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.
Wikipedia
The Pareto principle
The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes.
Concrete poetry
Concrete poetry is an arrangement of linguistic elements in which the typographical effect is more important in conveying meaning than verbal significance.
Pinkas Synagogue
Names of the Holocaust victims from Czech lands on the synagogue's inner wall.
During reconstruction in 1950–1954, the original floor-level as well as the appearance of the synagogue were restored. In following five years, the walls of the synagogue were covered with names of about 78,000 Bohemian and Moravian Jewish victims of Shoah. The names are arranged by communities where the victims came from and complemented with their birth and death date.
Saudade
Saudade is a deep emotional state of nostalgic or profound melancholic longing for an absent something or someone that one cares for and/or loves. Moreover, it often carries a repressed knowledge that the object of longing might never be had again.
Transclusion
In computer science, transclusion is the inclusion of part or all of an electronic document into one or more other documents by hypertext reference. Transclusion is usually performed when the referencing document is displayed, and is normally automatic and transparent to the end user. The result of transclusion is a single integrated document made of parts assembled dynamically from separate sources, possibly stored on different computers in disparate places.
Transclusion facilitates modular design: a resource is stored once and distributed for reuse in multiple documents. Updates or corrections to a resource are then reflected in any referencing documents. Ted Nelson coined the term for his 1980 nonlinear book Literary Machines, but the idea of master copy and occurrences was applied 17 years before, in Sketchpad.
Phonaesthetics
Phonaesthetics is the study of beauty and pleasantness associated with the sounds of certain words or parts of words. The term was first used in this sense, perhaps by J. R. R. Tolkien, during the mid-twentieth century and derives from the Greek: φωνή (phōnē, "voice-sound") plus the Greek: αἰσθητική (aisthētikē, "aesthetic").
Rage rooms
A rage room, also known as a smash room or anger room, is a business where people can vent their rage by destroying objects within a room.
Truchet Tiles
Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling.
Wang tiles
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.
The linear city
The linear city was an urban plan for an elongated urban formation. The city would consist of a series of functionally specialized parallel sectors.
As the city expanded, additional sectors would be added to the end of each band, so that the city would become ever longer, without growing wider.
Tactical urbanism
Tactical urbanism includes low-cost, temporary changes to the built environment, usually in cities, intended to improve local neighborhoods and city gathering places. Tactical urbanism is also commonly referred to as guerrilla urbanism, pop-up urbanism, city repair, or D.I.Y. urbanism.
The Street Plans Collaborative defines "tactical urbanism" as an approach to urban change that features the following five characteristics:
- A deliberate, phased approach to instigating change;
- The offering of local solutions for local planning challenges;
- Short-term commitment and realistic expectations;
- Low-risks, with a possibly high reward; and
- The development of social capital between citizens and the building of organizational capacity between public-private institutions, non-profits, and their constituents.
Inglenook
An inglenook, or chimney corner, is a recess that adjoins a fireplace. The inglenook originated as a partially enclosed hearth area, appended to a larger room. The hearth was used for cooking, and its enclosing alcove became a natural place for people seeking warmth to gather. With changes in building design, kitchens became separate rooms, while inglenooks were retained in the living space as intimate warming places, subsidiary spaces within larger rooms.
Aedicula
Front of the Library of Celsus with aediculae in Ephesus.
In ancient Roman religion, an aedicula (plural aediculae) is a small shrine.
Many aediculae were household shrines that held small altars or statues of the Lares and Penates, household gods guarding the entire house.
Other aediculae were small shrines within larger temples, usually set on a base, surmounted by a pediment and surrounded by columns. In ancient Roman architecture the aedicula has this representative function in the society. They are installed in public buildings like the triumphal arch, city gate, and thermae.
From the 4th century Christianization of the Roman Empire onwards such shrines, or the framework enclosing them, are often called by the Biblical term tabernacle, which becomes extended to any elaborated framework for a niche, window or picture.
Caustic (optics)
Caustics made by the surface of water.
In optics, a caustic is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light.
Terroir
Terroir is a French term used to describe the environmental factors that affect a crop's phenotype, including unique environment contexts, farming practices and a crop's specific growth habitat. Collectively, these contextual characteristics are said to have a character; terroir also refers to this character.
Mondegreen
A mondegreen is a mishearing or misinterpretation of a phrase in a way that gives it a new meaning. Mondegreens are most often created by a person listening to a poem or a song; the listener, being unable to clearly hear a lyric, substitutes words that sound similar and make some kind of sense.
American writer Sylvia Wright coined the term in 1954, writing that as a girl, when her mother read to her from Percy's Reliques, she had misheard the lyric "layd him on the green" in the fourth line of the Scottish ballad "The Bonny Earl of Murray" as "Lady Mondegreen".
Parkinson's Law
Work expands so as to fill the time available for its completion.
Eating your own dog food
Eating your own dog food or “dogfooding” is the practice of using one's own products or services. This can be a way for an organization to test its products in real-world usage using product management techniques. Hence dogfooding can act as quality control, and eventually a kind of testimonial advertising. Once in the market, dogfooding can demonstrate developers confidence in their own products.
Illa de la Discòrdia
A city block on Passeig de Gràcia in the Eixample district of Barcelona, Catalonia, Spain. The block is noted for having buildings by four of Barcelona's most important Modernista architects, Lluís Domènech i Montaner, Antoni Gaudí, Josep Puig i Cadafalch and Enric Sagnier, in close proximity. As the four architects' styles were very different, the buildings clash with each other and the neighboring buildings.
Baumol’s cost disease
Baumol's cost disease (or the Baumol effect) is the rise of salaries in jobs that have experienced no or low increase of labor productivity, in response to rising salaries in other jobs that have experienced higher labor productivity growth.
The rise of wages in jobs without productivity gains derives from the requirement to compete for employees with jobs that have experienced gains and so can naturally pay higher salaries, just as classical economics predicts. For instance, if the retail sector pays its managers 19th-century-style salaries, the managers may decide to quit to get a job at an automobile factory, where salaries are higher because of high labor productivity. Thus, managers' salaries are increased not by labor productivity increases in the retail sector but by productivity and corresponding wage increases in other industries.
ƒ/8 and be there
"f/8 and be there" is an expression popularly used by photographers to indicate the importance of taking the opportunity for a picture rather than being too concerned about using the best technique. Often attributed to the noir-style New York City photographer Weegee, it has come to represent a philosophy in which, on occasion, action is more important than reflection.
Betteridge's law of headlines
Betteridge's law of headlines is an adage that states: "Any headline that ends in a question mark can be answered by the word no."
It is named after Ian Betteridge, a British technology journalist who wrote about it in 2009, although the principle is much older. It is based on the assumption that if the publishers were confident that the answer was yes, they would have presented it as an assertion; by presenting it as a question, they are not accountable for whether it is correct or not.