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.
Why Keep a Field Notebook?
Pick one thing
I recently started a field notebook assignment for my upper-level Ecology class at the University of Montana. I asked my students to pick one “thing” and observe it carefully over the entire semester.
In addition to their field notebooks, the students also had to suggest at least ten research questions inspired by their observations.
Lab notebooks
Most of my colleagues who conduct laboratory research not only keep extremely thorough and complete lab notebooks, but they teach their students how and why to keep data in them. Some labs even have friendly competitions in which prizes for the best-kept notebooks are awarded.
In stark contrast to the vibrant culture of keeping lab notebooks in molecular biology, my informal polling suggested a lack of interest in notebooks in field biology.
“I have a GPS for that.”
“My data are in a spreadsheet.”
“I write things down when I get home.”
“I have a computer.”The general consensus seemed to be that field notebooks are quaint, archaic, and obsolete in field biology.
Hybrid journals
The most useful and interesting notebooks of field biology are hybrids; as well as recording details and data of field research, they record the observations, thoughts, musings, and peregrinations of the author.
A fertile incubator
Another value of field notebooks is their ability to serve as an incredibly fertile incubator for your ideas and observations. By jotting down interesting observations, questions, and miscellaneous ideas, your field notebook can serve as a powerful catalyst for new experiments and projects.
Best practices
- Use a hardbound notebook.
- Keep your contact information in a prominent location.
- Write for yourself and for posterity.
- Write pertinent field information with every new entry. You should enter the date, time, and location at the top of every page.
- Add information on your location.
- Record your methods.
- Make backup copies.
- If you use abbreviations, make sure there is a key in your field notebook.
- Don’t leave home without it.
- Form a writing habit. Thomas Jefferson was such an inveterate chronicler of daily events in his notebooks that he even took the time to record the weather four times on the day he helped write the Declaration of Independence. So unless you have something far more pressing than writing the Declaration of Independence, you have no excuse for avoiding your field notebook!
- Set up a structure for your field notebook.
- Create an index.
- Treat your field notebook like a scrapbook. You should view your field notebook as a central clearinghouse for miscellaneous information that is relevant to your research project. If there are related bits of information that you will find useful later on, sketch them, write them down, photocopy them, and staple or tape them in your notebook.