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.
Linking Researchers Across Generations
Future value
In the field, there is a continuous flow of information that consists of daily observations, insights, and data. How can I capture these data and thoughts in notes, maps, and images so that they will be of value both to me and to future generations of scientists?
Time capsules
In recording fieldwork I was creating my own time capsules.
Tools of the digital age
The myriad tools of the digital age that provide quick ways to capture words, images, and data have added to the perception that handwritten field notebooks are passé. As someone who routinely encounters objects that can speak to us over millions of years, I may have a bias towards things that have stood the test of time. That said, it is clear that there is still much to recommend preserving records and information in traditional paper field notes.
Over the course of my career, I have developed a habitual field note protocol in which a paper notebook is used both to record information and to integrate records made on standardized data sheets, in computer files, and in photographs.
Five basic rules
Five basic rules:
(1) Record your work as notes to your future self and colleagues.
Write notes so that someone fifty years from now (or more) will understand and be able to use the factual information you collected, perhaps for purposes quite different from the original reasons.
Clearly separate facts from interpretations so these are not confusing to a future reader.
(2) Establish a clear and consistent notebook format and process.
I always include the data, place, main activities or events, weather conditions, and other people involves. The day, month, and year is the most important link between that particular point in time and other people’s records, separate data sheets that I filled out myself, photos, and most important, collected specimens.
Documenting collecting strategies and protocols receives special attention. In the moment, these may seem like common knowledge for the field team, so sometimes no one bothers to write them out.
(3) Don’t lose your field records!
(4) Pack a camera, create a visual record.
No matter how many words you write to describe a fossil locality, you can’t beat an actual photo, taken on the spot, annotated in pen, and pasted into your notebook.
There is no substitute for a photograph you actually mark in “real time” in the field as the best way to preserve a lasting, accurate record for yourself, or for someone who has never seen the site or object in question.
(5) Learning through sketches and diagrams.
Photographs are great, but drawn what you see is a more powerful way to learn about spatial patterns and relationships.
Even if you are not an expert at drawing, you can make sketches that are much more informative than words would be.
Always include a scale, an orientation, and labels in your diagrams.
Bonewalks
Example of a standardized field data collection form used to record all the fossil bones encountered along a transect.
Informally I refer to these as “bonewalks.”
Microstratigraphic
A "microstratigraphic" diagram from Olorgesaille, Kenya.