A few nights ago I met a young man who teaches glass blowing workshops at an arts centre. I asked him if he has ever made a Klein Bottle. He admitted that he hadn’t heard of the thing, and then googled it. His answer to me was that it would undoubtedly require what is referred to in the industry as a “scientific lathe.”
I looked into the technique today and found that the only way that people seem to be capable of making the Klein Bottle, using the “scientific lathe,” is to produce it in parts. The process begins with a sealed tube, and then two pieces are inserted inside of that tube (which constitute the pieces which will later be joined to produce the ‘extimate’ surface), and worked with in that way. The process is outlined in the following website: http://www.kleinbottle.com/making_a_klein_bottle.html
This is curious. If, at one time, it was thought that a Borromean Knot could only be produced by taking three pieces of string (or more) and tying them together, or, in a strange way, of taking a single piece of string and producing a trefoil knot, then, in recent years, a simple technique was invented by sculpture artists which demonstrates that a single torus may be split from within to produce the Borromean surface. More on this can be found here: http://graphics.berkeley.edu/papers/Sequin-STK-2005-07/Sequin-STK-2005-07.pdf
In the latter case, I have extended the Lacanian concept of “splitting” or “split subject” and rejected any discussion of the “barred subject.” In the age of the sinthome, of ordinary psychosis, etc, all that makes sense is “splitting” of subjectivity.
I am seeking any information on alternative processes to make a Klein Bottle which does not consist of piecing it together in the way outlined above. If you have such information, please share it with me.