Mathemagenic

My thinking about trees vs. webs was a bit implicit till I saw Clay Shirky pointing to A city is not a tree where Christopher Alexander talks about tree vs. semilattice structures. As I don't have a good mental model of semilattice (and Google doesn't give many pictures ;), I'll talk about trees and webs. Or, to be more specific about tree-structures and web-structures.

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.

I'm thinking about tree vs. web structures in my own work:

About filers and pilers (longer abstract if you can't access it full-text) when it comes to sorting out papers.

About saving a file on my hard drive, where I always have to remember specific folder I used, vs. adding a document to Docushare (used as a document management system in my company), which allows "placing" one document into several folders (e.g. if you scroll you'll find out that this paper is available in four folders).

About using Favourites in IE vs. del.icio.us, which is free of "I have to decide in which folder it should go".

And finally about using categories vs. liveTopics to organise my thinking in this weblog.

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...

Tree-relations may be easier to grasp than more complex structures. They are also easier to unfold into linear structure (think how you were taught to write an essay: introduction - body - conclusion, body consists of X parts, each of them is subdivided...). Trees are easy to draw. Easy to program.

But for me ideas live as webs. Tree structure of a paper is good to help others understand creative mess of ideas in my head, but it pains every time I try to squeeze a web of ideas into a tree structure when writing (I guess that's why hyperlinks and cross-references were invented ;).

When I think about webs of ideas I associate a lot with Christopher Alexander talking about cities:

When we think in terms of trees we are trading the humanity and richness of the living city for a conceptual simplicity which benefits only designers, planners, administrators and developers. Every time a piece of a city is torn out, and a tree made to replace the semilattice that was there before, the city takes a further step toward dissociation.

In any organized object, extreme compartmentalization and the dissociation of internal elements are the first signs of coming destruction. In a society, dissociation is anarchy. In a Person, dissociation is the mark of schizophrenia and impending suicide. An ominous example of city-wide dissociation is the separation of retired people from the rest of urban life, caused by the growth of desert cities for the old like Sun City, Arizona. This separation is only possible under the influence of treelike thought.

It not only takes from the young the company of those who have lived long, but worse, it causes the same rift inside each individual life. As you pass into Sun City, and into old age, your ties with your own past will be unacknowledged, lost and therefore broken. Your youth will no longer be alive in your old age - the two will be dissociated; your own life will be cut in two.

For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not, cannot and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make cities which are trees, they will cut our life within to pieces.

Site note: Thinking about writing texts, I think about stories that somehow fit linear format without breaking a web of relations. For me there is a lot to read and to think about to understand how stories emerge from webs and is there "tree" stage in between...