ARTWORK by Murray Young.
Most of these works are mathematical, dealing with fascinating, important and useful concepts; my hope is that these works stimulate an interest in those concepts yet can also be enjoyed by anyone who has no interest in Mathematics whatsoever. The artistic quality here is mediocre at best; I have known at least four people who are better artists than I am so this is not false modesty. The best part of these works are the ideas they play with, ideas to do with music, imagination, culture and philosophy as well as mathematics.
ONE OFFS:
- Bachanalian Melodies
- Terror Horror
- Selene Neon
- Digitesselation
- Pythagorean Regression
- Yang Hui’s Triangle Too
- Young Owl With a Horn
DRAGON CURVES
- Anarchist Dragon Swimming Against the Current
- Contrarian Barbarian Reptilian Gargantuan Leviathan
- To Boldly Go Where No One Dimensional Line Has Gone Before
1. BACHANALIAN MELODIES. Januaey 3, 2020. 45.7 cm by 61 cm
This is a graphic illustration of the three intertwining melodies in Sinfonia number 11 in G minor by Johann Sebastian Bach. Each of the coloured lines represents a melody and the melody lines are displayed as a function of the distance of each note from the tonic note of the G minor scale as measured in semitones, each semitone represented by a distance of one millimetre. The dotted line in the middle of the melodies represents the tonic note.
The opening notes of the composition are pictured in the centre but then the music staff lines anarchistically begin to act in interesting and unusual ways. One line wanders up to complete the depiction at the top of an object that could never exist in the real world. Two lines wander down, become the cracks between piano keys, then the keys themselves morph into the front door of a house. Two other staff lines drift down to become the smoke coming out of the chimney of that same house while two more lines become the sides of a lighthouse. A final line wafts down to be swallowed up by the sea. The notes on the right are taken from one of the bars near the end of the composition. The sign BONZO LIVES on the zeppelin is a reference to John ‘Bonzo’ Bonham, the drummer of Led Zeppelin, who died at the age of thirty-two after a night of heavy drinking.
2. TERROR AND HORROR. October 2, 2015. 30.4 cm by 30.4 cm
This is an early work, based on the symbol for the transcendental number pi, reflected downward then transformed into an object which could never exist in the real world. The blue and green spheres represent the two moons of Mars. These moons were named for two figures from Greek mythology, Deimos (representing horror) and Phobos (representing terror). The digits of pi form the background.
Pi has been over-hyped with connotations of mathematical nerdiness. Mathematicians, however, are often more interested in the constant tau (pi times two) which makes more sense geometrically. Pi is still rather enigmatic, however. Pi is usually depicted as the ratio of the diameter of a circle to its circumference, but it surfaces in places that have nothing to do with circles. For example, draw lines on a sheet of paper equally spaced and drop a handful of toothpicks onto the sheet an infinite number of times. The number of times toothpicks cross lines turns out to be an expression containing pi (this is Buffon’s Needle Problem). Pi’s decimal expression never ends and never repeats, and pi has proven extremely useful in the practical world.
3. SELENE NEON. January 12, 2016. 30.4 cm by 30.4 cm
Another early work, this features segments of three of the four Conic Sections – parabolae (y = ax squared), ellipses (x squared / a squared + y squared / b squared = 1) and circles (x squared + y squared = r squared where r is the radius). Selene is the Greek deity of the moon.
4. DIGITESSELATION. November 14, 2015. 30.4 cm by 30.4 cm
This early work features all ten digits positioned together to form a shape which dovetails precisely with itself top and bottom, left and right. That means that this shape could be replicated in all directions infinitely without any gaps or overlaps.
5. PYTHAGOREAN REGRESSION. November 3, 2017. 45.7 cm by 61 cm
Here are two examples (mirror images) of nested right-angled triangles that can be generated in smaller and smaller forms forever. Pythagoras (570 BCE – 495 BCE) was an early mathematician and mystic whose good ideas were revolutionary and influential, so much so that the great logician Bertrand Russell considered him to be incredibly important and somewhat under-rated. We do know that at a time when women were for the most part invisible and powerless, and barred from the public sphere (including the educational world). Pythagoras welcomed women as equals into his secret society which studied Mathematics, among other things, twenty-five centuries ago.
Pythagoras is also known for The Pythagorean Theorem but that theorem was known to the Babylonians more than a thousand years before Pythagoras was born. An Indian work, the Baudhayana Sulba Sutra, dated as early as the eighth century BCE, also contains a statement of the theorem as well as lists of Pythagorean triplets. There is also evidence that the theorem arose first in China, where it is known as the Shang Gao Theorem. At least Pythagoras himself never claimed to have been the originator of the proof of the theorem.
6. YANG HUI’S TRIANGLE AS WELL. 45.7 cm by 61 cm
Various mathematical discoveries have been made by different people independently and often the person given credit, or the person whose name is attached to the discovery, isn’t always the first person to come up with the discovery. To be fair, the people given credit inaccurately sometimes make an attempt to correct the record and give credit where credit is due.
The triangle in this artwork was constructed and analysed by Blaise Pascal (1623 – 1662) and the triangle came to be known as Pascal’s Triangle in the West. As a mathematical idea the triangle embodies dozens of valuable mathematical processes. However, this same triangle was analysed by the mathematician and poet Omar Khayyam (1048 – 1131), someone who is fairly well known in the West. It was also analysed in China by Yang Hui (1238 – 1298), someone essentially unknown in the West. It was most likely not Pascal’s fault that those two earlier mathematicians did not get the recognition in the West that they deserved. Many mathematical patterns and relationships embedded in the triangle are displayed in this work but there are many more that there was no space for. It is an amazing entity.
7. YOUNG OWL WITH A HORN. February 18, 2017. 45.7 cm by 61 cm
The joke here is obvious as long as you know who Louis ‘Satchmo’ Armstrong is, and he had a huge international fan base. He also went by the nickname Pops. Armstrong is one of those rare individuals from the world of music whose influence and raw musical talent went beyond performing or composing and changed the direction of the entire field. Purandara Dasa, J.S.Bach, Beethoven, Paganini, Bessie Smith, Gershwin, The Beatles, Jimi Hendrix and Glenn Gould also come to mind.
Louis Armstrong changed the direction of the entire genre of jazz. He was breathtakingly talented as a trumpet player and he also composed music. He invented a new style of singing as well, including scat singing, which influenced many who came later. He was also a man who emphasized the positive, who was quick to laugh, and laugh with not at, and who would probably have smiled at this particular illustration.
The deep and lethal racism of the United States that he grew up surrounded by as a black man meant that he was forced to take on an affable, simple and non-threatening persona. He was anything but. His knowledge and skills were easily underestimated. He grew up in extreme poverty in an orphanage yet was classically trained and he had formidable self-discipline. His recording of ‘West End Blues’ is considered by many musicologists to be the greatest jazz recording ever made.
He was also not the Uncle Tom that some accused him of being. He was principled, and he was defiant when it mattered. When he was asked to tour the Soviet Union during the Cold War by his government at a time when that same government was doing little about the racism of the southern states, this affable musician told the government to go to hell. Those were strong and dangerous words for a black man in those days when lynching still happened and patriotism and conformity were mandated.
DRAGON CURVES
1. ANARCHIST DRAGON SWIMMING AGAINST THE CURRENT. January 29, 2019. 45.7 cm by 61 cm
A dragon curve is a space-filling curve in that it starts as a short, simple line, then a simple set of procedures, an algorithm, is applied to it and it expands and twists, and after an infinite number of repetitions of the algorithm it covers an area of two dimensional space, as impossible as that sounds. A line has one dimension (length), a square has two dimensions (length and width), and a cube has three (length, width and height). The dragon curve has 1.52 dimensions which becomes two at infinity. The curve gets its name because after a fair number of iterations of the algorithm it resembles a dragon, with its head and snout on the left, tail on the right, and feet paddling under the water at the bottom.
This close-up shows that the dragon curve is indeed curved. Often dragon curves are depicted as a series of sides of miniscule squares periodically turning at right angles (see TO BOLDLY GO WHERE NO ONE DIMENSIONAL LINE HAS GONE BEFORE) but that is actually not quite accurate.
2. CONTRARIAN BARBARIAN REPTILIAN GARGANTUAN LEVIATHAN. January 3, 2019. 45.7 cm by 61 cm
This is another rendering of a dragon curve (see the previous work Anarchist Dragon Swimming Against the Current for a definition and descruption of dragon curves).
3. TO BOLDLY GO WHERE NO ONE DIMENSIONAL LINE HAS GONE BEFORE. December 17, 2018. 45.7 cm by 61 cm
Please see the work Anarchist Dragon Swimming Against the Current (work 7) for a definition and description of a dragon curve. This present work is actually a set of four dragon curves. One dragon is joined snout to snout to a second one that’s upside-down, right in the cenntre of the work. These two dragons ar joined in turn, connected tail to tail, to two other dragons. These dragons are illustrations of the tenth iteration of the algorithm, and after an infinite number of iterations the one dimensional curve covers two dimensional space, hence the title. The work also displays a parable about an imaginary nasty leader who acts a lot like Donald Trump, written before the pandemic and the death of George Floyd. Little did I realize how bad it would get.
According to The Kidd 