Fractional Dimensions

By Tom Peters |

When I was in grade school in the 1960s, we learned the basics about must have been in math class. It seemed like every math teacher I had used an overhead projector with water-soluble colored pens as a pedagogical aid. A one-dimensional object was a line, like the x axis on a graph. A two-dimensional object had height and width, but no depth, like a sinusoidal curve drawn on an x/y graph. A sheet of paper was, for all practical purposes, two-dimensional, even though you could add a z-axis to your graph to create a sense of depth. A three-dimensional space like a classroom had height, width, and depth. The fourth dimension, which always seemed a little suspect to us, was time.  The fifth dimension, of course, was a musical group. It was the Age of Aquarius. 

Recently I have been  thinking about virtual worlds and how librarianship is evolving and how it might continue to evolve in light of these worlds. There are scads of them out there: Second Life, Active Worlds, Lively, Whyville...the list goes on. Some of these virtual worlds seem to be  two-dimensional like cloth figures on a felt board. Other virtual worlds are three-dimensional, more like the real world. 

One day a new idea hit me: Dimensions may include fractions. There may be 2.3-dimension virtual worlds, or even 3.3-dimension virtual worlds. Let me explain.

Dimensionality, it seems, is how one is able to perceive the dimensional object, coupled with how one is able to navigate around and act in that object. If we think of the real world as a three-dimensional space (let’s not worry about time for the moment), it is possible to perceive that three-dimensionality through sight and touch. We can navigate around the three-dimensional real world as well as act in it.

When it comes to the real world, using whole numbers to describe dimensions makes sense. The first and fourth dimensions are a little weird. Most of the action is between two-dimensions and three-dimensions; in fact, it seems like we toggle between them. This distinction kept me in good standing from college through adulthood. For example, in a paper written for the ebullient Professor Cervene’s 8 a.m. Art Appreciation course, I wrote something transplendent, “Note how the artist uses perspective to project a three-dimensional scene onto the two-dimensional canvas.” 

When it comes to virtual worlds, the 2D/3D toggle seems insufficient. In Whyville, for instance, there are intimations of a 3D space, and you can move your avatar from the back bench to the front row of the Greek Theatre, but you cannot really change your perspective on the scene, and you cannot really explore the scene in great depth and variety. Whyville may be something like a 2.3-dimension virtual world.

If we take the real world and consider it the 3D gold standard, some virtual worlds seem to move fractionally beyond 3.0D. In Second Life, for instance, you can view the space through the eyes of your avatar, or from almost any other vantage point, so that you are looking at your avatar in the virtual environment. This happens in the real world only when you look at yourself in the mirror or when you see yourself in some security camera display in a retail store. Second Life may be approximately 3.3-dimensions.

Applying fractions to the right of the decimal point of dimensions may be a new art or science, with opportunities for discussion. It reminds me of the situation where athletes recovering from injuries describe themselves as performing at 80 percent capacity. How did they arrive at that figure? Why not 75 percent, or 85 percent?

Even if you tentatively agree with me that fractional dimensionality may be a useful tool to help us make sense of things in this age of virtual environments, you may be asking: What does this have to do with librarianship? 

I firmly believe that human interaction with information in virtual environments will become immersive and experiential in ways that are radically different from the ways we currently interact with written and other visual information on printed pages and computer screens. Information experiences in virtual environments are going to take the best aspects of both the “school of hard knocks” (learning from direct experience) and “book learnin’” (vicarious learning) and meld them into some new forms of information experience.

If this happens, the dimensionality of the virtual environment used to create and deliver these information experiences will be a crucial component both for the design and the experience. If we thought it was tough to transform an online catalog or electronic resource display from an 800x600 pixel screen to the small screens of PDAs and cell phones, wait until we try to convert an immersive information experience from a 2.3-dimension virtual world to a 3.3-dimension virtual world. And what happens if we are able to add incrementally to the basic 4.0 dimensionality of real-world height/width/depth/time? If that happens, we’ll all be up, up, and away.