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.
Cubed
A dry, husky business
Despite the furor over their aggressive unmanliness, clerks, and with them the office, crept silently into the world of nineteenth-century America. Moral philosophers were mostly preoccupied with the clang of industrialization and its satanic mills, and most regarded as negligible the barely audible scratch of pens across ledgers and receipts that characterized the new world of clerical work. It was only a “dry, husky business,” as the narrator of Bartleby had it.
A segment of the enormous file
As office buildings grew taller, and flammability became a problem, steel file cabinets replaced wooden ones – the tall cabinets mimicking the shape of the skyscraper, such that the “file” seemed to be a metaphorical stand-in for the office itself. “Each office within the skyscraper,” C. Wright Mills would argue some years later, “is a segment of the enormous file, a part of the symbolic factory that produces the billion slips of paper that gear modern society into its daily shape.” Aldous Huxley, in his dystopian novel Brave New World, could imagine no more powerful symbol of a totally bureaucratized world than the idea of each person having his or her name on a file.
Taylorism
“In the past the man has been first. In the future the system must be first.” — Fred W. Taylor
Taylorism was a way of thinking that came at the expense of the workers’ own knowledge of their system. Taylor summed up his philosophy thus:
“It is only through enforced standardization of methods, enforced adoption of the best implements and working conditions, and enforced cooperation that this faster work can be assured. And the duty of enforcing the adoption of standard and enforcing this cooperation rests with the management alone.”
The unscripted practices of the old offices would remain, but as a kind of subterfuge: in the future, a leisurely pace wouldn’t be the norm; time would not be given, but stolen.
Divided against itself
By separating knowledge from the basic work process (“the separation of conception from execution,” as Harry Braverman once put it), in the factory as well as the office, the ideology of Taylorism all but ensured a workplace divided against itself, both in space and in practice, with a group of managers controlling how work was done and their workers merely performing that work.
Somewhat more dangerously, this division put into serious doubt the notion that office workers were, as a whole, on the way up. It became increasingly clear from the shape of the offices themselves, and from the distance between the top and the bottom rungs of the “ladder”, that some workers were never going to join the upper layers of management. For some, work was always, frankly, going to suck.
Form follows finance
The formula that Sullivan coined to explain this individualist-conformist principle has become a commonplace of architectural history: “Form follows function.” The envelope of the building was to reflect no particular style, no empty ideal, but rather, with as pure a transparency as possible, the shape and feel of the interior. It was the office that determined the skyscraper – a fact that might have had a beneficial effect on the form of the office itself.
But the result was the opposite: few conceptions of the office have had a more deleterious effect on the human work environment. The title of an influential work by the architectural historian Carol Willis gives us a better, if less palatable, explanation: Form follows Finance. For by and large, making an office “functional” had less to do with making it serve the needs of a particular corporation and much more with serving any corporation. The point was not to make an office building per specification of a given company, but rather to build for an economy in which an organization could move in and out of a space without any difficulty. The space had to be eminently rentable.
Serendipity
This was not meant to be like Bell Labs; there were no expectations that the clerical workers would run into their managers in a “serendipitous encounter” and produce a new innovation. The ideas was rather to create a workplace in which status barriers seemed to dissolve, in which participation and friendliness all around made the work environment look less like the white-collar factory it was.
Office survival
“The caveman was undoubtedly very pleased to find a good cave but he also undoubtedly positioned himself at the entrance looking out. Protect your back but know what is going on outside is a very good rule for survival. It is also a good survival rule for life in offices.” — Robert Propst, The Office: A Facility Based on Chicago
The office landscape
An organic, almost forest-like office layout.
There is an affinity with certain planned “landscapes” of the natural world – namely, the classic Italian Baroque garden. In the sample plans the Schnelle brothers devised, the arrangement of desks seems utterly chaotic, totally unplanned – a mess, like a forest of refrigerator magnets. But, as with the seemingly “wild” overgrowth of a “natural” garden, the office landscape is more thoroughly planned than any symmetrical and orderly arrangement of desks. Imaginary lines wend their way around every cluster, delineating common pools of activity; between and through the undergrowth of clusters are invisible, sinuous paths of work flow.
Open-plan the world
In the end, noise would always be a problem, when quiet was not placed at a premium. Interaction and communication were conceived of as norms in the landscaped office; introspection and concentration were sidelines. In the rush to open-plan the world, some crucial values for the performance of work were lost.
The cubicle
The cubicle had the effect of putting people close enough to each other to create serious social annoyances, but dividing them so that they didn’t actually feel that they were working together. It had all the hazards of privacy and sociability but the benefits of neither. It got so bad that nobody wanted them taken away; even those three walls offered some kind of psychological home, a place one could call one’s own. All these factors could deepen the frenzied solitude of an office worker.
Chilled-out anxiety
Working in the typical dot-com office was an admixture of frenetic pace and a relaxed overall atmosphere, exemplifying that chilled-out anxiety which was the general mood of the 1990’s.
A resource
The office, Chiat argued, had become the site of a turf war, not a place to do work. Changing the office “means focusing on doing great work instead of focusing on agency politics,” he argued. “You come to work because the office is a resource.”