The new [physics-based] viewpoint is so potent that it has perhaps, caused too many metallurgists to forsake their partially intuitive knowledge of the nature of materials to worship at the shrine of mathematics, a trend reinforced by the curious human tendency to laud the more abstract.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.
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.
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.
One 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.
One 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.
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.
This 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.
Besides being unlikely to work for you even if someone is able to describe what makes their writing tick, most advice is written by people who don't understand how their writing works. This may be difficult to see for writing if you haven't spent a lot of time analyzing writing, but it's easy to see this is true if you've taken a bunch of dance classes or had sports instruction that isn't from a very good coach. If you watch, for example, the median dance instructor and listen to their instructions, you'll see that their instructions are quite different from what they actually do. People who listen and follow instructions instead of attempting to copy what the instructor is doing will end up doing the thing completely wrong. Most writing advice similarly fails to capture what's important.
What keeps me busy in my classes is trying to help my students learn how to think. They say, "Rob holds his hands like this...," and they don't know that the reason I hold my hands like this is not to make myself look that way. The end result is not to hold the gun that way; holding the gun that way is the end result of doing something else.
…The more general issue is that a person who doesn't understand the thing they're trying to copy will end up copying unimportant superficial aspects of what somebody else is doing and miss the fundamentals that drive the superficial aspects. This even happens when there are very detailed instructions. Although watching what other people do can accelerate learning, especially for beginners who have no idea what to do, there isn't a shortcut to understanding something deeply enough to facilitate doing it well that can be summed up in simple rules, like "omit needless words".
Swearing or saying that something "is cancer" or "is the Vietnam of X" or some other highly emotionally loaded phrase seems to be particularly effective
Talk-up prestige/accomplishments/titles
Use an authoritative tone and/or style
Write things with an angry tone or that are designed to induce anger
Write frequently
Get endorsements from people
Write about hot, current, topics
Provide takes on recent events
Use deliberately outrageous / controversial framings on topics