How Man Ray Made Art of Math and Shakespeare

While advanced math and Shakespeare combine to make a nightmare curriculum for some students, for artist Man Ray, one of the most intriguing minds of 20th century art, they were “such stuff as dreams are made on,” or at least art could be made from. A new exhibition at The Phillips Collection reunites the objects and photographs with the suite of paintings they inspired Man Ray to create and title Shakespearean Equations. Man Ray—Human Equations: A Journey from Mathematics to Shakespeare traces the artist’s travels between disciplines, between war-torn continents, and between media that became not only a journey from arithmetic to the Bard, but also a journey of artistic self-discovery.

While advanced math and Shakespeare combine to make a nightmare curriculum for some students, for artist Man Ray, one of the most intriguing minds of 20th century art, they were “such stuff as dreams are made on,” or at least art could be made from. A new exhibition at The Phillips Collection reunites the objects and photographs with the suite of paintings they inspired Man Ray to create and title Shakespearean Equations. Man Ray—Human Equations: A Journey from Mathematics to Shakespeare traces the artist’s travels between disciplines, between war-torn continents, and between media that became not only a journey from arithmetic to the Bard, but also a journey of artistic self-discovery.


Man Ray’s long, strange trip begins in Paris in 1934. Art historian Christian Zervos commissions him to photograph a collection of three-dimensional mathematical models at the Institut Henri Poincaré. Originally made to serve as algebraic and geometric teaching tools, the models immediately strike the Surrealist photographer with greater artistic potential. Zevros publishes the photographs in 1936 in an issue of Cahiers d’Art centered on the “Crisis of the Object.” That same year, Man Ray’s original photographs appear in several Surrealist exhibitions.

Yet, in 1937, just one year later, Man Ray renounces photography as his main medium in the manifesto titled La Photographie n’est pas l’Art, L’Art n’est pas de la Photographie, literally announcing that photography is not art, and vice versa. After philosophically leaving photography behind him, Man Ray physically left his photographs and other artworks behind as he fled France at the start of World War II for America. By late 1940, Man Ray settled in the then (and now) Surrealist place on earth—Hollywood. “There was more Surrealism rampant in Hollywood,” Man Ray joked later, “than all the Surrealists could invent in a lifetime.” As Andrew Strauss writes in the catalog to the exhibition, Man Ray “reinvented” himself in Hollywood, not only marrying a young dancer but also wedding himself to the idea of working in different media in new and exciting combination.

In 1947, Man Ray returned to France to retrieve his pre-war oeuvre, including his mathematical photographs. Back in America, Man Ray reevaluated the potential of those decade-old pictures. Fellow Surrealist André Breton suggested titles such as “Pursued by her Hoop,” “The Rose Penitents,” and “The Abandoned Novel” back when the mathematical photographs were first taken, but Man Ray went in a different direction when titling the paintings inspired by those photos. “While such poetic titles echoed the playful Surrealist spirit of the mid-thirties,” Strauss writes, “Man Ray felt that refreshing new titles in English could add to their potential popularity and commercial appeal in his new environment.” Man Ray then hit on the idea of using the titles of Shakespeare’s plays for the paintings. “The mathematical models would then become specific personalities featured in Shakespeare plays that would be familiar to his audience and invite curiosity,” Strauss continues.

The Shakespearean guessing game quickly aroused the inner critic of viewers. “We would play games, trying to get people to guess what play belonged to which picture,” Man Ray admitted later. “Sometimes they got it right; sometimes of course, they didn’t, and it was just as well!” Man Ray—Human Equations invites the same guessing with the same ambiguous, same fittingly Surrealist results. By bringing together more than 125 works, the exhibition allows you to take in for the first time ever the original models from the Institut Henri Poincaré Man Ray photographed, the photographs, and the paintings they inspired.

Despite having all the facts before you, however, things never truly add up in a convincing way, just as Man Ray intended, thus calling into question the long-perceived, unjustified differences between “solid” math and the “squishy” liberal arts of literature and painting. For example, on the blackboard shown in Shakespearean Equation, Julius Caesar, writes the illogical equation “2 + 2 = 22” beside rational formulae “a : A = b : B” and “a : b = A : B,” thus introducing us to a whole new world of math merged with art. As exhibition curator Wendy A. Grossman writes in her catalog essay, “Squaring the Circle : The Math of Art,” “Devices such as inversion, negation, doubling, disjunction, and symbolic form common to mathematicians are techniques equally employed by Surrealists in order to achieve the movement’s professed goal of going beyond the real.” If the Surrealists used modern math in pursuit of unreality, Grossman argues, “Is this confluence merely coincidental, or do Surrealism and modern mathematics share something of the same spirit? Or is there something Surreal about mathematics that drew these artists to this realm?”

Just as the idea of modern math and modern art intersecting challenges common assumptions, stirring Shakespeare into the equation adds another intriguing dimension. There’s a long tradition of paintings of Shakespeare’s plays. Shakespeare scholar Stuart Sillars cites in the catalog epilogue William Blake and Henry Fuseli as notable examples, and powerful contrasts to Man Ray’s approach. “Trying to place Man Ray’s Shakespearean Equations series within the tradition of paintings that illustrate or are inspired by Shakespeare’s plays is at once pointless and essential,” Sillars writes, “pointless because the originality and zest of the images, like all his work, argues against such placement, and essential because by comparison the sheer originality of his work becomes clearer.” Despite titling and suggesting Shakespearean qualities, Man Ray’s paintings tell but don’t tell us anything about the plays in a direct or obvious way—a paradox as mathematically modern and as conceptually complex as Shakespeare’s works themselves. The Bard himself would be proud.

One example of Man Ray’s paradoxical, quintessentially Shakespearean method in action is Shakespearean Equation, King Lear (shown above). Strauss sees King Lear’s famous “tears speech” depicted “by means of a diluted pigment dripping down the canvas” and even suspects that this “presumably fortuitous effect provided inspiration for the choice of title.” Grossman sees Man Ray’s affixing of the canvas to a large wooden hoop—“a geometric figure known to mathematicians as a Kummer surface”—as the artist’s attempt to “turn[] the work into a three-dimensional object that, like so much of his work, defies easy categorization and belies a common perception that his canvases from this series were simply cerebral and literal transfers of his photographs involving little artistic mediating vision.” In essence, Man Ray’s King Lear shows off his mathematical knowledge in the name of artistic independence, all, of course, while depending on a Shakespearean allusion—a paradox neatly holding together right before your eyes. Or, as Sillars neatly puts it, “[H]ere, the Shakespearean equation is the image, not a pedestrian decryption.” As much as you try to solve the puzzle, the puzzle remains bigger and more powerful than any single answer, making this exhibition both frustrating and irresistible.

To accompany these paintings’ first exhibition, Man Ray designed a fittingly different album. On the front cover appeared a yellow, triangular flap with the words “TO BE,” the first half of Hamlet’s famous quote and the most immediately recognized line in all of Shakespeare. Man Ray deflated all expectations, however, when readers lifted the flap to find the words “Continued Unnoticed,” a confession of the artist’s disappointment over the failure of the paintings to reach a wider audience. By bringing these works and Man Ray’s methods to public notice, Man Ray—Human Equations: A Journey from Mathematics to Shakespeare introduces the artist to the public he’s been waiting for—a 21st century audience more comfortable with the surrealism of post-modern life and accepting of the intersection of math and art in the magical electronic devices it wields. The world of easy answers is gone, even when we have the whole world just a few clicks away. Man Ray—Human Equations: A Journey from Mathematics to Shakespeare demonstrates that embracing the paradox can be challenging, fun, and undeniably human.

[Image: Man Ray, Shakespearean Equation, King Lear, 1948. Oil on canvas, 18 1/8 x 24 1/8 in. Hirshhorn Museum and Sculpture Garden, Smithsonian Institution, Washington, DC. Gift of Joseph H. Hirshhorn, 1972. © Man Ray Trust / Artists Rights Society (ARS), NY / ADAGP, Paris 2015. Photography by Cathy Carver.]

[Many thanks to The Phillips Collection, Washington, DC, for providing me with the image above from, other press materials related to, and a review copy of the catalog for Man Ray—Human Equations: A Journey from Mathematics to Shakespeare, which runs from February 7 through May 10, 2015.]

[Please follow me on Twitter (@BobDPictureThis) and Facebook (Art Blog By Bob) for more art news and views.]

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Political division is nothing new. Throughout American history there have been numerous flare ups in which the political arena was more than just tense but incideniary. In a letter addressed to William Hamilton in 1800, Thomas Jefferson once lamented about how an emotional fervor had swept over the populace in regards to a certain political issue at the time. It disturbed him greatly to see how these political issues seemed to seep into every area of life and even affect people's interpersonal relationships. At one point in the letter he states:

"I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend."

Today, we Americans find ourselves in a similar situation, with our political environment even more splintered due to a number of factors. The advent of mass digital media, siloed identity-driven political groups, and a societal lack of understanding of basic discursive fundamentals all contribute to the problem.

Civil discourse has fallen to an all time low.

The question that the American populace needs to ask itself now is: how do we fix it?


Discursive fundamentals need to be taught to preserve free expression

In a 2017 Free Speech and Tolerance Survey by Cato, it was found that 71% of Americans believe that political correctness had silenced important discussions necessary to our society. Many have pointed to draconian university policies regarding political correctness as a contributing factor to this phenomenon.

It's a great irony that, colleges, once true bastions of free-speech, counterculture and progressiveness, have now devolved into reactionary tribal politics.

Many years ago, one could count on the fact that universities would be the first places where you could espouse and debate any controversial idea without consequence. The decline of staple subjects that deal with the wisdom of the ancients, historical reference points, and civic discourse could be to blame for this exaggerated partisanship boiling on campuses.

Young people seeking an education are given a disservice when fed biased ideology, even if such ideology is presented with the best of intentions. Politics are but one small sliver for society and the human condition at large. Universities would do well to instead teach the principles of healthy discourse and engagement across the ideological spectrum.

The fundamentals of logic, debate and the rich artistic heritage of western civilization need to be the central focus of an education. They help to create a well-rounded citizen that can deal with controversial political issues.

It has been found that in the abstract, college students generally support and endorse the first amendment, but there's a catch when it comes to actually practicing it. This was explored in a Gallup survey titled: Free Expression on Campus: What college students think about First amendment issues.

In their findings the authors state:

"The vast majority say free speech is important to democracy and favor an open learning environment that promotes the airing of a wide variety of ideas. However, the actions of some students in recent years — from milder actions such as claiming to be threatened by messages written in chalk promoting Trump's candidacy to the most extreme acts of engaging in violence to stop attempted speeches — raise issues of just how committed college students are to
upholding First Amendment ideals.

Most college students do not condone more aggressive actions to squelch speech, like violence and shouting down speakers, although there are some who do. However, students do support many policies or actions that place limits on speech, including free speech zones, speech codes and campus prohibitions on hate speech, suggesting that their commitment to free speech has limits. As one example, barely a majority think handing out literature on controversial issues is "always acceptable."

With this in mind, the problems seen on college campuses are also being seen on a whole through other pockets of society and regular everyday civic discourse. Look no further than the dreaded and cliche prospect of political discussion at Thanksgiving dinner.

Talking politics at Thanksgiving dinner

As a result of this increased tribalization of views, it's becoming increasingly more difficult to engage in polite conversation with people possessing opposing viewpoints. The authors of a recent Hidden Tribes study broke down the political "tribes" in which many find themselves in:

  • Progressive Activists: younger, highly engaged, secular, cosmopolitan, angry.
  • Traditional Liberals: older, retired, open to compromise, rational, cautious.
  • Passive Liberals: unhappy, insecure, distrustful, disillusioned.
  • Politically Disengaged: young, low income, distrustful, detached, patriotic, conspiratorial
  • Moderates: engaged, civic-minded, middle-of-the-road, pessimistic, Protestant.
  • Traditional Conservatives: religious, middle class, patriotic, moralistic.
  • Devoted Conservatives: white, retired, highly engaged, uncompromising,
    Patriotic.

Understanding these different viewpoints and the hidden tribes we may belong to will be essential in having conversations with those we disagree with. This might just come to a head when it's Thanksgiving and you have a mix of many different personalities, ages, and viewpoints.

It's interesting to note the authors found that:

"Tribe membership shows strong reliability in predicting views across different political topics."

You'll find that depending on what group you identify with, that nearly 100 percent of the time you'll believe in the same way the rest of your group constituents do.

Here are some statistics on differing viewpoints according to political party:

  • 51% of staunch liberals say it's "morally acceptable" to punch Nazis.
  • 53% of Republicans favor stripping U.S. citizenship from people who burn the American flag.
  • 51% of Democrats support a law that requires Americans use transgender people's preferred gender pronouns.
  • 65% of Republicans say NFL players should be fired if they refuse to stand for the anthem.
  • 58% of Democrats say employers should punish employees for offensive Facebook posts.
  • 47% of Republicans favor bans on building new mosques.

Understanding the fact that tribal membership indicates what you believe, can help you return to the fundamentals for proper political engagement

Here are some guidelines for civic discourse that might come in handy:

  • Avoid logical fallacies. Essentially at the core, a logical fallacy is anything that detracts from the debate and seeks to attack the person rather than the idea and stray from the topic at hand.
  • Practice inclusion and listen to who you're speaking to.
  • Have the idea that there is nothing out of bounds for inquiry or conversation once you get down to an even stronger or new perspective of whatever you were discussing.
  • Keep in mind the maxim of : Do not listen with the intent to reply. But with the intent to understand.
  • We're not trying to proselytize nor shout others down with our rhetoric, but come to understand one another again.
  • If we're tied too closely to some in-group we no longer become an individual but a clone of someone else's ideology.

Civic discourse in the divisive age

Debate and civic discourse is inherently messy. Add into the mix an ignorance of history, rabid politicization and debased political discourse, you can see that it will be very difficult in mending this discursive staple of a functional civilization.

There is still hope that this great divide can be mended, because it has to be. The Hidden Tribes authors at one point state:

"In the era of social media and partisan news outlets, America's differences have become
dangerously tribal, fueled by a culture of outrage and taking offense. For the combatants,
the other side can no longer be tolerated, and no price is too high to defeat them.
These tensions are poisoning personal relationships, consuming our politics and
putting our democracy in peril.


Once a country has become tribalized, debates about contested issues from
immigration and trade to economic management, climate change and national security,
become shaped by larger tribal identities. Policy debate gives way to tribal conflicts.
Polarization and tribalism are self-reinforcing and will likely continue to accelerate.
The work of rebuilding our fragmented society needs to start now. It extends from
re-connecting people across the lines of division in local communities all the way to
building a renewed sense of national identity: a bigger story of us."

We need to start teaching people how to approach subjects from less of an emotional or baseless educational bias or identity, especially in the event that the subject matter could be construed to be controversial or uncomfortable.

This will be the beginning of a new era of understanding, inclusion and the defeat of regressive philosophies that threaten the core of our nation and civilization.