being a story submitted for the Space Bats contest sponsored by The Archdruid Report
[Note: this post was the official submission in a last-minute screaming drive for a deadline. As such, it was left unmodified until the contest was concluded. I was delighted when the story was selected for inclusion in After Oil 3: The years of Rebirth, which is now in print from Founders House Press. However, the "live" development version of the story was moved to https://github.com/whblondeau/memoria-interna/blob/master/stories/the-borax-road-affair/the-borax-road-affair.md. ]
'Everything seen through each kind of lens is actually there.' -Donnella Meadows 'Now this is not gonna be pretty. We're talking violence, strong language, adult content...' -Buffy Summers
Wednesday, April 30, 2014
Friday, January 10, 2014
Complex Systems: Feedback is Hard
This is a continuation of the series begun in A Motorcycle Tour Through the Museum. The convention of capitalizing terms of art that may have different meanings in other contexts (e.g., “System”, “Complexity”) remains in force.
The purpose of this article is an extension of the Motorcycle Tour: not to formally educate, but to provide reasonably accessible first-cut explanations of some aspects of Systems Theory. Accordingly, some of the terminology introduced here is nonstandard: adapted, or coined outright, for clarity and expressive convenience.
We’re not good at thinking in Systems. Some of this is, I suspect, a hard-wired predisposition in our neuroanatomy. However, humans are a fairly mentally flexible bunch. We can certainly learn to think in Systems; or at least I hope so. At least, better than we do now. (That hope is, after all, part of the reason for this series of articles.) And then, a lot of our ineptitude in Systems thinking is not a biological limit at all. Some of our inability is pretty clearly cultural. This we should be able to do something about.
What makes Complex Systems so alien to our normal habits of thought?
Answering that question has to start with a look at any System’s most fundamental attribute: Feedback.
Definition of Feedback
Feedback is the principle that any perturbing action can propagate through a System and find its way back to affect the initiator of that action… in such a way as to provoke, or modify, the very action that started the chain. In real life we say, “What goes around comes around” and it makes all the sense in the world. But real life is, of course, a Complex System. When that which goes around does, in fact, come around, we have observed a Feedback loop in action.
Feedback Loops: the basic mechanism
The simplest kind of Feedback loop is a dyad, one acting between two components. There are two interactions between them: one originating with the first component and sending a Signal or Flow to the second; and the other interaction doing the same kind of thing, but going back the other way, from the second to the first.
The simple and immediate question that most of us try to answer is, “Does the green action from A to B cause the blue, or does the blue action from B to A cause the green?” For a Feedback loop, the answer must, of course, be “Both”: if they have no mutual causal relationship, it’s not a Feedback loop in the first place.
The second question that often occurs to us is, “Which action happens first, and which action happens second?” The general answer here is, “Ordinarily, but not always, both at the same time”.
These two questions, and their answers, illustrate a key concept of Systems thinking: you can’t reason about these interactions in isolation or you’ll miss the point completely. You have to hold that mutual effect, and that concurrency, in mind.
A third, and somewhat more advanced, question would probably be, “Are they the same—is this a symmetrical interaction?” And to that the answer is, “Well, sometimes… but ordinarily not. In the general case, these are not necessarily the same kind of interaction, they don’t transfer information or other content at the same speed, and there’s no requirement that components A and B are much alike in the first place.”
How we think about these things
I’ve framed the above questions as being sort of naive, but they’re really not. They are basic and solid. They make complete sense when considered from the frame of reference of our particular culture’s modes of reason.
Questions like this are the result of a linear intellectual bias: our basic tendency to try to isolate causes and effects in order to investigate patterns and phenomena. Culturally, we’ve been on this path since the time of the Hellenic philosophers, who were the first to deliberately develop fully abstract forms of thought. (Earlier traditions, such as the Babylonian, Egyptian, and Chinese philosophers, chiefly focused on more pragmatic concerns: ethics, theology, spirituality, politics, divination, music, mathematics, and so on.) We owe the Classical Greeks much: we have gained great advantages from the rigorous forms of thought they pioneered.
- We learned to hold all significant aspects of a problem constant except one, and correlate changes to that variable condition with variations in the observed outcome. This is the basis of experimental science.
- We learned to classify things into meaningful categories: the essence of analysis. Analysis is the precondition of both inductive and deductive reasoning, and the founding premise of the descriptive sciences.
- We learned to subdivide problems into tractable parts. Parts often inhabiting entirely different disciplines. Composition of discrete solutions is the basic activity of engineering and technology.
So, linear reasoning clearly kicks ass, and we wouldn’t want it any other way. We’re not to be blamed for this glorious tradition of intellectual adventure and pragmatic benefit. However, it has left us awkwardly disadvantaged when it comes to Systems thinking, because:
- Systems resist selective stasis, so holding a single variable to a constant value tends to distort System behaviors, yielding false results;
- Analysis simply doesn’t scale well to the skyrocketing numbers of diverse interactions in a Complex System;
- Isolating a subsystem from a larger System will unavoidably change the subsystem’s behavior. Compartmentalization of cause and effect doesn’t tell us much about a System’s actual nature.
These are very real problems. They undercut our civilization’s most powerful problemsolving techniques. Feedback lies at the root of these incompatibilities; so, let’s unpack, if only briefly and only a bit, Feedback.
What are these interactions that are feeding back?
Feedback is a pattern of interaction between components of a System. Interactions can be treated as two kinds of thing: Signals and Flows. (These are not really different in kind, but the practical difference in their behavior, from the standpoint of any given model, is large enough to treat them as completely different things.)
Signals
A Signal is narrowly defined: an interaction that takes place in such a short span of time that it can be treated as effectively instantaneous. In other words, rather than being a process acting over time, it occurs in the model as an event having a timestamp but no meaningful duration. Its impact is to modify component behavior.
“Signal”, when you get right down to it, is merely a practical simplification: a statement that our model is ignoring any propagation or processing time associated with a particular interaction.
Stocks and Flows
A Flow is the more common and substantial interaction between components of a System. Rather than just a single item of information, it is an event of transference of some common quantitative property, or Stock, that is held by both parties to the interaction. Flows are understood as time-domain functions, infinitesimal in nature, subject to the familiar methods of differential and integral calculus. A Flow is a transfer of quantity, from one component to the other, over time.
Stocks are, generally speaking, conserved within a System. The special kinds of components in which a Stock enters or leaves the System—components, in other words, in which a Stock is created or destroyed—are called Sources and Sinks respectively. Sourcing and Sinking are, like Flows between components, time-domain functions.
For instance: a Feedback loop involving Flows and Signals
An example is probably good here. Let’s look at a fairly simplistic mechanism: a dam controlling flow volume for water management purposes.
Water flow through the dam’s spillway is modulated by a floodgate, which is under the direct control of some kind of observer: a human engineer, say, or perhaps an automated controller. Let’s posit that the floodgate is hydraulically powered, and the hydraulic rams are operated by a computer linked over the Internet. This simple system also has water level gauges which report upstream and downstream levels to the observer in real time.
So, rain falls (or doesn’t fall) upstream, and the controlling observer adjusts the floodgates according to water use policies: trying to sustain reservoir levels during dry times, trying to prevent disastrous flood crests during prolonged rainstorms, and so on.
The Feedback loop in the System is this:
The solid blue line is the downstream flow over the dam; the dotted lines are information about upstream and downstream water levels, going to the Observer; the dashed line is a control Signal from the Observer to the floodgate that throttles the downstream flow. It forms a loop, each element affecting the next:
water flow → water levels → observer response → floodgate position → water flow...
The point here is that, in our model, the observations, and the actuation of the floodgate, can be considered instantaneous, but the flow of water cannot. Water is a Stock; its transfer is a Flow, which has to be modeled over time. Level measurements and floodgate actuation, by contrast, are Signals, that in the context of our water flow model take no time at all.
So, why then does Feedback subvert our normal habits of thought?
Feedback, considered as a basic mechanism, is simple enough to describe. At the same time, it’s oddly slippery and hard to think about. The examples above (dyad abstract loop, and controlled dam floodgate) both pose the same difficulty for us. We have a tough time wrapping our heads around things happening mutually, over time, and concurrently.
We have learned not to think in terms of simultaneous, mutually affecting activities, because it’s so damned rewarding to go the other way, pursuing classical modes of analytical thought.
However, when Feedback enters the picture, we have to start reasoning about it in a way that does not exploit our familiar conceptual tools very well. We’ve historically treated Feedback as a special case, sort of like zero in arithmetic before the Indian mathematicians calmly unified it with the positive and negative numbers.
That’s only the beginning, though: it’s when we get to the point of considering Feedback from the point of view of the whole System—when we look at lots of those basic mechanisms, interconnected—that Feedback really blossoms into a much more formidable thing, which we call Complexity.
Friday, December 6, 2013
Complex Systems: A Motorcycle Tour Through the Museum
This is the first of a series of posts adapted from an article originally published on Kurt Cagle's XML Today blog.
In the articles I write, some key piece of reasoning usually depends on the properties and behavior of Complex Systems.
Partly it’s me (I find Systems Theory increasingly indispensable as an investigative, analytic, and descriptive model); but partly it’s that we live in a changing world. Systems are looming larger in human affairs.
In fact, it all seems to be coming together in a spectacular crunch, and that’s not coincidental: this global trend is driven by the increasing interconnection and scale of human activity. Systems behavior can, and does, occur in very simple contexts, but its occurrence increases nonlinearly as things get more numerous and interconnected. Bottom line: It’s getting harder and harder to ignore, or defer responding to, Systems-driven global phenomena that have real near-term consequences.
Which sucks, all things considered, because we’re just no damn good at Systems. Thinking in systems is not something that our species does well.
More than that, though, our contemporary culture is especially bad at it. Really, and c’mon: we’ve mostly been taught to think in Systems as little as possible. It's understandable: analytical, reductionist, linear thinking was much more profitable and effective during most of the thousands of years in which our primary intellectual traditions developed.
More than that, though, our contemporary culture is especially bad at it. Really, and c’mon: we’ve mostly been taught to think in Systems as little as possible. It's understandable: analytical, reductionist, linear thinking was much more profitable and effective during most of the thousands of years in which our primary intellectual traditions developed.
Problem is, we've changed the world. Now we really need to get a lot better at Systems thinking, fairly quickly—a hard thing to ask of people who’ve been trained against it. But if we can’t manage it, we’re facing worse times.
A Physics professor of mine once used the phrase “motorcycle tour through a museum” as a rueful lament about how small a glimpse, of how vast a subject, undergraduate Physics courses could actually provide. I’ve stolen this from him, and I hope he’d approve.
In that spirit, here’s a basic overview of the general nature, shape, and implications of Complex Systems. Don’t expect theoretical precision. I’ll just try to make things conceptually accessible at a pretty high level.
Now you probably know enough to decide whether to read further. If you do, grab your boots, jacket, do-rag, assless chaps, mirrorshades, whatever you think you need for the road; and let’s roll.
A note on terminology
The words “Complex” and “System” have specific technical meanings in the field of Systems Theory. They also, however, have different meanings in everyday speech. Complex and complicated mean the same thing in casual conversation; the Dewey Decimal System is certainly “systematic” in the way most people understand the word, but it’s got nothing to do with Systems Theory.
In order to emphasize the distinction, I am capitalizing the formal terms and any derived forms (e.g. “Complexity”) in this series of articles.
In order to emphasize the distinction, I am capitalizing the formal terms and any derived forms (e.g. “Complexity”) in this series of articles.
What's Complexity, eh Precious?
Any discussion of Complexity runs into the fish-can't-describe-water problem. Complexity is such a pervasive part of, well, everything, that it's hard to stand aside and talk about it.
We ourselves are, as individuals, biologically Complex organisms and psychologically Complex personalities. We work for Complex organizations, exchange information across Complex networks, buy and sell goods and services through Complex markets within Complex economies. We live in highly Complex societies governed by Complex political systems and sustained by Complex infrastructures. Our global civilization itself is Complex, immensely so.
That’s only the beginning, though. We are only a small fraction of the living organisms on the planet, and the ecologies of mutual interdependence in which those organisms live are always Complex—orders of magnitude more so than any of those human artifacts.
The planet itself is Complex in its responses to energy throughput, most especially its meteorological and oceanic systems. (It’s awfully hard to have anything that flows, be it a material gas or liquid; energy such as heat or electricity; or nonphysical quantities such as money, celebrity, or memetic content; that does not exhibit Complexity. Engineers work pretty hard to prevent, or reduce, or at least ride on top of, Complex behavior in any flow system.)
Personally and professionally, you yourself are a Complex System immersed in other Complex Systems. You are likely to behave in weird and unexpected ways; and so is just about everyone and everything else.
Welcome to the world of Systems thinking, you beautiful freaks.
What’s a System?
There are a lot of deep and technical descriptions of the nature of Systems. I will goose the throttle right by those, and just give some broad ideas and rules of thumb.
- A System is any grouping of identifiable components that interact meaningfully, in reasonably consistent ways.
- Components act on each other, usually altering one another’s state as they do; these changes in state kick off other interactions, and so on. In other words, interactions propagate from component to component, working changes as they go.
- A System is dynamic. If there’s no motion, if there’s no change, then the components can never interact. A static structure like that is not a System—not the kind Systems Theory studies, anyway, no matter what people call it.
- Very importantly: these dynamic interactions are not instantaneous. Systems act over time. This is particularly weird to those of us in IT, because we have gotten overwhelmingly accustomed to the logic of discrete states, i.e. the logically instantaneous execution of instructions in sequence.
- If state changes can cause interactions which lead to state changes which cause interactions which... then it’s usually the case that an interaction will sooner or later come around, full circle, and have a significant effect on the originating component. This is called a feedback loop. The presence of feedback loops is the fundamental characteristic of Complex Systems, and it leads to some very basic general behaviors:
- Oscillation
- Emergent behavior
- Self-organization
- Self-regulation.
- As a result, it’s usually the case that Complex Systems are behavior-dense: you get a lot of different behaviors out of a fairly modest set of components and defined interactions. And, as mentioned, the behaviors explode in profuse differentiation as the System’s size increased.
These points are all somewhat fuzzy. Don’t worry about it: in Systems thinking, fuzziness is a feature not a bug.
There’s a learning point to make here. This list has a remarkable defect, which is instructive to ponder: it's got its precedence of expression wrong.
We normally expect, given a sequence of assertions, that the first is the most fundamental, the most significant. Look at this list: the first point in this list is to define a System in terms of components. This tempts you, dear reader, to use that to frame the entire concept as you traverse the list.
You would be wrong to do that, though. The structure of the System is mostly defined by its internal interactions, especially feedback loops. In Systems thinking, component parts matter not because of what they are, but because of what they do.
You would be wrong to do that, though. The structure of the System is mostly defined by its internal interactions, especially feedback loops. In Systems thinking, component parts matter not because of what they are, but because of what they do.
To start the list with something like “A System is a set of mutual cyclic interactions” would have been more correct, but much less accessible. Leaving the concept of feedback loops to near the end of the list makes a much easier progression to grok.
This has some important lessons about the nature of Systems, not least of which is that entry points in Systems discussions are chosen for convenience. Ordered lists do not reflect System nature, nor structure, worth a damn. Which is inconvenient for us, who by nature (and much more by nurture and training) think in terms of linear sequences.
How do Systems behave, and how do we work with them?
Systems are things that buzz and wriggle and vibrate, things that don't hold still, things subject to damping and stoking of motion, things that try to get beck to business as usual, things that can suddenly collapse or fly into bits.
Systems are things that just can't be reasoned about with the tools we know best.
Systems are a source of bafflement and surprise. They cause us wonder and delight, and they cause us frustration and bafflement. Sometimes at the same time.
Systems teach a salutary intellectual humility.
If you want to think in Systems, you have a lot of unlearning to do.
If you want to think in Systems, you have to learn to see with different eyes. Or, ahem, through a different lens.
There are five things about Systems that deserve a bit more discussion to round out this introductory description:
Systems are things that just can't be reasoned about with the tools we know best.
Systems are a source of bafflement and surprise. They cause us wonder and delight, and they cause us frustration and bafflement. Sometimes at the same time.
Systems teach a salutary intellectual humility.
If you want to think in Systems, you have a lot of unlearning to do.
If you want to think in Systems, you have to learn to see with different eyes. Or, ahem, through a different lens.
There are five things about Systems that deserve a bit more discussion to round out this introductory description:
- Feedback
- Emergent behavior and self-regulation
- Stocks and flows
- Modeling vs. analysis
- Complex System representation in data and computation
So I will talk about those. But not today. Each of these topics can stand on its own.
Hey! I think I see a roadhouse up ahead. I can use a break. Maybe a drink too… Systems Theory gives me a thirst. You?
Sunday, July 21, 2013
The Crafted World of Analog Computing
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.
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.
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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