Notes on Complexity
What makes something physically complex? How can physical complexity be measured?
Let’s start with a typical dictionary reference. I have on hand Webster’s New Collegiate Dictionary (copyright 1980 by G. & C. Merriam Co.). There are three definitions, adjective, noun, and transitive verb. We are of course interested here in the adjective and noun. The etymology provided in the adjectival definition references the Latin “complecti, to embrace, comprise (a multitude of objects).” The root “plectere” means “to braid.”
The first definition includes objects that are very simple: “composed of two or more parts: composite.” The next two (as variations of the first) refer to specific English grammar uses, i.e. complex words and sentences. However, the second distinct definition is “hard to separate, analyze, or solve.” This sounds more like what I have in mind, as there is nothing hard to analyze or solve about something that has as few as two pieces. Even things that have a lot of pieces may be easy to solve or analyze. Thus, having multiple parts must be the barest minimum consideration. On the other hand, “hard to…” is very subjective and there’s no direct reference to physical properties.
The first definition in the noun entry is a bit more helpful, perhaps. “a whole made up of complicated or interrelated parts.” The use of “complicated” in the definition may seem circular at first (maybe it is), but upon consideration it reveals that a complex object may have parts that are themselves complex. Now we are beginning to get a more satisfactory picture of the difficulty in solving or analyzing what we generally have in mind when we call something complex. The other definitions (also) include the idea of a number of parts that can be considered as a group due to some relationship or interaction.
It might help to also consider what might be called the “opposite” of complexity, that is, simplicity. What might we consider the epitome of simplicity? Perhaps a total vacuum? But that may be going too far. How about something that’s singular, without sub-parts? The old idea of an atom would fit the bill. Perhaps these days we would think of quarks instead. But in acknowledging that change, we can see that “simplicity” can be dependent on scale, relative comparisons, or practical purposes. Protons and even atoms can indeed be considered ultimately simple within their own realms. What is relevant to something’s complexity depends on what qualities make it what it is.
Let us consider, then, sheets composed of the same atom, for example carbon in graphite film. In the broad sense of complexity, even a couple of atoms might technically qualify, but we would generally consider any number of atoms in this case to be simply one sheet of graphite. Furthermore, any part of the sheet would look identical to any other (not to be fussy about possible contaminants which arguably are irrelevant anyway).
So I would argue that in a very real, practical sense, sheer numbers of components do not relate to the useful, technical definition or conception of complexity that we are looking for. (“Sheer” indicating “by themselves, alone, apart from other considerations such as interrelationships.”)
Another method that might help trim sloppy usage and vague conceptions is to look at things which might be called complex and see if there are other words which might work better. For example, the relatively few snowflakes with highly branching structures are sometimes said to be complex. But they are essentially made of one kind of molecule (water), and are essentially static shapes. The so-called complexity of these shapes are better described as exhibiting “intricate order.” Probably the biggest problem in this area is this confusion of “order” with “complexity.” Something that is ordered merely has a regular arrangement of parts.
Another phenomenon sometimes called complex is the hurricane. Here again, though, we have only a couple of elements (in the old or general sense), air and water, and while they interact very dynamically, there is no fixed pattern (beyond the general circular swirl and shorter-lived smaller whirls) to the motion, and the elements behave en masse rather than as discrete components. Such highly dynamic phenomena that do not have many long-lasting distinct structures are better described as “chaotic.”
So, complexity should be identifiable and perhaps quantifiable, but not by simply counting the number of parts or anything like that.
1) The number of parts would probably be the place to start in an evaluation, taking into account the practical/scale consideration. A big pile of sand is not significantly more complex than a small pile of sand, at least not in any practical sense. (an example of “sheer numbers”)
2) The next consideration would be diversity of parts. Again, a simplistic reckoning would not be very useful, and practical application of scale would have to be taken into account. Does the diversity of parts affect or relate to the reactions and inter-relations of parts? A pile of garbage may have many, very different things in it, but they don’t move, and if they move (perhaps by sliding down the pile) there is no organization or fixed relationships.
3) Scale and dimensionality also need to be considered. More complex (that is, the most complex) objects will have parts interacting at various scales, in three dimensions, moving or varying systematically over time.
4) Intricate, stable, systematic order is also a factor, though not complexity itself (as noted above), as setting apart complex objects from chaotic phenomena.
5) Dynamism is also very important, although its presence must be taken into account along the way (in respect to the previous characteristics) to determine which parts/aspects are considered significant. The electrons in most things wouldn’t be counted, but some of them in electrical devices and photosynthetic processes might be considered as important parts, at least en masse. Thus, computers are considered very complex, not so much for their few moving parts (hard drives, fans) nor the intricate arrangement of their circuitry (okay, that too, in common usage), but because of their data storage and complex shuffling of electrons in a systematic fashion (data processing).
6) A final factor to consider is information content. Even something that is static may be considered to have some complexity if it is not merely regularly patterned, but takes its unique identity and form from being part of a coding or communication method, system, or technique. Thus, a page of writing may be considered more complex than one with a simple graphic design, and “a picture is worth a thousand words” because it conveys a lot of information about a complex scene. In a way, a novel that is a static pile of paper with ink could be considered more complex than a toy that has many different parts and can move if wound up or placed where its solar panel is in sunlight. We may need to specify different kinds of complexity to avoid such “apples to oranges” comparisons. Interestingly, the most complex things, living things, have a great deal of both kinds of complexity. Robots, which have information stored in ROM and RAM chips, sensors and microprocessors, also have both kinds, to a lesser extent. In living things, the information content of DNA is used by the biological system to produce the physical complexity, so perhaps there is some way to compare or equate information and complexity. There’s more to the process than “simply” translating the DNA code, however, and we still have much to learn.
You may have noticed this isn’t a means of detecting all examples of design — it leaves out very many designed objects. I do think it can help clarify that there is a quality to high-tech artifacts that is shared by living things, and not by anything else. I also think it can be used to clarify and evaluate what I mean when I say that evolution (as a story of the origins of all life) requires increases in complexity, to evaluate cases where such increase has been claimed to be observed, and to define which “evolutionary” changes are actually compatible with the creation framework. I think creationists have been too quick to deny the possibility of some things, such as flatfish “evolving” from upright fish, or the very existence of “half a wing.” Such things could be due to degeneration from the original created forms or other reasons that wouldn’t show evolution. (I’m not sure about the flatfish, there may be more to it than having a migrating eye and maybe losing a swim bladder, etc.) I also think there is no way to detect design in every case — things that seem to be totally chaotic messes, or very simple and unformed masses, might have been designed that way. It may be possible to define an upper limit to what inanimate (abiotic, non-living-thing-related) natural processes can produce, but what I’m attempting here is to show a kind of complexity which can only be created by design (or reproduced by a living thing with at least equal complexity) and is very far from what other processes can produce.
Okay, now I’m going to consider a few examples.
A lot of designed tools don’t begin to shape up. From stone tools to modern hammers and crescent wrenches, there are all sorts of objects clearly identifiable as designed, but verging on ultimately simple: one solid object. You can throw in handles, note that they have a stable order (but not an intricate one) in their structure… but these hardly make any difference worth considering.
Now, simple tools like pliers and scissors take a step in the right direction. There are at least two parts (depending on how they are joined) and the parts have different distinct shapes. But that’s it. No functionality on different scales, there’s only a bit of intricacy in the way they are joined, and they are not dynamic in themselves.
The mousetrap might be considered the simplest example of something that’s complex in the sense I am trying to develop here. It is usually made of more than two parts, and the parts have different distinct forms and usually are made of two or more different materials. They also have the capacity for dynamic “autonomous” action, although like all artifacts they require a human to at least prep them for action. This action is also triggered by a moving part reacting to an interaction with an outside source. Perhaps I should add something like “sensing” to my definition. I’d have to specify that the interaction causes an internal reaction, to clarify that a boulder being pushed off a cliff doesn’t count. I suppose such things could be subsumed under dynamism, combined with diversity. I’m not ready to stick numbers or other specific descriptors in here, but I think the potential is clear. Come to think of it, maybe the anti-irreducible complexity argment that a mousetrap can be used as a tie clasp indicates an even simpler example and one that can be quantified as the minimal level: Three parts, joined in a stable configuration, with at least one of the parts providing a systematic motion.
It might also help to show why I’m not impressed with a report of protists supposedly becoming colony creatures. Being stuck inside the membrane of the original cell for one or a few more replication cycles doesn’t really add anything. There are more cells forced into close proximity, but they don’t exhibit any diversity, new interactions, or functionality. Furthermore, since this first step occurs fairly quickly and regularly, I’m not impressed by the excuse that it’s only one small step toward greater complexity. Let’s see another step — why not? Perhaps if the one happens so quickly but the second refuses to appear, it’s because the first one is a designed ability to adapt, or a degenerative step which is easy to take and from which no evolutionary increase in complexity is to be expected.
Thinking about it again in 2013:
Since the beginning of the debate and the Watch on the Beach argument of Natural Theology, creationists have been championing what amounts to a common-sense, gut-level understanding that there is a certain category of object and recognizable hallmarks thereof, which can only be produced by the purposeful actions of an intelligent agent, and that living things belong in that category and have those hallmarks. It has always been an imprecise, analogical argument until recently, with the works of Gitt, then Behe, Dembski, and others in the ID group. The evolutionists’ response has always been to wave their hand at their “mounds of evidence” and the vague theory that depends on the untestable belief that small changes in living things can account for all the changes needed (by gradual accumulation). Oh, and for the origin of life… well, they got some building blocks to form and they’re still working on the rest, have faith, here we are so we must have (chemically) “evolved” at one point…
Well, there should be a way to set forth clearly and undeniably that the forces of nature just can’t produce life and then from a “simple” life form all other forms. As it is, evolutionists resort to hemming and hawing about the origin of life, proposing extremely different conditions and even contributions from outer space. They also refuse to discuss the differences in kinds of change, insisting that “big” changes can be accomplished by adding up all the little changes, and they even count changes of loss as evidence for what they believe evolution can accomplish.
SO, what we want is something clear and intuitively felt, like the Second Law of Thermodynamics (2LoT for short), and with the same degree of non-violation and inevitable one-way flow (and remember, at small time scales and individual particles even the 2LoT doesn’t hold, but nobody believes that larger natural violations could happen). It needs to be something that doesn’t require advanced math to understand properly, something concrete and objective.
I believe this careful defining of complexity is the key.
As we’ve seen with other important terms such as “information” and even “evolution” itself, a big problem is that there are already accepted terms, but the accepted ones only cloud the issue, and trying to re-define them doesn’t help. The solution seems to be in specifying the term for a given concept or context; this at least is accepted as a valid practice and elicits serious responses. The classic examples are “specified complexity” and “irreducible complexity.”
From what I’ve seen, “specified complexity” and “complex mechanisms” both are good concepts, but depend on assuming (more or less directly) an intelligent agent (to do the specifying or observing, or defining “function” in a way that implies intelligently-designed purpose). This is either begging the question, or too close for comfort. Evolutionists use terms and phrases all the time that fit ID better than evolution, such as “mechanism” itself — but if we point that out, they tell us it’s just a form of shorthand, and I have seen at least one article asking fellow evolutionists to STOP using such terms. We need a term and its definition that makes it clear that it’s not the baggage of the words used, their connotations, that matter, but the objective facts about the physical arrangements in question that matter.
“Irreducible complexity” is good, too, but it focuses on a specific, minimal kind of complexity, often so minimal that one might argue if it deserves the term “complex” at all. Some have sought an even simpler concept of minimal design, that would include even a basic doorway, nothing more than two uprights (or a hole) and a beam on top. It doesn’t take much to imagine nature forming such a natural bridge; in fact, there are many cases of something like that forming in nature.
What we need to establish is a simple but mathematical science of complexity that is based on the physical relationship of parts involved in any given object, and the processes involved in such objects and their alterations. This may seem like a daunting task, but I think we now have examples of previous works for guidance and for use. Thermodynamics of course set the example, and I’m sure when properly understood and applied will contribute to this new effort. Information science, again when properly understood and applied, is one area where we’ve already made a good deal of progress, from what I hear of Werner Gitt’s efforts. We need to translate the immaterial aspects to the physical manifestations. “Fuzzy math” and chaos theory are also examples of new ways of looking at things, and have been translated into popular investigations of nature and practical applications. Finally (or did I miss something?) fractal math has shown how physical arrangements (patterns) can be quantified or closely approximated in a quantifiable way. Oh, perhaps I should mention the math/science of dimensionality, which actually came before fractals and their surprising sort of in-between dimensionality.
Going into all that math or setting up a new, similar sort of math for the subject of complexity is totally beyond me, but these thoughts I’ve shared might help someone else start.
I think we need to have a system of ranking everything on a complexity scale that includes fractional values, directly related to fractal math in some cases. It might actual involve two or more kinds of complexity. I propose that everything that is not both organized and dynamic be given a value of less than 1 in physical complexity. I’m thinking a pair of scissors might be an example of 1 on the organized complexity scale: they consist of the minimum of two parts and have the minimal dynamic property of being capable of regulated movement upon application of an external force. The “regulated” (or perhaps “fixed” would be less suggestive) is the key here. Or perhaps that would be at 0.5 or 1/2 on the scale, with 1 being objects on the order of a mousetrap: capable of one independent motion, given an external input of energy followed by an external stimulus. Or consider a wind-up toy, which has more moving parts but cannot (does not, and doesn’t need to) react to an external stimulus. Either of them has at least one aspect of Systematically Organized Dynamic Complexity: (2 or more) differing parts connected in a way that converts an (external input of energy to an) internal source of energy to motion in a specific, consistent way. Computers have batteries or power supplies, and shuffle electrons around in consistent paths consisting of the different materials of transistors, diodes, capacitors, etc. What makes computers so much more complex is sheer number of parts, information content, and the variations in the possible electron flows.
As I’ve said, a simple scale might not suffice. We might need to define the complexity of things using multiple dimensions (scales, vectors, whatever you prefer to work with). Starting at the bottom, “zero complexity,” we might point to a single particle of one substance. Again, scale and boundary must be considered. At the very bottom might be an isolated photon, but even that is made of quarks, which can’t be isolated in nature. We could scale up to a planet, which is not only very large but consists of many different rocky materials, maybe even a coating of dynamic water and atmosphere and even be sprinkled with humans, the most complex known creatures — but on a solar-system scale, none of those matter; it can be considered a point or simple object for purposes of calculating its motion and those of the other bodies in the system. Nor does the presence or absence of liquids, gasses, or life affect the status of “planet.” Likewise, it doesn’t matter Jupiter and the other outer planets are mostly balls of swirling gas. So complexity can be contextual or vary with the scale or boundary of the system under consideration.
Likewise, for most purposes any ordinary rock can be considered as a totally non-complex singular object. However, for various technical purposes we could scale rocks and other solid objects according to the number of different interior components they have, and “components” again may depend on scale being considered. For a rock it might be how many different minerals make up the rock, for balls like golf balls and bowling balls it might be layers of materials. For snowflakes, the intricacy of the patterns can be measured by fractal math, whereas whatever different grains of dust trapped inside might be ignored. I suppose the way boundary conditions are defined for thermodynamics might be used or at least serve as a model for determining which scales are applied in a way that does not seem arbitrary or subjective.
Well, perhaps one or more people with the required knowledge, intellectual abilities and interest will pick up the ball and develop these ideas further.