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.
Letters to the Future
The lapse of many years
At this point I wish to emphasize what I believe will ultimately prove to be the greatest purpose of our museum. This value will not, however, be realized until the lapse of many years, possibly a century, assuming that our material is safely preserved. And this is that the student of the future will have access to the original record of faunal conditions in California and the west, wherever we now work. He will know the proportional constituency of our faunae by species, the relative numbers of each species and the extent of the ranges of species as they exist today.
— Joseph Grinnell, 1910
The Grinnell System
The recording of field notes was common practice for biological surveyors and naturalists generations before Grinnell. His system continues this tradition but is distinguished by its distinctive standardized format. It consists of three sections:
- The journal contains a narrative account describing the study site and summarizing each day’s activities and observations, including a list of species encountered. This section is often peppered with sketches, photographs, or maps.
- The catalog is a sequential record of all voucher specimens collected, each with a unique field number and the information needed for the specimen’s museum tag, such as its sex, mass, breeding status, and standard body measurements.
- Species accounts are species-specific summaries of information and observations, gradually accumulated over multiple days at a site or across multiple sites, that eventually grow to detailed summaries of physical description, seasonal behaviors, microhabitat associations, and other characteristics.
Separating the notebook in this fashion allows each section to have its own context-specific structure and format.
Jim's system
From the earliest days of my fieldwork until now, throughout a given day I jotted notes, typically in pencil, into a small, spiral-bound pocket notebook, remembering the admonition not to trust one’s memory but to record observations as continually as possible. I then transcribes these notes into my handwritten journal in the evenings on the best of days or every few days when an intense field effort allowed.
From 2000 onward, I would still takes pencil notes in a small pocket notebook in the field, but I transcribes these into a word-processor document with margins set for the size of our field note pages. I combined this document with my field catalog for a particular trip and eventually both would be bound in the same manner as standard, handwritten field notes.
This approach had the advantage of producing both an archival paper copy as well as an electronic copy. It was also easy to intersperse specialized maps and digital photographs, which had become the norm by this time, throughout the journal text.
John's system
I have two field notebooks: a “raw" notebook and my formal Grinnellian notebook.
In the field, I take all my raw notes in a waterproof notebook using a fine-point permanent pen (or pencil when its raining). The entries have virtually no structure other than the date at the top of (almost) every page.
At the end of the day, I transcribe the notes into my Grinnellian journal as if I were writing a latter to a colleague.
Record them all
You can’t tell often in advance which observations will prove valuable. Do record them all!
— Joseph Grinnell, 1908
Recommendations for field notes
Being an end-user of someone else’s field notes certainly gives you insight into the benefits of good note-taking skills. Our experiences as end-users and creators of archival field notes lead us to a few specific recommendations:
(1) Don’t get bogged down in the details of format or style.
Rules are counterproductive if they prevent a researcher from taking field notes in the first place.
You will get more return by focusing on your content than by refining your formatting.
(2) Compose your notes as if you were writing a letter to someone a century in the future.
Writing for an external audience requires you to be more explicit in your descriptions and to take less knowledge for granted. Avoid the use of abbreviations, symbols, and other shortcuts that only you will understand.
Ask yourself: How would you describe this to someone over the phone?
(3) It is better to spend five minutes writing the important details than twenty minutes writing the trivial ones.
Field notes
Field notes example.
Camp's notes
Grinnell-era field notes example, Charles L. Camp.