This piece pits two legendary beauties, Helen of Troy and Emily Ratajkowski. The central shape is an abstract representation of a scene in a music video featuring the latter. The shape itself includes two curves with circles rolling down them. One of those curves is a portion of a cycloid (aptly named the Helen of Geometry due to the number of epic math battles involving it). For example, Johann Bernoulli presented his Brachistochrone Problem as a challenge for the world's leading mathematicians. It asks to determine the curve a ball would descend fastest between two points under a gravitational field's influence. The writing on the work relates to this curve and the two belles. I'll explain some of these references and leave the rest for the viewer to unpack. Issac Newton, for example, received Bernoulli's problem at 4 PM and solved it later that night. So, while "nothing good happens at 4 AM", at 4 in the afternoon, Newton displayed his legendary mathematical genius. "Moby Dick" references the cycloid making a cameo in Herman Melville's famous work (in particular, its "equal time" property). While undoubtedly true, the title "Bad Spelling Is Particularly Atrocious When Writing Equations" was partially accidental. It was a response to the artist confusing the model's name and subsequently spelling Emily as Emma in the lower portion of the work.
This piece pits two legendary beauties, Helen of Troy and Emily Ratajkowski. The central shape is an abstract representation of a scene in a music video featuring the latter. The shape itself includes two curves with circles rolling down them. One of those curves is a portion of a cycloid (aptly named the Helen of Geometry due to the number of epic math battles involving it). For example, Johann Bernoulli presented his Brachistochrone Problem as a challenge for the world's leading mathematicians. It asks to determine the curve a ball would descend fastest between two points under a gravitational field's influence. The writing on the work relates to this curve and the two sex symbols. Sfumato is an art technique that was common during the Renaissance. Its Italian translation means "turned to smoke" or "blurred."
This collage combines three of the most important players in artistic love triangles: Shakespeare (Twelfth Night), Picasso (Marie Therese and others), and Jackson Pollock. The last two had tragic endings (gun and gin). The word "SHIP" references Lee Krasner leaving by ship right before Pollock's fatal car accident with his new lover and the shipwreck at the beginning of Twelfth Night. "Rapunzel loses her hair" refers to the blond beauty Marie Therese losing her hair after a tragic swim. The sheet of paper is from the "Twelfth night". Written on top of the paper is the phrase "Love triangle? No a couple to be exact" combined with relevant math symbols (in particular an exact couple which relates to another mathemtical concept called a spectral sequence). This refers to the love triangle and conclusion of the Twelfth Night. The word spectral also refers to the ghost like figure on the right of the work that comes from one fo Picassos’ paintings about love traingles. Almost drowned references Viola's brother in 12th and another's close call.
I added relevant math to Paul Klee's Two Men Meet, Each Believing the Other to Be of Higher Rank which features two men bowing at each other. Referencing the Birch Swinnerton Dyer conjecture, I sketch the “analytic” and “algebraic” ranks of an elliptic curve and draw arrows pointing to thought bubbles. Since it is unknown which value is larger (the conjecture hypothesizes they are equal) neither man knows which value is larger and hence bow.
This work is a clarion call for society to sober up and continue the fight against slavery.
Even though slavery was finally criminally abolished in 2007 there are tragically still 27,000,000 slaves in the world. Its time for us all to sober up and join the fight for a world where people cant invade another’s most intimate space whether for work or sex.
Displayed Oct 2020 at the Lincoln Memorial
This piece applies mathematics to argue for the fair representation of African-Americans in our integral businesses and throughout society. The math symbols that have been added to the computer printer paper hint at an important theorem from topology called Brown Representation, but its description is incomplete (topology is a modern form of geometry). This argues that as a society we must work to have African-Americans added and fully represented in technology companies and other thriving industries. The incomplete list of math conditions is symbolic of the fact that while some strides have been made in this regard (e.g., Brown v. Board of Education), more is needed. The Domino box, which has been X'd out, points to the sugar industry (and its role in slavery), and the arrow directed at the printer paper references the migration of African-Americans from one category to another: poorly treated slaves to successful leaders. The fact that some of the symbols were crossed out and then replaced (e.g., the "for all" symbol - upside-down capital “A") alludes to the tragic hiccups on the road to the achievement of these basic civil rights. Finally, the work's raw cotton canvas background points to slavery and the centrality of cotton to its vile practice, a symbolic gesture to describe where our society started. Among other mathematical motivations nestled in this piece, there is the word "monochromatic" (one color) crossed out and replaced with the word "spectrum" (range of color). While there are clear interpretations of this in the context of social justice, in topology, a spectrum is also intimately tied to Brown Representability, expanding this metaphor and the important range of work we must achieve as a society to move forward.
The aesthetic for the piece was motivated by the direct imagery often seen on demonstration or protest signs.
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This is a cursory first draft which serves as an incomplete introduction to the work. This art work focuses on Mickey Mantle, spheres, toplogy, and the number 7. Topology's first results come from the great Leonhard Euler: the seven Bridges of Konnisberg problem and his Polyhedron formula for the 2-sphere. John Milnor revolutionized topology with his discovery of the exotic 7-sphere in 1956, for which he won the Fields Medal and essentially every other prestigious math award. Mantle wore number 7, won 7 World Series, and achieved his best year in 1956, winning the Triple Crown. 7 years after discovering his exotic 7-sphere Milnor, jointly with Kervaire (M-K), went on to classify large swaths of these exotic spheres which also led tp the Kervaire invariant problem for framed manifolds. Their work relied heavily on mathematical surgery. Mantle tore his right ACL and badly needed surgery. One of many interesting aspects of M-K’s work is they show a portion of the classification of exotic spheres ties to the Bernoulli numbers. In essence constructing a “bridge” between topology and number theory. Several hundred years earlier, Euler gave an interesting definition of the Bernoulli numbers and he proved one of the first theorems of topology with the 7 bridges of Konnisberg problem.
Mantle's seven was retired in 1969. 1969 was also the year, Browder, who later chaired Princeton's math department, proved a substantial result in the continued classification of exotic spheres in particular the Kervaire invariant problem eg. showing it was necessary that n had to equal 2^k-2 for the Kervaire invariant to be nonzero.
The story continues starting with the hyperbolically named Doomsday Conjecture, an exaggerated name given to an esoteric conjecture in math about framed manifolds having nonzero Kervaire invariant. The horrifying, yet slightly humorous, tone is due to the fact that some important work on problems such as the homotopy groups of spheres, would be nullified if it were confirmed. An important paper written in 2009 shows there exists a spectrum (cohomology theory) with several interesting properties including a Gap theorem. This enabled the authors to resolve a large part of the Kervaire invariant problem, only leaving the case n=2^7-2 open.
Some other details in the artwork include the fact Mantle and Milnor were both born in 1931 and there were two Yankees players who had their number 8 retired.
notes:
Mantle twisted his knee his rookie year and badly needed surgery.
The statue that makes up Mantle’s body originally held a disc (discus).. And gloves are for catching a ball.
See piece Seven for info about Mantle and Milnor’s exotic 7-sphere.
Henry 7th (inside the dotted square) survived the war of the Roses. Does the element h7² in the Adams Spectral Sequence (7 in subscript) survive?
Exec Ord 6102 was signed on Apr 5 1933 the same year a theorem central to BTC was proven. Satoshi's bday is Apr 5. The Fed's inept actions helped worsen the great depression instead of dampening the business cycle. A motif in this work is a rat on a cycle...
A quick intro into the piece and then there are some hints below. This work is my first foray into. stable homotopy, First, the Tasmanian Devil’s explosive personality is anything but stable, but more importantly, the whirlwind behind him looks like a sequence of lowercase cursive e's (Cy Twomblyesque) or possibly a long loop. Central to Stable homotopy is an object called a spectrum, which is a sequence of CW complexes (CW, not Cy) with additional properties related to their loop spaces. that are typically denoted with a sequence of capital Es. While there are several interpretations of Taz, this one shows how he opens the conversation into an abstract field of math.
Extra Notes: The only stable portion of the work is a parachute slowly delivering an ACME spectrum. The parachute itself can actually be interpreted as a suspension of the 1 sphere? The suspension is integral to a spectrum? To the right we see Bugs Bunny dropping U-235 an unstable Uranium isotope, an element which would make quite a good bomb shell?
Exec Ord 6102 was signed on Apr 5 1933 the same year a theorem important for Bitcoin was proven. Satoshi's bday is Apr 5 (1975 see below). The Fed's inept actions helped worsen the great depression instead of dampening the business cycle. A motif in this work is based on a rat on a cycle...Lets start with Satoshis “birthday”: April 5, 1975. April 5th, 1933 is the day personal gold ownership in America was banned (Exec Ord 6102). Gerald Ford ended this ban starting in 1975. 1933 was also the year a theorem was proven central to Bitcoin. It essentially gives bounds for the number of points on an elliptic curve (over a finite field. I don’t want to go into this technicality but essentially think clock like arithmetic ie 12 plus any number still results in the original number on a clock, but something ill address in later works). Bitcoin is based on a particular elliptic curve. Ill now motivate the central “rat on a cycle“ motif. Warren Buffet famously called Bitcoin rat poison squared, but one might wonder if the Fed is a “rat” that might not be such a bad thing. There is a decent argument that the Fed’s inept actions worsened the Great Depression and more recently with the 2008 Crash iconic Fed Chairman Alan Greenspan admitted he made mistakes. Here he is represented as the famous yet ineffective duck hunter Elmer Fudd. In addition to overseeing a complete collapse of the price of the dollar over the last century these examples may question the effectiveness of the Fed to dampen the business “cycle”. In 1910, an ultra-secret meeting between a handful of the worlds top bankers disguised as duck hunters occurred at Jekyll Island. This led to the creation of the Fed in 1913. The word “fixed” has many interpretations eg the number of Bitcoin is “fixed” (21 million), the price of gold was “fixed” (eg $35/oz), does the Fed need to be “fixed”, some even argue the (economic) “game” itself is fixed eg who gets a Fed bailout and who does not. It also has a mathematical one, “fixed” points, which Ill get to later. The rat imagery is an altered from rats made by the famous street artist Banksy, a name which like Satoshi is a pseudonym (another unnamed pseudonym which ill address in later works relates to the math picture). Now for a tiny bit of the math. A program, undertaken by some of the 20th centuries foremost mathematicians to generalize the aforementioned theorem (Hasse) and revolutionize algebraic geometry, led to Grothendieck’s development of motives (same root as motif). One example of this is a motive which is based on rational equivalence on (algebraic) cycles (the former is usually abbreviated “rat” when writing math) ie “rat on a cycle. For example in the work you’ll see an M with a superscript rat and subscript k, it represents the “universe”, category, of these motives. To tie back to economics the large M should be juxtaposed with another “decorated” M, named M1 which is an important “measure” of the money supply which unlike in bitcoin’s case fluctuates and is impacted by the Fed. I mentioned “fixed” points in relation to the title: a deep observation about the “fixed” points of a particular map (Frobenius) and a "Lefschetz-like" fixed point theorem was important for the initiation of the program to generalize Hasse. Another of Gothendieck’s brilliant innovations (he was responsible for a significant amount of the work on this revolution) was the scheme. This "mathematical" scheme appears to be preferred to a Ponzi scheme, a term that is sometimes disparingly used in the context of economics and finance. The Standard logo has many relevant interpretations eg bitcoin standard, gold standard, a famous conjecture on cycles related to motives and the aforementioned program, and the idea of a monopoly. This can be interpreted in the context of the Fed’s monopoly” on "money printing" and some critic’s concerns about the Fed’s role in helping to determine who “wins” in our economy (eg with bailouts). There is much more to say but brevity is sometimes wit.
