Contemporary work in IT is based on discrete state computing: logically instantaneous transitions between members of a finite and countable set of states. This is based in turn on a mathematical construct called the Finite State Machine. This model of computation has been wildly successful as a problem-solving mode, and it’s easy to do using increasingly inexpensive digital electronic circuits, so it’s no surprise that it has become dominant. It’s so prevalent that it’s a bit of a stretch for us to think outside of that particular box.
However, it wasn’t always this way. Discrete state computation (with a few cool exceptions such as the abacus and other mechanical calculators) wasn’t practical at all until the switching times of digital electronics became fast enough that they could reasonably approximate “instantaneous”, thus performing a helpful number of computational steps in a sensible span of time. Electronics in the real world were not useful for discrete state computing until the 1940s.
Before digital electronics, there were other computers that worked fine, solving problems quite well, including problems that would be considered hard programming projects today. These were analog computers, which had a radically different approach. They are worth looking at, not least because they model the actions of Complex Systems much more directly than anything we can do in the discrete state world.
Analog computers started out as purely mechanical devices. A slide rule is a fully mechanical analog computer, and a damned powerful one (which in skilled hands outperforms an ordinary keypad calculator for a lot of work, simply because punching all those keys can take longer than a few slipstick/graticule manipulations.) (Of course, you have to know what you’re doing, which is a hellish disadvantage in the minds of some.)
That is the essence of analog computing: there are moving physical parts. Instead of writing abstract logic to a universal logic machine, analog computers use real, physical length and angle to represent the state space of a problem.
When you add electrical machinery such as servos and synchros, you can do all kinds of new things.
Analog electromechanical computers, in their heyday, got quite large and complicated. They could solve dauntingly hard problems in real time: the most famous examples are probably the 20th Century naval gunnery fire control computers, which resolved the dizzying problems of throwing ballistic artillery shells dozens of miles from the guns of a rolling, pitching, maneuvering ship, through sea air of varying humidity and wind, in the direction of a target that was similarly maneuvering (and trying to work out where that target was going to be when the shells actually finished their trajectory.) The fire control computers actually moved the guns and turrets robotically to train them on the computed elevation and azimuth.
If you think about the problem in those terms, it seems kind of amazing that battleships and cruisers ever got sunk at all except by sheer accident; but analog technology was up to the grim task.
A less martial, and much more more charming, use of high-end analog computing was the tide-predicting machine. Not only did it embody something very close to what we today would call a Steampunk aesthetic, it carried out immensely complicated calculations in an elegant way. People relied on such machines up into the 1970s, when the digital revolution finally overturned their economic justification. Beautifully tooled, purpose-built electromechanical artifacts, all wires and gears and scaled pointers, just couldn’t provide the same ROI as software running on general-purpose digital computers.
Analog computers differ from discrete state computers in four main respects:
Hardware. Analog computers express algorithms in hardware, not in software.
Infinitesimal math. Where discrete state logic performs transitions between distinct states, analog computing treats state as an infinitesimally varying quantity. Discrete computing uses integers, and has to emulate the real numbers to any necessary precision; analog computing, by contrast, has no natural concept of integers. In an analog computer, a number is simply a mark engraved on a scale.
To put it another way: analog devices use calculus and trigonometry natively and have to emulate simple algebra by carefully machined markings; discrete state computing, quite the other way, must use numeric methods to emulate anything beyond algebra.
Domain input. An analog computer performs its actions over a continuous independent domain. Traversing that domain is the essential action of an analog device. This domain is sometimes time, as in the real-time resolution of multiple inputs in a fire-control computer; it’s sometimes some kind of master driving input standing in for time’s progress, as with the cranks that moved the early tide machines; and sometimes it’s just the dimensions and position of physical devices in motion - a scale’s linear position in a slide rule, the angular position of a synchro-servo controller, and so on. In no case is this domain discontinuous: instantaneous operations have no place in analog computing.
Holistic operation. Analog devices do not operate as separate parts. This is perhaps the oddest thing, from a digital computing perspective, because our first move, when looking at a programming problem, is to break it into separate subproblems. This doesn’t work in analog computing, which is actually analog’s biggest drawback (aside from the whole hardware-vs-software cost thing.) An analog computer has to be conceived and built as a whole in order to make sense, which is just a lot harder than the piecewise techniques we ordinarily use.
It’s significant that these characteristics of analog computing are also entirely true of Complex Systems.
Now, before anybody gets suspicious, I’d better say that I am emphatically not saying that we should throw out our existing machines and go back to analog computing in order to perform Systems modeling and computation. Digital logic is perfectly capable of emulating analog devices, and perfectly capable of modeling Complex Systems.
What I am saying is that thinking about the nature of analog devices can teach us a great deal about how to think about Systems; and that’s something we need, especially in light of the last 50 years or so of information processing practices. Everything we’ve done in computing for a long time has been oriented, not towards effective consideration of Systems, but towards how best to exploit the prodigious power of discrete state computation.
That tends to leave us a bit behind the curve when we do think about Systems. Given the nature of our world, I suspect we’ll need to find ways of modeling Systems better and better in years to come, and a lot of us will need to study some things that are, at this point, little-known and difficult specializations.
Sunday, July 21, 2013
Saturday, April 27, 2013
Lenses
When I was a little kid, perhaps five or six, my uncle Don gave me a magnifying glass. The handle was wood painted black, and the lens was bound with a flat steel band. It was a secondhand item, somewhat worn and with a few conchoidal fractures around the edge of the lens where the band had apparently transmitted a few hits. I loved it and used it for years growing up.
It was more than just a tool for viewing things up close. It was of course very detective-story in form and function, and I had acquired from somewhere a precocious fascination with detection, both as drama and as tales of intellectual puzzles. That was my initial attraction - here I was, with an accoutrement favored by various of my heroes. It was a numinous object, a connection with fiction and fable, as much as any contemporary kid’s toy light saber. It goes without saying that I understood as little of the realities of detection as a proud lightsaber wielder would understand of the realities of physical combat. Less, probably.
But the more I used it, played with it, contemplated it, the more I found fascination with what lenses do. I tried to magnify objects as much as I could, marveling at textures and grain entirely invisible to my unaided eye. Of course I burned intricate designs on pieces of paper - what child doesn’t? - and was awed to be informed that the tiny burning dot was actually a photographic image of the sun. When the magnifying glass was not closely focused, I could see the shadow cast by the chipped spots on the edge. I could twist the handle so that the light splayed out into fantastic geometrical sweeps. I experimented with focal length, watching magnification blur out into chaos and then suddenly reappear upside down (and reversed right to left as well, although I didn’t grasp that right away) as I moved the lens further from my eye. In my own way, I was getting an introduction to ray optics that was perhaps more emotional than mathematical. That magnifying glass was my hands-on teacher about light, years before I took anything remotely resembling a physics course. A scientifically literate family is a wonderful thing.
Besides its optical magic, the lens afforded me the opportunity to study glass itself, especially as revealed by those chipped places around the rim. When another childish passion, rockhounding, emerged in my life, the lesson of those fracture patterns gave me a boost in understanding mineralogy and geology. Fresh fractures tell secret lessons about the behavior of materials under stress. When I saw conchoidal fractures in obsidian and anthracite, I got it right away. Descriptions of paleolithic flintworking made intuitive geometric sense. And of course, few things are as rewarding to inspect with a trusty magnifying glass as bits of rock. Things that seem drab to the naked eye sometimes, under magnification, become wondrous tiny mazes of intricate crystalline structure. The magnifying glass was not only numinous, it was arcane: a possession serving as a window on previously unrevealed worlds, a magical key to things hidden from ordinary sight.
Later I learned about telescopes and microscopes and prisms, and put things together mentally and physically. When I did get to physics in school I learned to solve equations of refraction and focus. I found it pretty easy stuff, and I give a lot of credit to the magnifying glass that Don gave me.
There was more to it though. That magnifying glass had shaped my imagination much more than I had realized. The Lens, as a concept, remained numinous and arcane. Always stories with observatories and spyglasses held a special power for me. And then, of course, E. E. Smith’s Lensman series came along. Smith’s “Lens” was neither an optical nor a focusing device, getting its name from its lenticular shape; but it made complete talismanic sense to me - I was smitten by the word “Lens” in the title alone when I discovered those in the Public Library in Los Alamos. I was fourteen, I think.
Smith’s work has a lot of cringeworthy elements in it, mostly deriving from the patriarchal norms and excruciatingly dorky slang of mid-20th century American engineering culture. Smith as a writer was more notable for his headlong vigor than for the quality of his prose; he gushed far too much, and far too phallically, about titanic applications of imaginative physics; but without his work we’d never have had Star Wars, Babylon 5, nor Star Trek, let alone the rich body of Space Opera fiction that needs a post of its own. Smith set the stage for all of those, so our star-roaming imaginations owe him an incalculable debt.
Donnella Meadows was a writer of a very different sort. She was the lead author of the 1972 book Limits to Growth, a formal application of Systems Theory to natural, economic, and human activities and resources on the planet. That book, which used early computer models to illustrate the intellectually unremarkable idea that infinite growth is not possible on a finite planet, provoked a very shrill firestorm of scorn and denunciation. As a result, a lot of people still vaguely recollect that “Limits to Growth was debunked”; it never was. (A neat illustration of how the effectiveness of propaganda seems to have an inverse relationship to its factual accuracy.) Limits to Growth’s main premises have proven out. They are unexpectedly, and unpleasantly, close to the actual data curves from 1972 to the present.
As a scientific and imaginative device, lenses were a recurring motif in the back of my mind. So it was happily breathtaking, in the introduction to Donnella Meadows and Diana Wright’s seminal book Thinking in Systems: A Primer, to read this passage:
I do have a lot of lenses that are important to me, and any or all of them are likely to appear in these pages. Systems Theory, semantics, information work both pragmatic and theoretical, human ecology, fantasy and science fiction, history, contemporary civilization, music, handwork, politics, shade-tree philosophy, whatever. I will be resurrecting and sometimes rewriting old content from other places.
One of my pronounced ethical interests is feminism, so it’s pleasant to include, as the other guiding motto here, another female (albeit fictional) voice. Please heed that. Whiny-assed pearl-clutchers will probably want to spend their precious internet time elsewhere. I have some vehement ideas about things, and no compunctions about resorting to NSFW vocabulary.
Picturesque language, after all, is another interesting lens in its own right.
It was more than just a tool for viewing things up close. It was of course very detective-story in form and function, and I had acquired from somewhere a precocious fascination with detection, both as drama and as tales of intellectual puzzles. That was my initial attraction - here I was, with an accoutrement favored by various of my heroes. It was a numinous object, a connection with fiction and fable, as much as any contemporary kid’s toy light saber. It goes without saying that I understood as little of the realities of detection as a proud lightsaber wielder would understand of the realities of physical combat. Less, probably.
But the more I used it, played with it, contemplated it, the more I found fascination with what lenses do. I tried to magnify objects as much as I could, marveling at textures and grain entirely invisible to my unaided eye. Of course I burned intricate designs on pieces of paper - what child doesn’t? - and was awed to be informed that the tiny burning dot was actually a photographic image of the sun. When the magnifying glass was not closely focused, I could see the shadow cast by the chipped spots on the edge. I could twist the handle so that the light splayed out into fantastic geometrical sweeps. I experimented with focal length, watching magnification blur out into chaos and then suddenly reappear upside down (and reversed right to left as well, although I didn’t grasp that right away) as I moved the lens further from my eye. In my own way, I was getting an introduction to ray optics that was perhaps more emotional than mathematical. That magnifying glass was my hands-on teacher about light, years before I took anything remotely resembling a physics course. A scientifically literate family is a wonderful thing.
Besides its optical magic, the lens afforded me the opportunity to study glass itself, especially as revealed by those chipped places around the rim. When another childish passion, rockhounding, emerged in my life, the lesson of those fracture patterns gave me a boost in understanding mineralogy and geology. Fresh fractures tell secret lessons about the behavior of materials under stress. When I saw conchoidal fractures in obsidian and anthracite, I got it right away. Descriptions of paleolithic flintworking made intuitive geometric sense. And of course, few things are as rewarding to inspect with a trusty magnifying glass as bits of rock. Things that seem drab to the naked eye sometimes, under magnification, become wondrous tiny mazes of intricate crystalline structure. The magnifying glass was not only numinous, it was arcane: a possession serving as a window on previously unrevealed worlds, a magical key to things hidden from ordinary sight.
Later I learned about telescopes and microscopes and prisms, and put things together mentally and physically. When I did get to physics in school I learned to solve equations of refraction and focus. I found it pretty easy stuff, and I give a lot of credit to the magnifying glass that Don gave me.
There was more to it though. That magnifying glass had shaped my imagination much more than I had realized. The Lens, as a concept, remained numinous and arcane. Always stories with observatories and spyglasses held a special power for me. And then, of course, E. E. Smith’s Lensman series came along. Smith’s “Lens” was neither an optical nor a focusing device, getting its name from its lenticular shape; but it made complete talismanic sense to me - I was smitten by the word “Lens” in the title alone when I discovered those in the Public Library in Los Alamos. I was fourteen, I think.
Smith’s work has a lot of cringeworthy elements in it, mostly deriving from the patriarchal norms and excruciatingly dorky slang of mid-20th century American engineering culture. Smith as a writer was more notable for his headlong vigor than for the quality of his prose; he gushed far too much, and far too phallically, about titanic applications of imaginative physics; but without his work we’d never have had Star Wars, Babylon 5, nor Star Trek, let alone the rich body of Space Opera fiction that needs a post of its own. Smith set the stage for all of those, so our star-roaming imaginations owe him an incalculable debt.
Donnella Meadows was a writer of a very different sort. She was the lead author of the 1972 book Limits to Growth, a formal application of Systems Theory to natural, economic, and human activities and resources on the planet. That book, which used early computer models to illustrate the intellectually unremarkable idea that infinite growth is not possible on a finite planet, provoked a very shrill firestorm of scorn and denunciation. As a result, a lot of people still vaguely recollect that “Limits to Growth was debunked”; it never was. (A neat illustration of how the effectiveness of propaganda seems to have an inverse relationship to its factual accuracy.) Limits to Growth’s main premises have proven out. They are unexpectedly, and unpleasantly, close to the actual data curves from 1972 to the present.
As a scientific and imaginative device, lenses were a recurring motif in the back of my mind. So it was happily breathtaking, in the introduction to Donnella Meadows and Diana Wright’s seminal book Thinking in Systems: A Primer, to read this passage:
You can see some things through the lens of the human eye, other things through the lens of a microscope, others through the lens of a telescope, and still others through the lens of systems theory. Everything seen through each kind of lens is actually there. Each way of seeing allows our knowledge of the wondrous world in which we live to become a little more complete.This book is intensely important in many ways - a commonsense, nontechnical, accessible exposition of the basics of Systems Theory - but it was the unexpected emotional impact of that simple metaphor, weaving together as it did a lot of threads from the slow development of my thought over a lifetime, that stayed with me. So much so that I excerpted a bit of it as one of the guiding mottoes of this blog.
I do have a lot of lenses that are important to me, and any or all of them are likely to appear in these pages. Systems Theory, semantics, information work both pragmatic and theoretical, human ecology, fantasy and science fiction, history, contemporary civilization, music, handwork, politics, shade-tree philosophy, whatever. I will be resurrecting and sometimes rewriting old content from other places.
One of my pronounced ethical interests is feminism, so it’s pleasant to include, as the other guiding motto here, another female (albeit fictional) voice. Please heed that. Whiny-assed pearl-clutchers will probably want to spend their precious internet time elsewhere. I have some vehement ideas about things, and no compunctions about resorting to NSFW vocabulary.
Picturesque language, after all, is another interesting lens in its own right.
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