Joho the Blog: Are trees natural?

May 17, 2006

Are trees natural?

EirePreneur has a fascinating post on research by the Weizmann Institute of Science that a "tree-like hierarchy...may be a basic underpinning of language."

There's no question in my mind that arranging concepts so that A includes B which includes C is fundamental to how we think. But I'd only call that a tree if C can only hang from one branch. If it can hang from lots of branches simultaneously, we have something way messier and more complex.

From the article about the article:

Mathematically, these concept vectors can go in many directions, and reading the text can be thought of as a tour along paths in the resulting network. The multidimensional concept vectors seem to span a "web of ideas." The scientists' work suggests this network is based on a tree-like hierarchy that may be a basic underpinning of language. The reader or listener can reconstruct the hierarchical structure of a text, and thus the multidimensional space of ideas, in his or her mind to grasp "the author's meaning."

Hard to to tell from this exactly what the research showed. I haven't yet found the original... (Thanks to Lisa Williams for the link.) [Tags: taxonomy everything_is_miscellaneous eirepreneur]

Posted by D. Weinberger at May 17, 2006 09:47 AM

Comments

I'd only call that a tree if C can only hang from one branch. If it can hang from lots of branches simultaneously, we have something way messier and more complex.

Possibly a directed acyclic graph? (I only discovered DAGs a couple of months ago, but I think they're very cool indeed.)

Posted by: Phil | May 17, 2006 12:13 PM

There's a deep issue here. I suspect that we humans constantly try to create simplified models of what we see. It's why we constantly try to reduce 3D to 2D so we can draw it on flat pieces of paper. In the same way we constantly try to reduce meshes to trees because they are easier to understand. The problem is that reality isn't tree structured, it's mesh structured.

This then results in some patterns that get used over and over again in computing. A flat layered desktop. Outlines. XML instead of RDF. This doesn't mean trees aren't useful but as a simplification they are limited and inaccurate. The map is not the territory.

I bet you could work something in there about art and scratches in the sand. If your art is 2 dimensional it encourages you to draw two dimensional diagrams that tend towards trees and outlines. Meshes get horribly messy in 2D.

Posted by: julian bond | May 17, 2006 03:51 PM

I agree that paper has a lot to do with it. In fact, paper is why our ways of organizing knowledge generally share the limitations on organizing physical objects. That's a big theme in the book I'm writing. (Trees are made out of paper, as well as vice versa.)

But I don't think reality is mesh shaped either, although meshes capture much more than classical trees can. Meshes have nodes and lines, but reality doesn't. Reality has words and meanings. Reality is shaped like language. What a coincidence! :)

Posted by: David Weinberger | May 17, 2006 04:40 PM

You're right. Reality isn't mesh shaped. The map is not the territory. And a mesh is just as much a symbolic simplification of reality as a tree. And our view of reality is defined by the symbols we use to describe it, which in most cases means words.

But I'm arguing that the interconnectedness and messiness of reality is better modeled by meshes than trees. Even in family trees where the parent-child relationship is defined by biology the tree quickly becomes mesh like with enough points. The problem is that we find it harder to think about meshes than trees. So we constantly try to reduce the multi-dimensional interconnectedness to simpler patterns in order to be able to think about it.

These thoughts are giving me a deep mistrust of tree structured tools like Outliners, BrainMaps and Categories. They are useful for brainstorming because they appeal to our 2D symbol manipulation abilities. But they encourage us to ignore half the links.

Posted by: julian bond | May 18, 2006 02:30 AM

Well I must admit that my approach to the topic may not be mathematically rigorous and already this talk of directed acyclic graphs is taking it well over my head ;-)

In my earlier hypothesis about "How Social Bookmarking can lead to the Semantic Web" I demonstrated how hierarchical tag trees evolve on del.icio.us. Of course any tag can belong to numerous trees at once in that scenario but each URL has a single 'tag DNA'. Each leaf (tagged article) can only belong to a single branch extremity but of course that branch extremity can hold numerous leaves.

I see them more as multidimensional trees than meshes and I use the metaphor of a long term timelapse to observe how the tree grows and mutates over time. Some branches grow stronger and longer as others decay or diminish. Tag hierarchies are evanescent, biotic entities wriggling and jiggling according to the vagaries of the hive mind.

Neither have I found the original research from the Weizmann Institute of Science but I would guess they're arriving at discrete tree-like hierarchies. My bet is that the wisdom of the crowd can arrive at the same results through the mechanism of social tagging (as the crowd tends to infinity).

Posted by: James Corbett | May 18, 2006 05:41 AM

Julian, I totally agree that meshes are usually more accurate representations than trees (except in special cases, of course). And we do seem to need models that simplify the buzzing, blooming confusion. The map isn't the territory, but we do sometimes need maps, and how simplified a map is has little to do with reality and lots to do with what we need the map for. (I'm agreeing with you.)

James, I agree that we are going to learn a huge amount by analyzing tags, especially "as the crowd tends to infinity," as you nicely put it. We will be able to build meshes and maps and (yes) trees based on what we see. And thesauri and gazetteers as well. Lots and lots of them, different ones for different groupings of people. It's going to be a fascinating 100 years.

PS: I will take on all comers for the title of Least Mathematically Competent.

Posted by: David Weinberger | May 18, 2006 10:03 AM

Posted by: CONNIE | May 30, 2006 05:08 PM

Posted by: ALAN | May 30, 2006 05:09 PM

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