Linearity (or whatever it is)
This page is about a property of systems that is important to scientists and engineers, most of whom will immediately recognize the term ‘linearity’ and agree that it is very important. I have spent years trying to explain that importance to non-technical people, but without much luck.
In the process, I have taken some liberties, and I am guilty of trying to extend this term in ways that technical people may not approve of. Strictly speaking one is not supposed to talk about linearity without reference to the underlying field, (e.g. the field of real numbers under ordinary addition and multiplication), but engineers may recognize that it is quite possible to get a strong impression that you are dealing with a linear system long before the underlying field is defined. I think this is legitimate and strongly believe that there is some such property that can be identified without reference to the underlying field.
Over the years I’ve played with several alternative terms, such as pseudo-invertibility, or structure-preserving, but nothing I’ve tried quite satisfies me, so for the moment I’ll stick with linearity.
It seems that linearity is not an absolute, all-or-none property, and there can be quite a sharp threshold separating linear and non-linear behaviour. For systems with feedback there can be a distinct threshold beyond which non-linearity and feedback combine to create chaotic behaviour. When we know that a system includes lots of feedback but do not detect chaotic behaviour we can infer that the system is almost linear.
The idea of such threshold behaviour reminds me of the threshold for neutron multiplication in a nuclear reactor. In the early days of nuclear physics an important issue was the amount of neutron multiplication in fissionable elements like uranium. An encounter with a slow neutron will induce a uranium nucleus to split, and a by-product of that fission is some number of neutrons. If each fission produces one neutron on average, no chain reaction happens, because a few neutrons are lost. If each fission produces 2 or 3 neutrons the result can be explosive, so the neutron multiplication factor is the critical difference between an amusing experiment and a deadly weapon. Various arrangements of control rods and moderators can determine how many neutrons are lost and how many reach the speed at which they are easily absorbed.
As people have often talked about, society is a network — but is this just an amusing thing to joke about, as in the 6-degrees-of-Kevin-Bacon game, or does it mean something important?
I see an idea multiplication factor or conversation multiplication factor as critical. If you have a close friend full of ideas and you are foolish enough to discuss those ideas with other people, then there is some chance that ideas will flow from person to person in a sort of chain reaction, but it all depends in a complex way on the compatibilities of individual people, their proximity in time and space, and many other factors, some of which we can vary at will, but most of which depend on our ability to find compatible people to talk to.
By ideas, read not only the real inspirations, but also the political views, the amount of pleasure or displeasure with our surroundings, and all the rest of it. For me a real democracy is not just a society in which you have a vote, but one in which every idea you have floats around the net and eventually tickles the ears of people who can change things.
I say that the connectivity and compatibility of people — the way they are tied into the net — is very much more important than people think, if they think of it at all. Intellectual history is less a history of ideas, as such, than it is a history of some part of the social network; who passed what ideas to whom is mostly what intellectual history is about, not the ideas themselves.
There is a model of the world in which the social connections are the whole of it, not just the most significant part. I mean of course the neural network model or analogy, human society as a neural network, human beings as neurons — because in a neural network it is the actual synaptic connections that matter, and learning is growing the right connections.
I resist this model very strongly even though it would be one in which my emphasis on social connections would be obviously right — if growing the right connections is all there is to it, then we should use whatever works to do just that. This comes down to a very fine point, which I place somewhere between James Mill and his son John Stuart — between the pure and simple association of ideas, (one might say the free association of ideas had, that term come to mean something else), and J.S. Mill’s “mental chemistry” in which the whole can be more than the some of its parts (or at very least not equal to the sum of its parts) — between, in other words, the free association of free men and the Leviathan.
The question is whether the association of ideas is just a mixture, like the mixture one might make of powdered sulphur and zinc filings, a very explosive mixture that used to be used in toy rockets, or is more like the result of some chemical reaction, like the zinc sulphide used as in popular skin creams for medicinal purposes. But the notion that the whole can be much more than the sum of it’s parts is almost a textbook definition of non-linearity.
The attraction of the atomic nucleus for the electrons is a nonlinear one, obeying a square law, like gravity, and all that happens when you light the fuse to the zinc/sulphur rocket is a result of that fact.
So I find myself at a very fine point, a narrow piece of territory in which I can on the one hand sense the importance of social connections and on the other hand hope that we are basically linear, so whatever chain reaction might occur in a well-connected net is not just an explosion.
To me, network effects can be non-linear and there can be a Leviathan which can do incredible harm. Did you know that during the Bosnian civil war (I mean the most recent one!) the Serbs fired incendiary shells into the Bosnian National Library, causing its almost total destruction?
I think a network of people can resemble an organism, and I know many people feel that such an organism must be “greater” than the beings which compose it, but I don’t agree with that.
To me the composite or hive organism is an organism subject to Brooks’ law. Just as adding more programmers to a late project makes it later because of communications problems, I believe a hive-organism is not necessarily a better or more worthy organism. I think the three competing organisms, Serb, Croatian, and Muslim, having a few hundred thousand people each, behaved a lot like a organisms like salamanders which have a few hundred thousand neurons each.
If you look at the things which turned a society of reasonably peaceful Yugoslavians back into the warring hordes of past ages, almost all of them are tools of cultural dissemination, including that library, but more importantly the radio and television and newspapers which artificially propagated quite ancient and erroneous ideas. As much as I like such media myself, I can see they have a non-linear effect, that is to say, the result of one bigot sitting in front of a microphone is blown out of all proportion. The idea that effects must in some way be proportional to causes is another textbook definition of linearity.
What I’m trying to get through to here is something about machines, related to George Dyson’s views, and the views of any of the other people who have talked about the separate evolution of machines — a key idea in several books by Asimov, Brunner, and Simak, to name just a few recent people. I don’t know about the future evolution of machines, but I suspect they may be up against the same problem we have faced, in which nonlinearity is not helpful, perhaps is just the opposite.
I know that individual human beings unaided by vacuum tubes or transistors are reasonably linear because I see feedback everywhere I look, but I don’t see chaos. People are constantly getting feedback from friends, spouses, teachers, students, co-workers, and so on. But feedback plus nonlinearity equals chaos, quite literally. To generate the Mandelbrot set you use the simplest non-linear equation and apply feedback, looking for convergence or divergence. But any non-linear equation will do, and perform similarly. Only linear equations are different.
Linear equations are equations of the first degree and so by the fundamental equation of algebra have one solutions — equations of the second degree (quadratic equations) have two apiece, third degree (cubic equations) three apiece and so on. But if you apply feedback even equations of the second degree with only two solutions quickly become chaotic because at each act of feeding back the output to the input the number of possible solutions is multiplied by itself. So equations of any degree other than the first, with enough feedback, have infinitely many solutions.
I see linearity as an evolutionary choice, which social organisms have taken — the essence of linearity is the ability to guess at the inputs given the outputs, even in the presence of feedback (perhaps especially in the presence of feedback). It is just the opposite to determinism, which is means the output is more or less determined by the input. The ability to guess the input from the output is — at its best — what I described on another page , the ability to deconvolve the distortions of personality, something that can only happen with linear systems. So we have to be more or less linear to be able to function as social organisms, and I suspect machines will have to become more and more linear as well, with all the consequences of it.
See philosophical thoughts on recursion for more musings along these lines, if you can take any more of this!
Copyright © 1998 Douglas P. Wilson
Copyright © 2009 Douglas Pardoe Wilson
Other relevant content:
Please see these web pages:
The main Social Technology page.
Find Compatibles , the key page, with the real solution to all other problems explained
Technological Fantasies , a page about future technology
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 :
Social Technology the main blog, hosted on this site, with posts imported from the following blogger.com blogs, which still exist and are useable.
Find Compatibles 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.
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 Find Compatibles , 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.
Copyright © 2009 Douglas Pardoe Wilson