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.
The Pale King
We change them and are changed
"We fill pre-existing forms and when we fill them we change them and are changed."
— Frank Bidart, Borges and I
Displacement
...the man fitted to his job like a man to the exact pocket of space he displaces.
What's wrong?
Pay attention, boy. The next suitable person you're in light conversation with, you stop suddenly in the middle of the conversation and look at the person closely and say, "What's wrong?" You say it in a concerned way. He'll say, "What do you mean?" You say, "Something's wrong. I can tell. What is it?" And he'll look stunned and say, "How did you know?" He doesn't realize something's always wrong, with everybody. Often more than one thing.
Narrative codes
The idea, as both sides' counsel worked it out, is that you will regard features like shifting p.o.v.s, structural fragmentation, willed incongruities, & c. as simply the modern literary analogs of 'Once upon a time...' or 'Far, far away, there once dwelt...' or any of the other traditional devices that signaled the reader that what was under way was fiction and should be processed accordingly. For as everyone knows, whether consciously or not, there's always a kind of unspoken contract between a book's author and its reader; and the terms of this contract always depend on certain codes and gestures that the author deploys in order to signal the reader what kind of book it is, i.e., whether it's made up vs. true. And these codes are important, because the subliminal contract for nonfiction is very different from the one for fiction.
An enormous machine
The couple of years in question here saw one of the largest bureaucracies anywhere undergo a convulsion in which it tried to reconceive itself as a non- or even anti-bureaucracy, which at first might sound like nothing more than an amusing bit of bureaucratic folly. In fact, it was frightening; it was a little like watching an enormous machine come to consciousness and start trying to think and feel like a real human.
Abstruse dullness
Consider, from the Service's perspective, the advantages of the dull, the arcane, the mind-numbingly complex. The IRS was one of the very first government agencies to learn that such qualities help insulate them against public protest and political opposition, and that abstruse dullness is actually a much more effective shield than is secrecy. For the great disadvantage of secrecy is that it's interesting.
To hide or dissemble
Fact: The birth agonies of the New IRS led to one of the great and terrible PR discoveries in modern democracy, which is that if sensitive issues of governance can be made sufficiently dull and arcane, there will be no need for officials to hide or dissemble, because no one not directly involved will pay enough attention to cause trouble.
Distraction
To me, at least in retrospect, the really interesting question is why dullness proves to be such a powerful impediment to attention. Why we recoil from the dull. Maybe it's because dullness is intrinsically painful; maybe that's where phrases like 'deadly dull' or 'excruciatingly dull' come from. But there might be more to it. Maybe dullness is associated with psychic pain because something that's dull or opaque fails to provide enough stimulation to distract people from some other, deeper type of pain that is always there, if only in an ambient, low-level way, and which most of us spend nearly all our time and energy trying to distract ourselves from feeling, or at least from feeling directly or with our full attention.
The Manual
I don't believe I have anything to say that isn't in the code or Manual.
In a stare
Being in a stare referred to staring fixedly and without expression at something for extensive periods of time. It can happen when you haven't had enough sleep, or too much sleep, or if you've overeaten, or are distracted, or merely daydreaming. It is not daydreaming, however, because it involved gazing at something. Staring at it. Usually straight ahead—a shelf on a bookcase, or the centerpiece on the dining room table, or your daughter or child. But in a stare, you are not really looking at this thing you are seeming to stare at, you are not even really noticing it—however, neither are you thinking of something else. You in truth are not doing anything, mentally, but you are doing it fixedly, with what appears to be intent concentration. It is as if one's concentration becomes stuck the way an auto's wheels can be stuck in the snow, turning rapidly without going forward, although it looks like intense concentration. And now I too do this.
We infantilize ourselves
Here in the US, we expect government and law to be our conscience. Our superego, you could say. It has something to do with liberal individualism, and something to do with capitalism, but I don't understand much of the theoretical aspect—what I see is what I live in. Americans are in a way crazy. We infantilize ourselves. We don't think of ourselves as citizens—parts of something larger to which we have profound responsibilities. We think of ourselves as citizens when it comes to our rights and privileges, but not our responsibilities. We abdicate our civic responsibilities to the government and expect the government, in effect, to legislate morality.
Doubling
Obetrolling didn't make me self-conscious. But it did make me much more self-aware. If I was in a room, and had taken an Obetrol or two with a glass of water and they'd taken effect, I was now not only in the room, but I was aware that I was in the room. In fact, I remember I would often think, or say to myself, quietly but very clearly, 'I am in this room.' It's difficult to explain this. At the time, I called it 'doubling', but I'm still not entirely sure what I meant by this, nor why it seemed so profound and cool to not only be in a room but be totally aware that I was in the room.
Strings and clots
The walls' texture was mostly smooth, but if you really focused your attention there were also a lot of the little embedded strings and clots which painters tend to leave when they're paid by the job and not the hour and thus have no motivation to hurry. If you really look at something, you can almost always tell what type of wage structure the person who made it was on.
More by accident
In an intentional bout of concentrated major thinking, where you sit down with the conscious intention of confronting major questions like 'Am I currently happy?' or 'What, ultimately, do I really care about and believe in?' or— particularly if some kind of authority figure has just squeezed your shoes—'Am I essentially a worthwhile, contributing type of person or a drifting, indifferent, nihilistic person?', then the questions often end up not answered but more like beaten to death, so attacked from every angle and each angle's different objections and complications that they end up even more abstract and ultimately meaningless than when you started. Nothing is achieved this way, at least that I've ever heard of. Certainly, from all evidence, St. Paul, or Martin Luther, or the authors of The Federalist Papers, or even President Reagan never changed the direction of their lives this way—it happened more by accident.
Wisdom
This remains largely theory, but my best guess as to his never dispensing wisdom like other dads is that my father understood that advice—even wise advice—actually does nothing for the advisee, changes nothing inside, and can actually cause confusion when the advisee is made to feel the wide gap between the comparative simplicity of the advice and the totally muddled complication of his own situation and path.
No-nonsense
Admittedly, though, however alert and aware I felt, I was probably more aware of the effects the lecture seemed to be having on me than of the lecture itself, much of which was over my head, and yet was almost impossible to look away from or not feel stirred by. This was partly due to the substitute's presentation, which was rapid, organized, undramatic, and dry in the way of people who know that what they are saying is too valuable in its own right to cheapen with concern about delivery or 'connecting' with the students. In other words, the presentation had a kind of zealous integrity that manifested not as style but as the lack of it. I felt that I suddenly, for the first time, understood the meaning of my father's term 'no-nonsense', and why it was a term of approval.
The pie has been made
"In today's world, boundaries are fixed, and most significant facts have been generated. Gentleman, the heroic frontier now lies in the ordering and deployment of those facts. Classification, organization, presentation. To put it another way, the pie has been made—the contest is now in the slicing."
Midwest sunset
For those who've never experienced a sunrise in the rural Midwest, it's roughly as soft and romantic as someone's abruptly hitting the lights in a dark room. This is because the land is so flat that there is nothing to impede or gradualize the sun's appearance. It's just all of a sudden there.
Test anxiety
It was part of a larger discussion about younger examiners and television and the theory that America had some vested economic interest in keeping people over-stimulated and unused to silence and single-point concentration. Shackleford's observation was that the real object of the crippling anxiety in 'test anxiety' might well be a fear of the tests' associated stillness, quiet, and lack of time for distraction. Without distraction, or even the possibility of distraction, certain types of people feel dread—and it's this dread, not so much the test itself, that people feel anxious about.
To fill in the gaps
It would be easy to impose on the office a whole welter of detail, explanation, and background that was actually gleaned only later and not part of my arrival and dazed scurrying about with the Iranian Crisis at all. Which is a quirk of temporal memory—one tends to fill in gaps with data acquired only later, sort of the same way the brain automatically works to fill in the visual gap caused by the optical cord's exit through the back of the retina.
Every love story is a ghost story
What hell is
He felt in a position to say he knew now that hell had nothing to do with fires or frozen troops. Lock a fellow in a windowless room to perform rote tasks just tricky enough to make him have to think, but still rote, tasks involving numbers connected to nothing he'd ever see or care about, a stack of tasks that never went down, and nail a clock to the wall where he can see it, and just leave the man there to his mind's own devices.
No place it hadn't already been
He imagined that the clock's second hand possessed awareness and knew that it was a second hand and that its job was to go around and around inside a circle of numbers forever at the same slow unvarying machinelike rate, going no place it hadn't already been a million times before, and imagining the second hand was so awful it made his breath catch in his throat and he looked quickly around to see if any of the examiners around him had heard it or were looking at him.
The word invents itself
Posits certain neologisms as arising from their own cultural necessity—his words, I believe. Yes, he said. When the kind of experience that you're getting a man-sized taste of becomes possible, the word invents itself.
Unborable
The underlying bureaucratic key is the ability to deal with boredom. To function effectively in an environment that precludes everything vital and human. To breathe, so to speak, without air.
The key is the ability, whether innate or conditioned, to find the other side of the rote, the picayune, the meaningless, the repetitive, the pointlessly complex. To be, in a word, unborable. I met, in the years 1984 and '85, two such men.
It is the key to modern life. If you are immune to boredom, there is literally nothing you cannot accomplish.
Institutional structure
'That was all he said it seemed like I needed, just to talk to somebody with no bullshit, which was what the Zeller Center doctors didn't realize, or like they couldn't realize it because then the whole structure would come down, that here the doctors had spent four million years in medical school and residency and the insurance companies were paying all this money for diagnosis and OT and therapy protocols, it was all an institutional structure, and once things became institutionalized then it all became this artificial, like, organism and started trying to survive and serve its own needs just like a person, only it wasn't a person, it was the opposite of a person, because there was nothing inside it except the will to survive and grow as an institution.'