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.
Premium Mediocre
Cupcakes and froyo
Premium mediocre is the finest bottle of wine at Olive Garden. Premium mediocre is cupcakes and froyo. Premium mediocre is “truffle” oil on anything (no actual truffles are harmed in the making of “truffle” oil), and extra-leg-room seats in Economy. Premium mediocre is cruise ships, artisan pizza, Game of Thrones, and The Bellagio.
Maya Millennial
But the demographic at the very heart of the phenomenon, the sine qua non of premium mediocrity, is the young, gentrifier class of Blue Bicoastal Millennials. The rent-over-own, everything-as-a-service class of precarious young professionals auditioning for a shot at the neourban American dream, sans condo ownership somewhere at a reasonable distance from both the nearest meth lab and minority ghetto.
The essence of premium mediocrity is being optimistically prepared for success by at least being in the right place at the right time, at least for a little while, even if you have no idea how to make anything happen during your window of opportunity. Even if you know nothing else, you know to move to San Francisco or New York and hoping something good happens there, rather than sitting around in some dying small town where you know nothing will ever happen and being curious about anything beyond the town is a cultural transgression. This is a strategy open to all.
What premium mediocre is not
So premium mediocrity is not clueless, tasteless consumption of mediocrity under the mistaken impression that it is actual luxury consumption. Maya Millennial is aware that what she is consuming is mediocre at its core, and only “premium” in some peripheral (and importantly, cheap, such as French-for-no-reason branding) ways. But she consumes it anyway. She is aware that her consumption is tasteless, yet she pretends it is tasteful anyway.
Second the distinguishing feature is that premium mediocrity only signals an appearance of striving upwards. Everybody in the premium mediocre world recognizes that it is not a reliable indicator of actual upward striving, such as number of code commits on github, or non-bot retweets achieved by on a tweet.
In other words, premium mediocrity is dressing for the lifestyle you’re supposed to want, in order to hold on to the lifestyle you can actually afford — for now — while trying to engineer a stroke of luck.