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.
On Motivation
I’ve had this (semi-vague) idea that I want to write about what keeps us excited to work on Are.na, on the occasion of its 10th (yes 10th) birthday. While writing generally is a tricky process for me, this subject motivation is even trickier.
In turning this subject around in my mind, and thinking about all the people and things that have been influential, I have some idea about what keeps us going.
Nodal points
I started thinking about all the other important “nodal points” (I don’t know what else to call this) of people, places, books, albums, websites, etc. that all played a part in shaping who I am as a person and what I think is important. These points are a combination of seeking things out myself and getting a recommendation that felt like it was actually for me. A mixture of both passive and active knowledge acquisition.
ultimately, it's the totality of those “nodal points” that indicate one’s own unique perspective. It doesn’t matter if you specifically sought out the nodal point or not, it’s the recognition that counts. When you encounter a piece of life-changing information (no matter how large the change part is), you are simultaneously discovering and creating “yourself,” becoming incrementally more complete. Your perspective (where your gaze is directed) is made up of a meandering line through these points. Learning (or maybe some precursor to learning) is a lot about developing the intuition to recognize when something you find in the world is going to be a nodal point for you.
Infinite varieties of contexts
Over the course of 10 years of using Are.na, I have fully adopted the view that any piece of information can be important to a person given the right context. And on Are.na, pieces of information can be arranged in infinite varieties of contexts – their respective meaning shifts as the proximate information shifts. In other words, the more connections a block has, the more opportunities it has to be a nodal point.
A lifelong project
One question that is still hard to answer after 10 years of working on Are.na is “what is the long term vision?” This is difficult for a few reasons.
One reason is that we have to calibrate our definition of long term with the person who is asking the question. Are.na is a lifelong project. Our ideal outcome as a company is not becoming the next Facebook (god forbid), it’s becoming the next Nishiyama Onsen Keiunkan, a hot spring hotel in Japan, and one of the world’s oldest businesses (founded in 705 AD).
Growing in the correct way
It often feels like Are.na itself has its own needs and desires—that Are.na has its own personal intuition. And that we (you and I) are figuring out what it wants to be together. We (the organization that works on Are.na) have a very defined sense of how things should be done and why building Are.na is important, but we try not to be overly dogmatic about what exactly it should evolve into.
…We’ve long had the sense that it’s possible to cultivate an experience on the Internet that is more calm, thoughtful, and introspective. And we’ve long had the view that this is possible not from a technology-oriented approach, but from an approach that is more soft, more personal, and more intuitive.
…If we are the blade, what is the shield? I think it’s speed: The dominant model for online platforms (especially social platforms) is speed and scale at all costs. But to us, growing Are.na in the correct way is more important than growing it quickly.