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.

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.

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.

Well, that and most elegance inherently has some degree of complexity.

Of course; like I said, complexity is like heat, there’s always some degree of it.

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, allow me to now repeat your definitions (an impressive list, BTW), with commentary….

the quality of being intricate and compounded; “he enjoyed the complexity of modern computers”
[url]wordnet.princeton.edu/perl/webwn[/url]

Focuses on number of elements.

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]

“Detail complexity” measures number of elements; “dynamic complexity” boils down to not being reducible.

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]

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.

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]

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.

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]

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.

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]

This one gets us back to emergent properties (explicitly), and self-regulation (implicitly, in the delineation from chaos and its predictability).

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]

Irreducibility as it haunts a scientist’s nightmares, perhaps?

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]

This is the definition used in mathematics and computer science, already considered in full in the article.

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]

So, complex systems have emergent properties and self-regulate.

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]

So complexity measures the number of elements in an irreducible system?

over 30 measures of complexity have been proposed in the research literature

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.

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.

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…

Python is Better.

[i]Python is Better. [/i]

Ah, well, hopefully, we can at least agree on that!

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.

Sorry, jhereg, I have no idea how Akismet became so convinced you’re a spambot—I rescue what I can.

eh, np, I s’pose I could deal with existence as spiced ham, at least not many people would want to eat me!

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.

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?

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.