Can scientists compare complexities?

May 25, 2007 9:33 AM

Do scientists have an accurate way to measure complexity? Are they able to compare a human body with a city, for example, and say that one is more or less complicated or complex than the other?
posted by cgc373 to science & nature (22 comments total)

I doubt it, because "complexity" is an umbrella term, even in science, much like "solar phenomenon." You can't measure complexity, because complexity is not a specific thing. It's a useful word that describes a conceptual framework.
posted by grumblebee at 10:04 AM on May 25, 2007

If the word means anything at all, it must describe a multi-dimensional value -- and that means that magnitude comparisons are meaningless.
posted by Steven C. Den Beste at 10:10 AM on May 25, 2007

There wouldn't generally be much use in such comparisons, so I don't think there's much discussion of such things in most sciences. However, in computer science and mathematics, this kind of question does come up.

If you consider more abstract objects than the human body and city mentioned in your question, say a paragraph of written words, then it makes sense to ask what is the smallest possible encoding of that paragraph. (This becomes of particular interest in computer science, since it's often useful to compress some information before sending it to someone else.)

Now, in order to call a piece of data, call it D, an encoding of our paragraph, we'll need some program that can take D as input and recreate the original sentences. In other words, we need some program that can uncompress the compressed paragraph. In fact, there are a whole bunch of different programs that could do the job.

To narrow down the field, let's consider only the programs that could handle, not just this particular paragraph, but any paragraph in the same language. That eliminates consideration of a lot of possible programs, but there is still a large set of programs that would work. However, we can now take the smallest of these programs, call it P, and use it to get some measure of the complexity of the paragraph. You can think of the complexity of the paragraph as the size of P plus the size of the data D. That gives a value by which the complexity of the given paragraph could be compared to any other collection of words or sentences in the language. (This value is called the Kolmogorov complexity of the paragraph.)

You can see how it might be difficult to apply this outside of computation, to the body and city example you mentioned. In fact it's difficult to apply even to mathematical cases, since the complexity turns out not to be a computable function! As the wikipedia page notes, it is possible to compute upper bounds on the complexity, but that's the best you can get.

I suppose biologists might have a less general concept of complexity they invoke in such cases, but it sounds like you're interested in the most general conception of complexity -- i.e., allowing for comparison between arbitrary objects. I think Kolmogorov complexity might be the most general in that respect.
posted by voltairemodern at 10:12 AM on May 25, 2007 [2 favorites]

I don't think there's an accurate or robust way, but since science is all about making predictions, I don't think it would be too far off to define a system's complexity as roughly the inverse of its predictability. As in, the more complex something is, the more difficult it is to make accurate predictions about its behavior, even if lots of information is known. For example, a billiard ball is fairly non-complex, and if you know its trajectory, mass, etc. you can predict its behavior in a very accurate way. Less so with an automobile, which is still highly predictable, but less so than the billiard ball by dint of its complexity (more parts and variables). Humans and cities are both incredibly complex since accurately predicting how both will behave is far beyond current capabilities. It's still a relative term and subject to all kinds of value judgements, so I don't think there's a "complexity number" or anything.

That's a bit handwaving, but with as vague a term as "complexity" I think it might be tough to get a more descriptive answer.
posted by SBMike at 10:13 AM on May 25, 2007

Here are some notes and references on measures of complexity
posted by euphotic at 10:15 AM on May 25, 2007 [1 favorite]

voltairemodern has it. Complexity and Order and Entropy of a system are things which can be dealt with mathematically, either as Shannon Entropy or Kolmogorov complexity.

These are measures of mathematical information however, not physical systems. You could extract all possible information from physical systems in order to extract their complexity but such a transformation is not well-defined. That doesn't mean there aren't sub-realms where the activity is useful: For example, these doctors developed a measure of an aging heart which reveals older hearts to be less complex systems.

There are entire fields devoted to answering your question and so its not easily answerable in a few paragraphs. The gist is that Complexity can be defined in different ways and each way brings slightly different and even contradictory results.

For example:

1. One measure says the body is more complex because it is more highly ordered: Move a few houses around in a city and its still a city, move a few organs around in a body and its dead.

2. Another measure might say the body is very simple because it can be easily "compressed" into some DNA and some generator functions. A city may actually be less compressible this way but then again, maybe someone hasnt found the right generator functions....
posted by vacapinta at 10:25 AM on May 25, 2007 [1 favorite]

I don't believe there is a universal measure of complexity for the reasons grumblebee mentions, although there are different ways of measuring complexity within a particular problem domain, such as computer science or biology. Eric Chaisson has proposed that complexity be defined as the energy density of a given system. This might be one way to compare the human body with a city. For more background on why measuring complexity is hard, see this.
posted by steadystate at 10:25 AM on May 25, 2007

The closest that you can probably come is something like voltairemodern was describing, which falls under the category of information theory.

However, trying to apply this to something like human cities would probably be an exercise in futility. Thinking through the problem yourself will give you some idea of the number of variables one might consider. Number of people, number of chinese restaurants, types of building materials used, pigeon droppings per square foot, (continue ad naseum).
posted by chrisamiller at 10:25 AM on May 25, 2007

Kinda what grumblebee said. Complexity, like entropy, are terms we tend to throw around but not really have a good gut feelign for. (Then there is the evolution / creationism debate where they really take a beating.) It can be used to mean highly ordered or a convoluted mess.

Scientists can calculate the entropy of a chemical system (though there is no entropometer you could use to take a direct reading). But in the sense I think you mean the city is going to be more "complex" every time just based on the number of atoms in play.
posted by Kid Charlemagne at 10:27 AM on May 25, 2007

Hausdorff Dimension/Fractal Dimension is how some of us in mathematics do that sort of thing. I hate to link to the W but it's a good list. It's used mostly in man-made fractals, but stuff in creation like clouds, vascular systems, rivers, and coastlines can be viewed from the same perspective.

Get it? Fractals, perspective?
posted by monkeymadness at 11:03 AM on May 25, 2007

A system must be more complex than it's most complex component. If humans are the most complex component of a city, than a city must be more complex than a human.

@ vacapinta about the "move a few houses around"

Also, you can perform the equivalent of "moving a few houses around" on a human - from cutting one's hair to losing a limb. An amputee is still a human.
posted by JacksonEsquire at 11:11 AM on May 25, 2007

I'll throw something out there. Big O Notation for computational algorithms. This measures the complexity of a given algorithm based (I generalize greatly here) on the number of inputs and how long it takes to complete the algorithm.
posted by boo_radley at 11:27 AM on May 25, 2007

A system must be more complex than it's most complex component.
Of course this depends on your meaning of complex. I'd argue that a simple tower built out of LEGOs is not very complex but the chemical and physical properties of each LEGO are very complex. If you look at the tower you generally think "that's a bunch of LEGOs" instead of "that's a big pile of molecules all interacting in X way".
posted by monkeymadness at 11:41 AM on May 25, 2007

I would say that they are apples and oranges. You could boil it down to the complexity of the molecules, and in that case, I would say that anything animated would be more complex.
posted by clearly at 12:30 PM on May 25, 2007

It's all a matter of definition, assumptions, and criteria. If there's a formula that can be applied to both cities and the human body then sure you can compare. But as others have noted, there are a lot of definitions of complexity and some of them are mentioned. In my work, the definition is related to the information/communication theory of entropy. It's adaptable and can be applied to a lot of things, but is only used where it makes sense.

But even if you could apply the same formula to both different types of items it may not make the comparison meaningful. E.g. the number of bits it would take to encode a complete description of a human may be much greater or much smaller than a complete city, depending on the detail... but it's not clear that comparing the two numbers is really meaningful in context because cities don't think or act.
posted by mikshir at 12:48 PM on May 25, 2007

Folks are right in that you can't measure the "actual" complexity of a real-world thing like city--the closest that you can really do is build a mathematical model that approximates some aspects of a city, and then apply one of the math approaches described to that model. The more usefully your model describes the thing, the more relevant the calculated measure, but you're still not ever really measuring the object itself.

Measuring complexity isn't like measuring square miles. You've got to put a lot of effort into building the model, and then take the answer with a huge grain of salt. For me, it puts this sort of question into the "It's not the destination, it's the journey" category.

Calculating that your model of the city has some complexity coefficient of exactly 4.625, while the body model comes out at 5.684 is pretty much meaningless. Working out the logic of good models, identifying which aspects make your "city" model rate come out lower than your "body" model, and then identifying how those aspects let you better understand the real-world objects--that's where you find the real point of an exercise like this.

_{[On preview, basically what mikshir just said]}
posted by LairBob at 1:36 PM on May 25, 2007

_{As a somewhat tangential aside, I just wanted to toss out that "thinking about complexity" brought up fond memories of reading Gregory Bateson back in my undergrad days. His thinking hasn't aged all that well (for me, at least), and I totally understand why he's kind of a loopy outlier on topics like "complexity", but man...I did really enjoy having my mind blown reading his stuff back then. Figured if any group were going to have similar fond memories of reading Bateson, it'd be folks on this thread.}
posted by LairBob at 1:52 PM on May 25, 2007

Calculating that your model of the city has some complexity coefficient of exactly 4.625, while the body model comes out at 5.684 is pretty much meaningless.

Exactly. It's all about context.
posted by Mr. Gunn at 9:48 PM on May 25, 2007

An newish paradigm in the study of complex systems is looking at systems from a network perspective. There is a lot of work right now looking at complex networks.

For example, you can look at the social network of a city, transportation network, electrical network, etc. In a similar way, you can look at gene regulatory networks, neural networks, or other networks in the human body.

Either way, like others have said, it's still about context. You still need to define your question well. You could ask, "Is the human vascular network as complex as the city's water system?" Of course, this raises another question, how do you measure the complexity of a network? I'm not that familiar with complexity measures in networks, but a lot of them are based on ideas from statistical physics, thermodynamics and information theory.
posted by formless at 2:22 AM on May 26, 2007

Just took a class on this, actually.

Check out Wm. Wimsatt's "Complexity and Organization" (pdf here, but it doesn't have the included figures) and Simon's Architecture of Complexity (JSTOR here).

(Wimsatt was my professor, FWIW.)
posted by rhoticity at 12:20 PM on May 26, 2007

I just realized that JSTOR might not work for you if you don't have an educational affiliation--sorry.
posted by rhoticity at 12:21 PM on May 26, 2007

Now that I've finally registered I wanted to come here toa say that complexity is actually a pretty big deal in ecology right now--but not in the apples-to-oranges manner of your example. For instance, ecologists are beginning to think that physical complexity of certain habitats (forests, reefs) may be linked to biodiversity and/or ecosystem health. This might also have practical implications for human management of such systems, since traditional management techniques often cause their simplification.

People do try to compare complexities of, say, different reefs, but they're only just beginning to develop quantitative techniques for doing this--and such work is much more circumscribed than your example. However, the topic is generating a lot of interest.
posted by Herkimer at 1:33 PM on July 18, 2007