It's easy to end up focusing all your design resources on making VRML-space easy for humans to use. (This is not to say it's easy to succeed there.)

But who is cyberspace for anyhow? If you count the number of visitors and viewers of VRML worlds over the next year, I expect we will see the number of visits from robots exceed the number of visits from humans.

In cyberspace, who takes out the garbage? Bots. What are bots? They are sources of action not driven by humans. Can you imagine worlds personalized for humans? Then how about worlds that are personalized for bots?

Already, HTML pages have bots visiting them on a regular basis. For instance, indexing robots from search sites such as Altavista regularly visit pages. In addition, other robots visit sites for users at times. For instance, when you submit a VRML URL to BOOM!, the Aereal server goes to your URL to look at the world and make sure that the URL is there and that your server transmits a VRML MIME type header when your HTTP it delivers the file. In addition, proxy servers on Intranets are sort of like bots (loosely speaking).

It all becomes very neat when bots are able to replicate. I'd like to create the first self-replicating, multi-level marketing robots. Would you like some vitamins, water-filters, air purifiers and prepaid internet service cards with your pass to Krustyland?

Is Cyberspace-time curved?
The Cartesian coordinate system we are using for VRML has its limits. It's ok for local space -- the space closest around you. However, if you can travel millions of miles in VRMLspace, and change your scale from a human to a pea to a microbe, the coordinate system doesn't work well. You run out of digits and life gets screwey.

Physicists spend a lot of time thinking about curvature of space and time... will they start talking about cyberspace? An interesting starting point would be a metric to determine the distance between any two points in cyberspace. In the Cyberspace Protocol that Pesce, Kennard and Parisi dreamed up way back when, there was a coordinate assigned to various objects and objects were referenced by the coordinate rather than by URLs.

However, in VRML we have two coordinate systems going on -- URLSpace and VRMLSpace. URLSpace is the set of all valid URLs. VRMLSpace is the set of all points in all VRML coordinate systems. A point in VRMLSpace must be referenced by both its URL and its local VRML coordinate.

One possible way to create a distance mechanism would be to use complex numbers, numbers which have a "real" part and an "imaginary" part. The definition would be quite difficult, and the distances between places could change very easily, merely by the addition of a hyperlink or an inlining.

What are some of the properties we'd want the distance in cyberspace to have? We'd want to have it reflexive, commutative and also triangular. It should also be non-negative. The distance from one point to itself should be 0. The distance between points A and B should be equal to the distance between points B and A. Also the distance between points A and B should be less than or equal to the distance between A and a third point C plus the distance between C and B.

One way to start could be to do something as follows:

The distance between two points A and B in cyberspace is the minimum of the number of hyperlinks between the worlds containing A and B expressed as the real part of the complex number, and the sum of the Euclidean distances between A and B and their world centers expressed as the imaginary part of the complex number.

This is just an initial thought and there are some severe flaws in it, but it's something we should start thinking about. Dynamically-generated URLs and VRML 2.0-movements add complexity too.

So that's a little bit about defining distances in Cyberspace. The next step would be to define a metric for the volume of matter. Another step would be to define what an open set in cyberspace is, thus giving us a topology for cyberspace.

Adrian Scott
adrian@aereal.com
Publisher