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.
Deadlines are bullshit
In software development deadlines are a necessary evil. It is important to understand when they are necessary, and it is important to understand why they are evil.
- External vs. internal deadlines
- Why are internal deadlines evil?
- Engineers who love their work
External vs. internal deadlines
When are deadlines necessary?
- Contractual obligations
- Technical liabilities (e.g., dependency EOL)
- Compliance, government, investors, and other external stakeholders
What do all of these deadlines have in common? They are all important. They are all deadlines that cannot be missed. They are all external.
When are deadlines evil?
- Your manager says you have a deadline
- Your software development methodology says you have deadlines
What do all of these deadlines have in common? None of them are important. They are arbitrary. They are all internal. They are all bullshit.
Why are internal deadlines evil?
- Estimation: When estimating engineering work a substantial time investment is required by an engineer in order to get an accurate estimate.
- Misaligned Incentives: There is an incentive to lie and give estimates much longer than the feature is truly expected to take.
- Low Morale: Deadlines are likely to be missed often. Repeated failure has a cost to the morale of the team.
- Micromanagement: Deadlines are wielded by middle managers as a whip to harass and annoy engineers working on features.
- High Stress: When engineers feel the pressure of other stakeholders holding deadlines over their heads it creates an environment of high stress.
- High Turnover: On teams with high turnover rates the best engineers have an easy time finding new work and leave quickly, the worst engineers have a difficult time finding work and remain. This selects for a lower quality team over time.
Engineers who love their work
The resolution is simple. Never have internal deadlines. Operate on a prioritized and ordered list of features. Estimate only when necessary to prioritize and do so in a t-shirt sizing way. Trust your engineers and they will begin to love their work. Engineers who love their work are happy and productive.