math
On beauty bare
Wang tiles
Trees and graphs
A tree is a kind of graph, but a graph can be considerably more complex than a tree.
I have reason to believe, which for brevity’s sake I will treat elsewhere, that the most complex class of processes and structures we humans can consciously prescribe, reduces mathematically to a tree. A tree has a top, bottom, left and right. Its branches fan out from the trunk and they don’t intersect with one another. They are discrete, contiguous, identifiable objects which persist across time. Trees are Things.
Software and websites, however, reduce to arbitrarily more complex structures: they are graphs. A graph has no meaningful orientation whatsoever. No sequence, no obvious start or end—at least none that we can intuit. It is better considered not as one Thing, but as a federation of Things, like the brain or a fungus network, or perhaps a composite artifact left behind from an ongoing process, like an ant colony or human city.
Trees and semilattices
The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shall contrast it with another, more complex abstract structure called a semilattice.
Both the tree and semilattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system.
A collection of sets forms a semilattice if, and only if, when two overlapping sets belong to the collection, the set of elements common to both also belongs to the collection. That is, if [234] and [345] belong to the collection, then [34] belongs to the collection.
A collection of sets forms a tree if, and only if, for any two sets that belong to the collection either one is wholly contained in the other, or they are wholly disjoint. Every tree is trivially a simple semilattice.
We are concerned with the difference between structures in which no overlap occurs, and those structures in which overlap does occur.
The semilattice is potentially a much more complex and subtle structure than a tree. It is this lack of structural complexity, characteristic of trees, which is crippling our conceptions of the city.
A City Is Not a Tree
An Essay by Christopher Alexander- Strands of life
- Impending destruction
- The right overlap
- The difficulty of designing complexity
- Political chains of influence
Notes on the Synthesis of Form
A Book by Christopher AlexanderVisualizing Data
A Book by William S. ClevelandExploratory Data Analysis
A Book by John TukeyPlus Equals #4
An Article by Rob WeychertOne of the seeds for Plus Equals was planted a few years ago with Incomplete Open Cubes Revisited, my extension of a Sol LeWitt work. I learned a lot about isometric projection from that project, but my affection for the concept didn’t begin there. Whether I’m looking at a Chris Ware illustration or an exploded-view technical drawing of a complex machine, an isometric rendering always stirs something in me.
A brief foray into vectorial semantics
An Article by James SomersOne of the best (and easiest) ways to start making sense of a document is to highlight its “important” words, or the words that appear within that document more often than chance would predict. That’s the idea behind Amazon.com’s “Statistically Improbable Phrases”:
Amazon.com’s Statistically Improbable Phrases, or “SIPs”, are the most distinctive phrases in the text of books in the Search Inside!™ program. To identify SIPs, our computers scan the text of all books in the Search Inside! program. If they find a phrase that occurs a large number of times in a particular book relative to all Search Inside! books, that phrase is a SIP in that book.
tixy.land
A Websitesin(t * x) * cos(t * y)
Creative code golfing.
Rafael Araujo's Golden Ratio
A GalleryBlue Morpho Double Helix & Icosahedron
The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy
A Research Paper by Cyril Stanley SmithA pattern of tiles illustrated by Douat in 1722.
A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.
Everything and More
A Book by David Foster WallaceInfoCrystal
A Research PaperThis paper introduces a novel representation, called the InfoCrystal, that can be used as a visualization tool as well as a visual query language to help users search for information. The InfoCrystal visualizes all the possible relationships among N concepts.
Rethinking Repair
This chapter is an exercise in broken world thinking. It asks what happens when we take erosion, breakdown, and decay, rather than novelty, growth, and progress, as our starting points in thinking through the nature, use, and effects of information technology and new media.
The modern infrastructural ideal
The form and possibility of the "modern infrastructural ideal" is increasingly under threat, as cracks (sometimes literal ones) show up in our bridges, our highways, our airports, and the nets of our social welfare systems. For these and other reasons, broken world thinking asserts that breakdown, dissolution, and change, rather than innovation, development, or design as conventionally practices and thought about are the key themes and problems facing new media and technology scholarship today.
Attached to this, however, comes a second and more hopeful approach: namely, a deep wonder and appreciation for the ongoing activities by which stability (such as it is) is maintained, the subtle arts of repair by which rich and robust lives are sustained against the weight of centrifugal odds, and how sociotechnical forms and infrastructures, large and small, get not only broken but restored, one not-so-metaphoric brick at a time.
The fulcrum of these two worlds
Here, then, are two radically different forces and realities. On one hand, a fractal world, a centrifugal world, and always-almost-falling-apart world. On the other, a world in constant process of fixing and reinvention, reconfiguring and reassembling into new combinations and new possibilities...the fulcrum of these two worlds is repair.
A creature of bones, not words
In building connections, [articulation work] builds meaning and identity, sorting out ontologies on the fly rather than mixing and matching between fixed and stable entities. Articulation lives first and foremost in practice, not representation; as its proper etymology suggests, it's a creature of bones, not words. When articulation fails, systems seize up, and our sociotechnical worlds become stuff, arthritic, unworkable.
The world is always breaking
So the world is always breaking; it's in its nature to break.
A side that goes unrecognized
Edward Burtynsky, Shipbreaking #4.
Burtynsky's [shipbreaking] photos tell us important things about the themes of breakdown, maintenance, and repair raised here. The first is the extent to which such work is rendered invisible under our normal modes of picturing and theorizing technology. Burtynsky's photos share, in exquisite detail, a side or moment of technological life that goes for the most part unrecognized.
If we are to understand maintenance, repair, and technology more broadly, scenes such as Burtynsky's must be made empirically and conceptually familiar, even normal.
Turned into other things
Ask yourself this: for all the representations of great ships in history you've encountered, at what times and in what forms have you seen such vessels? In almost every instance it will be at moments of birth, or at the heights of strength and glory: the christening before the maiden voyage, rounding the cape, facing down the Spanish fleet, and so on. But what happens (or happened) to these ships? Save for the special cases of hostile sinking, shipwreck, or honorable retirement and preservation, it was this: they were disassembled, repurposed, stripped, and turned into other things.
An engine of technological difference
Whether at the level of national "technological styles" that shape and differentiate the nature of "same" technologies in different national contexts, or the simple but consequential variations by which industrial commodities are brought into, enlivened, and sustained within the circumstances of individual homes and lives, repair may constitute an important engine by which technological difference is produced and fit is accomplished.
The internet grew by breaking
The Internet grew by breaking, bumping up against the limits of existing protocols and practices and working around them, leaving behind almost by accident some of the properties that we now enumerate as key and distinctive virtues of the Internet as infrastructural form. Far from being a generalized cultural tendency or a property of individual minds, innovation in the technology space, as in culture more generally, is therefore organized around problems. This makes innovation simultaneously specific and in some measure collective in nature. And its engine is breakdown and repair.
What the fixer knows
Can repair sites and repair actors claim special insight or knowledge, by virtue of their positioning vis-à-vis the worlds of technology they engage? Can the fixer know and see different things—indeed, different worlds—than the better-known figures of "designer" or "user"?
Tool-being
Take Heidegger's notion of "tool-being", built around the central distinction between tools that are "ready-to-hand" versus "present-at-hand".
In the former state, technologies function as anticipated, do and stay where they're supposed to, and therefore sink below the level of conscious reflection. In the latter, the material world resists, obstructs, or frustrates action, and therefore calls attention to itself (precisely because we must now work to figure out and overcome barriers in our no-longer seamless world).
An ethics of mutual care
Foregrounding maintenance and repair as an aspect of technological work invites not only new functional but also moral relations to the world of technology. It references what is in fact a very old but routinely forgotten relationship of humans to things in the world: namely, an ethics of mutual care and responsibility.
To love deeply a world of things
Care brings the worlds of action and meaning back together, and reconnects the necessary work of maintenance with the forms of attachment that so often (but invisibly, at least to analysts) sustain it.
...What if we care about our technologies, and do so in more than a trivial way? This feature or property has sometimes been extended to technologies in the past, but usually only ones that come out of deep folk or craft traditions, and rarely the products of a modern industrial culture.
...Is it possible to love, and love deeply, a world of things?
We live in the aftermath
So do we live in later modernity, postmodernity, alternative modernity, or liquid modernity? Knowledge societies, information societies, network societies, or risk societies? New media, old media, dead media, or hypermedia? The world of information, the world of search, the world of networks, or the or the world of big data?
The answer is simple: like every generation before, we live in the aftermath.