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.
It's All Over
It has come to seem to me recently that this present moment must be to language something like what the Industrial Revolution was to textiles. A writer who works on the old system of production can spend days crafting a sentence, putting what feels like a worthy idea into language, only to find, once finished, that the internet has already produced countless sentences that are more or less just like it, even if these lack the same artisanal origin story that we imagine gives writing its soul. There is, it seems to me, no more place for writers and thinkers in our future than, since the nineteenth century, there has been for weavers.
Into the system of flight
It seems this transformation, from physical object to vector of data, is a general and oft-repeated process in the history of technology, where new inventions begin in an early experimental phase in which they are treated and behave as singular individual things, but then evolve into vectors in a diffuse and regimented system as the technology advances and becomes standardized.
In the early history of aviation, airplanes were just airplanes, and each time a plane landed or crashed was a singular event. Today, I am told by airline-industry insiders, if you are a billionaire interested in starting your own airline, it is far easier to procure leases for actual physical airplanes, than it is to obtain approval for a new flight route. Making the individual thing fly is not a problem; inserting it into the system of flight, getting its data relayed to the ATC towers and to flightaware.com, is.
The gutting of our human subjecthood
Someone who thinks about their place in the world in terms of the structural violence inflicted on them as they move through it is thinking of themselves, among other things, in structural terms, which is to say, again among other things, not as subjects. This gutting of our human subjecthood is currently being stoked and exacerbated, and integrated into a causal loop with, the financial incentives of the tech companies. People are now speaking in a way that results directly from the recent moneyballing of all of human existence.
A performative contradiction
I have found myself coming away from discussions with my good PR people feeling vaguely guilty that I do not have enough followers on Twitter (five thousand is the cut-off, I think) to be considered an “influencer,” or even just a “micro-influencer,” and feeling dismayed to learn that part of what is involved in launching a book like this into the world is strategizing over how to catch the attention of a true influencer, for a retweet or some other metrically meaningful shout-out. You would be a fool to think that it is the argument of the book, the carefully crafted sentences themselves, that are doing the influencing.
And yet for me to try to insert myself into the metrics-driven system would be a performative contradiction, since the book itself is an extended philippic against this system. And so what I do? I play along, as best I can, until I start to feel ashamed of myself. I contradict myself.
The one reveals a subject and the other reveals an algorithm
My own book may be crap, but I am certain, when such an imbalance in profitability as the one I have just described emerges, between photojournalism and selfies, that it is all over. This is not a critical judgment. I am not saying that the photos of Pol Pot are good and the selfies are bad. I am saying that the one reveals a subject and the other reveals an algorithm, and that when everything in our society is driven and sustained in existence by the latter, it is all over.