Right now we hope that this project will give a clearer sense of the classical geometry of Euclid's Elements. In the future we hope that this project will give people a clearer understanding of a more modern networked geometry and its conceptual underpinnings.
In short, it's important to remember where we came from.

It is interesting to notice that The Elements, one of the first sincere efforts at using logic to construct an insular environment, works (for most intents and purposes) as an Object Oriented Programming Language. The postulates and common notions can be understood as classes, and the propositions as these classes' respective instances.
This is a nice metaphor, but it also leaves us less work to do the more we embellish this project. Plus it offers a strong framework for conceptual rigor: in other words, it's good proving ground for programmatic thinking.

It's also interesting to notice that there are relations that exist between the proofs. These can be illustrated with hyperlinks. Each of the propositions rely on previous propositions.
But The Elements is not just about these conceptual structures. It is also about space - both 2 dimensional and 3 dimensional.
So we thought it would be good to do Euclid in a hyperlinked scene description language. VRML, only about a year old as of this writing, has been useful for this.

In addition to this there are some intellectual sideshows of minor interest, each of which is a result of the fact that spacial dimensions in networked digital media differ from their euclidian beginnings. Perhaps this is because of the metaphors we have chosen, or it may be the nature of this new "space" itself.
  1. The rapid-transit "space" of the Internet is non-euclidian.
    The distances of the Internet are measured by the time it takes for a packet to travel from one machine to another, not by the space between the the two computers. In some cases it will take as long for a packet to travel from San Francisco to Los Angeles as it will for travel from San Francisco to Sydney. But we try to translate this "space" into a Euclidian metaphor for ease of understanding. Some dataspace visualisations such as an internet map or internet topology make an intuitive sense since we are able to see similirities and differences between servers.
    And it still makes sense to us to do this - we are able to ignore the non-euclidian elements since we are functioning on a conceptual rather than a spatial level. At least for now. The shortcoming seems to be more in our intuition than in the metaphor.

  2. Several of Euclid's Common Notions evaporate in cyberspace.
    Though all of the definitions, postulates and propositions remain true there are several Common Notions that seem to change. For example: Things that coincide are not necessarily equal, parts can be greater than wholes.
    The reason for this is that the interior dimensions of a space can be greater than its exterior volume. This is a result of several operations that include inlining files, proximity switches, and other procedures that allow space to actually be added into itself. Which introduces another problem of relative space.

  3. As the user moves towards an object is the object getting closer or is it just getting bigger?

There are many questions that still need to be asked. We hope that this small project offers an inroad to the development of geometric spaces, both conceptual and digital (if, in fact, there is a distinction). There are a wide range of similar thoughts that are well worth addressing so that as we continue to build 3D spaces we are acquainted with the issues that go into authored environments.

This project has been an experiment as much as an education. It was done as a collaboration between Construct and the following volunteers:
    Jeth Odom: Project Director
    Josh Draper: Models
    Tim Riley: HTML and CGI Scripts
    Patrick Mahoney: Cheerleader
    Kari Friedman : Production Assistant
    Lisa Goldman: Real World Relations
    Mark Meadows:  Obi-Wan
    Todd Goldenbaum:  Project Manager
One of the uncanny results of this experiment was the formation of dFORM. If there are any parts that you feel need to be added, subtracted or otherwise edited, please let us know.