Complexity & Elegance
by Jason GodeskyJoseph Tainter’s Collapse of Complex Societies offers the most widely-accepted view of why civilizations collapse in archaeological discussion; already summarized in greater detail elsewhere, for now, it is sufficient to recall that Tainter’s primary argument rests on the idea that social complexity is subject to diminishing returns, beyond which further investments in complexity become less economical, leading to collapse. This is a powerful explanatory framework, and while social complexity is a well-defined and even quantifiable criteria, “complexity,” as a whole, is often muddled and weighed down by more colloquial understandings. If we are to compare social complexity to other forms of complexity, then we must investigate further the broader definition of complexity in general, and its counter-balance, elegance.
The definition Tainter used for social complexity offers one key starting point for our discussion. It is the most generally accepted definition of social complexity in anthropology.
Complexity is generally understood to refer to such things as the size of a society, the number and distinctiveness of its parts, the variety of specialized social roles that it incorporates, the number of distinct social personalities present, and the variety of mechanisms for organizing these into a coherent, functioning whole. (McGuire, 1983)
In biology, the definition of “complexity” is subject to greater debate.
However, biological complexity has been widely accepted to be a function of the range of subcellular structures (prokaryotes versus eukaryotes), increasing numbers of cell types, organ structures, the functional repertoire of the organism, neural and immune function, and the intricate developmental processes necessary for the generation of these characteristics. The recent advent of the genomic era, however, has shifted discussions of complexity to genomic composition. Perhaps the most valuable genomic definition of biological complexity stems from an information theoretic approach. This definition suggests that an organism’s complexity is a reflection of the physical complexity of its genome, i.e. the amount of information a sequence stores about its environment . (Taft & Mattick)
Complexity has become a major issue in many fields, from computer science, to biology, to anthropology, and others; yet, a single definition for complexity that cuts across these varied uses remains elusive. In his consideration of John Horgan’s general dismissal of the term, D. C. Mikulecky, a Professor of Physiology at Medical College of Virginia Commonwealth University noticed that the key to understanding complexity lay in the failure of the Cartesian “machine” to adequately explain the world. “Ironically, not only do we not have a good definition of complexity, but we also lack one for a machine. The importance of this metaphor is in the intuitive concept of machine that almost everyone shares. A machine is built up from distinct parts and can be reduced to those parts without losing its machine-like character.” Complexity defies this, because in a complex system, losing one of the parts breaks the system. Complex systems are more than the sum of their parts. Thus, Mikulecky offers this general definition:
Complexity is the property of a real world system that is manifest in the inability of any one formalism being adequate to capture all its properties. It requires that we find distinctly different ways of interacting with systems. Distinctly different in the sense that when we make successful models, the formal systems needed to describe each distinct aspect are NOT derivable from each other.1
This harkens back to the etymological roots of “complexity,” in the Latin complexus, meaning “entwined” or “twisted together.”
We may conclude that complexity increases when the variety (distinction), and dependency (connection) of parts or aspects increase, and this in several dimensions. These include at least the ordinary 3 dimensions of spatial, geometrical structure, the dimension of spatial scale, the dimension of time or dynamics, and the dimension of temporal or dynamical scale. In order to show that complexity has increased overall, it suffices to show, that—all other things being equal—variety and/or connection have increased in at least one dimension. (Heylighen, 1996)
If we take this definition and apply it back to the definition of social complexity offered by McGuire, and generally accepted in anthropology, we can see the unspoken tenet that bridges the gap. Namely, that cultures are reflexive, nearly organic systems, where every cultural element interacts with and helps shape all others. Changes in religion will have effects on art, architecture and tool making, and changes in how food is gathered will change social structures, locality and religion. So anthropologists already understand that all cultural elements are fundamentally interrelated, and have neglected that element from their discussion of social complexity, because for them, it is redundant.
How does this change our understanding of social complexity and biological complexity, and diminishing returns? It’s worth noting that biological complexity exhibits much of the same behavior towards complexity that we see in human societies. All systems have some degree of complexity, so like heat, we can speak of one thing as “more complex” or “less complex” than something else, but these are comparative measures.
Many have pointed to biological evolution as a constant escalation of complexity: that evolution somehow innately favors greater complexity. Stephen Jay Gould (1997) has rebutted this perspective by pointing out that throughout history, the overwhelming majority of life on earth has been minimally complex. There’s a certain amount of complexity chemicals need to be truly alive, and overwhelmingly, most living things by numbers and type hug this boundary. Rather, Gould says that evolution maximizes diversity, not complexity, thus creating our anthropocentric perspective by way of the “Drunkard’s Walk.” If a drunk stumbles out of the bar, going this way and that down a side walk with a wall on his left, and a gutter on his right, then he will end up in the gutter on the right every time. The reason is not because his movements arent’ random, or that he favors the right, but because there’s nowhere else to go on the left because of the wall. Likewise, Gould discusses a “left wall” of biological complexity, the minimum complexity necessary for a chemical reaction to still be alive. With nowhere else to go in that direction, increasing diversity means that evolution will lead to more complex traits.
Gould’s “Left Wall” of biological complexity.
This idea has not gone completely uncriticized, of course.
There is a kind of “just-so” quality to this notion (to borrow a metaphor from Gould). It implies that systematic size/complexity increases in nature could occur without being “tested” and winnowed by natural selection. On the contrary, any such changes always entail bioeconomic “costs” (energy, for instance) that have to be offset by at least equivalent “benefits.” (There are no free lunches in nature.) (Corning, 2001)
This is an important point, and one that definitely needs to be added to Gould’s metaphor to make it fully work, because while there is a complexity minimum in biology, there is also an effective maximum, measured not in any absolute terms, but rather, in efficiency and diminishing returns. Let’s take one of the most complex systems evolution has yet developed, the Homo sapiens brain.
A brain, energy-wise, is an enormously costly organ. That is, pound for pound, it takes far more energy to keep it running than any other organ. It accounts for about 3 percent of our body’s mass, yet close to 20 percent of our energy needs. The quantum leap in brain size brought with it a stiff increase in the individual’s need for calories. Thus, if that bigger brain did not bring with it at least a proportional leap in our ability to feed it, there would be no net gain, and it would not confer fitness, would not survive evolution’s merciless test. (Manning, 2004)
The marginal return on the human brain is very slim: for all the power it gives us, it also requires an enormous input of energy. It just barely breaks even, and that only because we, as nomadic, social omnivores, were able to put it to use in a tribal context to share risk, wealth, hunger and plenty, to the benefit of all. The egalitarian social networks that our big brains allowed us to form were all that made its enormous energy costs worthwhile. So we can see already that anything much more complex would be much harder to feed, in terms of the added energy cost. So besides the left wall of minimal complexity, biology also has an ill-defined right gutter, where the marginal returns on further complexity become too small, and such varieties die out.
The biological process of succession essentially “fills in” the maximal ecological complexity a particular place can sustain, based on geological, climatological and similar constraints. Early stages begin with less complex systems, such as grasses, that move in quickly after a catastrophe, fix the soil in place, and prepare the way for slightly more complex brush and small trees. These give way to new growth forests with somewhat more complexity, and finally reach maximal complexity in old growth forests. Of course, local conditions may have different energy caps. Climate (rainfall, average temperature, and so forth), geology (soil quality, minerals, and so forth), geography (latitude and the angle of the sun, rivers, mountains, and so forth) all set constraints on how much energy is available to the local ecology, and by extension, how far along the process of succession can go. But even under “ideal” conditions for maximal complexity, ecologies reach a maximal level of complexity and then stop. Beyond that, the complexity becomes too costly, and the marginal return too low. Even where energy abounds, ecologies do not move beyond a level of complexity very far beyond an old growth forest. Even without civilization’s influence, only 60% of the earth’s land area is covered with forest, and only a portion of that is old growth at any given time.
Human societies, like any other kind of animal society, build on this ecological complexity, and depend on it for sustenance. Like biological communities and organisms, human societies likewise have a “left wall” of minimum complexity. The Ik of Uganda, or the South Fore of Papua New Guinea, for instance, hug this wall tightly (interestingly, both show signs of having once had much more complexity in their cultures, but to have then collapsed to their current levels). Most of the world’s cultures fall into a range of complexity slightly higher than this, ranging from hunter-gatherer bands to horticultural tribes. Civilizations may account for the most people, but they are a distinct minority of cultures. As we have already seen, and as Tainter (1988) discussed in much greater detail, civilizations are likewise subject to diminishing returns.
What does this mean? Does it mean that complexity is “bad”? Obviously not; complexity is present to one degree or another in every society, in every ecology, and in every organism. Rather, it implies that complexity is an investment, and subject to diminishing returns, whether we are talking about societies, organisms or ecologies. Complexity can provide extra energy, but it also entails an energy cost. Lower levels of complexity always provide the highest marginal costs; higher levels always entail the lowest marginal costs. What matters, then, is not trying to “eliminate” complexity, but rather, adopting a more nuanced view of it—neither as an evil to be stomped out, nor as a good to be pursued. Rather, it must be approached as an investment: sometimes wise, and just as often, not.
Does this mean we are fundamentally limited in our capacities, that we must bound our dreams? To some extent or another, our Icarian enterprise could do with a bit of wing-clipping, but this would likewise be an incorrect conclusion to draw from complexity’s limitations, because we also have available to us the opposite of complexity: elegance.
Gregory Chaitin proposed a formal definition in computer science, stating that the most elegant program in a particular language was the shortest one that could achieve the same result. Another mathematician, Edsger Dijkstra, said, “The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.” The anthropologist Clifford Geertz related these ideas as well: “The way in which mathematicians and physicists and historians talk is quite different, and what a physicist means by physical intuition and what a mathematician means by beauty or elegance are things worth thinking about.”
Elegance achieves the same end with fewer parts, making it the opposite of complexity in approach, but not in nature. To achieve that result, elegant solutions emphasize the non-mechanistic nature of systems. Because elegance works with systems as they are, there is no steady escalation that it drives towards, as complexity does. That makes elegance a sustainable trajectory for a society. While ever more complex solutions eventually become too costly to pursue, ever more elegant solutions will always be available.
Elegance is a solution to the problems of hierarchy. Because elegance is, by this definition, contained, it will foster localized, self-sufficient, and independent societies. Elegance is the feedstock of rhizome. And elegance is a concept that, if we set it as our goal, can steer the vast potential of human innovation to a positive, sustainable end that is compatible with human ontogeny. (Vail, 2006)
Greer’s (2007) definitions for “sustainable technology” likewise fit the criteria of elegance: durability, independence, replicability, transparency all follow from elegant design. As computer programmers are painfully aware, greater complexity in a piece of software brings with it exponential increases in its fragility. Simpler programs are the most robust, because there are fewer places where something can go wrong. With each new class, function, or even line of code, a program introduces not only the potential of a mistake in itself, but of unexpected problems in how it interacts with other parts of the program. Those potential problems points of interaction increase exponentially as the number of parts increases. Elegance is a programmer’s highest virtue, because a simple program that can achieve the same ends does so with far greater reliability and robustness. The 10 million new lines of code in Windows Vista may awe the uninitiated, but for programmers, they are not a signal of vast improvements, but a red flag of new bugs, pains and headaches.
An example of elegance: The use of primitive windmills in Michael Green’s “Afterculture.”
Some have suggested that our understanding of complexity in human cultures is probelmatized by the greater complexity in ecological systems. Of course, the fact that human societies already begin on top of those ecologies must certainly not be forgotten. But the most diverse ecology on earth, the Amazon, is made up of millions of species; modern, Western civilization encompasses millions of cultural elements. What makes ecology seem to “work” with such seeming effortlessness is not the complexity of the solutions evolution has provided, but their elegance. Ecologies are complex, and as we’ve already seen, they likewise suffer from diminishing marginal returns on that complexity. That is why evolution, not sharing our biases, began exploring a new avenue: elegance. This is likewise why indigenous cultures and modern permaculturalists alike look to ecological systems as the pre-eminent teachers of elegant design.
In the Northwest, salmon swim at the center of the stream ecosystem, linking the land with the sea. Born and reared in the clear, cold waters of our rivers and streams, most juvenile salmon species feed on aquatic insects - mayflies, stoneflies, caddisflies, and others. These insects feed upon the detritus of decaying leaves, wood, and other stream life. The decayed carcasses of adult salmon returned from the ocean to spawn and die are transformed into nutrients for the stream and food for their own offspring. It is a web of ecological elegance, and is the foundation of a great Northwest mythology centuries old.2
An example of elegance: The use of hangliders in Michael Green’s “Afterculture.”
In his imagination of a post-civilized North America, Michael Green’s “Afterculture” consistently invokes the possibilities of elegant technology, rather than complex technology. The windmills and hangliders that appear in Green’s paintings are not complex: a few stout branches, some properly tanned leather, and some good cordage to put them together properly are all either of them require. Yet their ability to use something as simple as the passing wind and the laws of aerodynamics allow them to achieve remarkable feats with very little in the way of complexity. These are both excellent examples of elegance.
The problem with complexity does not lie with complexity, but in our relationship with it. We have idolized complexity as an absolute good. Our civilization is systemically driven to pursue greater complexity no matter the cost, even at the risk of collapse and ensuing “gigadeath.” Complexity to one degree or another is necessary, but it is not simply “good.” It is an investment, and taken too far, it can become a bulky overhead—one that can come at far too high a cost.
The finer things in life can generally be divided into two categories: material and experiential. Despite the relentless psychological barrage of advertising, most of us can readily admit that it is the experiential that is truly rewarding and fulfilling. Many even recognize their own predilection to fulfill their desire for the experiential by compensating with an excess of the material. Commercialism tells us that the experiential–that which requires time–is too costly, out of our reach. Our time, we are led to believe, must be sacrificed to meet the demands of the economy. But time is free for all of us. It is the great equalizer, something to which we all have equally random access. But in the modern economy, where average individuals cannot directly provide for themselves, they are duped into trading time for the basic necessities of life–necessities that are directly available to the poorest of the Earth. As this economic hierarchy has intensified over time, we continue to be duped into trading our time for material possessions–far beyond those required to survive. The memes of our economic culture have convinced us that the material is a fine substitute for the experiential. A nagging doubt, dissatisfaction with our own suburbanization, some unknown, unfulfilled yearning tells us that, despire the overtures of mass-media, even the materially rich among us still long for the experiential. (Vail, 2004a)
Vail also offers us some points on how we can begin to repair our dysfunctional relationship with complexity and elegance:
- Elegant simplicity: some things work better, are more efficient when they are simple. Simple may not serve the needs of hierarchy, but it often does serve the needs of the individual, family or community. We need to develop and explore these instances when simple is more efficient than complex. I won’t go into examples here, but this is a body of knowledge that must be developed, remembered, etc.
- Conspicuous simplicity: replace the cultural ethos of “conspicuous consumption” with “conpicuous simplicity”. If it is desireable to have a flashy and showy level of simplicity, to have as high a standard of living as possible in a “simpler” manner than your neighbor, then we may be able to make the transition from hierarchy and complexity to rhizome and simplicity. It CAN happen–take a look at advertising all around you and look at how attractive the “simplicity” is, how hard the advertisers have to work to make that rolex or ferrari stick out of the beautiful nature scene, how difficult it is to brand your hotel when the real attraction is a quaint seaside locale. How the real star of that diamond commercial is two people in love–or at least the nice meal they’re sharing. (Vail, 2004b)
A dedication to ever-increasing complexity defeats itself, not because complexity is “bad,” but because it is subject to diminishing returns. A sustainable society cannot be rooted in any kind of continual escalation; rather, a sustainable society must move naturally towards a dynamic equilibrium. The blind pursuit of complexity will not suffice for this end, since a dynamic equilibrium will require a society to reduce complexity as often as it increases.
The fact that social complexity has both a left wall and a right gutter does not imply stasis, or limit the possibilities for the future. It does not imply an atavistic throw-back to the stone age. Rather, the principle of sankofa means that primitivism is a new starting point, not an end. From there, our future prospects could lead us anywhere. We have seen that constantly increasing anything cannot work sustainably. That said, there is great cause for hope and excitement for what we might be able to invent and devise when we have adopted elegance as our measure of success.
Bibliography
- Corning, P.A. 2001. “The ‘Drunkard’s Walk’ Theory of Complexity.”
- Gould, S.J. 1997. Full House: The Spread of Excellence from Plato to Darwin. New York: Three Rivers Press.
- Greer, J.M. 2007. “Principles for Sustainable Tech.” In The Archdruid Report.
- Heylighen, F. 1996. “What is Complexity?” In Principia Cybernetica Web
- Manning, R. 2004. Against the Grain: How Agriculture has Hijacked Civilization. New York: North Point Press.
- McGuire, R. H. 1983. “Breaking down cultural complexity: inequality and heterogeneity.” In Advances in Archaeological Method and Theory, volume 6, ed. Michael B. Schiffer, pp. 91-142. New York: Academic Press.
- Taft, R. J. and Mattick, J.S. “Increasing biological complexity is positively correlated with the relative genome-wide expansion of non-protein-coding DNA sequences” [PDF]
- Tainter, J.A. 1988. The Collapse of Complex Societies Cambridge: Cambridge University Press.
- Vail, J. 2004a. “Vernacular Zen.” In Energy Intelligence.
- Vail, J. 2004b. “Conspicuous Simplicity.” In Energy Intelligence.
- Vail, J. 2006. “Elegant Technology.” In Energy Intelligence.
Dave Pollard has written about complex versus complicated systems, and the distinction he draws has carried some weight in certain online circles of the sustainability movement. I believe his distinction obscures more than it reveals, and this is the perfect place to say why.
The Northwestern Institute on Complex Systems distinguishes “complex” from “complicated” as such:
So again, we return to the defining, non-mechanistic nature of complex systems. Both complicated and complex systems are made up of many parts, and both are difficult to understand, but complicated systems operate mechanically; complex systems do not.
CSIRO offers emergence and self-organization as the criteria that distinguish complex systems from complicated systems, which again brings us back to the distinction of mechanistic vs. non-mechanistic systems.
Why, then, does Pollard draw the line between “knowable” and “unknowable”? In actual fact, we can and do know how complex systems operate. We know how climates, ecologies and societies all function, and though we can’t follow all the variables in our own heads, we’ve made fairly successful computer models that predict what happens to complex systems. They are knowable.
Cultures are not mechanical. They self-orgaize, adapt to outside pressure, and have emergent properties (including Daniel Quinn’s “Mother Culture”). The elements of culture interact with one another dynamically; changing one creates cascading changes throughout the culture in response. Cultures, therefore, cannot be complicated; they are complex.
An epistemological division between complicated and complex begins to redefine these terms from their normal usage, and serves to obscure much more important divisions, like the mechanical or adaptive nature of a system. When disturbed, does a system move back towards equilibrium (like an organism or an ecology or a culture)? Or does a slight disturbance lead to escalating problems and quickly catastrophic breakdown (like a jet)? This is a much more important distinction. By obscuring this in favor of an epistemological division that doesn’t even hold true, we essentially create a new jargon, which becomes all the more problematic as we try to cross-check our conclusions against the growing literature of others’ work on similar problems, who use the more established meanings for these terms. If a word hides more than it reveals, then it has failed in its most important task. When that happens, we need to abadnon that usage, in favor of those meanings that help us communicate more easily, rather than those that hinder communication.
Comment by Jason Godesky — 24 April 2007 @ 10:35 AM
Hey –
hmmm… well, you hit on biology and mathematics, but you completely ignored what physics and chaos theory have to say about complexity (which is, for me, where a lot of my thoughts originate….)
I still have some issues here, but I am going to take a little time to put my thoughts in order on this one.
Interesting article, even if I am going to be compelled to argue
Janene
Comment by janene — 24 April 2007 @ 10:39 AM
Really, chaos theory has a lot more to do with complicated systems than complex ones. Chaos theory deals with dynamics that are sensitive to initial conditions. Weather, for instance. Of course, weather is part of the complex system of climate—climate self-regulates, and that makes climate much easier to predict than weather. The way that a problem on a jet escalates into catastrophic breakdown, that’s a property of a complicated system. Complex systems are not sensitive to initial conditions. Their defining property is their self-regulation, the means by which they eliminate the effect of initial conditions.
The CFTC Conference brought together physicists, biologists and social scientists to compare notes on what “complexity” is all about, and they operated under the definition, “the collective behaviour of many interacting units that evolve towards self-organised steady states, whose global properties cannot be described at the level of the individual units.”
Physicists admit to having no good definition of complexity. But they also point to self-regulation and emergent properties as prime indicators.
Sounds to me like the physics definition of complexity doesn’t actually differ all that much.
Comment by Jason Godesky — 24 April 2007 @ 10:58 AM
Hey –
Okay, let’s take this by the numbers
Yes…. and no. The problem with Anthropologies take on complexity is that they subsume the meaning of complexity with their language and assumptions. By counting discreet elements, they are reinforcing the assumption that those discreet pieces are complexity in and of themselves, whereas, in fact, complexity is about the relationships, NOT the elements.
What this says to me is that while they may intuitively grasp that cultures are complex (which of course they are) there is no reason to assume that a culture with 10,000 artifacts is more complex than a culture with 1,000 artifacts. I know that is going to sound really wrong to you and that is the core of our disagreement. The more complicated an artifact (material or not), the more linear the relationship between that artifact and others becomes. So, for example, the relationship of an atlatl within a primitive culture to the other elements of that culture is far more complex (because it impacts most characteristics of the culture) than the relationship matrix between a moon lander and American culture.
…..Right Gutter of Maximal Complexity. Nice. Good to see that getting more airplay
And of course, I agree with all of that….
hmmm. I have a bit of a problem with this. I understand where this definition of elegance comes from… and I understand why it has been formulated this way. But this gets into the distinction between designed and evolved systems. Sure, the most elegant math equation or computer program IS defined by fewer parts. However, what can you think of that is more elegant than an ecosystem? And it is decidedly NOT defined by fewer parts. It is defined, quite specifically by simple interactions. Each piece of the whole just going about its own business, while other parts do the same, and yet, at the end of the day – wow. Just try and tell me that it is not complex. But it is also, quite obviously, elegant as well.
This is where physics comes in as well. Another data point where it is quite obvious that simple interactions (every interaction at the subatomic level) create the entire freaking universe out of, probably, just one fundamental ‘thing’, based entirely on the relationships between different bits of that one thing (I’m talking about strings, here)
I think you are going to need to back that one up a bit. I agree entirely that individual organisms have to deal with cost-benefit when engaging in increased complexity. But I would submit that this is because individual organisms do not have the same level of elegance (or, at least, may not….) and that it is the lack of elegance that creates the ‘right gutter’. By comparison, an ecological system has exactly as many pieces as it can use and no more. But there is no diminishing marginal returns inherent, aside from the most basic level wherein a given organisms will not survive if it is not able to establish a useful role in the ecology.
I think, perhaps, this is pushing against my alert flags re: evolution of populations. Can’t happen. And suggesting that an entire ecology ‘evolves’ as a whole is absolutely beyond the pale. What I don’t know is whether you intended to go that way. Or realized that you might be……
Re Dave Pollard. I agree with everything you are saying there…. but what Dave writes about is how we solve complex vs complicated problems. And points out that complicated problems are easy whereas complex problems must be addressed in a different way. (A non-linear, intuitive way, rather than a linear, bandage approach) So I am not quite sure what you are trying to dispute with him on?
Sure. Absolutely. Or put in another way, as I am so fond of doing…. complex systems are defined by non-linear equations. Scientists try to solve those equations all of the time, bu they do so by cheating – by fudging the equations to make them linear. This is the fundamental problem our culture has with trying to understand complexity. We see it, and then we ‘make it go away’ because our reductionist approach to, well, everything, does not have an adequate way of dealing with complexity.
No. I’m sorry, Jason. But that is simply not true.
Dividing weather and climate? That is reductionism at its finest. Sure, we can talk about the two things as if they were discreet, but quite clearly they are not. Climate is nothing more or less that thousands, millions (or whatever) of nested weather patterns. If enough changes occur in those nested sets then the macro system is said to change as well. But WE create that distinction. Not the universe. We decide when ‘climate’ has changed from A to B, based upon distinctions that we create so that we can decide when it has changed.
I know…. that’s a lot of semantics. But that does not make untrue. We could just as easily say that climate is constantly changing. And it is.
Complex systems are absolutely sensitive to initial conditions. You are describing it as if initial conditions (always) create positive feedback loops, but in fact, they simply create feedback – and this feedback is part and parcel of what allows complex systems to self regulate.
Oh sure. I was pointing more to what physics (or more properly quantum physics and cosmology) have to show us about complex systems and how they work.
Janene
Comment by janene — 24 April 2007 @ 12:16 PM
Errr … yes and no. Cultural elements aren’t entirely discrete in anthropology, because culture is adaptive. Morever, complexity is distinguished by its relationships, but it’s still a question of how many elements. It simply adds the stipulation that the elements do not contribute to the system in a merely additive fashion. But complexity is still measured by the number and distinctiveness of those elements.
On the contrary, that’s precisely what it means. Every culture is adaptive, meaning that every one of those artifacts has more than a simply additive relationship to the culture. The culture is more than just the sum of its elements, the culture itself has emergent, self-regulating properties. But complexity is still the measure of the number and distinctiveness of those elements. What distinguishes complexity is the type of system those elements add up to, not the count of elements involved. So a culture with 10,000 elements is definitely more complex than one with 1,000, because all 9,000 of those added elements also make more than a simple additive contribution to the adaptive system.
An atlatl might impact a larger percentage of a culture, but that’s only because the culture has fewer elements. The NASA program has impacted nearly every aspect of our culture, and is composed of other elements that had similar impacts. Burke’s Connections series is a great illustration of this. I see your point, but for once, I can actually stand up in defense of civilization. It’s no less reactive as a culture than any other, and the introduction of any new element, in any culture, has culture-wide ramifications, so an atlatl cannot be more complex than a lunar lander because it affects the culture more widely. Both impact their cultures equally.
As I pointed out, ecosystems achieve elegance through reduction of parts. The same elements come into play again and again. Of course, ecologies also show a good bit of complexity, so they ultimately balance the two. There’s quite a few things more elegant than ecosystems, then. A lever, for instance: no balance of complexity vs. elegance, just elegance in nearly its purest form.
Which is why complexity has its limits. Elegance is the opposite of complexity, so the more elegant you make some parts, that frees up more potential complexity in other parts. But even where the energy is there, you don’t see ecologies going beyond old growth forest complexity. Succession stabilizes there, it doesn’t keep on going. That’s a fairly clear indication that increasing complexity in an ecosystem passes a point of diminishing returns, so the trend towards complextiy in succession stops there.
Well, that’s diminishing returns, isn’t it? As niches are filled, the roles available for new species dry up. There’s no need for more species, and complexity stops escalating. In fact, old growth forests actually reduce their complexity somewhat from maximal biodiversity, right? The first phases of succession go quickly; grasses are there for months, shrubs for years, new growth for decades and old growth for centuries. The trend of complexity slows down, and then settles into equilibrium. Classic dimishing returns, no?
I’m not entirely sure what you mean–populations are the only things that can evolve. Individuals can’t. We know that ecologies move towards “equilibrium,” this is what succession is all about (and what makes them complex systems, e.g., self-regulating). The first grass communities have an evolutionary niche, but the system isn’t stable. Brushes come in the same way, then new growth trees, then old growth. There’s escalating complexity as more and different species are introduced to the ecological system, but eventually you begin to reach a point of diminishing returns. Niches are being filled, the system is stabilizing, there’s less and less room for new species, and increases in complexity level off.
I think his way of dealing with them is slightly off, because his delineation is slightly off. Complex systems break our assumptions of reductionism. They can only be studied as a whole system. But they can be understood: it just requires consilience, rather than reductionism.
Every climatologist I’ve ever talked to went to great pains to make clear that climate is different from weather.
Well sure, but it’s not simply additive. Those weather phenomena that make up climate are more than just additive. The climate they create is self-regulating, and it has emergent properties. The weather may be chaotic, but the climate eliminates the impact of initial conditions.
The key is “sensitive to initial conditions.” What makes a system chaotic is that initial conditions produce positive feedback loops, resulting in big changes from little inputs. What makes a system complex is that it self-regulates, so even big inputs are absorbed, reduced, and their impact is eliminated.
Wikipedia puts it this way:
What I take from that is that complexity is the opposite of chaos: chaotic systems are easily pushed out of equilibrium, while complex systems regain their equilibrium.
Comment by Jason Godesky — 24 April 2007 @ 1:02 PM
Certainly it makes sense that scientifically organized efforts to deal with human problems must take account of manifold interconnected events. Although it is necessary to recognize and acknowledge the complexities
inherent in cultural life and the natural world, it is equally important that a
dizzying array of variables not blind us to certain scientific facts of biophysical reality. Humankind could be bound by such predominant facts because the workings ofthe natural world exist independently of human
wishes and beliefs.With this in mind, please note that Russell Hopfenberg has provided
an elegant model that accounts for the salient factors governing the dynamics of global human population numbers. According to his findings, the size of the human population is determined primarily by food availability. The realization that complexity and elegance are derived from different points of view—that there is complexity and
simplicity in the world we inhabit—does not necessarily mean that one is correct and the other incorrect. To the contrary, it could be
that each point of view is valid based on the scope of observation.
According to Hopfenberg, the dynamics of human population
numbers is no longer a preternatural phenomenon but a knowable one, and that human population dynamics is not essentially different from the population dynamics of other species in both the complexity and the simplicity
of the governing elements.
A point in human history may have
been reached when the current scale and anticipated growth rate of
economic expansion worldwide, increasing per human consumption
of limited natural resources, and skyrocketing absolute global human population numbers can be seen as soon to become patently unsustainable.
Regardless of how long a predominant culture of the human
species prizes certain of its unbridled growth activities and CHOOSES TO LEAVE THEM UNCHECKED, surely it is not too late to accept limits to growth of the human economy, human consumption, and human numbers
worldwide by altering human behavior accordingly.
Thanks,
Steve
Comment by Steven Earl Salmony — 24 April 2007 @ 1:06 PM
Of course elements are not simply additive. But you are making no distinction between elements that are related in linear fashion and those that are related fractally (for lack of a better word). Note, I did not say NASA or the space program, I said “A moon lander�. Because, specifically, you are talking about elements. And that particular element may have relationships with 100 other elements. By comparison, something like, say, a television may have billions of interactions. So when, where, how do anthropologists recognize this discrepancy?
The only way to take that into consideration is to focus attention on relationships rather than elements. Or perhaps we should be talking about nodes and connections.
Now, I do need to clarify, I am not actually suggesting that it is common or likely that a culture with 1000 elements is more complicated than a culture with 10,000. But I AM suggesting that you cannot necessarily make that distinction based on simple, quantitative data.
That’s not really, actually true, though. An early succession ecology is no less complex, no less elegant than an old growth forest. It is in the self regulating behavior, redundancy and resiliency that all ecologies share. As you pointed out elsewhere, only a small portion of a truly healthy biosphere is taken up by old growth forest – but I don’t think it has anything to do with diminishing returns and has everything to do with diversity. All things must pass. The old gives way to the new and whatever other cliches you want to throw out there.
Ah ha! The core of our miscommunication… or is it real disagreement?
An individual cannot evolve. Sure. Leave Lamark at the door. However evolution can only express itself in individuals. Populations change as the result of selection at the individual level. There has been some pretty heavy debate about this one…. but I see it as one of those ‘no duh’ questions. A trait cannot become dominant in a population because it is advantageous to the group — traits can only be selected for when they are advantageous to the individual. And the same dynamic occurs in ecologies. The ecology as a whole DOES NOT evolve. The individuals within the community change in dynamic relation to one another, therefore the ecology as a whole can be said to change. Again…. lots of simple elements nested together in a complex pattern – this is where complexity (and elegance) comes from.
Again… this is the reductionistic view of what is occurring. In fact, no ecology is ’stable’ – like Gaea itself, ecologies exist in dynamic dis-equilibrium. No less the original grasses than the later old growth forest. It is only from our human-centric view that we can look at it and say that a grass community that survives for a few seasons is less stable (or less complex) than a forest community that survives for thousands of years. The difference is not in stability so much as it is in life cycle.
Yes.
Of course they did. And in one context that is correct. But in context of the nature of complexity and elegance, it’s too simplified.
In what context have I suggested that ANY of this is additive? Of course it is not. Climate and weather are both self-regulating, its merely a difference in scale. And no… climate does NOT eliminate sensitivity to initial conditions except in our description of it.
No, see this is exactly what I suggested was wrong with your argument and now you throw it back at me as self-evident: initial conditions do NOT specifically create positive feedback loops. They simply create feedback — and of course feedback is equally necessary for BOTH positive and negative loops. Ergo, complex systems ARE sensitive to initial conditions… but you need to look deeper to see if they will self correct or if they will spiral out of control. Both possibilities exist for a time…. but eventually a dynamic dis-equilibrium will be achieved.
Well, yeah, there is a problem because I reject outright that commentary for Wikipedia….
This goes back to my initial research into Chaos Theory…. and the insight I had that Chaotic Systems are no more Chaotic than any other complex system…. they are simply complex systems caught up in positive feedback. And they are, intuitively understandable and predictable – just not mathematically predictable. Watch a fractal for a few hours… and then tell me that there is no way to determine where it is going to go next…….. mathematically it is true, but I bet you money, that you could still do it
Part of the problem, of course, is that Chaos Theory, as it stands, is pretty much ‘dead’ science. They realized that it really did not describe very much, once they explored further into other related fields… so they never really went back and ‘fixed’ it to take new understandings into account. They just let it dry up and die. Of course, we can still read about it and that leaves us with the impression that the info from two decades back is still cutting edge – but it is not.
Janene
Comment by janene — 24 April 2007 @ 2:32 PM
Hmm, my “Complex Analysis” and “Chaos Theory” is pretty rusty, but I thought that all mathematically complex systems were sensitive to initial conditions…?
What’s more, I don’t see how weather, forests, or cultures are not sensitive to initial conditions, perhaps I’m being dense here. If so, could someone provide a more illustrative example?
Also, I thought that “Chaos Theory” was picked up by Artificial Life researchers. For some reason I was under the impression it factored into genetic algorithms. That seems like a loooong time back that I was paying attention to that scene, tho’.
Comment by jhereg — 24 April 2007 @ 4:03 PM
This is fascinating stuff! I’ve been following Jason’s writings here and Janene’s on IshThink. If I can jump in here, I think there is another piece to the puzzle: complexity requires resources. The available resources determine the point of diminishing returns.
For example, start out with a bare piece of land. The ecology will get more and more complex until the scarcest resource limits the marginal return on additional complexity. In a rainforest, the limiting resource is sunlight. In a desert, it’s water. Change the climate (resources), and the system will reach a new equilibrium, either more complex or less complex depending on the resources available.
Similarly, one can argue that it is not complexity per se that leads to a civilization’s collapse, but complexity PLUS a loss of resources.
Comment by Danneau — 24 April 2007 @ 4:53 PM
Hi again,
I am getting a sense of the ‘complex analysis’ and ‘chaos theory’ in this discussion. What appears to be missing from this thread is attention to what is elegant. Perhaps Jason can help us here.
Thanks,
Steve
Comment by Steven Earl Salmony — 24 April 2007 @ 7:42 PM
There is a metaphysical assumption behind Gould’s thesis, which is that the universe is cosmologically bounded, i.e., that it has limits in scope, duration, and scale. This is understandable, given the muddled state of cosmological theory, but it does not make him correct. The floor he posits — and by extension, the ceiling you posit — are horizon artifacts. Gould selects an arbitrary scale — e.g., the biological — and concludes that there is a minimum threshold of complexity below which evolution does not function. But this is nonsense. Evolution, in its most generalized sense, is a process of variation and selection, and it can be observed at all levels of reality, from the quantum foam to galactic superclusters. Life, as a thermodynamically-driven autopoietic process, is scale-independent; it can exist anywhere along the continuum from the immeasurably small to the immeasurably large. The life with which we are most familiar is biological life, composed of organic compounds, but this is not the only possibility the universe has to offer. There are other substrates, with their own distinct properties, that can achieve structural efficiencies and utilize power sources not readily accessible to organic life forms. Human technology demonstrates this principle quite nicely. If biological succession leads to climax ecosystems in which matter and energy are maximally recycled, what is to say technological succession doesn’t lead to the same? What if the human race is a bridge between substrates, a pioneer species for a latent synthetic ecology? In this context, the ordeal we experience as civilization is a necessary process by which the ground is prepared for more mature successors. It’s painful and destructive, yes, but little different from the experience of lichen, which ultimately “ruins” its habitat by churning bedrock into soil.
Life is life. The form it takes is cosmically irrelevant. Why invest so much in a form of life that, as you describe it, is doomed to perish with the next cometary impact, or when the oceans photodissociate into space, or when the sun swells into a red giant and consumes the Earth? Why not migrate to a new substrate with an expanded range and spread throughout the galaxy? If the universe is doomed to inevitable heat death (which I don’t believe it is, but we’re addressing the prognosis for the cosmos implicit in your curiously deterministic worldview), what difference does it make?
Comment by Anonymous — 24 April 2007 @ 9:50 PM
According to Edible Forest Gardens, a permaculture book, old growth forests have been shown to be somewhat less complex than more open systems. A fairly continuous canopy is not conducive to complexity. If the old growth forest is in an area that has lots of disturbances to break up the canopy then it can be very diverse, but without high winds, lightning, elephants, or humans complexity will decline as the trees cast their pall.
Comment by Scott — 25 April 2007 @ 9:16 AM
Hi again,
Perhaps an example of elegant research will be useful here.
According to Hopfenberg, global population growth of the human species is a rapidly cycling positive feedback loop in which food availability drives population growth and this growth in human numbers gives rise to the misperception that food production needs to be increased even more.
Data indicate that the world’s human population grows by approximately two percent per year. All segments of it grow by about 2%. Every year there are more people with brown eyes and more people with blue ones; more people who are tall and more short people. It also means that there are more people growing up well fed and more people growing up hungry. The starving segment of the population goes up just like the well-fed segment of the population. We may or may not be reducing hunger by increasing food production; however, we are most certainly producing more and more hungry people.
Hopfenberg’s evidence suggests that the magnificently successful efforts of humankind to increase food production in order to feed a growing population results in even greater increase in human population numbers.
The perceived need to increase food production to feed a growing population is a widely shared and consensually validated misperception, a denial of the physical reality and the space-time dimension. If people are starving at a given moment of time, increasing food production cannot help them. Are these starving people supposed to be waiting for sowing, growing and reaping to be completed? Are they supposed to wait for surpluses to reach them? Without food they would die. In such circumstances, increasing food production for people who are starving is like tossing parachutes to people who have already fallen out of the airplane. The produced food arrives too late; however, this does not mean human starvation is inevitable.
Consider that human population dynamics are not biologically different from the population dynamics of other species. Human organisms, other species and even microorganisms have essentially common population dynamics. We do not find hoards of starving roaches, birds, squirrels, alligators, or chimpanzees in the absence of food as we do in many civilized human communities today because these non-human species are not annually increasing their own production of food.
Please take note that among tribal peoples in remote original habitats, we do not find people starving. Like non-human species, “primitive” human beings live within the carrying capacity of their environment. History is replete with examples of early humans and other ancestors not increasing their food production annually, but rather living successfully off the land for thousands of years as hunters and gatherers of food.
Prior to the agricultural revolution and the production of more food than was needed for immediate survival, human numbers supposedly could not grow beyond their environment’s physical capacity to sustain them because human population growth or decline is primarily a function of food availability.
Hopfenberg’s research appears to provide virtually irrefutable, uncomplicated support for Jason’s Thesis # 4: Human population is a function of food supply.
As ever,
Steve
Comment by Steven Earl Salmony — 25 April 2007 @ 9:32 AM
…. Huh?
First of all, WTF? Trying to follow your comment damn near made my head ‘asplode. That came out of nowhere! We’re not even talking about population here!
Secondly, you do know that the idea of human population being bound to food supply greatly predates Hopfenberg, right? His study is great because it so clearly shows what’s going on, but he’s nowhere even close to having come up with the idea. It’s been a well-known fact in biology since at least the days of Lotka & Volterra that every other animal population is determined by food supply. We like to think we can get an exemption from that thanks to our “intelligence,” and Hopfenberg—and others—have done an excellent job of showing that isn’t so. Hopfenberg cites some of the many researchers who made this argument before him in his own paper. I mean really, this is a positively common idea with a history long before Hopfenberg’s work. You might as well attribute the idea of evolution to Richard Dawkins!
I appreciate his work, but your hero-worship is rather unseemly. You make it sound as if Hopfenberg’s the first person to ever suggest this; he’s not, not by a long shot.
Their position is that the discrepency doesn’t really exist. Every element has an impact on every other element. There’s no such thing as two unrelated cultural elements. The moon lander has an impact on every single element of our culture. The meaning of a washer has been changed by the lunar lander. Our religious beliefs have been impacted by the lunar lander (think of hubris). Every political office we have has been slightly redefined by the lunar lander (think of JFK).
The point made in anthropology is that it’s a complete graph. Every node has a connection with every other node. That means that the number of nodes is really all you need to know.
It’s much less complex than an old growth forest. You can’t say it’s less elegant, because it doesn’t achieve the same ends, and as important to elegance as simplicity, is effectiveness. Grasslands don’t support anything like the same biodiversity, they don’t have anything like the same energy throughput, etc. But they’re also not nearly as complex as old growth forests. There are far fewer species and far fewer types of interaction to be found in a prairie than in an old growth forest. Mind you, there’s still a lot more going on in a prairie than most civilized folk would ever notice, and even that is fairly complex, but that complexity is nothing compared to an old growth forest.
All those cliches are really just folksy ways of pointing out diminishing returns, though. That’s why the old has to pass away.
That’s not really true. Look at recessive traits. This is probably how homosexuality evolves, and why it’s in pretty much every social animal species. Sure, you’re not passing on the Fabulous Gene personally, but your nieces and nephews who had the benefit of you helping to raise them (since you had no kids of your own), carry the recessive gene, and they do much better thanks to their gay uncle, than the kids in a completely straight family. So homosexuality evolves because it’s advantageous to the group, even though it’s a real death knell for the individual’s genetic legacy. There’s plenty of other traits that have evolved along similar lines, despite their cost to the individual, precisely because they’re advantageous to the group.
Not at all; dynamic equilibrium is stability. Your body is always shifting, but you still have a homeostatic movement towards dynamic equilibrium. Ecologies are always shifting, but they gravitate towards a dynamic balance.
I disagree. Even if nothing happens to it, a grassland is not going to remain that way in most areas. Succession will move it past that. Old growth forests are stable: they don’t keep going on their own, they need to be “knocked down” by some catastrophe, otherwise they’ll keep chugging along indefinitely. Since over time the probability of something happening approaches 1, that never entirely plays out, but we can see it in old growth forests around the world. There’s no ecological process that changes them due to their own imbalances, the way the early stages of succession do.
If that’s true, then why do we have winter and summer? These should not be nearly so regular. Chaotic systems are not predictable, because any tiny difference in initial conditions can change everything. If a butterfly flaps its wings in the Amazon, shouldn’t we have twelve feet of snow in August? If climate’s really chaotic, then on any given day, it should be just as likely to be at -40 C or 80 C. August 31 or February 18 shouldn’t make any difference at all, right?
Of course, a self-regulating system is defined by the way it eliminates initial conditions. Sure, your body may start off with a bacterial infection, but your body is self-regulating. It has an immune system that seeks to restore your body’s homeostasis by removing the infection. Complex systems self-regulate: they use negative feedback loops and response systems to try to return to their original, dynamic equilibrium. You’re not as likely to die from the flu as to recover, because your body is a complex system: it has means of maintaining its status quo. It’s the opposite of sensitivity to initial conditions, because it actively works to eliminate the effect of initial conditions. Just like the climate: a butterfly flapping its wings may cause a tornado in Kansas, but the overall effect of all the various weather phenomena out there creates emergent properties. So twelve feet of snow on August 31 is not as likely a hot summer day, because climate as a whole actively works to eliminate the random, chaotic effects of weather.
Or, to quote John Robb:
The classic designs emulate the behavior of complex systems: they dampen the effect of random factors in order to remain stable. That’s what self-regulation is all about. Chaotic systems are more like the high-performance aircraft: they are sensititve to initial conditions, meaning that “the system’s interaction with the environment can create uncontrollable loops that tend towards infinity.” That’s why a butterfly flapping its wings in the Amazon leads to a tornado in Kansas.
If an initial condition created a negative feedback loop, it would eliminate its own effects, and the system would not be sensitive to it. For a system to be sensitive to an initial condition, that initial condition’s effect needs to be amplified over each iteration. It has to be a positive feedback loop. That’s the only way that a small initial difference can have a big effect. If it’s a negative feedback loop, then what little effect it originally had is extinguished. Such a system would be marked by how insensitive it is to initial conditions. Even very large impacts–ecological catastrophes, bacterial infections, and so forth–would be eliminated by such systems. And that’s exactly what complex systems do; that’s what self-regulation means. Chaotic systems are unpredictable because the smallest initial difference can have enormous consequences, and the initial condition can never be perfectly known. Complex systems are eminently predictable, because random events are absorbed, downplayed, and their effects eliminated. So, we have a very hard time predicting the weather for next week because the system is chaotic, but we can be fairly confident that August will be hot because climate is complex.
Well, you know I like open source too much to reject Wikipedia, but in this case, there’s sources cited. It was apparently Colander’s 2000 The Complexity Vision and the Teaching of Economics that outright called complexity the opposite of chaos theory, while Cilliers’ 1998 Complexity and Postmodernism : Understanding Complex Systems makes similar conclusions, while Buchanan’s 2000 Ubiquity : Why Catastrophes Happen discusses how complexity and chaos differ in that chaos arises from an imperfectly known history, while complexity tries to eliminate the impact of history.
Absolutely not; then the definition of chaotic systems as those sensitive to initial conditions would be meaningless double-talk. The key word there is “sensitive.” If you’re sensitive, then a small thing can have a big effect. You see that in chaotic systems. Complex systems, though, are insensitive to initial conditions. Even big things have very small effects. That’s what self-regulation does.
Weather is a chaotic system. Very small things can have big effects, as with the famed “butterfly effect” example.
But look at a forest. If a tree falls in the woods, does that escalate into some major shift of the whole forest? Not at all; it’s incorporated, absorbed, and the overall ecology goes on. Even if we introduce something very big, like a forest fire, you have the process of succession which moves the forest back towards something like it used to be. Small things have very little effect, and even big things have very little effect. The system self-regulates, it eliminates the impact of initial conditions and tends towards its own dynamic equilibrium.
Likewise, culture is a complex system. Changes in culture are absorbed. The introduction of Christianity did not significantly changed Roman culture; rather, Roman culture absorbed Christianity. Cultures try to maintain their status quo; Quinn anthropomorphized this emergent process as “Mother Culture.” Just like succession in a forest, culture adapts to changes by absorbing them and trying to maintain its normal state.
Absolutely–that’s rather the point. Complexity is a function of energy. Whether we’re talking about biological complexity, cultural complexity, or any other kind, the amount of complexity possible is determined by the amount of energy available. Complexity is always an investment, and when it begins to cost more energy than it returns, that’s when you cross the point of diminishing returns, and that’s when complexity stabilizes. If you happen to be talking about cultures, then continuing to push complexity beyond that leads to collapse.
Elegance arises from two factors, like complexity: effectiveness, and simplicity. Achieving the same end with less complexity, or achieving more with the same complexity, are both ways of increasing elegance.
But it does limit our focus. This isn’t a metaphysical assumption, but when we’re talking about the “complexity of life,” then things that are not complex enough to be alive are hardly germane.
Because civilizations are created on the assumption of unlimited growth. When they stop growing, they implode. Ecologies have no such dedication to growth for its own sake, so if they stop growing, they’re quite capable of maintaining a dynamic equilibrium. Civilizatons can’t do that.
Now, elegant technology does leave room for that possibility–which was rather the point of the article.
Which illustrates rather nicely that ecological complexity is subject to diminishing returns. The point at which an ecology “stabilizes” is not the point of maximum complexity, but after that, at a somewhat lesser level of complexity.
Dude. This is not about population. Give it a rest!
Comment by Jason Godesky — 25 April 2007 @ 11:51 AM
Hmm. Okay, so I’m thinking of Conway’s “Life”, you know that really, really old model of cellular automata. And I’m having difficulty figuring out how you would classify it as a system. It’s certainly sensitive to initial conditions. It may go to a zero bound, it may go to infinity. It may end up in total statis or in a dynamic equilibrium. It can be used to create calculators and operating sytems. It doesn’t seem to clearly fall into either “chaotic” or “complex” as they are being defined here, but it seems to me (and maybe this is where I’m wrong) that we [b]should[/b] be able to call this one or the other (or both). I guess I’m not sold on the idea that complex vs chaos is entirely valid. It seems to me that complex systems are sensitive to initial conditions. If a tree falls in a forest, the forest can deal, but, you know, it’s a forest. Isn’t that an initial condition too?
I’m not trying to argue with your conclusion, I’m trying to understand your reasoning (and hopefully help others understand it as well).
Comment by jhereg — 25 April 2007 @ 12:24 PM
Wolfram has the best discussion of cellular automata I know of, but I’m also unsure where they would land.
“Initial” is fairly arbitrary in these discussions; it wasn’t always a forest. Succession and evolution built up that forest because once life existed, its dead, non-forest state became unstable. Life could grow there, so it did, and continued to do so until there was a forest. A new dynamic equilibrium emerged, one that regulates itself, so that now, things that might impact it–big or small–have very little effect. Some take longer to work out than others, but the system is set up to eliminate those factors.
That’s very different from your classic chaotic system, which is very sensitive to those kinds of factors, and easily escalates into some massively different state because of a very small change.
Chaos theory is very often used to assert that predictions about complex systems are impossible, when they quite clearly are possible. Not only possible, but downright commonplace. We predict them all the time, and we’re almost always right. Pittsburgh is not going to see twelve feet of snow this August. I can make that prediction, and I can almost guarantee it will be correct. The reason I can be so sure is because it’s a complex, self-regulating system. When things happen, complex systems eliminate their effects. That’s the opposite of classic chaotic systems, which are unpredictable precisely because small effects escalate, rather than extinguish.
If complexity were the same as chaos, then that would mean that if I push you with my pinky finger, you’re as likely to spontaneously combust as just stand there looking at me like I’m crazy. We know that these two are not of equal probability, because your body maintains its homeostasis. Climate maintains itself; ecologies maintain themselves. The self-regulation of complex systems oppose chaos, they bracket chaos theory. It’s not that chaos theory isn’t true, it just moves it to a lower level so it’s no longer relevant.
Comment by Jason Godesky — 25 April 2007 @ 12:34 PM
Ok, I’m going to do this a little out of order, so bear with me
I understand that it was well cited. I was saying, quite frankly, that I reject the source material as well. Has nothing to do with it being wikipedia
Just to give you an idea of where I am coming from…. all of this ties together in my mind with animism and intuitive thinking. The questioning of science and scientific process discussion we had with Willem et al. I’m still having a hard time explaining the depth of my thoughts, but I think I might be getting a little closer to being able to do so. So we can consider this an exercise in that ongoing process.
But don’t you see how fundamentally linear that is? Ok, fine, every element is related, but that gives no credence, whatsoever, to qualitative properties. And it is the qualitative properties that make the difference.
To draw from a different discussion: it is the difference between somebody within your monkeysphere and someone without. The depth and importance and power of each relationship is fundamentally different and those differences are the real determining point of effect, neh?
How so less complex? If you are merely counting elements, a prairie is FAR more complex. The number of species in a square mile of prairie is hugely greater than the number of species in the same space of old growth. Remember, it’s the edges where everything happens. So on the scale of biodiversity, the old growth forest is at the bottom, then the prairie, then the boundary between the two. Check it out. Seriously. (Yes, Tropical Rain Forests are THE most diverse ecology, but I am not disputing that energy plays a role in all this. Compare temperate forest and temperate prairie and prairie has a much higher degree of diversity)
hmmm… that’s an interesting thing to say, particularly when you also concede that:
So are you saying that old growth forest dies because it is past the point of diminishing returns, or are you saying that it is the result of more complex systems dying back from diminishing returns? If the later, then why do the forests eventually die as well? Hmmmm?
I submit that the cycle of succession is nothing more or less than a cyclical system where the most efficient species within the current context of an ecological system prosper. And sometimes that means prairie, other times it means forest and yet others it means desert, etc. So…. if you really want to call that diminishing returns, so be it…. but that is watering down the theory a whole lot if you say that any move towards efficiency is an example of the same thing, don’t you think?
But it is not ‘advantageous to the group’ it is advantageous to those specific nieces and nephews… and their, individual success is what changes the make up of the group as whole. Same thing with grandparents, or altruism etc. It is the individual effects playing out on individual organisms. Re-read your Gould. Re-Read your Dawkins. This is a REALLY important piece of modern evolutionary theory.
Ho’d up. Big difference between dynamic equilibrium and dynamic dis-equilibrium – and I was not using it accidentally. Dynamic dis-equilibrium specifically refers to balance points that are completely impossible without active and constant reinforcement. So something like a Lotka/Volterra Cycle is a dynamic equilibrium. The oxygen content of our atmosphere, however, is dynamic dis-equilibrium. Because there is no ’stable’ volume of oxygen in our atmosphere. It always bonds with other elements – so in order to have free oxygen it MUST be constantly replaced. Basic Gaea Theory.
A grassland or a prairie? Does grassland actually even exist, or is that just a mis-nomer? Probably somewhere in between. I don’t think that is true about old growth forests, however. If it were, well, most of the world would have been old growth when we came along. In fact, long before we came along, and in the absence of constant crises, old growth forest gave way to other ecologies. Takes a long damn time, but it still does happen.
When is the last time that you watched a fractal? A subtly changing but mostly repeating sequence. Classic non-linear equation, classic example of chaos in motion. But the cycles still repeat, they just repeat imperfectly. Just like climate. August is warm in the Northern Hemisphere, while February is cold. But you cannot know what the exact temperatures will be six months ahead, NOR a few days ahead (although the closer you get to the date, the more accurately you can make some kind of guess.
So let’s talk initial conditions. The Butterfly Effect does not say that a butterfly WILL cause a hurricane. It says that something as simple as a butterfly flapping its wings could impact a hurricane half way around the world. So let’s look at ecologies in that sense.
Imagine two different ecologies (pretending for a moment that we can segregate one from the next….)
(Note: example taken completely from my ass, so please no quibbles on the details)
One has soil with an iron component of 1%.
The other has soil with an iron component of 3.5%.
Pretend everything else is exactly equal.
Do you honestly believe that these two ecologies will develop in exactly the same way? Or do you think that the second will magically make that iron disappear? Or that the iron will create a positive feedback loop that leads to a completely different result? No. In fact, both will gradually move through the stages of succession, but the exact plant components and life cycles will vary slightly because of the iron difference. This is a ’sensitivity to initial conditions’. It does not require a positive feedback loop… just a continuing variation.
That’s where I am quibbling with language, though. Because complex systems ARE chaotic systems and vice versa. All complex systems are sensitive to initial conditions. Not meaning that they fly out of control, but that they respond differently depending on ALL of the relationships inherent to the system. Something like the jet – well, that is a merely complicated system with a chaotic element introduced intentionally……………
No… it merely needs to maintain an influence. It does NOT need to spiral out of control.
Comment by janene — 25 April 2007 @ 1:17 PM
But in that analogy, everyone’s in someone’s monkeysphere. Every cultural element has essentially the same number and weight of connections to every other cultural element. You might be able to talk about this or that element as “more important” to one area of a culture, but not to the culture as a whole. That’s the important part.
Old growth forests don’t just die off from old age. They die when something happens to them, not from internal causes.
Well, that’s only because you’re pretty radically redefining succession here. Succession always moves from grasslands, to new growth, to old growth. In different places, it may stop at some point along the way because that’s all the local resources will support, but it’s not a cycle that stops relatively randomly: it is a very linear process, that goes further in some places than others.
I fail to see the difference. That’s just dynamic equilibrium between two imbalanced forces. One is much stronger than the other. The forces putting out new oxygen are greater, so the equilibrium struck is on the positive side. There’s still a mean that the value modulates around. It sounds like the difference is simply whether or not the equilibrium is at zero. I don’t think that makes much of a difference, though. The key point here is that there is a value that is always approached, and even when knocked away from that, the system tries to return to it.
No; old growth might be the “ideal” for succession’s ultimate “goal,” but the earth isn’t “ideal.” Actually, you’d really expect old growth to be in the minority before humans, since it would only be in those places where the conditions were all right, and nothing had happened recently to knock it down.
No, but the one with more iron in the soil is going to have more plants that use more iron, until they start using it up. Then new plants will prosper, plants that take up what those iron-hungry plants left in the soil. As time goes on, the soils begin to look more alike, because the ecological system is washing out the initial conditions.
In what way is that sensitivity to initial conditions? They both end up roughly similar, despite the difference in initial conditions. The makeup of species varies slightly, but they are still mostly similiar. We don’t end up with one a rain forest and the other a desert. That would be sensitivity to initial conditions: small initial differences leading to vastly different outcomes. But here, small initial differences leads to very little difference in outcomes. How is that sensitive to initial conditions?
They’re certainly not identical, but sensitivity implies that small differences will lead to much bigger differences. Instead, self-regulating, complex systems minimize those differences. That’s not sensititivity. There’s some difference to begin with, and there’s still some difference at the end, but it’s generally less difference; sensitivity would imply more.
How can you say it’s sensitive to something, when all it does is maintain it? When my skin is sensitive, than a very minor impact will produce disproportionate pain. If my teeth are sensitive, a slight difference in temperature will produce a massive sensation of hot or cold. Sensitivity means that the effect is disproportionately greater than the cause; how can a system be sensitive to slight changes in initial conditions, when all it actually begins to minimize the effect of those conditions?
Comment by Jason Godesky — 25 April 2007 @ 1:50 PM
That doesn’t seem reasonable to me. Not that it is (or isn’t) [b]used[/b] to assert that predictions about complex systems are impossible, but rather the conclusion itself that chaotic systems are inherently unpredictable. From the background I have, chaotic systems allow for different levels of prediction (usually, with a time or iterative aspect attached), but any chaotic system [b]of interest[/b] has some amount of predictability; if one is literally talking about random chance, that’s probability and statistics, not chaos theory.
Ok, so, a system that maintains an equilibrium until such point that it is [b]no longer capable of doing so[/b] is complex, and that once it is no longer capable of maintaining that equilibrium it becomes chaotic? That doesn’t seem right, and I’m reasonably certain you don’t think so either.
Hmm, okay, so, initially we have a chaotic system that grows until it’s in equilibrium (due to finite resources, physical restrictions, etc), at which point it becomes complex? That doesn’t seem right either….
I think I understand what you (and obviously, the Wiki article) are driving at by using sensitivity to initial conditions as a defining characteristic, but I’m just not getting it.
As I understand it, all complex systems are sensitive (in varying degrees) to initial conditions, and chaotic systems are a subset of complex systems.
I’m going to go back and review my advanced math, maybe I’ll find
something that clicks….
Comment by jhereg — 25 April 2007 @ 2:26 PM
Ok. Have you ever actually READ the data that inspired chaos theory? Let’s start with the real basics.
Edward Lorenze was running weather modeling on a computer system. He ran the same sequence dozens of times with the same results. But at some point, he decided he didn’t want to wait for the earlier part of the sequence to run over and over, so he picked an iteration, printed out the data values, had his assistant type those values into fresh and then ran the sequence again… and everything was different.
That is not to say that the system broke, or lost continuity or in any way was radically changed…. just that the results were suddenly not the same anymore. Still a stable system. Still repeatable, as many times as he ran it, the new results recurred.
So now he had to figure out why. Turns out, when he sent the data values to the printer it chopped them off at eight or ten decimal places. So he lost the fine details in his data points and that made all the difference.
NOT the same thing as a positive feedback loop. Just different.
Now jump forward a little and look at Strange Attractors. Very simple pattern. I could ell you with absolute certainty that the next point to fall is going to fall somewhere within the parameters of the pattern, and I would be correct 99.999% of the time (and when I was wrong, it would only be marginally outside of the pattern). However, there is absolutely no way to tell precisely where the next point will fall. Can’t even say if it is going to be on the right or the left loop. It could, literally, be anywhere.
The ‘point’ is weather. The Attractor as a whole is climate.
Now back to it………
You’re looking at the opposite side of the analogy from what I was trying to invoke. I’m not looking at culture as a whole (in the analogy) I am looking at you as an individual. Makes a HUGE difference in your life whether an action takes place within or without your monkeysphere.
To take it back to artifacts, it also makes a huge difference to you if a tool you use everyday is improved. Not so much, if there is a subtle, third generation change to a tool you use on occasion, or not at all.
Of course they do. Just not in a timeframe that we humans relate to well.
Forget ideal. If eventually succession will always getting to its ‘highest’ possible state, and then only slips back to any earlier stage as the result of catastrophe, then shouldn’t maximal succession be the norm at some point in ‘history’? When more so than after a period with minimal catastrophe’s to muck it up?
Equilibrium, even dynamic equilibrium, settles into a relatively stable state.
Dis-equilibrium, however, is a loss of stability. When you talk about dynamic dis-equilibrium, therefore, you are talking about a constantly changing unstable state.
Put another way, dynamic equilibrium is established, then occasionally tweaked to maintain the status quo. (Basic, negative feedback)
Dynamic dis-equilibrium is NEVER ‘established’, it is constantly pushing a pulling from various points, always staying just outside of a feedback loop – or maybe one could even say that it is multiple positive feedbacks interplaying just so to prevent any of them from spiraling out.
You could even say that the difference is in energy. The first is pretty energy savy, while the later is energy intensive.
ahem. And where, pray tell, is the iron going? You have made a number of points over the years based upon the basic understanding that elements don;t get used up. They just cycle. Granted, the soil may have less iron, but the ecology maintains that higher level throughout. And the difference in species is exactly the kind of change that occurs as the result of differing initial conditions.
Chaos Theory does not really deal with Chaos. That’s the point I have been trying to make, seems like for years, now. See above.
But this is not, in fact, what they found. Not more difference. Just difference. Remember these are scientists that HAD BEEN quite happy with a clockwork universe. Even after Quantum Mechanics came on the scene they could dismiss that as not-relevant to the macro scale. Chaos Theory changed that. But not by actually introducing random chance, but simply by recognizing that we are not smart enough to understand it all. At least not from a mathematical/scientific perspective. And perhaps, when you get far enough down on the decimal places, perhaps they even opened a door for quantum fluctuation. But I have never seen anyone actually suggest that…………..
Sensitivity can be used to mean hyper-sensitivity. Like your poor tooth. But all it really means is that something is capable of responding to stimuli. Look it up.;-)
Comment by janene — 25 April 2007 @ 2:34 PM
That’s not what I said. Complex systems self-regulate. They move towards a given point of equilbrium: succession moves towards a given ecological state, homeostasis moves towards a given biological state, etc. Chaotic systems don’t. If we introduce something new to a chaotic system, it will drastically change the shape of the chaotic system, because it’s sensitive to such stimuli. If we introduce something to a complex system, the complex system will try to regain its former state. That’s not to say you can’t introduce something so overwhelming that the complex system’s self-regulation fails, but when you do so, you’re working against a complex system. A chaotic system would escalate the impacts for you.
No, it’s a system gaining in complexity. You’re assuming that everything is complex or chaotic. That’s not the case. Many things are too simple to be either one.
Well, that is how chaos theory defines chaotic systems, as I understand it: systems are chaotic in that they are sensitive to initial conditions. They’re unpredictable because the initial conditions cannot be perfectly known. Small things have big effects.
That’s very different from complex systems, where even big things have small effects, because the system works to minimize those effects.
Well, initial conditions have an effect. Does any effect count as sensitive? If I shout in your ear and you barely hear a whisper, is that sensitive? Doesn’t sensitivity imply that the effect is disproportionately larger than the cause?
If so, then complex systems cannot be chaotic, because they’re not sensitive to initial conditions. They have an effect, but they’re not sensitive to them. They self-regulate, they minimize the impact. They tone it down. They go back to their equilibrium state as much as they can. They make those conditions as unimportant as they can.
Chaotic systems don’t have self-regulation, which is one of the defining characteristics of complexity. Chaotic systems escalate the impact of initial conditions, so that very small initial differences end up having drastically different outcomes. It’s like that old sci-fi story about going back in time and changing the past. Push someone out of the way of a moving car in the past, and if history’s a chaotic system, then you might end up with some vastly different present. Of course, cut down a tree in the past and come back to the present, and what was a forest before hasn’t suddenly become a desert. The forest is complex. It absorbed that change, and in the end, whether you cut down that one tree or not, the forest looks pretty much the same. That tree over there is two inches more to the right, and this one has moved a whole foot to the left—there is an effect, but it’s been minimized. There used to be a cut down tree here; centuries later, the difference betweeen “forest with tree” and “forest without tree” would take some careful observation to notice. Because the forest self-regulates. So in what way does that display sensitivity to such changes?
Comment by Jason Godesky — 25 April 2007 @ 2:39 PM
from:
[url]http://www.cna.org/isaac/Glossb.htm#Complexity[/url]
Emphasis mine.
Note that if I were to really run with this, I would say that “Elegance” should be defined as anything with a low static complexity relative to a high dynamic complexity.
Comment by jhereg — 25 April 2007 @ 2:48 PM
It kind of is, isn’t it? The initial difference was .000127, yet the outcome was substantially different. Each iteration of the model the computer went through, the difference increased, and as that iteration’s difference increased, it made the next iteration even more different. The more iterations you run, the greater the difference becomes. Very small initial difference gets bigger and bigger, constantly. Isn’t that the definition of a positive feedback loop?
By the same token, if we were looking at healthy person, and his perfect clone, and we introduced a massive bacterial infection to the clone, then each iteration (let’s say, day), the clone’s immune system has eliminated more of the bacterial infection, so that day he’s stronger, and his immune system is able to eliminate even more of the pathogens. Eventually, the clone’s immune system wins, and the clone and the original healthy person are once again essentially identical. Over each iteration in a complex system, the difference is diminished, and each iteration makes the difference diminish that much faster. And isn’t that the definition of a negative feedback loop?
Sure, but we’re not talking about individuals, or even subcultures. We’re talking about the complexity of cultures. If we wanted to take subgraphs, we could certainly say that models of cultural complexity don’t explain units smaller than cultures, but that would be fairly disingenuous. After all, we’ve already established that as a complex system, there’s more than a simple additive property here. It can only be understood as a whole system.
When? Where? I’ve heard of old growth forests drying up due to global climate shifts and the like, but just withering up and dying because they got too old? I’ve never heard of that.
No, because catastrophes are too frequent, and besides, only a small fraction of the earth’s surface has the resources to support maximal succession at any given point even under the best of circumstances. You’re not going to get it at the poles, for instance, becasue the angle of the sun is all wrong; neither in mountains, because the air is too thin, and so on. Take all that into account, and there’s really only a small percentage of the earth’s surface where it would ever be possible, and even there, catastrophes are fairly commonplace. Floods, fires and avalanches are annual occurences in some places. Succession might be pushing everything towards old growth, but it’s far from the only factor in play, and because of that, it doesn’t always get its way.
So what do you call eternal fluctuation about some mean, regardless of what that mean is? Because that’s what I thought dynamic equilibrium was. Sometimes it settles to just a static balance, but I was under the impression that was pretty rare, and that we were almost always talking about sometimes above, sometimes below, but always hovering around some basic mean.
Like oxygen. Sometimes it’s higher, and sometimes it’s lower, but we don’t have 0.001% of the atmosphere oxygen today, and then it’s 75% oxygen tomorrow, right? There’s variation about a mean.
But that’s much less difference than the original soil makeup. The species distribution is a little bit different; all the species tend to be storing more iron than they otherwise would. But the ecology follows the same pattern. You still get an understory and a canopy, you still have the basic successional process taking place. As the ecologies mature, they become more alike. The initial difference is minimized. Are you saying that a system that minimizes differences in initial conditions is sensitive to initial conditions?
Kansas with tornado vs. Kansas without tornado is a much bigger difference than butterfly flapping its wings vs. not. The difference gets bigger. The differences Lorenz modeled got bigger. Every example of an undeniably chaotic system I know of revolves around differences getting bigger.
But to use that meaning of sensitivity makes it tautological. It’s just saying that causes have effects (which is already implied in “cause”). By that, anything and everything is a chaotic system, so it means nothing at all. All you’re saying is that a cause will have an effect.
Comment by Jason Godesky — 25 April 2007 @ 3:02 PM
Okay, do I really need to point out that there’s another ending here? How about “Eventually, the clone dies….”? And before you point out that you specified a [b]healthy[/b] person, may I remind you of the [b]germs[/b] portion of “Guns, Germs, and Steel”?
Comment by jhereg — 25 April 2007 @ 3:07 PM
Now, if you wanted to make the point that the human body is actually chaotic and sensitive to initial conditions, you’d have to say that the clone dies because the immune system helped the bacteria reproduce, because then the system would be showing sensititivity to the initial difference. Whether the clone’s immune response succeeds or not, the fact remains that the immune system is trying to re-establish homeostasis. It is trying to fight off that bacterial infection: it is trying to eliminate the effect of the initial condition. The difference may be too great; it may fail. That doesn’t change the fact that the complex system was trying to eliminate it, it just means you overwhelmed it.
Likewise, you can rip out a forest and plow it under and keep succession from restoring it through active effort. That doesn’t change the fact that succession keeps trying to re-establish that forest, and that you have to fight it every inch of the way. That’s why farmers pull weeds and buy herbicides.
Whether or not the clone dies is irrelevant to the point at hand. He has an immune system that tries to re-establish equilibrium. He’s self-regulating. It might fail, but the system tries to self-regulate, nonetheless.
Comment by Jason Godesky — 25 April 2007 @ 3:14 PM
At this point, I think I’m trying to say that I’m not satisfied with your definitions of complex system and chaotic system. You seem to be trying to say that complex is bounded and approaches some value, whereas chaos is unbounded and doesn’t approach any value (except, perhaps infinity, but I’m not even sure about your stance on that), but that really doesn’t jive with what I remember of either complex analysis or chaos theory.
Comment by jhereg — 25 April 2007 @ 3:31 PM
Chaos theory is defined in terms of sensititivity to initial conditions. That isn’t my definition, that’s what I keep seeing in everything I read. So when a difference is introduced, the difference between two chaotic systems approaches infinity: they grow more divergent with each iteration. Complex systems are defined by self-regulation and emergent properties (again, not my definition). Self-regulation means that when differences are introduced, the difference approaches zero over increasing numbers of iterations. One is a positive feedback loop in which a small difference leads to a slightly bigger difference, leading to still greater difference, versus a negative feedback loop in which the difference is extinguished. Perhaps not perfectly; it may only approach zero, but it’s certainly minimized.
I’ve certainly provided plenty above to suggest that complexity has everything to do with self-regulation and emergent properties. If you don’t think chaos theory has anything to do with sensitivity to initial differences, here’s a few pages I found quickly:
Wikipedia: Chaos theory & Butterfly effect”
Chaos Theory: A Brief Introduction
Wolfram Math World: Chaos
Chaos theory
Introduction to Chaos Theory
I’m not a physicist or a mathematician, and I’ve never studied Chaos theory closely, but sensitivity to initial conditions sure seems like a well-established defining criterion of a chaotic system.
Comment by Jason Godesky — 25 April 2007 @ 3:43 PM
hmmm… remember way back when, when I said:
This is important, too. I do not, for a minute, believe that they were right back when they ‘determined’ that Chaotic systems are unpredictable. Mathematically, quite difficult, sure. But in no way unpredictable in the real world…. much like weather and climate. Weather, well, the closer you get to time, the easier it gets – even if it is still susceptible to unexpected changes. Climate – quite predictable so long as you don’t try to predict it too precisely. That’s how ALL chaotic systems are. Try to pinpoint the details and you are going to get hosed. Try to predict to far away from real time, with accuracy, you’re gonna get hosed. Not because it is impossible, but because we don’t have the neural capacity to deal with that many variables (and there is that quantum variation possibility)
So, to go back at it:
Of course the difference got bigger. Not ‘outside the norm’ but the variation between the two models increased. Of course they did. Let’s go back to your chopping down a tree 100 years ago. On the grand scale of the whole forest, that is a tiny little change. So let’s look at the iterations, say a year at a time….
In the first year, the difference in the forest is: one chopped down tree.
In the second year, the difference is: one chopped down tree, filled with decompositional life forms, a couple of new saplings and some other plants growing in the sunlight afforded.
In the third year: more saplings competing for sunlight, a huge fungal colony, lots more understory plants.
In the fourth year: an older tree falls down (would have anyway) but because both trees have opened up the canopy, you now get a nice big raspberry patch establishing itself, plus all of the previous years changes.
And so on and so forth.
You are looking at the forest before and after and saying ‘it still looks like a forest so nothing has changed. And that’s pretty much true.
Chaos Theory looks at the elements in the model and says there are 100 discreet elements that are different, and that is a big change. Which is also true.
But both describe the same system.
In Chaotic systems, the overall pattern DOES NOT change. Only the fine details. That’s why they ARE predictable, within a certain level of detail, and that is why Chaotic Systems ARE complex systems and vice versa. Because in both cases, the defining characteristic is that overlying pattern.
To be perfectly frank, I’ve kinda lost the initial point of this whole piece of the discussion…… oh, yeah… okay….
The point was the qualitative difference in different depths of relationships. No, we are not talking about individuals, but the point of the metaphor was to direct your attention to those qualitative issues. Cultural objects do not (cannot) exist as a flat matrix, not if we are talking about a complex system. Three, four, maybe more dimensions, with connections that vary from very weak to very strong. That is the kind of information that describes complexity… and so I think that Anthropologies desire to ‘count’ objects erases all of the real information about complexity.
If ‘catastrophes’ are so common, then they are not really ‘catastrophes’ are they?
Have you considered that this is part of the system? Just a few needles…. of course we are not gonna find old growth at the poles, or in the deserts… that’s why I suggested ‘maximum possible’ not simply ‘old growth everywhere’. However, forest is the primary ecology of the mountains. Not above the tree line, obviously, but of the places you still find old growth, its almost all in the mountains………
Both describe eternal fluctuation around a mean. I thought that was clear. The question is how and why… are they held relatively static via negative feedback? Or is it something else? How much energy does that relative stasis cost? And what and wherefore is causing the psuedo stability? Push or pull? If you stop feeding in energy what happens?
With D equilibrium, if you stop feeding energy, the system falls into entropy and gradually becomes disordered.
With D dis-equlibrium, if you stop feeding in energy the system dies.
Sez who? A slight variation in the soil composition is a greater divergence than a completely different guild? Yes, the basic pattern is similar. Just like a fractal. But the quantitative and qualitative difference are far greater in an established system than they were with just soil composition!
You put too much credence into the butterfly. That is no more than a vague possibility, thought up as a cute (and BTW intimidating) way to describe what they were talking about. The chances of any butterfly (or seagull, or any of the other animals they have used in the parable) actually creating a tornado or a hurricane etc are infinitesmally small. And even then, it wouldn’t be an animal creating the weather, it would simply be one tiny difference out of hundreds and thousands that all feed into one single, complex (chaotic) system.
Hell… you want an analogy? Tell me how a forest in Colorado responds to a stray spark in August. Oops.
But that IS the meaning of sensitivity. And no, it does not make it tautological, although I find that the more I read into a lot of this stuff, the more it appears tautological to me (I have an upcoming article on evolution exactly about that…..), all it says is that different systems are more or less able to respond to stimuli. Complex (and Chaotic) systems are defined as quite responsive to stimuli. That does not mean that they cannot handle stimulation
Comment by janene — 25 April 2007 @ 3:49 PM
From the “Chaos Theory: A Brief Introduction” url you posted:
So, okay, it’s not a steady state, and it’s non-periodic, so, yes, mathematically it’s chaotic, but it’s still bounded, see?
Comment by jhereg — 25 April 2007 @ 3:51 PM
Another one from the same url:
So, it isn’t [i]per se[/i] either/or in relation to complex & chaotic. Complex systems can become chaotic, and chaotic systems can stablize.
Comment by jhereg — 25 April 2007 @ 3:58 PM
It’s precisely that profligation of dimensions that makes every cultural element’s impact equal and total. Every new element affects every part of the culture, and viewed across all dimensions and the whole culture, every element has an equal impact on the culture as a whole. So the number of elements still remaisn the primary indicator.
In one sense, they are. They’re part of the global system. But they’re not part of the ecology: the organic communities that live together. The ecology has to adapt to changes in that larger system that contain it.
Above the treeline was precisely what I meant, though.
I think of this as pulling in opposite directions. The resting point could be positive, zero or negative, depending on which side pulls more strongly, and it’ll go this way and that, depeneding on how things go, but so long as each force remains viable, the equilibrium remains the same. When one of those forces fails–auto-immune diseases in organisms, removal of keystone species in ecologies, and so forth–you see the order suddenly collapse, the same as if a tug-of-war team all suddenly let go.
It’s not a completely different guild. Lots of guilds can “swap” members, with relatively similar plants playing the same role. All plants have certain tolerances, and can absorb more iron when necessary. So we’re not talking about entirely different guilds. We’re talking about more iron-friendly alternatives and subspecies in the same guilds, and everything picking up more iron than it might otherwise.
On the grounds that complexity minimizes the impact of stimuli? That’s the part I don’t get.
OK, so chaotic systems are not sensitive to initial conditions?
Comment by Jason Godesky — 25 April 2007 @ 4:06 PM
I’m sensing some frustration ;-(
You completely ignored the bit about the forest…. did that not help you to see what I am trying to say?
But it does not minimize the impact of stimuli, it incorporates it into the whole. Think Borg.
The only real difference between complex systems, and their subset, chaotic systems, is how deeply nested the sets are. Is it simple enough for us to grasp, or not?
Why do you see sensitivity to initial conditions as equivalent to unbounded?
Janene
Comment by janene — 25 April 2007 @ 4:15 PM
I’m not saying that chaotic systems aren’t sensitive to initial conditions.
I’m saying that complex systems, in general, are sensitive to initial conditions, that chaotic systems are a subset of complex systems, that chaotic systems have variable degrees of predictability, and that chaotic systems may or may not have a “Strange Attractor” (analogous to being bounded). At least, that’s what I’ve been able to dig out of this lump 3 feet above my ass.
Comment by jhereg — 25 April 2007 @ 4:18 PM
Little bit, yeah; it’s starting to seem like all this chaos theory stuff is either (a) tautological and therefore meaningless, or (b) contradictory and therefore meaningless. I’d like to think there’s something useful to it, but if it’s not sensitivity to initial differences, I don’t know what it is.
No, not really, because by the time you get to year 100, you’re well on your way to having a new tree growing up there, probably of the same species. Its shade will lead to the early successional species dying off. A few centuries out, the difference will be that a different tree of the same species stands within a few feet of where the old tree stood. If we look at some intermediate point, we might find greater difference, but the system is moving to eliminate the effect of the change as much as possible.
Because if the effect of initial conditions is extinguished, then it’s insensitive to such changes. You recover from disease; a forest regenerates after a fire. Even with massive differences, the impact is minimized. You’re more or less the same before and after a disease, even though the disease itself introduced a big change. Same for the forest fire. In both cases, a big difference was turned into very little difference. This is an insensitivity to differences in initial conditions. It makes initial conditions mostly irrelevant.
It may be extinguished eventually, there may be some asymptote, but to my mind, if a system is sensitive to initial changes, that means that initial differences need to have bigger effects. So, if a forest were sensitive to initial conditions, and we introduced a forest fire, then the burning forest would be different from the pre-fire forest, but the difference would continue to get bigger. So it’d become, I dunno, a tundra. You’d get the flu, and grow a second evil head. If the difference is extinguished, then how is that sensitive?
This is the part I don’t get. If you’re an eighth of a pound smaller than me at birth, that’s not something that’s going to lead to escalating differences. On the contrary, that’s something that’s going to be accounted for and largely eliminated over time. You can take two complex systems and even introduce very large differences, but because they’re self-regulating, over time, they’ll become more alike. The differences get worked out, rather than compounding. How can that possibly fall under the heading of “sensitive to initial conditions”? Wouldn’t that be the very definition of insensitivie to initial conditions—no matter what the initial conditions, the system will tend towards the same equilibrium state?
Comment by Jason Godesky — 25 April 2007 @ 4:32 PM
Hey –
hmmm… you took the wrong angle on what I was trying to say, once more. Damn, I gotta figure out how to express this better….
Sure… but go back to the forest. Yes, eventually another tree will spring up, or the same species or of another common variety to the forest, serving the same role in the guild. To you or me, the change seems minimal, minimized, even. But to the mathematician, that tree and all of the other living things that have come and gone, (differently from what they would have without the tree being cut down) are, in fact, different. Each object or entity has a mathematical significator. Doesn’t matter that 1A and 1B function in the same way in the system. It only matters that 1A is not 1B. That’s where the mathematical statement that the divergence increases come from.
Now, you and I, well, we know that its mostly semantically BS, even if the language is math. And yeah, mostly Chaos theory is not terribly useful anymore. It has been supplanted by complexity theory. Partly, that’s what I have been trying to express — that they really are the same thing, but with different assumptions and (therefore) different conclusions.
The important thing I have taken from Chaos Theory is the understanding that even mathematically complicated systems are understandable by the human mind — so long as we don’t try to analyze the details too strictly. So that opens up huge potentials for the way our descendants might be able to incorporate the ideas of modern science without getting bogged down in the cost and reductionism that it is currently defined by.
And of course, this means we’ve gotten way off track the original discussion, but I’m gonna let that lie until we can find some consensus on this bit
J
Comment by janene — 25 April 2007 @ 4:47 PM
Well that’s just not a very good mathematical model–even anthropologists counting up cultural elements do better than that; “number and distinctiveness of its parts.” Two trees of the same species should be related, if the model’s going to hold well. Sure, there’s some difference, but less than there was initially. The difference is minimized. Imperfectly, but minimized.
Taken to this level, it seems like chaos theory just says that causes have effects. Which seems like tautological nonsense to me.
Heh, I got the same thing from complexity. You look at the system as a whole; you don’t necessarily need to understand all of the individual parts. It may not even help you that much, even if you could.
Comment by Jason Godesky — 25 April 2007 @ 4:55 PM
Hey –
Well, yeah, that’s a basic problem with math because there is NO qualitative analysis, ever. It’s not elegant enough
The thing about Chaos Theory is that it presents a way to conceptualize that which appears to have no pattern whatsoever. It gives us the ability to see that it really is nested sets, just very very complicated ones. Watch an animation plotting out a Strange Attractor, sometime, and you’ll see where I got all excited about it.
Now… its gonna take me some time to figure out where exactly it was that we got sidetracked into a debate on chaos……
Janene
Comment by janene — 25 April 2007 @ 5:03 PM
Not necessarily. You could do this with a weighted graph, for instance. What you’d see is a small initial difference, perhaps an intermediate expansion of difference, and then an extinction to almost no difference at all. It could be done, but not by the model you suggested. That would just roll over everything. It really says more about a bad mathematical model than it does about anything real.
I guess I don’t get it because that was my operating assumption from about age 3 or so.
Comment by Jason Godesky — 25 April 2007 @ 5:08 PM
Braggart
J
Comment by janene — 25 April 2007 @ 5:11 PM
Okay, hopefully, 3rd times a charm*….
from cna corps’s website:
The important thing I’d like to bring up with the 2 types of complexity proposed here is that it leads directly into a good definition of elegance: low static complexity, but high dynamic complexity.
Better yet, think of an evergreen sapling. Now, predict ([b]precisely[/b]) where every brach, stem and needle will be in 10 years. You can’t do it. But you [b]can[/b] describe the most likely general shape of the tree. There you go, chaos theory in action, right there.
See the big take away is that reductionism fails inside a complex system. It isn’t tautological, it’s a bridge from mechanistic thinking to organic thinking. You may well say that this is a blinding flash of the obvious, and you’d be right, this is pretty obvious to most children (and is a direct segue to animism, imho). And, of course, because a reductionist society has difficulty knowing what to do with such forms of understanding, we really haven’t done much with it (not nothing tho’, it crops up in some unexpected places, but relatively speaking, not much).
How does this impact our understanding of cultural complexity? I have no proof whatsoever, obviously, but I [b]suspect[/b] that dynamic complexity is either a fixed value for human culture or close to a fixed value for human culture. Additionally, I suspect that static complexity is primarily a function of available energy. I also think that the ratio of static to dynamic complexity can be used as anthropologists use the counting up of distinct artifacts. I think this is the kind of complexity Jason’s talking about in regards to civilization: high static complexity, high dynamic complexity. Similarly, I think Jason’s view of elegance could legitmately be described as low static complexity, high dynamic complexity.
Comment by jhereg — 26 April 2007 @ 9:31 AM
*yeah, forgot the postscript: Jason, does the spam filter have something against CNA? Not that I could blame it, mind you, but I tried to include the link twice and nada….
Comment by jhereg — 26 April 2007 @ 9:32 AM
Hey Jhereg –
Wonderful. Yes, you pulled a lot of that together brilliantly
And the high dynamic complexity/low static complexity…. that makes a lot of sense to me and if Jason agrees, I may well be done here for now
Janene
Comment by janene — 26 April 2007 @ 9:47 AM
Thanks Janene :-), it took a lot of dredging around in the mental attic; I haven’t given any of this much thought in, oh… well over 5 years, so it took me awhile.
I’m very much hoping that Jason does agree :-), because, like I said I really don’t take issue w/ the conclusion, just some of the defintions along the way….
Comment by jhereg — 26 April 2007 @ 9:58 AM
Hmmm … this is getting somewhere. My one remaining problem is that what your source is calling “dynamic complexity” seems like a misnomer. What you’re calling “structural complexity” is precisely what I came up with for complexity above—a system that defies a reductionistic approach. But this concept of “dynamic complexity” seems unnecessarily, well, complicated.
What I mean is that it’s derived above from some of the furitive and ultimately confused attempts to define “complexity,” and those definitions that turned on defining it in terms of how it could be described or encoded. So, biological complexity as the amount of genetic information. This seems like a confused grasp, that we’re now codifying, rather than just confronting the original confusion.
What we’re essentially talking about with “dynamic complexity” is simply effectiveness. And in those terms, we’re absolutely getting to elegance: low complexity and high effectiveness. It just seems like using the word “complexity” here confuses the issue more than anything else.
You’re also somewhat right in that this effectiveness of culture is somewhat fixed. It’s rather more accurate to say that it’s a function of the (static) complexity of the culture. The ROI on complexity gives you a general idea of how effective (dynamically complex) each new cultural element will be, so you can always determine the effectiveness (dynamic complexity) of a culture based on its (static) complexity. This is precisely what the diminishing returns curve on complexity gets into.
But to just call them all different types of “complexity” seems to obscure far more than it reveals.
Comment by Jason Godesky — 27 April 2007 @ 11:44 AM
True, I mentally glossed over “information” and replaced w/ function (or effect).
/shrug
Well, you did see my comment about “blinding flash of the obvious”, right?
There’s a reason I left all this behind so many years ago: it’s not exactly nessecary to a full and meaningful life.
On the other hand, what you’re doing with “The 30″ sort of requires a certain amount of reference to reductionist thinking, which, this essentially is. There’s no question that it can make your head hurt (certainly hurts mine), but there are gains in specificity to be made by separating out the different aspects. This is a technique that mathematics does frequently and when there is a disagreement about something as open as “what is complexity?”, is often the best way to disambiguate statements.
As to “official” definitions of complexity in the hard sciences, I don’t think there’s complete agreement (even within the individual science in question), and that disagreement becomes more pronounced once you start crossing the boundaries. Chaos Theory does a better job than anything else I’ve seen at trying to unify the various brances of human knowledge as relates to complex/chaotic systems, but since it’s really only a fringe branch, it still hasn’t been very codified. So I’m not really sure you can rely on a simple citation to backup any particular defintion, imho.
Comment by jhereg — 27 April 2007 @ 12:09 PM
Hey –
I don’t think you can say that “dynamic complexity” is simply effectiveness.
I’ve been racking my brain for an example and maybe I found one….
Imagine a quartz crystal, the structure of molecules all lined up in a perfect crystalline form.
Now imagine the cellular structure of an organism. The structural image is very similar. Same number of elements (in a perfect case scenario), aligned in basically the same form…
But you and I know, intuitively, that the cellular version is far more complex, because it does things, interacts, creates etc etc, whereas the crystal is static.
So the “static complexity” is the same in both instances, but the “dynamic complexity” is very different. (At the same time, you cannot say that is merely elegance, because the crystal is more elegant than the organism….)
Janene
Comment by janene — 27 April 2007 @ 12:12 PM
Perhaps function is a better phrasing. Organisms have more functions than quartz, a knife can be used to perform more functions than an glock, and I suspect that human beings & their cultures have a fairly narrow region of functions that we do/require. This last point would be difficult to prove, but Dunbar’s Number seems to be good supporting evidence.
Comment by jhereg — 27 April 2007 @ 12:18 PM
Hey –
Not sure I follow…. I mean, a glock is also more complex that a knife, whereas the knife is more elegant. So how does this apply to the purpose/usefulness of the dynamic vs static complexity model?
Janene
Comment by janene — 27 April 2007 @ 12:27 PM
Yes, exactly, the knife would have both a lower static complexity (form) and a higher dynamic complexity (function), so it would actually be considerably more elegant.
At least, that’s how I read it.
Comment by jhereg — 27 April 2007 @ 12:29 PM
Hey –
hmmm…. I’m not sure I buy that, either…. is dynamic complexity the number of uses to which a ’system’ can be put, or does it more properly refer to the inherent functioning of the system?
My gut says the latter…
Janene
Comment by janene — 27 April 2007 @ 12:39 PM
From JMG’s discussion on sustainable tech:
[url]http://thearchdruidreport.blogspot.com/2007/01/principles-for-sustainable-tech.html[/url]
Where he goes on to discuss his criteria for sustainable tech (pruned back considerably):
Most of these have a pretty direct impact on complexity: independent, replicable, & transparent.
IMHO, not being independent would increase both forms of complexity; replication is directly tied into form, and a simpler form (or lower static complexity) would be more replicable*; transparency is a bit more indirect, but I think that anything not transparent is pretty much inevitably going to have more static complexity, if only because something(s) has been added to prevent transparency.
Comment by jhereg — 27 April 2007 @ 1:42 PM
Hmm. Maybe. Of course, from a cultural complexity POV, I think it means “to which”, rather than inherent functioning. Then again, I’m a little hard put to think of a situation where inherent functioning would be separate from form (static complexity).
Comment by jhereg — 27 April 2007 @ 1:49 PM
In a crystal, doesn’t the pattern just keep repeating? Cells make up tissues, and tissues make up organs. Each of the cells has sub-cellular components, like the nucleus and the cell wall; they might even have mitochondria, an ancient bacterial symbiote. That’s much more complex than a quartz crystal, even if we’re just counting the elements.
As for “dynamic complexity,” I think you’re illustrating here why it is it’s setting off all my B.S. alarms.
Comment by Jason Godesky — 27 April 2007 @ 2:21 PM
Ah, well, I still don’t see how to define complexity in a clear, concise universally acceptable manner. That’s probably why it’s mostly stuck at the “I know it when I see it” stage (which it is, even for the hard sciences that try to deal with it directly).
Comment by jhereg — 27 April 2007 @ 2:26 PM
But that’s really not the case at all. There’s lots of competing definitions, but all the good ones start to line up under “a count of the elements in a system that defies reductionism.” It’s not just “I know it when I see it,” it’s not an arbitrary definition at all. We have a very good, solid definition for it. It just doesn’t stretch as far as you’re trying to stretch it, and I’d say that’s because you’re trying to cram things under the “complexity” heading that just plain don’t belong there.
Comment by Jason Godesky — 27 April 2007 @ 2:34 PM
Sorry, jhereg, I have no idea how Akismet became so convinced you’re a spambot—I rescue what I can.
Actually, transparency is something of an opposite of complexity. Things that are too complex become too difficult to understand; that’s the essnece of Arthur C. Clarke’s “any sufficiently advanced technology is indistinguishable from magic” comment. “Advanced,” for him, means complex.
Complexity’s also opposed to durability, since the more complex a system is, the more points of failure it will generally have (this is at least true of technological complexity, because it has so few good self-regulating systems). See the discussion of complexity in computer programs above, for example.
Replicability of complex systems gets back to the same point as transparency, since a system too complex to understand is too complex to replicate as well.
And in terms of independence, this again is fundamentally opposed to complexity. Complexity is all about building technologies on top of one another—another way of saying, making them less independent.
So, like I said, complexity and elegance are two opposing forces that are balanced in the creation of any tool, system, culture, etc.
Comment by Jason Godesky — 27 April 2007 @ 2:49 PM
Okay, so a cursory search of definitions of complexity:
the quality of being intricate and compounded; “he enjoyed the complexity of modern computers”
[url]wordnet.princeton.edu/perl/webwn[/url]
We can say there are two kinds of complexity. Detail Complexity is when there are many variables. Dynamic Complexity is situations where cause and effect are subtle, and where the effects over time of interventions are not obvious.
[url]www.worldtrans.org/whole/wholedefs.html[/url]
Poor Terminology! Like `specificity’, the term `complexity’ appears in many scientific papers, but it is not always well defined. (See however M. Li and P. Vitanyi, A Introduction to Kolmogorov Complexity and Its Applications, second edition, Springer-Verlag, New York, ISBN 0-387-94868-6, 1997) When one comes across a proposed use in the literature one can unveil this difficulty by asking: How would I measure this complexity? What are the units of complexity? …
[/url]www-lmmb.ncifcrf.gov/~toms/glossary.html[/url]
is a measure of the number of possible states a system can take on, ie, the condition of a system, situation, or organization that is integrated with some degree of order but has too many elements and relationships to understand in simple analytic or logical ways.
[url]www.mountainquestinstitute.com/definitions.htm[/url]
A set of structure-based metrics that measure the attribute of the degree to which a system or component has a design er implementation that is difficult to understand and verify. IEEE96
[url]www.hi.is/~oddur/spisland/ref/def.htm[/url]
domain of emergent properties and non-linear relationships between factors; unlike chaos, which is inherently uncertain, may often create an illusion of predictability, especially where linear analysis is applied within a short-term, narrow set of assumptions
[url]www.soul-dynamics.com/glossary[/url]
Complex Systems Articles, Papers, Books & Bibliographies
“Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side — these have been puzzles to science, or worse, monstrosities.”
– Jame Gleick in Chaos: Making A New Science
[url]http://www.brint.com/Systems.htm[/url]
Definition: The intrinsic minimum amount of resources, for instance, memory, time, messages, etc., needed to solve a problem or execute an algorithm.
[url]http://www.nist.gov/dads/HTML/complexity.html[/url]
Excerpts: Complex engineered and biological systems share protocol-based architectures that make them robust and evolvable, but with hidden fragilities to rare perturbations.
Chaos, fractals, random graphs and power laws inspire a popular view of complexity in which behaviours that are typically unpredictable and fragile ‘emerge’ from simple interconnections among like components. But applied to the study of highly evolved systems, this attractively simple view has led to widespread confusion. A different, more rewarding take on complexity focuses on organization, protocols and architecture, and includes the ‘emergent’ as an extreme special case within a much richer dynamical perspective.
[url]http://www.comdig.com/[/url]
The aspects of distinction and connection determine two dimensions characterizing complexity. Distinction corresponds to variety, to heterogeneity, to the fact that different parts of the complex behave differently. Connection corresponds to constraint, to redundancy, to the fact that different parts are not independent, but that the knowledge of one part allows the determination of features of the other parts. Distinction leads in the limit to disorder, chaos or entropy, like in a gas, where the position of any gas molecule is completely independent of the position of the other molecules. Connection leads to order or negentropy, like in a perfect crystal, where the position of a molecule is completely determined by the positions of the neighbouring molecules to which it is bound. Complexity can only exist if both aspects are present: neither perfect disorder (which can be described statistically through the law of large numbers), nor perfect order (which can be described by traditional deterministic methods) are complex. It thus can be said to be situated in between order and disorder, or, using a recently fashionable expression, “on the edge of chaos”.
[url]http://pespmc1.vub.ac.be/COMPLEXI.html[/url]
And from the CNA link I tried to include earlier:
over 30 measures of complexity have been proposed in the research literature
I think at best you could say “a count of the elements in a system that defies reductionism”. But I fail to see that it’s a huge step up from “I’ll know it when I see it”.
Now, if you don’t like the static complexity/dynamic complexity, fine, that was a freeform attempt on my part to try and tie this back to the topic. All it really means is minimize parts, maximize function, and you find elegance.
Well, that and most elegance inherently has [b]some[/b] degree of complexity.
But, seriously, my point is that if you want to define complexity, please be my guest, just don’t try to say that there’s a lot of widespread agreement.
Well, that, and be really, really careful when referencing anything on Chaos Theory.
Comment by jhereg — 27 April 2007 @ 3:52 PM
eh, np, I s’pose I could deal with existence as spiced ham, at least not many people would want to eat me!
I suppose. I don’t really see complexity being “opposed” to durability, so much as I see durability arising from elegance. And since I don’t think that elegance is opposed to complexity….
So, wasn’t it Donald Knuth that said?:
1) Simple is better than Complex
2) Complex is better than Complicated
3) Simple tends towards Complicated
What would be your take on that? How does that fit into your view of complexity? Where does elegance fit in?
Comment by jhereg — 27 April 2007 @ 3:59 PM
No, I think it was Tim Peters’ “Zen of Python”:
Beautiful is better than ugly.
Explicit is better than implicit.
Simple is better than complex.
Complex is better than complicated.
Flat is better than nested.
Python is Better.
Comment by Jason Godesky — 27 April 2007 @ 4:06 PM
Ah, well, hopefully, we can at least agree on that!
Comment by jhereg — 27 April 2007 @ 4:09 PM
This is all in PHP ’round here.
Comment by Jason Godesky — 27 April 2007 @ 4:14 PM
Yeah, I know, but…
Comment by jhereg — 27 April 2007 @ 4:23 PM
I don’t know. Is it really not possible for suitably [b]elegant[/b] technology to be indistinguishable from magic…? I mean, elegance doesn’t really say anything about how obvious something is; in fact, often times, the most elegant tools (or methods or whatever) are non-obvious. Hmm… I don’t know…
Comment by jhereg — 27 April 2007 @ 4:32 PM
Elegant technologies are simpler, and thus more transparent. A slide rule is extremely elegant, for example.
Comment by Jason Godesky — 27 April 2007 @ 4:35 PM
I’m with you on the second sentence; it’s trying to cram the idea of effectiveness under the heading of “complexity” that bothers me. Effectiveness isn’t a kind of complexity.
Of course; like I said, complexity is like heat, there’s always some degree of it.
Well, allow me to now repeat your definitions (an impressive list, BTW), with commentary….
Focuses on number of elements.
“Detail complexity” measures number of elements; “dynamic complexity” boils down to not being reducible.
Well, we do have means of measuring it, don’t we? So this is really poking at popular conceptions of complexity, rather than the precise term we’re using here.
The first definition I think we can dismiss with a counter-example of a paper clip. Really, about as simple an element as this world provides, but able to be bent and placed into an infinite number of states. So I’d say the first definition is simply ill-considered.
The second just restates the irreducibility of a complex system.
This is just plain messy. Any number of simple things might be difficult to understand or verify. To the degree that this definition has value, it lies in the reference to a complex system’s irreducibility.
This one gets us back to emergent properties (explicitly), and self-regulation (implicitly, in the delineation from chaos and its predictability).
Irreducibility as it haunts a scientist’s nightmares, perhaps?
This is the definition used in mathematics and computer science, already considered in full in the article.
So, complex systems have emergent properties and self-regulate.
So complexity measures the number of elements in an irreducible system?
And all of them grope around the same aspects: the definition of complexity in number of elements in a system that cannot be analyzed in a reductionist fashion, and the two main properties of such a system, emergence and self-regulation.
Comment by Jason Godesky — 27 April 2007 @ 5:55 PM
Okay, I had to get away from this for a couple days, then get back to it.
After getting a little perspective, I agree that that’s as good a definition of complexity as we could ask, and it should serve it’s purpose. I think I’ve almost gotten to the point where I agree that elegance is opposed to complexity. I think that one is going to need to “cook” a little longer.
Comment by jhereg — 30 April 2007 @ 8:33 AM