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.
Managing Oneself
Only from strength
Most people think they know what they are good at. They are usually wrong. More often, people know what they are not good at—and even then more people are wrong than right. And yet, a person can perform only from strength. One cannot build performance on weaknesses, let alone on something one cannot do at all.
Feedback analysis
The only way to discover your strengths is through feedback analysis. Whenever you make a key decision or take a key action, write down what you expect will happen. Nine or 12 months later, compare the actual results with your expectations.
Taking pride in ignorance
First and foremost, concentrate on your strengths. Put yourself where your strengths can produce results.
Second, work on improving your strengths.
Third, discover where your intellectual arrogance is causing disabling ignorance and overcome it...First-rate engineers, for instance, tend to take pride in not knowing anything about people. Human resources professionals, by contrast, often pride themselves on their ignorance of elementary accounting or of quantitative methods altogether. But taking pride in such ignorance is self-defeating. Go to work on acquiring the skills and knowledge you need to fully realize your strengths.
But bulldozers move mountains
A planner may find that his beautiful plans fail because he does not follow through on them. Like so many brilliant people, he believes that ideas move mountains. But bulldozers move mountains; ideas show where the bulldozers should go to work.
Waste as little effort as possible on low competence
One should waste as little effort as possible on improving areas of low competence. It takes far more energy and work to improve from incompetence to mediocrity than it takes to improve from first-rate performance to excellence.
How do I perform?
For knowledge workers, How do I perform? may be an even more important question than What are my strengths?.
A few common personality traits usually determine how a person performs:
- Am I a reader or a listener?
- How do I learn? Writing? Taking notes? Doing? Talking?
- Do I work well with people, or am I a loner? And if I do work well with people, in what relationship?
- Do I produce results as a decision maker or as an adviser?
- Do I perform well under stress, or do I need a highly structured and predictable environment?
- Do I work best in a big organization or a small one?
To improve the way you perform
Do not try to change yourself—you are unlikely to succeed. But work hard to improve the way you perform. And try not to take on work you cannot perform or will only perform poorly.
The mirror test
In the early years of this century, the most highly respected diplomat of all the great powers was the german ambassador in London. He was clearly destined for great things...yet in 1906 he abruptly resigned rather than preside over a dinner given by the diplomatic corps for Edward VII. The king was a notorious womanizer and made it clear what kind of dinner he wanted. The ambassador is reported to have said, "I refuse to see a pimp in the mirror in the morning when I shave."
This is the mirror test. Ethics requires that you ask yourself, What kind of person do I want to see in the mirror in the morning?
Your organization's values
Organizations, like people, have values. To be effective in an organization, a person's values must be compatible with the organization's values. They do not need to be the same, but they must be close enough to coexist. Otherwise, the person will not only be frustrated but also will not produce results.
Values vs. strengths
There is sometimes a conflict between a person's values and his or her strengths. What one does well – even very well and successfully – may not fit with one's value system. In that case, the work may not appear to be worth devoting one's lift to (or even a substantial portion thereof).
Values are and should be the ultimate test.
Successful careers are not planned
Successful careers are not planned. They develop when people are prepared for opportunities because they know their strengths, their method of work, and their values. Knowing where one belongs can transform an ordinary person – hardworking and competent but otherwise mediocre – into an outstanding performer.
The best-laid plans
It is rarely possible – or even particularly fruitful – to look too far ahead. A plan can usually cover no more than 18 months and still be reasonably clear and specific. So the question is most cases should be, Where and how can I achieve results that will make a difference within the next year and a half?
The second half of your life
Today, most work is knowledge work, and knowledge workers are not "finished" after 40 years on the job, they are merely bored.
There are three ways to develop a second career. The first is to actually start one. The second is to develop a parallel career. Finally, there are the social entrepreneurs.
There is one prerequisite for managing the second half of your life: You must begin long before you enter it. If one does not begin to volunteer before one is 40 or so, one will not volunteer once past 60.