# linear abstractions

Linear.  Ajo, AZ

Around the corner, in the back… Cheers!

Please Help, I lost Everything with the Protect/Attac crash. I am now selling my abstract linear minimalism pepe. Please, it’s all I have left!

Rudolph Schaeffer School of Design, Linear Abstract Design Study, ca. 1920–1930

Hey, hope you are doing well ^^ this September I'll start uni and I'll also be studying maths!! I'm so excited haha ^^ How is it for you? How different do you think is math in uni compared to math in high school (I'm from a french system so our curriculum might be different though) Thanks in advance!

Hey,

I’ve typed a reply to this message three times now because I’m so clumsy and keep accidentally closing this tab!! 😂

Firstly, congratulations on your achievements!! 🎉🤓 I hope you enjoy studying maths at uni!! (Feel free to message me about it whenever you want!!)

For me, pure maths is really different to high school maths. It’s a lot more wordy and more about definitions, statements and proofs than actual calculation. So far in my pure maths career, I’ve studied Abstract Algebra, Linear Algebra and Analysis. I think most universities (at least in first year in the UK) split pure maths into Algebra and Analysis.

Abstract Algebra involves Set Theory, Number Theory and Group Theory. Linear Algebra is about linear spaces (it involves vectors and matrices). Analysis is about the properties of sequences, series and function.

I’ll show you some questions to demonstrate what I mean when I say pure maths is wordy:

These are two Abstract Algebra questions on Group Theory.

This is a Linear Algebra question.

These are two Analysis questions. The first is about the convergence of sequences and the second is about the continuity of functions.

As you can see, all these questions build on definitions and statements. None of them require calculators. In fact, I think only the Linear Algebra question involves any arithmetic at all and that’s only basic arithmetic in part (f) of the question.

Seeing these kind of questions was scary to me at first. I barely understood the language they were presented in; the wording of questions wasn’t what I was used to and there were so many new symbols to learn. It was almost like learning a new language!!

for all real numbers x there is a real number y that is greater than x

you can just write:

This literally translates to:

for all x in the set of real numbers, there exists a y in the set of real numbers such that y is greater than x.

It’s quite convenient actually but might take time to get used to if you haven’t seen it before.

Because of this new “language”, I definitely struggled with pure maths in the beginning of my first semester. For me, Analysis got better and easier to understand (in fact, Analysis is my bae at the moment 💛) but Abstract Algebra was the opposite. To this day, I hardly understand it. I think I just overcomplicate things in Abstract Algebra. Sometimes another student will explain something to me and it’ll seem so simple, but my brain just can’t see simple explanations. I don’t think Abstract Algebra is for me. (But other people love Abstract Algebra and that’s completely fine!) I’m finding Linear Algebra to be much better and I’m really enjoying it at the moment.

On the other hand, applied modules e.g. calculus, statistics, probability, are very similar to high school. They build on what you learnt in school (but don’t worry; the lecturers will (or at least they should) do recaps of what you learnt at school so it’s okay if your high school maths knowledge is a little foggy). I actually find applied modules a little tedious sometimes for this reason. Applied maths at school was never really my favourite, so to have to study it still kinda sucks, but sometimes it’s a nice relief from pure maths. I used to enjoy differentiation and integration in high school, but now not so much!! I would much rather be doing Analysis proofs than complicated calculus these days! If your first year doesn’t count, use it as a way to experiment to see what you enjoy and what you don’t. Your opinion and perspective on maths will probably change!

Also, another thing I want to say: don’t worry if you don’t immediately understand things. I feel like a lot of maths students grew up having a relatively easy time with mathematics and so university maths can be quite a shock to the system sometimes (it was for me!). Take your time with it. I felt like I was the only one struggling and for most of semester 1 I felt so dumb. I didn’t have much confidence going into my exams. Everyone around me seemed to understand what was going on, whereas my brain hurt just trying to do abstract algebra homework questions. But actually, I think most people felt like this, and people just didn’t and still don’t talk about it which sucks. Don’t be embarrassed if you’re struggling - maths at university isn’t easy at all and I don’t know anyone who hasn’t struggled at least a little bit. Talk about it with others - talking about it helps you learn and fill in gaps in your knowledge, and it helps you realise that most people are in the same boat as you!! ⛵️ (Talk to me about it if you so wish!!)

I hope that helps and all the best with your studies!! 😃

8

Stephen Felton!

Rudolph Schaeffer School of Design, Linear Abstract Design Study, ca. 1920–1930

from the [ Brasilia, 1961-63 ] series

*full photographer feature: here

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Naum Gabo.  Linear Construction No. 1, Red Kinetic Painting, Wire Abstract Sculpture, Head No. 2, MoMA Book by Pevsner, Head No. 2, Proof of Opus 3, Kinetic Construction (Standing Wave), Opus 3 Relief Print, Head No. 2 (top to bottom). 1915-1950.

Rudolph Schaeffer School of Design, Linear Abstract Design Study, ca. 1920–1930

No Future / No Past: “Tomorrow” Turns Towards the Present

Anna Valdez, Laptop with Landscape, 2014

Though it may only have ever been an illusion, the hermetically-sealed white cube once proved a singularly-authoritative curator. Temporalities traced lineages through its empty space, an art-world riff on the adage that past performance predicts future success. Even after legions of “outsider artists” began to expand the traditional art-space, the gallery continued to offer a singular site in which to consider art, outside of the entropy of time, paradoxically detached from and enmeshed in its histories.

It fell to the iPhone to tear these fantasies apart. No single work of institutional critique, neither a Michael Asher nor a Rirkrit Tiravanija, could so wholly destabilize the premise of the gallery as an internet connection. It is not only that creation now happens continuously throughout the showing of a work, or that that creation is democratized, or that it can occur at the hands of third-parties who have never once stepped foot in the gallery. It is that the internet is better at playing the gallery than the gallery is, that it offers us all possible futurities, founded on every conceivable point of reference, simultaneously.

How then does an exhibition take the internet as its subject matter and, further, elevate its artists over the multitude of content-creators we encounter in the digital age? “Tomorrow”, the in-quotations title of Hashimoto Contemporary’s new group painting show, tackles these dual conceits with a certain irony. In the same breath, we consider the manner in which the digital world increasingly compresses the timescale of lived experience into a “forever-present”—an aesthetic of the sleep mode, our constant half-awareness of all things, always—alongside the young artists who play to the art-world’s foundational entrancement with the avant-garde.

While at first glance the show may evoke memories of Forever Now, the Museum of Modern Art’s widely-panned contemporary painting survey that opened nearly a year prior, closer inspection reveals a crucial difference: curator Jessica Ross’ aims, though unstated, succeed on precisely the same grounds on which Laura Hoptman’s (curator of the MOMA show) failed. In Hoptman’s introduction, she elaborated a theme of atemporality, the “new and strange state of the world in which, courtesy of the Internet, all eras seem to exist at once.”

Where Hoptman followed that premise to exhibit inarticulate works whose meanings decayed rapidly in the now-unsealed museum space, Ross delivers works that move fluidly into and out of the digital realm. Hoptman’s determination to show Art failed in a grand, Modernist sense—the loss of the thesis; in effecting a more rhizomatic survey, Ross apprehends a multitude of stories without the assumed burden of assembling a narrative.

Though the paintings in Ross’ show vary widely, engaging with repetition and patterning, analogue accumulations and digital artifacts, the space between reality and the rendering of the computer screen, they carry forward a common conceptual through line. It is an opposition to definition, the paradox of circumscribing the infinite, that lends the digital world its depth as a sociological and artistic concern, and, in its breadth, “Tomorrow” develops itself as that world’s appropriate analogue.

Anna Valdez’s two paintings offer a particularly engaging introduction to these themes. Stack depicts eight art books stacked atop one another in a domestic scene, covers obscured but for the top book. That book features a crop of Paul Gauguin’s Spirit of the Dead Watching; the leftmost half, including the spirit, is omitted, leaving the viewer to take up the absent gaze of the reclining woman and occupy the (abandoned) phantasmic space of consumption. Gauguin once commented that his painting could either depict the spirit imagining or being imagined: viewing Valdez’s work, the viewer wonders if he creates the world through watching or if it is through watching that he himself is created.

Valdez encourages both claims, empowering us as authors as well as viewers. Read together, the books present an encyclopedia of indexicality, references made inaccessible. As we read the titles and recognize the names of artists (which Valdez leaves legible, even as other identifying ephemera on the spines devolve into marks), we access the unknowable complexity of our minds, adorning the names with images and details they have accrued through our particular experiences. Resting on a tree stump, the stack executes a further trick: where the leaves of the tree might have sprouted, we find the exotic floral print of Valdez’s facsimile of Gauguin’s bedspread, referring us to the leaves of the potted shrubs. Spliced onto the trunk of the tree, the painting books become a (re-)domesticated knowledge, taking root in our lived experience.

Similarly, Valdez’s Laptop With Landscape offers representation in place of representation, toying with the circularity of the digital as well as its ability to bridge modes and mechanisms of experience. Here, Valdez is more forceful, losing the viewer in a labyrinth of repetitions without signposts. To start, the laptop denies any true functionality—the screen lacks icons, the keyboard lacks inscription. As the eye moves through the composition, it becomes lost, as so often happens, in the seeming infinitude of the screen, whose figuration destabilizes into perspectival blobs, unable to return to the (figurative) “reality” that circumscribes it.

The yucca plants and grasses that reiterate one another into abstraction on the computer screen find mimics both in the imperfectly repeated patterns of the fabrics as well as in the more literal repetition between the potted cactus and its mirror, the yucca-like form of the lavender that spreads from the vase. The vase, in turn, is adorned with the decoration of yet another spreading flower, leading us back down through to the floral print on which the laptop sits. We cede our autonomy as viewers, led forth by the painting’s directive: like so many stitches in a blanket, our separate selves recede increasingly into the background of a world in which we have all lost ourselves.

Moving through the gallery, we find these ideas taken up repeatedly, though with less precision than in Valdez’s paintings. Valdez’s concern with fabric and the imprint of the human finds itself literalized in Amir H. Fallah’s series of covered forms, molded hoods standing in for heads. Personages disappear behind patterns, limbs become color fields, action and object become identity (his titles: Hold On, Necklace, Internal Expressionist). Though there is an enticingly exotic aspect to the veilings, Fallah directs us back upon ourselves, showing in the absence of his figures the reductive tendencies of our gazes. In the discourse of the larger show, we see anonymous bodies give way to words and images which, once collected, manifest our digital personalities.

The language of patterning appears effectively in the work of Matthew Craven and Sarah Bowser as well. Like Fallah’s paintings, Craven’s Portrait (TOTEM) brings to mind a particular decorative lineage, namely the geometries and color palette of the indigenous Southwest, the Hopi, the Navajo. His appropriated portrait recalls a bearded hipster or, less flatteringly, an Urban Outfitters graphic, but the context of the show makes his irony more legible. Sarah Bowser, in turn, offers a masterfully executed screen print—or perhaps it is a “screen” print—“stamped” linear and abstract shapes invoking the early Microsoft program Kid Pix. The technical proficiency of Bowser and Craven’s works on paper accent the flat dimensionality of their renderings, drawing out engaging compositions from combinations of simplified forms.

These lead easily into the compositional echoes between two of Michelle Fleck’s paintings across the room—Trees That Bloom Outside The Window, which depicts an “X” (one leg aerosolized, the other painted precisely in acrylic) behind a cluster of branches spreading out before it, and Black Cars, which offers a still life with two branches that form the selfsame “X” atop a perspectivally impossible table. Hung one above the other, the paintings speak to the interaction of the organic and the inorganic, the invented realities of the artist and the “objective” reality of experience, and dialogue nicely with Valdez’s own plants.

In form and content, the show repeatedly conjures the internet-age sentiment of aesthetic assemblage, the totalizing impulse that attempts to collate everything in one place and at one moment. Casey Gray’s twin corkboards, Trompe l’oeil with Head Shot and Trompe l’oeil with Mixed Feelings, achieve a simple and compelling iteration of this theme through collages of personal and cultural references rendered in a hyperreal aerosol acrylic. Gray’s work highlights the manner in which specific collections of mass objects often stand in for genuine individuality: think of the collaged quality of a Twitter page where tweets (themselves often commentary on events external to the user) and retweets intermingle or, quite literally, a Pinterest page.

It is no longer the role of a painting survey to singlehandedly recreate a culture, as MOMA’s earlier show, “The New American Painting,” did in 1958. And yet, “Tomorrow” argues compellingly for painting’s place in the increasingly diffracted arsenal of social criticism. Though the prospect of a more considered reaction to media may seem inconsequential to an age of present shocks and hyperobjects, that stance assumes the logic of Hoptman’s earlier fallacy.

We face grand problems, it is true. But it is precisely their scope that precludes grand solutions. Only by defining their periphery, by collecting and assembling all manner of counterarguments, at the smallest of scales, can one hope to expose their weaknesses. There is still a place for us to live and act and paint—here, now.

“Tomorrow” runs through December 19th at Hashimoto Contemporary, 804 Sutter St., San Francisco

Necklace by Marie Křivánková

Gold, emerald, mother-of-pearl. Circa 1910-12

Additional information from the Museum of Decorative Arts In Prague:

Marie Křivánková was a great name in Czech jewellery of Late Art Nouveau and Modernism. Her unmistakable, stylised designs based on geometric patterns influenced Prague jewellery production for several decades.

Křivánková’s participation in a contest announced by the Museum of Decorative Arts in 1908 was her first public presentation. She entered her designs for hair ornaments, featuring an abstract linear composition made of Bohemian garnets. At the time, she was still employed in the Max Schober jewellery house that specialised in Empire Revival jewellery.

Křivánková’s designs soon enriched the company’s output with minute, almost ethereal pieces made of meticulously coiled spirals and regularly arranged chains, encrusted with garnets and tiny pieces of mother-of-pearl. Her inspiration in ancient ornamentation and the granulation and filigree techniques led to objects that boasted an entirely modern appearance, in many aspects reminiscent of the Wiener Werkstätte aesthetic.

Pitchfork: What happened to the songs you wrote after Aeroplane? Will you ever use them?

Jeff: I don’t know if I’ll use them or not. Probably not. They are what they are, but I just feel really different now. One weird thing about those songs is that they were so linear. They weren’t abstract in any way, and they weren’t really fragmented, either. They just came out like [makes long farting noise] .

—  Pitchfork, 2001

Female freshman math major here, I just found your blog and I love it. I don't understand all of the concepts or topics but your blog has gotten me way more pumped for future classes. What were some of your favorite classes that you would recommend?

Woo! Welcome to the world of math majoring!!! In my experience, the first part of journey is figuring out what flavor of mathematician you are, because the world of math is large and beautiful. There are two main branches, each with sever sub-branches: Applied (Stats/Probability/etc) or Abstract/Pure (Analyst, Algebraist, Geometer). Like most flavors of flavored things, you can mix several categories together and end up with something great, too. I really like this map of Prof. Alexandru Buium’s on the matter of categorizing pure math, and seeing how each subject combines:

In the process of determining the color of your mathematical parachute, I would recommend taking both proof-based classes and more interesting computation classes. In a semester, I had Probability, Discrete Mathematics, and a proof-based Linear Algebra course. They were all great classes, but I found I had a distinct preference for the abstract linear algebra course (particularly the bit about linear transformations), which sort of cued me in that I might be an algebraist or topologist. That hypothesis has held so far :)

Let me know if you have questions about any specific classes or family of classes. Godspeed on your quest to discern your mathematical hat!

- Mallorca -

`Cube Movement - 150119`

Artist: Ryan Hewett

Title: Fig