It's like comparing a normal toy with something built with Lego pieces. If the toy fits your needs is perfect but only has a specific use. It looks like reality externally but not in its internal structure. Moreover, although a construction with Lego pieces is apparently more complex is just a set of simple bricks.

Keep it simple, let it crash and recover.

We try do develop our systems as simple as possible and accept the fact we cannot avoid every type of error. Recovery is an important thing to keep the system alive.

If a short crash with immediate recover to a stable state is an acceptable option to reduce system complexity: take your chance.

Dear Francisco and all:

As some other colleagues have commented before, it depends largely of course on the sense in which you use the term ‘complexity’.

Also other comments above interestingly approach us to Occam’s Razor, which I largely share, and relates to Godel’s Impossibility. If you can never buid a totally finished system of knowledge [i.e., a totally complete and conistent set of axioms] then the more rational solution is to work with the smallest set of consistent knowledge rules/axioms [i.e., the shorter model] that allows for a sufficiently precise modelling of the described phenomenon

Ok. Let us come back to the initial comment. What do you mean by complexity? I understand you use it in the sense of ‘being difficult to understand due to many interacting parts’, but let me use it in a broader epistemological sense, which allows us to highlight a wider range of issues.

Complexity Theory deals with everything we can know and model. Largely, because ‘knowing’ is a complex act but also because any model is built on rules [i.e., units of interacting phenomena] and usually the described phenomena [and the models used to describe them] are systems [i.e, sets of interacting elements].

That is the main reason why so many scientists claim to be leading the research in complexity while they work in quite different issues.

You can see it if you review a bit of the history of the relation ‘science-complexity’.

If we start from the well know Weaver’s article ‘Science and Complexity’, he already sets ground for an almost universal expansion of the term, since his article is epistemological [which can be rooted to Complex Thought, i.e., Morin], speaks about Organized Complexity [which best known later development is the idea of Complex Systems, i.e., Simon, Santa Fe Institute, Gell Mann, etc..] and also about Disorganized Complexity [this is a group where many different concepts fit, e.g. from statistical analysis, non-equilibrium thermodynamics –Prigogine-, and a bit of chaotic systems –Lorenz, Feigenbaum,…]

But though Weaver’s text marks the ‘official’ entry of ‘Complexity’ term in scientific texts, it does not limit its scope, which as I say, expands everywhere we can state knowledge.

In 1948 Shannon proposes his measure of Entropy [building on Gibb’s Entropy]. Initially developed to help Bell Telephone company better dimension the network wiring, soon becomes a tools widely used for trying to measure system’s organization.

In 1964 Solomonov proposes sort of a universal explanation [a formal theory] for enabling us to make logical inferences on a more consistent basis, building on Turing’s machine. One year later, Kolmogorov proposes his measure of Complexity building on Solomonov ideas. Though currently it is accepted that Kolmogorov’s proposal is not a measure of complexity but of Algorithmic information, still many proposals build on Kolmogorov’s ideas [Bennet, Kaplan, Gell-Mann,...].

So in parallel we have a systemic, a computational and an epistemological view of complexity. And the three of them are fundamental when building any model of reality.

Furthermore, more or less at the same time [1969], Zadeh [Towards a Theory of fuzzy systems] briefly proposes that almost everywhere reality seems to provide infinite amounts of information, and that our way to handle it is to convert it into measures we can manage through logical transformations.

Let me say that this proposal of Zadeh almost goes unnoticed, but still for me it is important. Somehow it is a nice effort to mathematise kant’s assertion; if we can only know through concepts, then we should model reality through concepts. It also approach us to another way of facing the problem of Sensitive dependence on initial conditions.

First highlighted by Pointcare in 1903, and being stated in more precise terms by Lorenz more or less at the same date [1962: Deterministic non periodic flow / 1973: does the flap of a butterfly in Brasil sett of a Tornado in Texas]. While a large branch of Compleity Science right now focuses on accurately modelling real world phenomena [Santa Fe Institute], Soft Computing focuses on 'fuzzily' modeling it. [Berkely Initiative on Soft Computing..

Let me skip the rest of the historical view that I just explained briefly. What I just wanted to highlight that the complexity of models materializes in different dimensions, with very different meanings and almost all of them must be considered when building a model, but their influence and the way they need to be dealt with is quite different.

Let me explain it in detail through an example. I am currently finishing a model for assessing urban sustainability. It is an operational model, i.e., its aim is to become a tool which can be used for helping decision making in many common processes in cities, though mainly in those referred to urban form, it can also be used in many other process.

For example, it can be used to assess the overall impact of a commercial product [e.g., the generalized used of electric cars, the conversion of roofs into green roofs...] it can be used to set the amount of official economic aids to commercial products based on benefits for the society, and a large etc…

 Ok, now let us get to the interesting part of the story that is how a model of this type relates to Complexity Theory:

From a systemic point of view,

• the object to be modeled [the city] can be understood as a Socio Ecological System [SES], which in usual terminology of currently so-called Complexity Sciences is a type of Complex Adaptive System [CAS], which incorporate Adaptive and Chaotic behaviours.
• the quality to be modeled [Sustainability] can be understood as an emergent property, hence a type of complexity manifestation that non linearly emerges from the interaction among parts of the system, requiring departure from thermal equilibrium [i.e., it can be measured in terms of neguentropy, building on Shannon’s Entropy].
• the sustainability of a certain city is highly conditioned by what other cities do, approaching us to networks analysis/theory of the games.

But also the decision to be made is a ‘complex object’:

• the dimensions that need to be evaluated interact among them [e.g., social/economic/environmental]
• the options that need to be assessed also interact among them, many times being able to combine in different ways [e.g., a city can decide to undertake a transformation that combines green roof, electric cars and other measures in different ratios, while each ratio provides a different result]
• the calculation of the best solution is an intractable computational problem [i.e., it does not belong to Computational Complexity Classes P neither NP] and being able to solve it, requires proposing simplified algorithmic solutions that can provide a solution using a reasonable amount of computational resources.
• the solution needs to be a rational decision making valid for public decision making, approaching us to the need to overcome Arrow’s Impossibility.

And last, the model is also a complex object:

• a model is an interpretation of reality which we understand mainly through comparison with already know concepts [of course, we always incorporate slight amendments, which is one of the reasons for the evolution of knowledge]. For such comparison, one of our most strong tools currently is Fuzzy Logic, as a framework that allows us assessing to what extent an object [in this case the city] has some qualities/concepts. This approaches us to Soft Computing and Artificial Intelligence.
• But also a model is a statement about reality, and interaction between reality and knower [von Bertalanffy] approaching us to some of the ideas of Complex Thought [Morin]

I hope this example has helped to explain a bit the many dimensions of Complexity that have to be correctly understood for making the best possible model of a real world object, but also the fact that some of them are not to be reduced , but just to be dealt with.

Best Regards

Dear Francisco

You can define completixy in science, social systems. In human-automation systems complexity is well defined from the point of view of objective and aubjective complexity. From the point of view of control theory a system is complex, for instance, controller, sensors, actuators, plant, (nuclear powet plant). From the point fo view of human facors and ergonomics is very important the subjective perception of complexity. In supervisory control tasks manage critical systems is a challenge for reserarchers.

Focusing on the two words: design and operation...

Good complexity should not be designed.In fact when it is, it becomes complicated.Good complexity should be bottom-up in construction.

The kind of bad complexity that comes to mind is usually connected to the notion of tight coupling. Where the margin for error is minimal.This lack of room for adaptiveness makes it highly fragile rather than resilient.Shocks to the system break it rather than remake it.

Complexity is not always bad, especially if we grasp how initiatives and shocks to the system "perturb" the stability of the system and anticipate/adapt to it.Some have chosen to call it anticipatory systems where the stress is on adaptive management rather than design.

Dear Francisco et Al:

I see other answers to the issue posed above, that in my view relate more to the system than to the model for assessing the system. So let me provide another alternative/complementary explanation to the one suggested above, which focus more on the complexity of the system, and not the complexity of the model.

From a physical POV, complexity is many times understood as the quality that enables building systems away from thermal equilibrium. Since thermal equilibrium is the state of maximum entropy [or disorder], complexity is many times considered to be equivalent to neguentropy [Bertalanffy, Foerster,...].

Neguentropy is a concept that relates mainly to organization. Any organization implies an expenditure in energy to be built [Lovelock] and creates a difference in information [which allows to understand why Shannon uses Entropy formula for measuring information].

But structures can be stable or instable; can tend to steady states or to critical points. In fact some authors question whether there are any steady states or all real systems tend to Self Organized Critical States [SOC, Bak], where collapse happens as an endogenous feature [i.e., collapse is generated by the usual dynamics that explain the system].

SOC theory is interesting and the economic system has been put as an example of a SOC system.

And relating to this issues, I am finishing a review of the economy of UE-28 countries that may shed some light to the above question from an empirical basis, which we can relate to two issues:

When we review countries’ evolution from classical economic indicators like GDP, employment,… SOC dynamics are clearly present. It seems like the economic cycle tends always to critical states and from time to time a collapse [crisis] is necessary [i.e, cannot be avoided] to adjust the system state [an easy eplanation is understanding that when too fragile structures are built too large, they necessarily collapse]. But…

When we use different variables, SOC dynamics do not appear, and the countries that best perform under classical economic indicators show steady equilibrium states using this other variables…

This is highly interesting. It relates to something many times discussed: the importance of the oberver as whom choses the variables to be reviewed. It also allows us to understand that a sustainability indicator shall be that which value can be stationary in an economic crisis, not which show SOC behaviour.

Of course, those two issues are very important, but they are not related to the issue discussed here, So.. which is the interest? Ok, let me explain it now... 

Any economic activity implies creating structures [i.e., departure from thermal equilibrium], or in other words, implies neguentropy or Entropy reduction. 

And any collapse [as SOC critical episode] implies a neguentropy destruction; a reduction in activity [hence approach to thermal equilibrium].

From a physical point of view, the first is equivalent to what the majority of scientists would consider an increase of the complexity of the system and the second to a reduction in the complexity of the system.

So, if we assess countries using classical economic indicators, we are indirectly measuring sort of their complexity [of course, not all their complexity]. But some of such complexity may be essentially fragile; the next economic crisis it will collapse with high probability [this could be consider as an example of what many people dessignates as 'bad complexity'].

Yet, if we assess countries using sustainability indicators, we are indirectly measuring ‘the part of their complexity’ that can be sustained over time; i.e., the part that can stand a crisis without collapsing [it somehow would be equivalent to what many people considers 'good complexity']

Hope this example provides some ‘empirical content’ to the issue asked above and I am sure that Francisco [a Spaniard as me] is convinced of the important of the above nowadays that Spain is struggling to overcome a devastating economic crisis, largely due to building too unstable structures [sort of 'bad complexity'...]

Regards.