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.
The Real World of Technology
Technology is a system
Technology is not the sum of the artifacts, of the wheels and gears, of the rails and electronic transmitters. Technology is a system. It entails far more than its individual material components. Technology involves organization, procedures, symbols, new words, equations, and, most of all, a mindset.
Fish and water
How does one speak about something that is both fish and water, means as well as end?
Defining activities
One has to keep in mind how much the technology of doing something defines the activity itself.
Holistic and prescriptive technologies
Holistic technologies are normally associated with the notion of craft. Artisans, be they potters, weavers, metal-smiths, or cooks, control the process of their own work from beginning to finish. Using holistic technologies does not mean that people do not work together, but the way in which they work together leaves the individual worker in control of a particular process of creating or doing something.
The opposite is specialization by process; this I call prescriptive technology. Here, the making or doing of something is broken down into clearly identifiable steps. Each step is carried out by a separate worker, or group or workers, who need to be familiar only with the skills of performing that one step. This is what is normally meant by "division of labor".
That which requires caring
Today's real world of technology is characterized by the dominance of prescriptive technologies.
The temptation to design more or less everything according to prescriptive and broken-up technologies is so strong that it is even applied to those tasks that should be conducted in a holistic way. Any tasks that require caring, whether for people or nature, any tasks that require immediate feedback and adjustment, are best done holistically. Such tasks cannot be planed, coordinated, and controlled the way prescriptive tasks must be.
Prescriptive technologies eliminate the occasions for decision-making and judgment in general and especially for the making of principled decisions. Any goal of the technology is incorporated a priori in the design and is not negotiable.
One-machine policy
Today population forecasts are based on extensive and reliable data. However, no such demographic base exists for the world's growing population of machines and devices. Now may be the time to take machine demography seriously and enter into real discussions about machine population control.
The downgrading of experience
Today scientific constructs have become the model of describing reality rather than one of the ways of describing life around us. As a consequence there has been a very marked decrease in the reliance of people on their own experience and their own senses.
The downgrading of experience and the glorification of expertise is a very significant feature of the real world of technology.
Reciprocity
Whenever human activities incorporate machines or rigidly prescribed procedures, the modes of human interaction change. In general, technical arrangements reduce or eliminate reciprocity. Reciprocity is some manner of interactive give and take, a genuine communication among interacting parties.
Instruments of cooperation
When work isn't shared, the instruments of cooperation – listening, taking note, adjusting – atrophy like muscles that are no longer in use.
When all you have is a hammer
The success and spread of a particular tool – and this tool can be organizational or administrative as well as mechanical – has another consequence. Any task tends to be structured by the available tools. It can appear that the available tools represent the best or even the only way to deal with a situation.
Thus is may be wise, when communities are faced with new technological solutions to existing problems, to ask what these techniques may prevent and not only to check what the techniques promise to do.
Consumption
The proponents of technology in the 1840s were very enthusiastic about replacing workers with machines. But somehow I find no indication that they realized that while production could be carried out with few workers and still run to high outputs, buyers would be needed for those outputs. The realization that though the need for workers decreased, the need for purchasers could increase, did not seem to be part of the discourse on the machinery question. Since then, however, technology and its promoters have had to create a social institution – the consumer – in order to deal with the increasingly tricky problem that machines can produce but it is usually people who consume.
Bridges as walls
The biographer of Robert Moses, Robert A. Caro, refers to the bridges and underpasses of the famed New York State parkways. These bridges and underpasses are quite low, intentionally specified by Moses to allow only private cars to pass. All those who traveled by bus because they were poor or black or both were barred from the use and enjoyment of the parkland and its "public amenities" by the technical design of the bridges. Even at the time of Robert Moses, a political statement of the form "We don't want them blacks in our parks" would have been unacceptable in New York State. But a technological expression of the same prejudice appeared to be all right. Of course, to the public the intent of the design became evident only after it was executed, and then the bridges were there.
Designed to be ruins
I don't want to talk here about the grand designs of the past – the sort of thing one finds in majestic cities, in palaces and temples; the sorts of layouts that brought a friend of mine to sum up his first impression of Washington D.C. by saying, "The place seems to be designed to be ruins."
Little sense of season
The real world of technology denies the existence and the reality of nature. For instance, there is little sense of season as one walks through a North American or western European supermarket.
Just as there is a little sense of season, there is little sense of climate. Everything possible is done to equalize the ambiance – to construct and environment that is warm in the winter, cool in the summer.
Humility
Maybe what the real world of technology needs more than anything else are citizens with a sense of humility – the humility of Kepler or Newton, who studied the universe but knew they were not asked to run it.
Technological middle age
In the automobile's technological middle age, it is hard, if not impossible, to tune or repair one's own vehicle. Technical standardization of cars has occurred, and with it the elimination of the user's access to the machine itself. At the same time, the infrastructures that once served those who did not use automobiles atrophied and vanished. Some may say they were deliberately starved out. Railways gave way to more and more roadways. And thus a technology that had been perceived to liberate its users began to enslave them.
All things change
The authors of this prognostication evidently assumed that the introduction of the sewing machine would result in more sewing – and easier sewing – by those who had always sewn. They would do the work they had always done in an unchanged setting. Reality turned out to be quite different.
It should be evident by now that there is no such thing as "just introducing" a new gadget to do one particular task. It is foolish to assume that everything else in such a situation will remain the same; all things change when one thing changes.
Exploiting emotion
There are no shortcuts to the investment of time and care in friendship and human bonding, and it is fraudulent to pretend otherwise. When human loneliness becomes a source of income for others through devices, we'd better stop and think a bit about the place of human needs in the real world of technology.
The receiving end
At times it helps to rephrase an observation in line with a perspective from the receiving end of technology. When my colleagues in the field of cold-water engineering speak of "ice-infested waters", I am tempted to think of "rig-infested oceans". Language is a fine barometer of values and priorities. As such it deserves careful attention.
Speaking people
Surely those who oversee and guide municipal transportation systems ought to use public transit during their work days. Why not put a clause to that effect in their job description or contract?
Requiring those whose work has a major impact on people's lives to experience some of the impact is really not too much ask. It means that they speak "people" rather than French, Cree, or Spanish.
Ping-pong patterns
The role of asynchronicity in unraveling social and political patterns without apparent replacement with other patterns cannot be overestimated. The ping-pong pattern of verbal communication is no longer tied to space or time.
Mechanisms and organisms
"Kant described a mechanism as a functional unity, in which the parts exist for one another in the performance of a particular function.
An organism, on the other hand, is a functional and structural unity in which the parts exist for and by means of one another in the expression of a particular nature.
This means that the parts of an organism – leaves, roots, flowers, limbs, eyes, heart, brain – are not made independently and then assembled, as in a machine, but arise as a result of interactions within the developing organism."
— Brian Goodwin, How the Leopard Changed His Spots