are different sizes Sierpinski triangles are irrep-tiles. There is also a three dimensional version of the Sierpinski Triangle called a Menger Sponge.

3. REPTILIAN REPETITION. October 2, 2020. 45.7 cm by 61 cm

The main large equilateral triangle here is divided up into four smaller equilateral triangles. Each one is subdivided into smaller and smaller equilateral triangles and one could continue subdividing forever getting infinitesimal triangles all different sizes so the original triangle you started with (one of the four making up the large equilateral triangle) is an irrep-tile. So are the shapes at the top on both sides. The lettering alternates right side up and upside-down because the first and last letters of the word IRREPTILES look the same right side up and upside-down. The giant triangle here is an irrep-tile but it could also be a rep-tile if you just stopped after subdividing it into the four smaller triangles.

4. REPTILIAN DUPLICATION. October 15, 2020. 45.7 cm by 61 cm

The main shape here, a hexagon, is subdivided into seven smaller hexagons leaving twelve triangles around the outside. Each of the twelve can also be subdivided into smaller and smaller hexagons and triangles, so the hexagons remain identical in shape but the sizes get smaller infinitesimally. Therefore this is a giant irrep-tile. The three triangles around the outside are also irrep-tiles, though they could also be re-configured as rep-tiles. At the bottom are infinity symbols swimming either toward the right or the left, depending on the viewer.

Replication Duplication detail

5. AMAZON ADVENTURE. December 1, 2020. 45.7 cm by 61 cm

Nine irrep-tiles are on display here. Usually the main starting shape is subdivided into brown shapes of different hues, and one of these shapes is subdivided again using purple / blue / green shapes which create an infinite regress, but if those regressions are omitted the shapes would still be irrep-tiles. Reptiles live in the Amazon jungle, and the mythological Amazon warriors, including Wonder Woman, lived on Paradise Island, hence the signpost.

6. AT INFINITY. October 10, 2020. 45.7 cm by 61 cm

The main shape here is highly unusual. It is a giant equilateral triangle with a large sort of growth at the top on the right. That growth consists of an infinite spiral of triangles which grow smaller and smaller infinitesimally. That same shape, duplicated three times, forms three infinitely long spirals inside the equilateral triangle as well. The perimeters of these four shapes are infinite so the shapes are called infin-tiles. The infinite decimal in light blue is phi, the golden mean, equal to the sum of the square root of five plus one all divided by two. The orange decimal on the left is the square root of two. The purple decimal is e, the base of natural logarithms, and the orange decimal on the right is good old pi. These are all non-repeating, non-terminating decimals but only pi and e are transcendental.

The smaller shape on the right is also an infin-tile but the top growth is constructed with a differently positioned sequence of smaller and smaller equilateral triangles. These things never get to infinity, of course, like the orange curve on the left, known as the Witch of Agnesi, discovered and analysed over two centuries ago by Maria Agnesi. The curve gets closer and closer to the blue baseline (we call it an asymptote) and it goes forever without ever getting to the blue line. There is also a saying in mathematical circles, that parallel lines meet at infinity.

At Infinity detail.

7. HEXTING. November 8, 2020. 45.7 cm by 61 cm

This is built up over four levels. There is a grid of hexagons that covers the entire page (Level One). The centres of some of those hexagons are joined to create a grid of larger hexagons primarily grey but some black nearer the bottom (Level Two). The centres of all of the Level Two hexagons have been joined to form dark brown hexagons (Level Three) and the centres of the Level Three Hexagons have been joined to create the main coloured shape which is itself subdivided into a triangular shape consisting of six hexagons. Those six hexagons are coloured using three colours. Eleven smaller coloured patterns consisting entirely of hexagons can be found around the outside. At the bottom are three bees. The largest one, on the right, is this hive’s Queen Bee which is why the name QUEEN VICTORIA can be seen emblazoned across her back. A second bee is labelled ‘Gordon Sumner’ because that is the real name of the British musician / actor Sting. Attached to the bee in the middle is a tag reading ‘IF FOUND PLEASE RETURN TO SHERLOCK HOLMES. That is because in the famous Sherlock Holmes stories by Sir Arthur Conan Doyle when Holmes retires he moves to the Sussex Downs and becomes fascinated with the art of beekeeping.

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8. THE MATHEMATICS OF RACISM / BLACK LIVES MATTER. July 2, 2020. 45.7 cm by 61 cm

This is a chronological list of historical events in black primarily American history from 1500 to 2020, each of which involves the death of black individuals because of racism. This is actually a small sample of a much longer and more detailed separate page entitled BLACK LIVES MATTER 1741 – 2020 which lists an historical event in black history / oppression for every day of the year.

Here is the text from this piece:

4 million slaves die in the Slave Trade, 1.2 to 2.4 million died during the Middle Passage, 10.2 million slaves were brought to North America during the Slave Trade. 1882 – 1968: 3446 African-Americans lynched. 5.4% of U.S. whites live in poverty but 9.7% of U.S. blacks live in poverty.

  1. 1619 – August – The first slave shaips arrive in North America.
  2. 1741 – June 4 – PEGGY KERRY executed for supporting a slave revolt
  3. 1811 – Jan. 6 – Slaves prepare for another slave revolt. It fails. 97 die.
  4. 1831 – Nov. 11 – NAT TURNER executed for starting a slave revolt
  5. 1836 – April 11 – Race riots erupt in Cincinnati, Ohio. Several people die.
  6. 1859 – Oct. 17 – Two of JOHN BROWN’s sons die in their father’s raid.
  7. 1859 – Oct. 18 – JOHN BROWN’s raid on Harper’s Ferry fails
  8. 1859 – Dec. 2 – JOHN BROWN is executed for his slave raid on Harper’s Ferry.
  9. 1863 – March 6 – Race riots erupt in Detroit Michigan. Two die.
  10. 1863 – July 14 – The New York Draft race riot begins. 119 dead.
  11. 1866 – May 1 – Race riots in Memphis, Tennessee. 48 dead, 75 injured.
  12. 1866 – July 30 -New Orleans race riot. 44 dead.
  13. 1868 – Jan. 7 – Race riots in Pulaski, Tennessee. Two dead.
  14. 1871 – March 8 – After a race riot breaks out in Meridian, Mississippi, the KKK kills wantonly for several days.
  15. 1873 – April 13 -Racial unrest in Louisiana. Between 62 and 153 blacks dead.
  16. 1876 – July 8 – Race riot in Hamburg, South Carolina. Seven dead.
  17. 1898 – Feb. 22 – FRAZIER B. BAKER and his infant daughter JULIA, African-Americans, are murdered in Lake City, South Carolina
  18. 1898 – Nov. 12 -The Phoenix election massacre. 13 dead, one by lynching.
  19. 1900 – July 24 – The Robert Charles race riot in New Orleans. 28 dead.
  20. 1906 – Sept. 24 – The Atlanta race riot starting Sept. 22 ends. 25 dead.
  21. 1908 – Aug. 14 – Race riots in Springfield, Illinois. 16 dead.
  22. 1910 – July 4 – JACK JOHNSON, black, defeats James Jeffries, white, for the world boxing championship. Riots ensue in fifty cities. 20 dead.
  23. 1910 – July 29 – Race riot in Slocum Texas. 100 dead.
  24. 1910 – Sept. 29 – Omaha race riots end with the lynching of WILL BROWN.
  25. 1916 – Jan. 29 – Six men are lynched in Lee County, Georgia.
  26. 1916 – May 15 – JESSE WASHINGTON lynched in Texas after hours of torture.
  27. 1917 – July 1 – Race riots in East St. Louis. Between 40 and 250 blacks dead.
  28. 1917 – July 24 – A race riot in Chester. Seven dead.
  29. 1919 – July 27 – Chicago race riot lasts 8 days. 38 dead.
  30. 1920 – Nov. 2 – The start of the Ocoee, Florida race riot. 60 – 70 dead.
  31. 1920 – Nov. 3 – the Ocoee riot ends with the lynching of JULY PERRY
  32. 1923 – Jan. 4 – Race riots in Rosewood, Florida. 27 – 150 blacks dead.
  33. 1921 – May 31 – The Tulsa, Oklahoma massacre of prosperous blacks. At least 300 dead. Many injured, many black homes and businesses destroyed.
  34. 1921 – June 1 – Day 2 of the Tulsa Massacre, which is later covered up.
  35. 1933 – Nov. 26 – THOMAS THURMAN and JOHN HOLMES are lynched.
  36. 1935 – March 19 – Harlem race riots. Three dead, hundreds injured.
  37. 1943 – June 15 – Race riot in Texas. Three dead.
  38. 1943 – June 20 – Detroit race riots. 34 dead.
  39. 1943 – Aug. 1 – Race riot in Harlem. Six dead.
  40. 1946 – Feb. 25 – The Columbia, Tennessee race riots. Two dead.
  41. 1955 – May 7 – Civil rights activist REV. GEORGE W. LEE is murdered.
  42. 1955 – Aug. 28 – Teenager EMMETT TILL is tortured and killed in Mississippi.
  43. 1956 – Jan. 30 – The home of DR. MARTIN LUTHER KING JR. is bombed.
  44. 1957 – Jan. 22 – The KKK hunt for WILLIE EDWARDS, murdering him the next day.
  45. 1960 – Mar. 21 – 69 protesters killed in Sharpeville, South Africa.
  46. 1961 – Sept. 25 – Civil rights activist HERBERT LEE killed in Mississippi.
  47. 1962 – Oct. 1 – JAMES MEREDITH becomes the first black to attend the University of Mississippi, triggering riots in which one person died.
  48. 1963 – June 12 – MEDGAR EVERS assassinated by the KKK, Mississippi.
  49. 1963 – Sept. 15 – The KKK bombs the 16th St. Baptist Church, Alabama, killing four children: ADDIE MAE COLLINS, CAROLE ROBERTSON, CYNTHIA WESLEY and DENISE McNAIR.
  50. 1964 – May 2 – The KKK murders CHARLES MOORE and HENRY DEE.
  51. 1964 – July 22 – Harlem race riot that started July 16 ends. 1 dead, 116 injured.
  52. 1965 – Feb. 18 – EL-HAJJ MALIK EL-SHABAZZ aka MALCOLM X is assassinated.
  53. 1965 – March 7 – Police attack protesters on the Edmund Pettus Bridge, Selma, Alabama. JOHN LEWIS and others badly injured. One dead.
  54. 1965 – March 25 – White civil rights activist VIOLA LIUZZO killed by the KKK.
  55. 1965 – Aug. 11 -Watts race riots last six days. 34 dead.
  56. 1966 – Jan. 10 – NAACP activist VERNON DAHMER killed by a bomb.
  57. 1967 – April 1 – DENZIL DOWELL killed suspiciously but police authorities refuse to investigate so the Black Panthers step in and do so.
  58. 1967 – May 12 – Racial unrest in Jackson, Mississippi. One dead.
  59. 1967 – June 14 – The fourth day of riots which erupted after the Tampa police kill black teenager MARTIN CHAMBERS.
  60. 1967 – June 18 – The second day of racial unrest in Atlanta after the arrest of STOKELY CARMICHAEL. One dead.
  61. 1967 – July 12 -Race riots in Newark last four days. 27 people dead, 1100 injured.
  62. 1967 – July 15 – Racial unrest in New Jersey. One dead.
  63. 1967 – July 23 – Detroit race riots last 5 days. 43 dead, 2000 injured.
  64. 1967 – July 31 – The second of three days of race riots in Milwaukee. Four dead.
  65. 1968 – April 4 -DR. MARTIN LUTHER KING JR. assassinated in Memphis, Tennessee. Racial unrest explodes in 125 cities nationally: Washington, D.C. (13 dead, 1097 injured, 7600 arrested), Chicago (9 to 11 dead, 500 injured, 2150 arrested), Baltimore (6 dead, 700 injured, 5800 arrested), Kansas City (5 dead, 80 injured, 100 arrested), Cincinnati (2 dead, hundreds arrested), Pittsburgh (1 dead, 36 injured, 1000 arrested)
  66. 1968 – May 29 – Racial unrest in Louisville, Kentucky. Two dead.
  67. 1969 – July 20 – York, Pennsylvania riots end with the death of LILLIE BELLE ALLEN.
  68. 1969 – Dec. 4 – Oakland police kill Black Panthers FRED HAMPTON and MARK CLARK.
  69. 1970 – May 11 – Police beating black teenager CHARLES OATMAN to death triggers riot in Augusta, Georgia. 6 dead.
  70. 1970 – May 14 – Black protests in Mississippi begin and the next day police open fire on protesters killing two.
  71. 1977 – Sept. 12 – Anti-Apartheid leader STEVEN BIKO is killed by South African police.
  72. 1980 – May 18 – Miami race riot. 18 dead.
  73. 1981 – March 21 – MICHAEL DONALD is lynched by the KKK.
  74. 1985 – May 13 – Police in Philadelphia drop a bomb on a building housing a Black Liberation group killing five children and six adults. No charges laid against the police.
  75. 1991 – March 3 – RODNEY KING taped being beaten by L.A. Police.
  76. 1991 – March 16 – LATASHA HARLINS killed by store owner who wrongly accuses her of theft. She was 15. He gets a slap on the wrist. This was a contributor to the L.A. riots.
  77. 1992 – April 29 – The police officers who brutalized unarmed RODNEY KING are acquitted, sparking the L.A. riots. 50 dead, 2000 injured.
  78. 1992 – Sept. 7 – South African police open fire on peaceful protesters in Bisho. 29 dead, 200 injured.
  79. 1992 – Nov. 5 – MALICE GREEN killed by Detroit police.
  80. 1993 – April 10 – Activist CHRIS HANI assassinated in South Africa.
  81. 1996 – Jan. 8 – Police kill OSCAR GRANT II in Oakland, California.
  82. 2000 – Nov. 7 – Police kill ROGER OWENSBY JR. in Cincinnati, Ohio.
  83. 2012 – Feb. 26 – Unarmed teenager TRAYVON MARTIN, 17, killed in Florida.
  84. From JULY 15, 2014 to MARCH 13, 2020 some of the African-Americans killed by the police: ERIC GARNER, JOHN CRAWFORD III, MICHAEL BROWN, TAMIR RICE (12 years old), FREDDIE GRAY JR., SANDRA BLAND, paraplegic JEREMY McDOLE, ELIJAH McCLAIN, BREONNA TAYLOR.
  85. 2017 – Aug. 16 – Memorial service for HEATHER HEYER. Though white, she was protesting against white supremacists. Donald Trump refuses to condemn the white supremacists.
  86. 2017 – Aug. 23 – Race riots in Houston, Texas. 11 dead.
  87. 2020 – May 25 – Unarmed GEORGE FLOYD killed by police in Minneapolis triggering international protests and some reforms.
  88. 2020 – June 12 – RAYSHARD BROOKS killed by the police.
  89. The future?

9. THE EXISTENCE SET

PART ONE – UNREALITY. April 7, 2018. 45.7 cm by 61 cm

The graphic features three Penrose (impossible) triangles. The text includes: fictional entities such as The Jabbewock and S.F.Sorrow, Anne of Green Gables and King Kong, Jack Frost and Circe; fictional places such as Strawberry Fields, Flatland, Gilead, Challenger Field, Midwich, Gormenghast, Vermilion Sands, Castra Sanguinarius and The Nine Circles of Hell; vehicles, devices and objects from fiction (e.g. The Time Machine, The Nautilus, one ring to rule them all and ruby slippers); poetry by Jim Morrison (aka The Lizard King) of The Doors aged 95 and Joan of Arc’s final inspiring words as she died age 67; The Protocols of the Elders of Zion, The Turner Diaries, The Camp of the Saints, The First Blast of the Trumpet Against the Monstrous Regiment of Women, The 100th Monkey Phenomenon, locations north of the North Pole, the date October 6, 1582, the divine image on the Shroud of Turin, intelligent design, homeopathy, astrology, the Bible Code, Velikovsky’s Jovian comet and The Green Children of Suffolk; mathematical impossibilities (e.g. the derivatives of a Snowflake Curve, a general quintic formula, a squared circle and doubled cube and trisected angle).

PART TWO – UNCERTAINTY. April 21, 2018. 45.7 cm by 61 cm

The graphic features a dodecahedron. The text includes: The fates of Raoul Wallenberg and Glenn Miller, miscellaneous missing ships and aircraft, what happens when the Red King awakes, The Continuum Hypothesis, the position and momentum of a subatomic particle, the still unidentified victims of the Shoah, many others who vanished, fate unknown: 30 000 Argentinians 1976 – 1983, 11 000 during the Sri Lankan Civil War, 8000 Colombians 1978-1992, 5000 Pakistanis since 2001, victims of the Nazi Nacht Und Nebel Program, and victims of the Anfal Genocide. Also the murderers of Olof Palme, Oscar Romero, Tupac Shakur, Notorious B.I.G. and Legs Diamond; upraised fingers in the Ministry of Love; Godel’s Incompleteness Theorems, Tarski’s Undefinability Theorem, The Hodge Conjecture, Goldbach’s Conjecture, and odd perfect numbers. The answer to the ultimate question involving life, the universe and everything (it wasn’t 42 after all). To be or not to be.

PART THREE – REALITY. May 7, 2018. 45.7 cm by 61 cm

The graphic features zero, one, two, three and four dimensional objects. The text includes: a one-sided Moebius Band, Climate Change, Evolution, a safe Bermuda Triangle, many wonderful people doing many actual wonderful things, wonderful animals, wonderful human-made structures and wonderful natural phenomena. A lot of horrendous things as well. Also, Alice Liddell, Dr. Joseph Bell, Chang Apana, King Macbeth of Scotland, J. Murrieta and Alexander Selkirk. Also the Banach-Tarski Duplication, Hempel’s Black Crow, Zeno’s Tortoise, An Unexpected Hanging, The Voters’ Paradox, The Thomson Lamp, quantum entanglement, teleportation and Cantor dust.

10. POLITICAL MUSIC. June 1, 2020. 45.7 cm by 61 cm

This is a miscellaneous collection of flags and symbols of a variety of political entities, both right wing and left wing. It also includes the names of eleven highly political songs from Nothing To My Name to Black Day in July. It was designed to accompany a series of posts I did in the latter half of 2020 on political music. The campaign buttons on the right read, in descending order, VOTE SENSIBLE, VOTE SLIGHTLY SILLY, VOTE SILLY, VOTE VERY SILLY which is a reference to a Monty Python sketch.

11. HARRY POTTER AND . . . – December 2, 2020. 45.7 cm by 61 cm

This is a collection of imaginary Harry Potter book titles along with an illustration from Book One of the seven coloured liquids puzzles that Hermione solves, using her brain to rescue Harry and allow him to have his dramatic final confrontation with Voldemort. This will be used to accompany a long series of posts I have written and will start to post in the new year (2021) dealing with gender / trans issues in the original seven Harry Potter novels. This work includes parody titles such as Harry Potter and the Deathly Terfs, Harry Potter and the Half-Eaten Mints, and Harry Potter and the Prisoner of Her Own Device.

The Klein Wine (second from the left) is contained in a Klein Bottle. This is an example of a Klein surface first analysed by Felix Klein. The neck of an actual Klein Bottle seems to intersect the side of the bottle but actually it doesn’t intersect itself at all. It bends through the fourth dimension to get from the outside to the inside. The concept is used to ghastly effect in the science fiction story The Last Magician by Bruce Elliott (in the anthology Fantasia Mathematica edited by Clifton Fadiman).