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Monthly Archives: July 2019

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by Richard Nilsen
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How many sides does a triangle have? Don’t be too quick; it’s a trick question.
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Usually, math is not thought of as something where you can have opinions over answers. It’s one of math’s most reassuring qualities.
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Too often, we take what we hear at face value. Facts turn out not to be facts. No one changed your family’s name at Ellis Island. Didn’t happen.
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These are not just myths, they are just things that sound like they could be true and so become embedded in our midden of common knowledge. No, Eskimos do not have 30 or 43, or 90 words for “snow.” Human beings do not use merely 10 percent of their brains. A triangle has three sides. This is all stuff for the Cliff Clavins of the world.
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Sometimes this stuff gets caught in our mental wheel spokes because we simply don’t look closely enough. Take the Fibonacci series. We are told that this interesting pattern of numbers governs much of what appears in nature, including the spiral patterns we see everywhere from whelk shells to spiral galaxies. The problem is, observation does not support this idea, at least not as it is usually presented.
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The series is created by starting with a zero and a 1 and adding them together, and continues by adding each new number with the previous, making the series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. The series has many interesting properties, one of which is the generation of the so-called “Golden Section.”
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To the Greeks, the golden section was the ratio ”AB is to BC as BC is to AC.” It also generates the Fibonacci series and is said to define how nature makes spirals.
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Look at the end of a whelk shell, they say, or the longitudinal section of a nautilus shell, and you will see the Fibonacci series in action.
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Yet it is not actually true. When you look at whelks, you find spirals and the Fibonacci series creates a spiral, but the two spirals are quite different:
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The mathematical spiral opens up much more rapidly. The shellfish has a tighter coil. The whelk’s spiral makes roughly two turns for every turn the Fibonacci spiral makes. Math is precise, but nature is various.
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What I am most interested in here is not just the agon of conflicting beliefs, but rather the faith in mathematics, and the sense that math describes, or rather, underpins the organization of the world.
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I cannot help thinking, in contrast, that these patterns are something not so much inherent in Creation, as cast out from our brains like a fishing net over the many fish in the universe.
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Take any large string of events, items or tendencies, and the brain will organize them and throw a story around them, creating order even where none exists.
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Consider the night sky, for instance, a rattling jostle of burning pinpoints. We find in that chaos the images of bears and serpents, lions and bulls. Even those who no longer can find the shape of a great bear can spot the Big Dipper. The outline seems drawn in the sky with stars, yet the constellations have no actual existence outside the order-creating human mind.
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Our own lives — which are a complex tangle of events, conflicting emotions and motives — are too prodigal to fit into a single coherent narrative, even the size of a Russian novel. Yet we do so all the time, creating a sense of self as if we were writing autobiographies and giving our lives a narrative shape that makes them meaningful to us.
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We usually believe the narrative version of our lives actually exists. Yet all of us could write an entirely different story by stringing events together with a different emphasis.
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The question always arises: Are the patterns actually there in life and nature, or do we create them in our heads and cast them like a net over reality?
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The issue is central to a brilliant movie made in 1998 by filmmaker Darren Aronofsky called Pi. In the film, a misfit math genius is searching for the mathematical organizing principle of the cosmos.
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His working hypotheses are simple:
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“One: Mathematics is the language of nature.
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“Two: Everything around us can be represented and understood through numbers.
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“Three: If you graph the numbers of any system, patterns emerge.
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“Therefore: There are patterns everywhere in nature.”
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The movie’s protagonist nearly drives himself nuts with his search until he cannot bear his own obsession anymore.
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But the film also questions in a roundabout way whether the patterns exist or not.
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In the film, when different number series — each 216 digits long — seem to be important, an older colleague warns our hero that, once you begin looking for a pattern, it seems to be everywhere.
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It’s like when you buy a yellow Volkswagen and suddenly every other car on the road is immediately a yellow VW. Nothing has changed but your perception.
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Mathematicians find patterns in nature, yet math itself is purely self-referential. It can only describe itself.
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As mathematician/philosopher Bertrand Russell put it: “Mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true.”
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In other words, “one plus one equals two” is no different from saying “a whale is not a fish.” You have only spoken within a closed system. “A whale is not a fish” tells us nothing about whales but a lot about our language.
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It is a description of linguistic categories, rather less an observational statement about existence. Biology can be organized as a system of knowledge to make the sentence false — indeed, at other times in history a whale was a fish.
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Before Carl Linne, who created the modern biological nomenclatural system, there were many ways of organizing biology. In his popular History of the Earth and Animated Nature, from 1774 and reprinted well into the 19th century, Oliver Goldsmith divided the fish into “spinous fishes,” “cartilaginous fishes,” “testaceous and crustaceous fishes” and “cetaceous fishes.” A mackerel, a sand dollar and Moby Dick were all kinds of fish.
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Let’s face it, although the Linnaean system is useful, it is kind of arbitrary to organize nature not by its shapes, or where it lives, but rather how it gives birth or breathes.
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“One plus one” likewise describes the system in which the equation is true. It is only a tautology. Real knowledge is metaphorical, hence, “artists’ math.”
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Artists have a different way of counting, of doing arithmetic and of contemplating geometry. It’s what makes them artists.
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For an artist, one plus one equals three. It is a very clear formula: There is the one thing, the other thing, and the two together — a knife, a fork and a place setting. Three things.
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And a triangle has five sides. There are the normal three, and then the front and back. You can turn any triangle over from its back and lay it on its belly. Cut a triangle from a piece of paper and hold it in your hand. Your thumb is on one side of the triangle and your index finger on the other. Add’em up: Five.
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Computer programmers talk about fuzzy logic as if they discovered it.
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It is artists who wake up each morning in a Gaussian blur, after all. It is artists who first understood that all numbers are irrational numbers.
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The primary difference between a mathematician’s logic and an artist’s is that the artist is unable to leave the world behind: The mathematician, the logician, the philosopher deal in abstractions; the artist deals in plums.
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The artist lives in a world of things. Real things: palpable, noisy, smelly, difficult and beautiful. He mistrusts any answers not rooted in them.
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The sentimental view of artists has them constructing “castles in the sky,” but the artist scratches his head over this, because to him, it is math and philosophy that are constructed out of thin air.
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“No ideas but in things,” wrote poet William Carlos Williams. Like the plums that were so cold and so delicious in his poem.
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Don’t get me wrong: One should not dismiss the practical world out of hand. It is good to know how to balance a checkbook, and artists’ math does not carry much clout with the bank.
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An artist is likely to use something called “gut mathematics.”
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The artist knows, as a banker usually doesn’t, that the shortest distance between two points is a leap of the imagination.
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She also knows that three is more interesting than four. It just is. Ask any artist.
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And when an artist talks of pie charts, she wants to know if it is cherry or lemon meringue.
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Like the old math gag: “Pi R square.” “No, pie R round, cake R square.”
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It’s fun to joke about artists’ idiosyncrasies, but there is a serious side to all this.
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When we see yammering faces on TV shouting each other down over ideology, the artist is the one who can remind us that the world isn’t made up of theory or system, but is made up of hubcaps and clamshells. Ideology means very little to an asparagus.
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The world falls into peril every time a system denies physical reality. It is abstractions, after all, that fueled the Cold War, abstractions that justify suicide bombing; it was theory that built Auschwitz.
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Artists remind us of flannel, of smoke, of mud. These are the things we share with our family and our friends. These are the things that ultimately count.
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No ideas but in things.
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It reminds me of a line written by the poet Tom Brown:
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Richard Nilsen inspired many ideas and memories at the salons he presented through the years when he was an arts critic and movie, travel, and features writer at The Arizona Republic.   A few years ago, Richard moved to North Carolina.   We want to continue our connection with Richard and have asked him to be a regular contributor to the Spirit of the Senses Journal.   We asked Richard to write short essays that were inspired by the salons.

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by Richard Nilsen
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There is no city more photogenic than Paris. New York does well by the camera, too, but Paris has that je ne sais quoi. London hardly shows up on the camera map; Los Angeles only serves as a set for movies. But Paris is the City of Light and untold photographers have asked it to be their model.
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I’m not talking here of travel photos — those gaudy, sunny-skied brochure pictures — nor of the vacation snapshots we bring home to show friends, but photographs made by artists, trying to find the visual metaphor for city-ness or life, or an armature to hang their shapes, colors and textures. These are photographers for whom the purpose of clicking their shutters is to capture some human emotion or intricate design.
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The city is also lucky to have had many photographers whose names are intimately tied to it and whose images have practically defined Paris for many of us. New York City may have had Joel Meyerowitz and Weegee, but Paris had Charles Marville, Eugene Atget, Brassai, Jacques-Henri Lartigue, Robert Doisneau, Andre Kertesz, Henri Cartier-Bresson and Willy Ronis, among many others.
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The earliest known photograph to contain an image of a human being was made in Paris in 1838 by Louis-Jacques Daguerre (the exposure was so long, no one on the busy street registered on the plate but a man standing still to have his shoes shined).
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So many others: Edouard Boubat; Jeanloup Sieff; George Hoyningen-Huene; Guy Bourdin; William Klein; Germaine Krull; Lucien Clergue; Gisele Freund; Edouard Baldus; Hippolyte Bayard; and Nadar (Gaspard-Felix Tournachon) who made the first aerial photos of Paris, from a gas-filled balloon in 1858.
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The greatest of the early photographers who have given us our Paris is Atget (1857-1927), a strange little man who took upon himself the project of archiving images of a city he saw disappearing before his eyes. The old city was giving way to the modern, and he dragged his camera all over the city to capture buildings, streets, doorways, windows, door knockers, fences — even peculiar trees and people. His work was little regarded as anything but the hobby of an eccentric, until American photographer Berenice Abbott discovered him as an old man, and bought his surviving prints and negatives and persuaded galleries and museums to exhibit them.
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But Atget was not the first to try to document old Paris. In 1851, author Prosper Mérimeé commissioned the Missions Héliographiques, to photograph French monuments needing restoration. He hired five photographers: Baldus, Bayard, Gustave Le Gray, Henri Le Secq and Auguste Mestral, who divided up the city and surrounding country to create a catalog.
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Better known is the work of Charles Marville (1813-1879), named official photographer of Paris in 1862, who was hired to photograph the city before the radical urban renewal undertaken by Baron Haussmann (the prototype of Robert Moses), who widened boulevards and tore down slums and narrow alleys.
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During La Belle Epoque, Jacques-Henri Lartigue (1894-1986) began photographing at the age of seven and captured life in Pre-WWI Paris. As an adult, he mostly gave up photography to be a painter, but it is the irrepressible pictures he made as a boy that he is remembered for.
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   After the War to End All Wars, Paris became the home of emigres and artists. A Hungarian, who called himself Brassai (1899-1984), came to love the bohemian underworld of the city and between the wars made the memorable photos of bars, prostitutes, artists and the city at night. His most famous book, Paris de Nuit (1933) practically invented the way we see the Paris of Hemingway, Pablo Picasso and Henry Miller.
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In 1925, another Hungarian, André Kertész (1894-1985), moved to Paris and carved out a career as a photojournalist with an experimental and artistic bent, often using unusual angles and designs. He later moved to the U.S., but his Paris is one of the visual landmarks of the century.
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Robert Doisneau (1912-1994) began photographing in the late 1930s, but the war interrupted his career and it is his photographs from the 1950s and after that are his legacy — a collection of photographs of visual puns, gentle mimicry and humanist concern. His jokes are never simply gags, but moments captured seemingly at random while people do the things that people do.
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It is that instant, called the “decisive moment” by Henri Cartier-Bresson (1908-2004) that define his work. One of the greatest photojournalists of the 20th Century, HCB, as he is sometimes called, filled his inch-by-inch-and-a-half Leica frame with designs so perfect, they seemed assembled like jigsaw puzzles. He intended to catch the perfect interaction of subject and motion to make a photograph that stands on its own as art, even when commissioned as an illustration to a magazine story or book.
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This is all a very short precis of Parisian art photography. There is so much more to say about it, including Richard Avedon’s use of the city as a backdrop to his animated fashion photos of the Fifties, and the crazy energy of the often out-of-focus black and white of William Klein. Or the photographs Swiss-born Robert Frank made in Paris before he moved to the U.S. and defined Eisenhower’s era in his book, The Americans(1958).
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Of course, Paris is a perfect subject for a camera. Many cities are interchangeable, and dropped into their downtowns unannounced, you would be hard pressed to tell which city it was. But Paris is unquestionably Paris, to the point of almost being a parody of itself. There is romance:
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There is the eucharist of bread and wine:
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When you enter Paris with your camera, you find there is little change between then and now:
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There are cafes, markets, fountains, boulevards, architecture and, most of all, people. The camera still has plenty to make a meal of.
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I’ve been to the city many times, and have made thousands of photographs, and almost every one of them says the one word, whispered in my welcoming ear: “Paris.”
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Perhaps you have a different favorite. Perhaps it is Rome that holds you tight, or Prague, or Dayton, Ohio. The job is to use your eyes and your lens to find what defines that spot, not only on the map, but in your affections and mind. Manhattan is surprisingly filled with trees; Chicago has its trains; New Orleans is framed by bridges; and Las Vegas is … well … very much itself.
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Even Phoenix has its visual soul, although it is often fried by the Sol. Take your camera out (or your phone — I know a photographer who has published an entire book of photographs of Havana taken entirely with his iPhone. The images are stunning). It matters less if it is Johannesburg, South Africa, or downtown Phoenix. There is something for the frame.
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Although in my book, Paris beats them all.
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Click on any image to enlarge
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Richard Nilsen inspired many ideas and memories at the salons he presented through the years when he was an arts critic and movie, travel, and features writer at The Arizona Republic. A few years ago, Richard moved to North Carolina. We want to continue our connection with Richard and have asked him to be a regular contributor to the Spirit of the Senses Journal. We asked Richard to write short essays that were inspired by the salons.

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