William Gibson’s Idoru and Felix Klein’s Erlangen Program
William Gibson is famous for the word cyberspace which he may have invented but certainly popularized, in his early science fiction novels Neuromancer, Count Zero, and Mona Lisa Overdrive . Apparently Gibson knew little about computers or networking at the time he wrote Neuromancer , but he got the single word ‘cyberspace’ right, at least. This one interesting case is not the only example of a word or expression he may have gotten right through clever ignorance. In the later novel Idoru he uses the phrase nodal points in many places, giving its meaning in the excellent prose for which Gibson is also justly famous, and again he seems to have gotten something very right, probably without much background knowledge to draw on.
This web page attempts to explain the relationship between nodal points in William Gibson’s novels, the ordinary mathematical use of this expression, and related mathematical concepts. Although the mathematics discussed here is quite real and should interest real mathematicians, there is no use of strange symbols or mathematical expressions in formal languages. Only plain English is used, and this page should be comprehensible to anyone who can read Gibson’s novels, though the title will scare off most non-technical readers.
‘Nodal Point’ is a well known mathematical expression, but the shorter term node is often used instead, even though nodes may be lines, planes, or even hyperplanes, the higher dimensional analogue of ordinary two-dimensional planes. There is nothing to be gained by restricting this discussion to nodal points so the broader term ‘node’ will be used here except when quoting Gibson’s text.
The most familiar use of the word ‘node’ is in music. A violinist or guitarist can produce a musical note of remarkable tone quality by gentling touching a string at a point which is one half or one third of the sounding length of the string. A nice image file of some musician doing this should be placed somewhere near the top of this page — can anyone contribute one? A diagram from a physics text will be inserted here soon, but it would still be nice to have an attractive photo.
Musical notes produced by touching strings at nodes are often called harmonics and our understanding of them goes back to Pythagoras. The ancient Greek analysis of the vibrating string that is associated with the school of Pythagoras is one of the high points of ancient science and is still the foundation of western musical theory. Pythagoras seems to have known that the distinctive harmonic notes are actually parts of the ordinary notes produced by bowing or plucking the string without touching the nodal points. We now know that touching the string at these nodes simply suppresses parts of the tone which have a significant amount of vibratory motion at those points — what we hear is what is left unsuppressed, the sounds produced by vibrations of the rest of the string which do not include a significant amount of vibratory motion at the nodes. (There is obviously some motion at the nodes, but it is more of an oscillating rotation than a vibration).
In a physics laboratory, using strings that are stretched only to very low tensions, usually driven by loudspeaker-like drivers at exact pitches, it is quite easy to see as well as hear the vibrations of the string. A nice image of this should be inserted here, or at least another diagram from a physics textbook — but you may have to settle for a hyperlink. By looking at such a string it is possible to see the absence of vibration at the nodes when the string is vibrating under the influence of some sounds produced by the driver. If the driver is producing an ordinary string-instrument-like sound all parts of the string will vibrate, but impressed sounds in which some components have been suppressed (or were just not generated at all) will cause the string to vibrate everywhere except at the nodes, and this will be visible.
The nodal points of a vibrating string are located in well-known and obvious places: the most important and commonly used one is the node halfway along the string, which is the node for “even-numbered harmonic partials”, that is to say, for parts of the tone at one or more octaves about the fundamental pitch. Unless you are specially trained to do so, it is not easy to tell by listening to a sound whether it contains even-numbered harmonics or not. The sound of a clarinet in the low or chalemeau register contains the fundamental tone and odd-numbered harmonics but only tiny traces of the even-numbered harmonics. By driving a suitably mounted and tuned string with the sounds from a clarinet, it is possible to see the lack of motion at the nodes and thereby detect the abscence of even-numbered harmonic that only experts can detect by ear alone.
… very unfinished.
Related Web Pages are:
The main Social Technology page.
FindCompatibles , the key page, with the real solution to all other problems explained
Technological Fantasies , a page about future technology
Practical Immortality , not the immortality of the body, nor making a copy of the mind in a machine, but actual transfer of a person, personality, memory and consciousness into a supercomputer
Social Tech a page about Social Technology, technology for social purposes. I think I was the first person to use this phrase on the Internet, quite a long time ago.
Roughly corresponding to these web pages are the following blogs :
FindCompatibles devoted to matching people with friends, lovers, jobs, places to live and so on, but doing so in ways that will actually work, using good math, good algorithms, good analysis.
Technological Fantasies devoted to future stuff, new ideas, things that might be invented or might happen, such as what is listed above and below.
Practical Immortality yes, practical immortality. Don’t write this off as insanity, please. See the first entry in the blog first.
Sex-Politics-Religion is a blog about these important topics, which I have been told should never be mentioned in polite conversation. Alright that advice does seem a bit dated, but many people are still told not to bring up these subjects around the dinner table.
I believe I was the first person on the Internet to use the phrase Social Technology — years before the Web existed.
Those were the good old days, when the number of people using the net exceeed the amount of content on it, so that it was easy to start a discussion about such an upopular topic. Now things are different. There are so many web pages that the chances of anyone finding this page are low, even with good search engines like Google. Oh, well.
By Social Technology I mean the technology for organizing and maintaining human society. The example I had most firmly in mind is the subject of FindCompatibles , what I consider to be the key page, the one with the real solution to all other problems explained.
As I explained on my early mailing lists and later webpages, I find that social technology has hardly improved at all over the years. We still use representative democracy, exactly the same as it was used in the 18th century. By contrast, horse and buggy transporation has been replaced by automobiles and airplanes, enormous changes.
In the picture below you will see some 18th century technology, such as the ox-plow in the middle of the picture. How things have changed since then in agricultural technology. But we still use chance encounters, engagements and marriages to organize our home life and the raising of children.
I claim that great advances in social technology are not only possible but inevitable. I have written three novels about this, one preposterously long, 5000 pages, another merely very very long, 1500 pages. The third is short enough at 340 pages to be published some day. Maybe. The topic is still not interesting to most people. I will excerpt small parts of these novels on the web sometime, maybe even post the raw text for the larger two.
This site includes many pages dating from 1997 to 2008 which are quite out of date. They are included here partly to show the development of these ideas and partly to cover things the newer pages do not. There will be broken links where these pages referenced external sites. I’ve tried to fix up or maiintain all internal links, but some will probably have been missed. One may wish to look at an earlier version of this page , rather longer, and at an overview of most parts of what can be called a bigger project.
Type in this address to e-mail me. The image is interesting. See Status of Social Technology
Copyright © 2007, 2008, 2009, Douglas Pardoe Wilson
I have used a series of e-mail address over the years, each of which eventually became out of date because of a change of Internet services or became almost useless because of spam. Eventually I stuck with a Yahoo address, but my inbox still fills up with spam and their spam filter still removes messages I wanted to see. So I have switched to a new e-mail service. Web spiders should not be able to find it, since it is hidden in a jpeg picture. I have also made it difficult to reach me. The picture is not a clickable link. To send me e-mail you must want to do so badly enough to type this address in. That is a nuisance, for which I do apologize, but I just don’t want a lot of mail from people who do not care about what I have to say.