It starts with a postcard.

In an 1890 paper, Italian mathematician Giuseppe Peano first described a plane-filling curve:

There exists a continuous curve which goes through every point of a plane ... This result is of interest in the study of the foundations of geometry, for there does not exist a specific character which distinguishes a curve from a surface.

This curve was a radical proposal. Peano asserted that a continuous one-dimensional line could be constructed in a specific way so that it would wind its way through every point of a two-dimensional square.



His curve suggested a mapping from the single dimension of points on a line to the paired dimensions of coordinates in a plane. Set theorist Georg Cantor had already devised in 1874 a one-to-one correspondence between the points on a line and the points on a surface, but the correspondence dissolved the continuity of the line. Peano built the argument in his 1890 paper strictly analytically using only the properties of the numbers between zero and one. He included no drawing of his curve. 

One year later, German mathematician David Hilbert offered a drawing based on the curves Peano had conjured. It is a recursive form beginning with a bent line where each segment is replaced by a smaller, self-similar bend, becoming denser and denser, continuing infinitely to completely fill a plane on its theoretical last iteration. The global trajectory of the path (in this case up, to the right, and down) remains unchanged throughout the iterations. Here is Hilbert’s drawing of the first three steps in the process:



Peano seems not to have drawn the curve himself, even in his own notes, until the fifth and final edition of his Formulario Mathematico, published almost two decades later, in 1908. Here are Peano’s drawings from the Formulario, which include Hilbert’s example using base two (c) and his own example using base three (d):



This drawing is from a family of curves most often referred to as a “Peano curve,” with which artist Tauba Auerbach has long been fascinated, incorporating them into their paintings, drawings, sculptures, and the occasional concrete poem.

Auerbach’s Ligature Drawings are something close to a writing practice, using markers on oversized graph paper to produce bent lines which develop as they are drawn. The lines often return on themselves, often repeat, and inevitably connect. Most are stamped with the date and they pile up. Their abundance, the programmatic movement of the pen, and the meandering compactness of the lines recalls something from Peano’s own description of his curve as

a point in n-dimensional space, which is a continuous function of a real variable, or of time, such that the trajectory of the moving point fills the whole space.

Continues in class . . .

Italian artist and designer Bruno Munari was also fascinated by Peano’s curious curve. This space-filling curve is a mathematical absurdity — a one-dimensional entity passing as a two-dimensional figure. I'd guess it was this paradox that drew Munari to the form starting in the late 1960s. Here’s a set of drawings attempting to understand the form [↓]:



Munari called these specific algebraic-geometric constructions "pathological curves." He began to explore them in his work. In December 1969 Munari made a print for La Rinascente department store in Milan called Arbitrary Variations on the Peano Curve. I expect “Arbitrary” is the key word here. Soon he started making paintings and prints based on Peano curves where he indulged his instinct to oppose the “scientific nature” of the mathematical forms with an irrational component:

My proposal, absolutely superfluous to mathematical speculation, but curious from an aesthetic point of view, is to place certain colors in the areas delimited by the line

Munari continues:

I wanted to try to insert in this very rigorous, mathematical structure an emotional fact based instead on the sensitivity of color. I asked myself: what happens if I insert a fact of chromatic sensitivity into a strictly logical problem? The truth that color finds its own structure even if it has an emotional origin because Peano can explain its structure with logic while I cannot explain in words what sensitivity is. So it is a relationship between sensitivity, intuition and logic.

He made a set of prints for Danese Milano based on the images. These are his color studies which give some slight insight to the process. And here is a finished picture [↓]. I love these so much.



All of this was research, design research, for Munari. Design research was an active concern for him from the 1960s onwards. In Codice Ovvio (1971), he described the research process:

Unlike artists, designers . . . do not come up with marvelous little sketches that someone else will later reproduce, they experiment with optical, physical, geometric, topological or mechanical phenomena . . . fine-tuning their components in order to maximize their effect, researching the material best suited to guarantee a maximum of communication at the lowest cost. They subsequently develop the best mechanical technique and finally create a prototype, which is not an artist’s unique masterpiece, but simply the model for the whole series. Whereas in art, reproductions are always inferior to the original, in this case the prototype is always inferior to the final products.

About ten years later, he became editor of a publication series which provided a platform for this work. From 1976, he was director of Quaderni di design (Design Notebooks) published by Zanichelli. It’s an exceptional collection, each issue presenting one single design research project. The second issue presented one of Munari’s own projects, The Discovery of the Triangle [↓]:



Continues in class . . .

Italian artist and designer Bruno Munari was also fascinated by Peano’s curious curve. This space-filling curve is a mathematical absurdity — a one-dimensional entity passing as a two-dimensional figure. I'd guess it was this paradox that drew Munari to the form starting in the late 1960s. Here’s a set of drawings attempting to understand the form [↓]:



Munari called these specific algebraic-geometric constructions "pathological curves." He began to explore them in his work. In December 1969 Munari made a print for La Rinascente department store in Milan called Arbitrary Variations on the Peano Curve. I expect “Arbitrary” is the key word here. Soon he started making paintings and prints based on Peano curves where he indulged his instinct to oppose the “scientific nature” of the mathematical forms with an irrational component:

My proposal, absolutely superfluous to mathematical speculation, but curious from an aesthetic point of view, is to place certain colors in the areas delimited by the line

Munari continues:

I wanted to try to insert in this very rigorous, mathematical structure an emotional fact based instead on the sensitivity of color. I asked myself: what happens if I insert a fact of chromatic sensitivity into a strictly logical problem? The truth that color finds its own structure even if it has an emotional origin because Peano can explain its structure with logic while I cannot explain in words what sensitivity is. So it is a relationship between sensitivity, intuition and logic.

He made a set of prints for Danese Milano based on the images. These are his color studies which give some slight insight to the process. And here is a finished picture [↓]. I love these so much.



All of this was research, design research, for Munari. Design research was an active concern for him from the 1960s onwards. In Codice Ovvio (1971), he described the research process:

Unlike artists, designers . . . do not come up with marvelous little sketches that someone else will later reproduce, they experiment with optical, physical, geometric, topological or mechanical phenomena . . . fine-tuning their components in order to maximize their effect, researching the material best suited to guarantee a maximum of communication at the lowest cost. They subsequently develop the best mechanical technique and finally create a prototype, which is not an artist’s unique masterpiece, but simply the model for the whole series. Whereas in art, reproductions are always inferior to the original, in this case the prototype is always inferior to the final products.

About ten years later, he became editor of a publication series which provided a platform for this work. From 1976, he was director of Quaderni di design (Design Notebooks) published by Zanichelli. It’s an exceptional collection, each issue presenting one single design research project. The second issue presented one of Munari’s own projects, The Discovery of the Triangle [↓]:



Continues in class . . .

Enzo Mari spent the year 1957 drawing an apple. The result, La Mela, is a large silkscreen print [↓] produced as an artist multiple by Danese Milano continuously since. 



Mari had the apple up in his studio [↓] for a year, considering and adjusting its form — trying to get the curve just right.



He lavished time on the drawing, preparing it for manufacture by abolishing detail and reducing it to an essential form. He was not looking to draw *an* apple, but rather *the* apple — a perfect symbol designed for the serial logic of industrial reproduction. In place of the unique work of art and its privileged market, multiples used contemporary manufacturing to produce many exact copies circulated as consumer products. The Apple was only the first in a series (Serie della Natura) of similar prints Mari designed over the next ten years. 

Curator and Enzo Mari archivist Francesca Giacomelli, describes his departure point for the series in the catalog for a recent comprehensive exhibition at The Triennale in Milan. He wanted a subject that was easily understood, and started from Caravaggio’s Basket of Fruit, a painting he thought everyone could recognize [↓]:



He continued with pictures of animals, vegetables, and other fruits, For each, Mari would start

a long process of research aimed at the simplification of form via the creation of hundreds of models of which he studied each and every detail (for the goose, for instance, he studied the eye, the beak, even the nostrils, etc.) 

He applied this research process to each image, since (now, Mari speaking):

quality does not reside in the grouping together of many elements but in the absolute perfection of only one element.

In a recent interview, Mari outlined the process. Describing his approach to research more broadly in his work, Mari offered this succinct theorem:

The research is the design, not the product.

Continues in class . . .

In 1958, Jock Kinneir said to Margaret Calvert:

If this takes off it’s going to be the biggest job that any graphic design team has ever tackled.

After working on the design of a comprehensive signage system for Gatwick Airport in London, Kinneir was tapped to design signs for the new British motorways. Motorways would have restricted access, wider lanes, and higher speeds and so, to be legible, the signs would need to be completely reconsidered. Kinneir hired his former Chelsea School of Art student Calvert to work on this project. It was a surprisingly small team, but this was also why it worked. (Calvert said later, “Anything bigger would just be another committee.”)



They [↑] worked intuitively and quickly. Calvert described their research and testing approach:

It required completely radical thinking. The information wasn’t there in terms of reading distance, clarity and letter spaces. We had to make up the signs and then test them. It was instinctive.

And Kinneir described their design method:

Style never came into it. You were driving towards the absolute essence. How could we reduce the appearance to make the maximum sense and minimum cost.

Maquettes were tested in an underground parking garage, a street near the studio, and in London’s Hyde Park where signs were propped up against trees to work out the most effective background colors. Reading distances were worked out ad hoc. Candidates were made, adjusted, re-adjusted. Here is a mockup [↓] of goache, paper, and cowgum.



The first signs appeared in 1958. Calvert and Kinneir drove up the motorway for its official opening, but never made it there. She recalls:

We were invited to the opening of the M1, and we had obviously special permission by the police to go on this motorway. It wasn’t open to the public at that point. It was a beautiful sunny day, blue skies, and then just us, noone else on the motorway. Then we’d see our signs up, and we thought, “Wow!” They just looked so good. They were big, and they sat there and they had their own presence. We just went on and on and on and on. We missed the turn-off or where the actual opening was, and I think we just ended at the end in a ploughed field. But we had a great day. And that’s probably a big moment in my life.

Continues in class . . .

Sylvia Harris flipped design around the other way. Instead of thinking from the point-of-view of the designer, she considered every project from the perspective of its user. Now, this was anything but standard practice at the time. Today “user-centered design” is ubiquitous, but this wasn't today — it was 1993, and I was lucky enough to be there.



I was fresh out of school and working at Two Twelve Associates, a graphic design firm in New York specializing in “Public Information Design” that she had founded with two Yale School of Art classmates, David Gibson and Juanita Dugdale. Two Twelve was a wonderful setting for a young designer, and I was able to not only work on projects but also observe the projects going on around me. One of these was the project to design the first touchscreen interface for Citibank ATMs. Sylvia led the effort, which started with research.



Existing ATM interfaces used the second-person imperative address of machines, with sequential screens of impersonal instructions telling the user what to do next. In distinct contrast, this interface [↑] spoke in the first-person, addressing the user directly. For example, it asks (in this polyglot metropolis), 

What language shall we speak?

The “we” here is important — this was generous design, a design that considered its user directly, as a partner rather than an operator. It was inclusive. And it was completely different from other bank machines at the time. It was an exceptional project, completed at a very high level for a very wide audience. Sylvia recalled:

My firm got a series of contracts with Citibank to work on the design of the first ATM. I learned everything I know about user testing, product design and strategic planning from that experience. It was like going to graduate school in usability and I made contacts that have lasted to this day.

Several years later, she was hired by the United States Census Bureau to bring this user-centered approach to the redesign of the U.S. Census 2000 forms. Sylvia was charged with making the forms easier to use, more legible, and in the process to collect a wider demographic population of responses from the 80 million forms sent out every ten years. As with most of her projects, she started with research. In this case that research started in a classroom at Yale School of Art, where she had introduced an information design class. Together with her MFA students, she developed the redesign of the census form. The results were powerful.

The 2000 U.S. Census looked considerably different from the 1990 version. Like the ATM interface, these begin with a plea to the user, “Your answers are important!” And indeed they were as political power depends on an accurate count of citizens. The stakes could hardly be higher.

Continues in class . . .

At the American Institute of Architects national conference in 1973, Sheila Levrant de Bretteville described her search:

I have begun to try to find an answer for myself as a woman designer. Designers must work in two ways. We must create visual and physical designs which project social forms but simultaneously we must create the social forms which will demand new visual and physical manifestations.

A printed version of her talk soon appeared under the title A Reexamination of Some Aspects of the Design Arts from the Perspective of a Woman Designer, published together with her students’ [↓] work in British design journal Icographic 6.



These were students in The Women’s Design Program at the California Institute of the Arts, a newly established program in a newly established art school which de Bretteville was instrumental in founding. The Women’s Design Program was meant to foster collective investigation between students and faculty. It was non-hierarchical, exploratory, participatory — a clearly distinct approach from the top-down knowledge transfer of more conventional teaching. And one that is neatly inline with de Bretteville’s call above. The two-sided model she suggests is powerful, recognizing that *how* design work gets done can carry as much meaning as *what* results.

On returning from Italy in 1969 after working with Olivetti, de Bretteville moved to Los Angeles to be involved in the formation of the new school. She was hired to design the printed materials to attract a new kind of student. She also edited an issue of Arts in Society. The issue has a wonderfully predictive subtitle, setting the stage for what’s to come. Again, the community, the setup, is as important as whatever teaching might happen there.

Not long after beginning to teach at CalArts, de Bretteville joined with fellow art faculty Judy Chicago and Arlene Raven to form a new offshoot, independent program they named the Feminist Studio Workshop. The initial brochure usefully repeats a picture of the three founding women together, each taking turns facing the camera. Here is the one with Sheila facing forward [↓].



The Feminist Studio Workshop met first in de Bretteville’s home, and soon was housed in the the Woman's Building, a collective site west of downtown Los Angeles. Here is a “video letter” from a participant who describes the setup. Again, the way the work gets done is what matters. 

Continues in class . . .

GPT 3.5 replies:

As of my last update in January 2022, Angie Keefer is primarily known for her work as an artist, writer, and editor. She has been involved in various projects in the contemporary art world. Keefer has contributed to publications, exhibitions, and collaborative projects, often exploring themes related to language, communication, and social structures. It's worth noting that Angie Keefer's work may have evolved or expanded since my last update, so I would recommend checking more recent sources for the latest information on her activities and projects.

So then you could read her collected writings, Second Thoughts — it‘s stellar [↓]:



Or you could look at a few of her previous exhibitions like this one, this one, or this one. You might just search the internet. Sandberg Instituut elaborates (full text here):

Angie Keefer (b. 1977, Alabama, USA) is an artist and teacher. In 2010, she co-founded The Serving Library, a not-for-profit artists’ organization dedicated to publishing, and, via publishing, to building an archive of materials to serve artist-run education. Keefer is the editor of History of an Art School (Konig, 2022), which chronicles fifty years of women students and faculty at the Yale School of Art as told through their testimony. Second Thoughts, a collection of her writings and visual works composed over the last ten years, was published in 2019. Version Space, an ongoing interview series (2019–) convened and edited by Keefer, brings graduate art students into conversation with artists working with Artificial Intelligence. 

Finally, look up her website (http://angiekeefer.com) which reports:

CHECK IS "N" THE MAIL!

Today in class, Angie is going to speak about Version Space, a collective investigation around artists working with AI via a series of interviews conducted by students. These are edited, formatted, and released on the project website and through Library Stack. Angie will fill us in around the project’s evolution and context, and offer another take on what (design?) research might look like.



 
That is the first half of class. In the second half, we are going make pinhole cameras and view an eclipse.



Continues in class . . .

In 2018 I was invited to join a team with artist Adam Pendleton and architect David Adjaye to design a monument to Dr. Martin Luther King Jr. and Coretta Scott King on a site at the northeast corner of Boston Common. It was more or less a dream project.



The speeches of the Kings inspired action, and the words they spoke now more than fifty years ago catalyzed a social movement which remains urgent. Their speeches were also virtuosic, moving oratory performances (Adam called them singing). They were calls to action, mobilizing allies in the fight for racial and economic justice. In place of concise quotations typically chosen, we wanted to include the context that surrounded the Kings’ spoken words. What did it sound like? How did it feel? What came next? To this end, we selected only generous excerpts and exclusively from the Kings’ speeches.

Public momuments typically use pithy statements and memorable quotes from written accounts. To honor the long-reaching effects of the Kings’ words, we chose instead to include long excerpts from their public speeches, not from written sources. Meanwhile, the translation of speech into physical text typically falls short. In place of the ubiquitous Roman square capitals carved into stone, I designed Speech-to-Text, a typeface that channels the vitality of the speakers and the era in which they spoke. 

Speech-to-Text is based on typewritten notes for the Kings’ speeches from the early 1960s. I adapted Artisan, a font commissioned by for the IBM Selectric typewriter [↑] and not previously digitized. The Selectric was state-of-the-art in 1961, intended to make typing faster and easier.



Speech-to-Text is both faithful to the practical documents of the time, and streamlined for contemporary computers. The new font software is also state-of-the-art, now, incorporating machine learning transcription into a dynamic typeface to produce variable letterforms.



Continues in class . . .

I saw the exhibition of Virgil Abloh [↓] at the Brooklyn Museum twice.



When you walk in, these shoes [↓] sit on a table just to the right, marked as what they are, a work-in-progress, one of many, a "prototype."



There are maybe 20 pairs of unreleased Nike shoes surrounding these, in various states of de- and re-construction, the fruits of an ongoing collaboration between the shoe-maker and Virgil Abloh’s label, Off-White. According the exhibition materials for Virgil Abloh, "Figures of Speech," these works-in-progress are typical of how he thought about design:

as much about the process of asking question and prototyping as it was about the final product.

The rest of the exhibition consists of so many prototypes. The materials are impressively mixed, inherently uneven, and all presented at the same level. This is one thing I really liked about it. It matched the similarly catholic approach to his work.

prototypes are presented alongside the finished works of art, products, and fashion designs to reveal his myriad inspirations — from centuries-old paintings to contemporary signage at construction sites.

Long tables collect the materials. For example, the first includes his high school sketchbook, a brass printing plate for the CD packaging of Watch the Throne (Kanye West and Jay Z), a small video screen showing a fashion shoot at Le Corbusier's Villa Savoye, next to a series of silkscreens used for his Pyrex Vision clothing line, sketches for a character called Jerry Curls, next to jewelry made from paper clips, a custom designed DJ setup, and a Nike tennis dress for Serena Williams. It is a dizzying array of materials and I’m guessing that’s the point. The exhibition design [↑] is by Abloh's studio, Alaska Alaska together with Mahfuz Sultan of Clocks.



Midway down the table, a set of silkscreens [↓] are laid out. One is a painting by Caravaggio (who you’ll remember from the Enzo Mari class), another combines the words ”Pyrex” and “23.” The constellation of references is (typically) mixed: ”Pyrex” refers to the glassware in home drug labs; “23” was the jersey number of basketball star Michael Jordan; and the Caravaggio painting is The Entombment of Christ (1603). 






Continues in class . . .

There’s a channel on Are.na called How do you describe Are.na at a party? Wonderfully self-reflexive, it’s also quite earnest. Here, a few descriptions I particularly like:

→ internet memory palace
→ random access memories
→ media without the social scramble
→ pattern recognition network
→ like del.icio.us, but better
→ research tumblr

Ten years into Are.na’s existence as a slow, considered social network of sorts, Charles Broskowski wrote a blog post, On Motivation, about why to keep going. His post is, naturally enough, illustrated with blocks from the site including this stunner by Bryce Wilner, called Plotter’s Tour (Spiral) (2017) [↓]:



To my eyes, this is a perfectly convincing picture of the process of design research. You will notice the lines are hand-drawn. You will notice that the dots that form the spiral are connected, but not in a route following the curve. You will notice the lines hop from dot to dot, connecting the parts in an ordered sequence which, only over time, reveals the big picture — in this case, a spiral. This is one in a sequence of works that Bryce describes in an interview with the Creative Independent.

We are at the end of the semester and I am guessing that each of your spirals has revealed itself. Today you will be showing your work in a 9-minute, scripted and precisely choreographed presentation. These will be recorded, collected, lightly edited, and posted back here on this website for the future to reconsider. 

I am very much looking forward.

Continues in class . . .