When it comes to representing virtual reality computers can be extremely helpful. But when working with mathematical notations and formulas, either directly or through a Graphical User Interface, it seems strange that we don't assume a more critical role. "Why does it work this way ?" , "What do the do the different elements of code mean ?" . On an emotional level I DO understand because it can be overwhelming to think about or in fact realize, the logic that saturates and often propagates through mathematical systems, and of which we often know little. There are obvious problems when using computer tools for geometric modelling without understanding the underlying implementation.
Architectural designers are focused on the quick fix in my opinion, trying all the time to "push the envelope" without knowing the basics of the different techniques and technology they are using. The use of 3d Graphics inside the establishments for Architectural design is and has been a sad affair. Anyone trying to tell you otherwise would be lying. That said the point of this is to start establishing some connections, between certain phenomena - in nature, in math, in geometry, in Computer Graphics and in Architectural design. Phenomena that are not just effects of the designer trying to imitate life. A good start would be to update your knowledge base if you need to. It sounds time- consuming, and it is.
Anyway, on the Turtle Graphics page I look at the connection between the rotation/transformation/translation - matrices, and the turtle and what it represents and helps to produce. When going through programming code for computer 3d software to modify or repair, I started to ask myself about the deeper meaning of the calculations that were being done, and eventually why it mattered. To cut it short, I have come to believe that in order for intuitive notions on these subjects not being completely arbitrary, you have to train that intuition. Now this is not a wild piece of speculation on my part, but is more or less common sense in other industries with analogous mathematical problems to solve. It's just that designers in general do not use the same process - confirmation in projects that other industries use, because it is all supposed to be "artistic". Of course the best designers, and artists for that matter, do certainly make use of clear- cut mathematical derivation processes, more akin to those found in the production and development industries.
More to follow.....