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This is a dictionary, or word-book. It is also a reccomendation on a new vocabulary for the higher dimensional geometries. Some comment is in order into the processing and formation of words.

Writing a Dictionary

Depending on one's fluency in the subject matter, one can sit down and write a fairly large glossary off the top of one's head. This is how the polygloss started life: one boxing-day, i sat down and churned out a sizable document of pages.

On reviewing of this glossing-fury, one sits down and looks through the work and say, 'this is missing' or 'that is missing'. Depending on the media, one may add the missing bits.

Eventually, it gets rather large and somewhat needing of reorganisation. By the time one gets around to it, it has become both large and useful. So it's not pretty much a case of tossing out the whole work.

The process takes years. This is much longer than the lifetime of many programs, and one starts to look for stable, long-term document forms. There are parts of the metegloss written in MultiMate III. None the same, the pages represent many hours of work, and they were largely reimported into ASCII web-pages.

Much attention has to be given to portability and local ease of use. KML was defined and written, largely as a way of creating a richer markup language, and extensible to boot. The reason for this, is that one can create special meanings for the markup, and then have the markup represent this how it should.

For example, we have a markup for a word-stem {stem word} gives [word]. This appears however the current implementation of {stem } base is. So if i decide to change how stems appear, it's pretty much a change of program for what stem is associated with.


Much of the work was done with an overloaded vocabulary on deep context. So one could talk about a 4D octahedron, or a octahedral product or a wide range of other things.

While such uses might be alright for a single user, it becomes rather hard to suggest this to the casual reader. So when i started to talk to other people in the field, i needed to invent a huge vocabulary. The polygloss holds some of it.

A dictionary is more like a butter-fly collection. One collects large numbers of words, and pins them to the pages. A vocabulary is a dynamic thing, readily changing, and having means to make words. We can partly show this by defining stems.

Take for example, horopetix. This is not a glossed word, but its meaning is understood from its two stems [horo-] zero-curvature + [petix] five-dimensional manifold. So what we have is a particular word describing the space E5 (5D euclidean geometry).

We can't rely on our experience

The existing vocabulary contains words that have multiple submeanings. When we try to take these meanings into higher dimensions, the diverse meanings are differently satisfied.

A line both unites, eg bus-line, railway line, and divides, eg dead-line, line in the sand, front line. In four dimensions, a line can only unite. We can readily wend our way around a road in 4D, because a road does not divide space.

Many words divide meanings, and so it is best to define stems with a specific meaning, and use it strictly like that.

The Multidimensional Glossary

George Olshevsky has a Glossary on his site. This glossary is a fairly accurate reflection of the terminology one finds in the more recent mathematical works, with a few extra words tossed in.

The work extends to a good deal of Jonathan Bower's work, which is on his hedrondude site. Jonathan did a lot of work enumerating the starry archimedean polychora. In a work like this, the mathematical names are extremely clumbsy, and a good deal of shortening of names, and inventing of concepts have gone on.

George and Jonathan worked on the extended vocabulary, which has been included in George's dictionary.

Their paritcular work is quite well executed, and full of cross-links to other pages. It's a fairly large site, not suited to dialup access, (which is why i made a local cache of it!). But whatever the eloquence and professionalism of describing a vocabulary-tarpit, does not make the tar-pit any more graceful.

The implementation of the current terminology in the mathematics, is a tar pit where words become stuck. One needs consider the series on the hyper- prefix, and how it got stuck in four dimensions, and looks rather silly when referred to in six dimensions! Four dimensions has no other name, so it got stuck there!

Multimate III: In the dim dark days of pre-windows computing, dear old Muttly was rated in the magazines as the last of the 29 available DOS word-processors. It was widely used in the real estate industry, and in the Government, probably because of this reason!
      None the same, importing MM documents into something else, like AmiPro, or WhingeWart, were none the less a frightning experience.

© 2003-2009 Wendy Krieger