It’s a moment of disorientation I’ve had a couple of times — you find a great piece of writing, and think “Wow, this is really going to change things!”, only to discover that it is in fact decades old. The clash of historical vertigo with Internet Now is both wonderful and daunting.

I had that moment yesterday with Christopher Alexander’s A City Is Not A Tree from 1965. Alexander argues that the hallmark of designed cities (Mesa City, Brasilia) is that their builders invariably gravitate to tree-structures, where all sub-units of a similar type roll-up into a single super-unit, und so weiter, which creates an artificial and ultimately damaging simplification. He contrasts this with the structure of organic cites (London, NYC), which are organized as semi-lattices, where overlap and shared function is the order of the day.

Whenever we have a tree structure, it means that within this structure no piece of any unit is ever connected to other units, except through the medium of that unit as a whole.

The enormity of this restriction is difficult to grasp. It is a little as though the members of a family were not free to make friends outside the family, except when the family as a whole made a friendship.

In simplicity of structure the tree is comparable to the compulsive desire for neatness and order that insists the candlesticks on a mantelpiece be perfectly straight and perfectly symmetrical about the centre. The semilattice, by comparison, is the structure of a complex fabric; it is the structure of living things, of great paintings and symphonies.

It must be emphasized, lest the orderly mind shrink in horror from anything that is not clearly articulated and categorized in tree form, that the idea of overlap, ambiguity, multiplicity of aspect and the semilattice are not less orderly than the rigid tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure.

The most startling proof that people tend to conceive even physical patterns as trees is found in some experiments of Sir Frederick Bartlett. He showed people a pattern for about a quarter of a second and then asked them to draw what they had seen. Many people, unable to grasp the full complexity of the pattern they had seen, simplified the patterns by cutting out the overlap. [T]he original is shown on the left, with two fairly typical redrawn versions to the right of it. In the redrawn versions the circles are separated from the rest; the overlap between triangles and circles disappears.

For me it mainly has to do something with classification. I believe that one of the reasons classifying information is difficult has something to do with the fact that in most cases tree structures are used for classification, so we have to find "unique folder" to put an idea or a document into it. And ideas never belong to "unique folders", they have multiple relations with other ideas, forming a web structure.[...]

It probably matter of personal preferences or thinking style, but I always have problems with tree structures. For example, I've got Typepad Plus account because it offers an easy way to put photos online only to discover that I can hardly use it because it forces me to organise my photographs into albums. And I always want to sort my photos by location, by date, by theme and by many other ways that I'll invent tomorrow.

Another example is about mind-mapping tools. Those that I tried force me to organise my ideas into tree structure. Of course, visualisation is nice to get an overview of ideas (especially if you use it for others), but forced tree structure makes these maps useless for (my) thinking. I tried to use mind-mapping software to structure my ideas for writing papers, but it didn't work. It's fine on paper for drawing a web of relations and thinking about steps of explaining them, but drawing a tree on my screen doesn't make any sense: I would rather start outlining directly in Word...