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.
Dieter Rams: As Little Design as Possible
Beyond improvement
In so many ways Dieter Rams’s work is beyond improvement. Although new technologies have since offered new opportunities, his designs are not undermined by the limits of the technologies of their time. The concave button top, designed to stop your finger from slipping as it made the long travel necessary for earlier mechanical switches, does not point to obsolete mechanisms. Instead, it reminds us how immediately and intuitively form alone can describe what an object does and suggest how we should use it.
Cardinal sin
Indifference towards people and the reality in which they live is actually the one and only cardinal sin in design.
The duty of industrial design is first and foremost to users and the users are, generally, human beings, with all their complexities, habits, ideas and idiosyncrasies.
On display
The SK4 record player, aka 'Snow White's Coffin'.
Instead of being hidden away in a piece of furniture, the controls and the functional aspects of the device were not only on display, but they were the predominant feature of the design.
Rams suggested making a transparent lid from a new plastic that had just come on the market and was being used for advertising displays. It was an inspired thought and lent the phonograph just the lightness needed to balance the metal and wood of the base, as well as helping to define the acoustics. It also set the standard for all record players that followed - a turntable without a Perspex dust cover is now almost unthinkable.
Long-term
"Apart from his own design work, this is the second greatest achievement of Dieter Rams: establishing a design department within a company, which succeeded for decades in preserving its own individual approach and rigorously advancing it, without really being influenced by changing market interests." — Klaus Kemp
He is right; it was a remarkable feat. It takes a considerable degree of doggedness and conviction to follow the ungratifying and difficult path of insisting on a consistently long-term view in a corporate world that is constantly shifting and full of short-term decisions.
Humble servants
Our electrical appliances should be humble servants, to be seen and heard as little as possible. They should ideally stay in the background, like a valet in the old days, that one hardly noticed. — Erwin Braun
They should accompany an individual over a long period of time without hindering or disturbing through ‘extravagant forms, loud colors or flashy proportions’.
Restrained beauty
Braun design had a beauty that was more than skin deep. It would be wrong to say that because the Braun approach spurned fashion in an ongoing quest for functional and useable perfection, it ended up with this beauty by accident. There is a very strong aesthetic sense in both the proportion and materials of nearly all the products of the Rams era. They have a ‘restrained beauty’, he admits.
Braun products designed by Rams and his team have a haptic aesthetic as well: when you pick them up, handle them, and use them as the tools they are supposed to be, you become aware of the effort that has gone into making them sit comfortably in the hand, of the texture, weight and balance they possess, and of the satisfying click of the control buttons.
Camels
When you look at the consumer products generated by many other manufacturers, and even by Braun today, there seem to be an awful lot of camels around. Maybe these companies are too diffuse, have the decision-makers in the wrong places or are continually making the wrong decisions and have no one to stop them. They make products with short-term goals in mind, seducing the eye of the buyer with fashionable colors, sensational curves or exotic surfaces. They may have external designers and, perhaps most significantly, the brand identity is defined by external marketing concerns, rather than design or user-related issues.
The lesson to learn from Braun is that allowing a consistent philanthropic design approach to define a company can be extremely successful if it is executed with discipline, flexibility and good timing combined with hard work and, not least, great talent.
A timeless quality
Of all Rams’s products, the 606 Universal Shelving System is perhaps his most successful in fulfilling his own principles of good design. It is still in production today, some fifty years after its conception. The system is distinctive yet unobtrusive, and when the shelves and cabinets are filled, its slim profile allows it to fade quietly into the background.
Its ‘plainness’ lends it a timeless quality that has transcended the vagaries of fashion like no other of Rams’s designs. It was conceived in such a way as to optimize its function as simply and in as many different situations as possible, while still permitting upgrades and alterations without falling into obsolescence: all later adaptations and additions could still be integrated into the original structure and sizes.
"Fashion objects are not capable of being long-lived," said Rams in 2007. "We simply cannot afford this throw-away mentality anymore. Good design has to have built-in longevity. I believe that the secret of the longevity of my furniture lies in its simplicity and restraint. Furniture should not dominate, it should be quiet, pleasant, understandable and durable."
A certain kind of world
Perhaps more directly than with the Braun products, my furniture arose from a belief in how the world should be ‘furnished’ and how man should live in this artificial environment. In this respect, each piece of furniture is also a design for a certain kind of world and way of living, they reflect a specific vision of mankind.
Designing detail
My heart belongs to the details.
I actually always found them to be more important than the big picture.
Nothing works without details.
They are everything, the baseline of quality.Truly functional design only comes from the most careful and intense attention to detail.
Although he did not directly design all products and even had very little to do with some of them, he constantly encouraged tiny improvements that could make a good design better. This attention to detail ranged from the acuteness of angles in forms; the size, feels and distances between switches; the integration of handle fixings; the placement and nature of graphic elements on the products themselves and extended to product photography and packaging.
Designing detail is about achieving a fine balance in all aspects and areas of the product, including those external to the object.
Controlled!
Braun design is greatly reduced - stripped of all that is unnecessary. Nevertheless, there is a strong aesthetic characterized by balance, order and harmony.
Self-control is very important. Although my own taste is involved it always has to be under control. Not suppressed though! Controlled!
Chromatic mutiny
Nevertheless there were a number of colorful appliances produced by Braun, particularly from the late 1960s onwards, when plastics in bright primary colors became fashionable and available.
T3 domino lighter
KMM 2 coffee grinder
HLD 4 hairdryer
KF 145 coffee maker
HT 95 pop-up toasterWhen Rams’s team used color in such a way, it was uncompromising in its intensity: loud and demanding. The highly reduced forms of the products that it clothed, which had gently rounded edges, smooth opaque surfaces and discreet (usually black) detailing only served to increase this intensity.
"The intention was to create product alternatives for people who wished for strong color highlights in their living environments. This impulse came from marketing - not from design,” says Rams, dissociating himself from this approach. This was one instance where marketing got the upper hand in the decision-making process and the design team had to bow to contemporary fashion.
Indeed, there is a defiant aspect to these chromatic exceptions; they are not so much compromises as mutinous responses. Nevertheless, the resulting products are beautiful objects in their stand-alone way.
Color codes
When not compelled to do otherwise, the Braun design team’s use of color in products was reduced to highly specific areas such as control switches. Restricting the use of color to small points on an otherwise neutral object concentrates its effect, which is shifted away from decoration and towards function, especially when each color is assigned a signal role such as green for ‘on / off' switches, red for ‘fm’ and yellow for ‘phono’ on hi-fis or yellow for the second hand on clocks and watches.
This color coding of operating details is a primary example of the self-explanatory nature of Braun products.
Shorten the wings
The labile tastes of certain decision-makers in a company are often a great burden for designers. Too many feel themselves qualified to pass judgment. And how insensitive, how superficial these judgments often are.
Taste, believes Rams, is something that needs to be trained, since the aesthetic decisions at this level in product design are intrinsically bound to the entire form and function of the object. It would be unimaginable, for example, that the management of an aerospace company would ask the designers of a new plane to shorten the wings because they think it would make it look prettier.
The evolution of Braun design principles
1975
Three general rules govern every Braun design - a rule of order, a rule of harmony and a rule of economy.1976
The function for us is the starting point and the target of every design.
Experience with design is experience with people.
Only orderliness makes design useful to us.
Our design attempts to bring all individual elements into their proper proportions.
Good design means to us: as little design as possible.
Our design is innovative because the behavior patterns of people change.1983
Good design is innovative.
Good design renders utility to a product.
Good design is aesthetic design.
Good design makes a product easy to understand.
Good design is unobtrusive.
Good design is honest.1985
Good design is innovative.
Good design makes a product useful.
Good design is aesthetic.
Good design makes a product understandable.
Good design is honest.
Good design is unobtrusive.
Good design is long-lasting.
Good design is thorough down to the last detail.
Good design is environmentally friendly.
Good design is as little design as possible.Less, but better
There must be millions less of things, less words, less gestures, less of everything. But every word and every gesture will become more valuable. If we can put it all into perspective we will need less things as a result.