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.
Brilliant Hardware in the Valley of the Software Slump
It begins with craft
Something strange is happening in the world of software: It’s slowly getting worse. Not all software, but a lot of it. It’s becoming more sluggish, less responsive, and subtly less reliable than it was a few years ago.
In some ways this is hyperbole. Objectively, we’ve never been able to do so much, so easily with our smartphones and laptops and tablets. We’ve never pushed more data between more places more readily. But while the insidious “worseness” I mention falls only in part on the engineering side of things, it falls harder on the more subjective, craft side of things, making it all the more worrisome.
Why should we care about this? Because the majority of our waking hours take place within the confines of applications. A truth recently amplified by the covid pandemic.
And I believe software used by millions (if not billions) has a moral duty to elevate the emotional and intellectual qualities of its users. That elevation begins with craft.
Penn Station
In the same way that physical architecture can affect a mind, so too can software. Slower, less reliable software is like Penn Station: Sure, you can catch a transfer from one train to another but the dreary lowness of the place, the lack of sunlight or sensible wayfinding will make you feel like a rat, truculent and worthless, and worse: You’ll acclimate to that feeling and accept it as a norm.
Edges
Hardware has literal and metaphorical edges — it must be fully complete and largely bug free to ship. Software? It’s far more amorphous, like mist. Patches can be endlessly pushed. It never ends. Faulty hardware can destroy a company. Faulty software can be patched. The butterfly keyboard debacle may never be lived down. Even as I type on this improved Magic Keyboard, I can’t help but wonder: Did they really test this thing? I had three butterfly keyboards die on me, twice in the field. Not fun. Hardware failures live long in the mind.
The business case for craft
macOS software that adheres to craft — Things or Carbon Copy Cloner or BBEdit or Sublime Text (which, despite not being “native native” feels so solid and so responsive you’re willing to overlook its quirks) or Bear or Alfred or iA Writer or Keynote (arguably one of the best pieces of macOS software of all time) or anything by Panic, heck, even Terminal or Quicken (which, against all rational expectations is just a joy to use)5 — exists in troves, the existence of such proves to the Slacks or Twitters or Adobes of the world that it’s not impossible nor rare to produce craft-oriented software in service to user fluency, and still make a profit.
In fact, there’s a business case to be made for being craft- and fluency-focused. We’ve seen entire companies with business models that could be summarized as “Bloat-Free X” emerge in recent years. Affinity is bloat-free Adobe. Install Adobe Creative Cloud on your laptop and marvel at the no fewer than a dozen processes whirling around in the background for unknown purposes. It’s no surprise Affinity Photo and Publisher and Designer have taken off. Sketch’s main feature for many years was simply: Not Adobe.
And the web! When you care — when you really give a shit — the web is awe inspiring. I still can’t believe Figma is web-native (also born from the Not Adobe camp). That an application can feel so powerful, so fast, so well-crafted and be fully web-based should be a kind of lighthouse-archetype for all other sites lost in a sea of complexity and muck and unnecessary frameworks.