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.
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The rapid-transit "space" of the Internet is non-euclidian.
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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.
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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.
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Several of Euclid's Common Notions evaporate in cyberspace.
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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.
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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.
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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.