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 small web is beautiful
I believe that small websites are compelling aesthetically, but are also important to help us resist selling our souls to large tech companies. In this essay I present a vision for the “small web” as well as the small software and architectures that power it.
Why aim small?
Why aim small in this era of fast computers with plenty of RAM? A number of reasons, but the ones that are most important to me are:
- Fewer moving parts. It’s easier to create more robust systems and to fix things when they do go wrong.
- Small software is faster. Fewer bits to download and clog your computer’s memory.
- Reduced power consumption. This is important on a “save the planet” scale, but also on the very local scale of increasing the battery life of your phone and laptop.
- The light, frugal aesthetic. That’s personal, I know, but as you’ll see, I’m not alone.
Features and complexity
Niklaus Wirth of Pascal fame wrote a famous paper in 1995 called A Plea for Lean Software. His take is that “a primary cause for the complexity is that software vendors uncritically adopt almost any feature that users want”, and “when a system’s power is measured by the number of its features, quantity becomes more important than quality”.
Solving the problem of software bloat
But instead of just complaining, how do we actually solve this problem? Concretely, I think we need to start doing the following:
- Care about size: this sounds obvious, but things only change when people think they’re important.
- Measure: both your executable’s size, and your program’s memory usage. You may want to measure over time, and make it a blocking issue if the measurements grow more than x% in a release. Or you could hold a memory-reduction sprint every so often.
- Language: choose a language that has a chance.
- Remove: cut down your feature set. Aim for a small number of high-quality features. My car can’t fly or float, and that’s okay – it drives well.
- Say no to new features: unless they really fit your philosophy, or add more than they cost over the lifetime of your project.
- Dependencies: understand the size and complexity of each dependency you pull in. Use only built-in libraries if you can.
Raw size isn't enough
A few months ago there was a sequence of posts to Hacker News about various “clubs” you could post your small website on: the 1MB Club, 512KB Club, 250KB Club, and even the 10KB Club. I think those are a fun indicator of renewed interested in minimalism, but I will say that raw size isn’t enough – a 2KB site with no real content isn’t much good, and a page with 512KB of very slow JavaScript is worse than a snappy site with 4MB of well-chosen images.
...[Instead, it's about] an “ethos of small”. It’s caring about the users of your site: that your pages download fast, are easy to read, have interesting content, and don’t load scads of JavaScript for Google or Facebook’s trackers.