April 15, 2000
Web Mind #2
by Rudy Rucker
In the Web Mind #1 column, I said that the Web might be a good model for the human mind. I said that one reason for this is that both the Web and the mind are like fractals. And then I spent the rest of the column explaining what a fractal is. Now let’s why the Web and the mind are indeed similar kinds of fractals.
Your Mind is a Fractal
There is a loose sense in which thinking is like moving about in a space of ideas. I visit this notion or emotion, then that one, and then perhaps I return to the first thought. My familiar thoughts are somewhat fixed and persistent, a bit like objects in a landscape. Suppose that I use the word “mindscape” to stand for the manifold of possible thoughts.
There’s clearly some overlap between my mindscape and yours. It’s suggestive to imagine that our mindscapes are really just different views of one Platonic super-mindscape. It’s like we’re in different rooms in a big town looking at the city outside. Though it’s hard for us to see the stuff hidden in each others’ rooms, when we look out our windows we pretty much the same collection of streets, buildings, clouds, mountains, pedestrians and so on. And if you can’t see a particular mindscape sight from where you are, I can tell you a way to get there.
But looking at the mindscape really isn’t very much like looking out a window after all. Things change, and split, and melt together. Each thought sets off fireworks of associations that in turn lead to further thoughts. You start out thinking about a soda, and the next thing you know you’re thinking about tap-dancing.
One of the reasons I love writing is because language is itself so slippery and fractal. Many words and phrases have the peculiar property of meaning, or at least suggesting, several different things. And a given passage of text can sometimes be interpreted at several levels.
Language evolved both to describe the world around us, but also as a way for people to represent the contents of their own minds. “What are you thinking?” “Well, let me tell you.”
Just like the mind, language itself has a branching quality. Suppose, for instance, you were to make a diagram with a word at each node. And now suppose you drew a line from each word to every other word that appears in, say, the standard dictionary definition of the first word. What a mess! Everything’s stuck to everything else.
In the Web Mind #1 column, I talked about a kind of fractal curve (the Koch curve) where a new bump buds out of the middle of every line. We can see this kind of thing happening in thought as follows.
Suppose I say that A (soda) reminds me of B (tap-dancing). Then I have a node A, a node B, and a line between them. But now you ask me about why A reminds me of B, I form a bump C, which holds a concept having to do with the connecting branch. C might be, for instance, the Rockettes.
Soda reminds me of tap-dancing because of the Rockettes. What could be more obvious? Obvious to me, but not to you! So now I make the bump bumpier. I’ve got an image of myself as a twelve-year-old boy at Radio City Music Hall drinking a Pepsi (sponsor product placement!) watching the Rockettes. Fine. But there’s another bump upon this. I’ve never been inside Radio City Music Hall. It was my boyhood friend Niles who went there, and he told me about it so vividly that I felt like I’d seen it myself. So now I better tell you about Niles and me back in 1950s Louisville...
A and B lead to C, D, E, and on beyond Z.
What Kind of Fractal is the Mind?
As it turns out there are many different kinds of fractals, so we might well ask which kind of fractal might best serve as a model for the Mind. The Koch curve in particular is not so well-fitting a model for the web as is a tree or a cloud.
As was discussed in Web Mind #1, you get a tree by repeatedly shooting new branches off the old branches, and this is a little like the way web-links (and mental associations) form. Viewed as a geometrical structure, this kind of tree is hard to draw, for if you try and draw a densely branching tree on a piece of paper, you quickly run out of room. Some of the lines end up crossing over the other lines. (To fit the extra lines in we can either ask for more room or we can bump our drawing up into higher dimensions.) But it’s easy to imagine such a tree. And the Web lends itself to representing a highly branching mind-tree because we can stick in as many links as we want.
But before committing to the idea of a tree, let’s think a bit about clouds. When I say that a cloud is a fractal, I have in mind a model in which we think of a cloud as a certain shaded volume of space. This shaded cloud region has a very complicated shape, with lots of holes and tendrils. One way to imagine mathematically constructing a cloud is to start with a cube of space and to then subdivide it into, say, twenty-seven subcubes (cutting it in three along each dimension, like a Rubik’s cube.). Remove each subcube that doesn’t have any of the cloud in it. Then take each of the remaining subcubes and divide it into twenty-seven subsubcubes. Again remove the pieces that don’t touch the cloud. Repeat the process of dividing and winnowing out for a number of levels. If done in a regular fashion this can lead to a regular fractal such as the “Menger Sponge.”
Figure 1: The Menger Sponge. From Rudy Rucker, Mind Tools (Houghton-Mifflin 1987) (Use Menger.jpg, sent in separate file.)
Of course you don’t have to build clouds up in such a regular way. You can use a more random process for removing subcubes, and then you end up with something more natural in appearance.
Maybe a mind is as much like a cloud as it is like a tree. You have some vague notion (like a cloud seen from a distance), and then when you examine it more closely it breaks into a number of denser regions. And these chunks in turn break into smaller chunks.
The Web is Fractal
Like the mindscape, the Web has a fractal quality to it. One starts out headed for topic A, but when you get to the page for A, you notice a link to topic B, and you go look at B before reading A, but on page B, you find a tempting link C that you just have to read first, and so on.
In some sense you never can get started drawing a true fractal like the Koch curve, because you always have to put in another bump before the bump you want to get to. This is similar to the experience you have when you try to fully explain any aspect of your mindscape. And this is an experience you can also have when you surf the Web.
The attractive thing about the Web as a model of the mind is that its a kind of “paper” where you never have to “run off the edge” or “run out of dimensions.” You can always add scrollbars or links to give yourself more room.
Certainly at this point in history, the Web doesn’t match the branching-tree structure of a real human mind, but a Web-like structure could be tuned to be a tree like this.
Or, again, if we want to think of the mind as being like a cloud, we can also think of a web page as being like a cloud. It’s a collection of concepts, and many of these can be hyperlinked to further web pages.
In other words, we can either think of a web page as branching like a tree or as having denser regions like a cloud.
The Web is Like the Mind?
Whenever I present these ideas to people I get a lot of objections. Here are a few of them, with my attempts an answers.
Objection 1. Just because the Web and the Mind are like fractals doesn’t mean they’re like each other. A Koch curve, a tree and a cloud are fractals, but they aren’t the same.
Answer 1. The Web is endlessly tunable. I’m not saying that the Web right now is like the Mind. I’m saying that it should be possible to use the Web to make a good representation of a mind.
Objection 2. What’s so special about the Web? Couldn’t you use a very fat book with a lot of footnotes to present a similar kind of branching hypertext?
Answer 2. Indeed you can make a printed model of a big hyperlinked Web site. You might, for instance, print out the text content and the images, and use footnotes for the hyperlinks. But it would be hard to maintain and cumbersome to read. This question suggests an interesting analogy. A good Web model of, say, Johnny X, would be something like The Encyclopedia of Johnny X, with lots of cross-references from article to article. How might Johnny X generate the content and the links for such a book? We’ll discuss some science-fictional methods for this next month.
Objection 3. A Web site is static. The essence of your mind is that it is continually changing and reacting to things.
Answer 3. If a Web site were really to be like a mind it would have to have a certain self-animating quality. It should “browse itself” and let you watch or, better, it should let you input things into it and watch it react. If you had the content and the links for a mind-sized website in place, writing some driver software in Java wouldn’t actually be that hard. Imagine, for instance, a background search engine that would keep popping up new associations to things on the screen.
(An aside. A product I’d really like to see is a Beavis and Butthead filter or a Mystery Science 3000 filter or a Popup Video filter. You’d hook this thing up to your TV set, and it would say funny things about whatever you were watching.)
Objection 5. The Web is all interconnected. So actually it is more like one mind than like a lot of minds.
Answer 5. You could indeed think of the Web as society’s mind. And then the most frequently visited sites are the public mind’s obsessions. But there will be individual pieces of the Web that correspond more to one individual’s mind.
There is a contemporary science-fictional dream sometimes called “uploading.” It happens a lot in my Ware novels, that is, in Software, Freeware, Wetware and Realware. You somehow put a copy of your brain’s software into a computer and this gives you a kind of immortality. The reason this is still science-fiction is that we don’t have the foggiest notion for how such a process might work. Thinking of the Web as a model for the mind seems like a good place to start.
Tune in next month for immortality.