# Complexity, discovered complications

Here more and less serious types of complexity are considered from different viewpoints.

## Definition

The term complex is often used for situations that appear quite different. Thus one has a broad range of different notions of complexity,  such that it is not always clear what is being claimed when a situation is said to be ‘complex’, even in strategic management.

## Complex versus complicated

According to the Concise Oxford Dictionary, the term complex derives from the Latin for ’embrace’, and is associated with the term ‘plaited’. The point here is that the whole is not composed of parts in a linear or sequential way (like a conventional building) but the parts ‘work together’ to form the whole (as in a geodesic dome). It is thus useful to distinguish between complex (parts are inter-dependent in a way that is hard to comprehend) and complicated (the whole is constructed sequentially, and challenges only in scale). In use a system with complicated but acyclic (‘linear’) causal relationships is ‘only’ complicated, whereas a complex has complex causal relationships. For example, if share prices only depended on earnings and other ‘concrete’ factors the stock market would be complicated, whereas because share prices depend on expectations which depend on performance (cyclically) there are (as Keynes noted) causal cycles, and hence the stock market is complex.

A petrol engine also has a causal cycle since the engine normally generates electricity which is used to ignite the fuel, but this cycle is ‘under control’ and hence ‘tame’ in a way that the stock market is not always. When we talk about complexity it is normally implicit that we are talking about untamed complexity, where either there is no regularity or deviations from regularity can propagate in unexpected ways, for example with positive feed-back. (Thus a tame system may be objectively complex but we may be able to treat it  subjectively as only complicated.)

Typically, a complicated problem can be solved if enough computational ‘horse power’ is thrown at it, whereas complex problems can at best be satisfactorily resolved, if tame, or need continual attention to keep ‘in check’.

## Complexity, uncertainty, pragmatism, logic and assumptions

For complicated systems, uncertainty may be nothing more than variability, represented by probability; pragmatic approaches tend to be adequate; and the implicit assumptions of classical analysis tend to be adequate, e.g. classical logic (with classical cause and effect) tends to be adequate.

For complex systems none of the above simplifications hold. Thus the distinction between complicated and complex is key, as it indicates which ‘intellectual tool-bag’ will be appropriate.

## Discovering complications

A complicated system is one which we could tackle conventionally. But often even if a situation is ‘only’ objectively complicated our ignorance may mean that we have to be careful in our analysis of it, almost as if – subjectively – it were complex. From this point of view, it is our ignorance that matters, not the ‘plaitedness’ of the system being observed. We have to try to discover what we can about a system, which may be unfolding.

## Entanglement

If consider ourselves to be ‘just’ discovering complications we are taking a ‘dualist’ view of our subject: that we are separate from it as a system. In particular, our subject is not responding to our understanding of it. Otherwise, we and our subject are entangled in a mutual embrace, with each responding to the other (or else why are we bothering to observe it?)

From this point of view even if an external system was merely complicated, our interaction with it would create a complex, unless we or it behave stereotypically. In designed systems (such as driving a car) the complexity may be tame, but for natural or accidental systems it may not be.

## Rules of the game

If an observed system reacts to us according to known rules, then by understanding those rules we could come to treat the situation conventionally, so that the situation would in that sense be merely ‘complicated’. Similarly, if we act stereotypical (e.g., following a given process) then the external system may come to an equilibrium with us in its behaviour, such that the situation appears merely complicated. (But it may be that we are missing an opportunity to ‘think outside the box’.)

This notion of ‘rules’ generalizes the notion of complexity as being about linkages, considering not only rules about linkages, but rules about processing. Thus a single process is complicated if the processing rules are definite but complicated, complex if the are no definite rules, such as if there is ‘open’ (unconstrained) learning from experience. Thus a system which only ‘adapts’ with set bounds is complicated, while one that exhibits ‘higher level learning’ or innovation is more complex.

## Comparison of discovered complications and complexity

Discovered complications challenge many of the same habits as complexity, so is there a significant difference?

An approach to complexity could also be used to tackle discovered complications: one might simply waste some time on esoteric thinking that wasn’t actually required. So one might learn to tackle complexity and treat discovered complications as a lesser included case. But the problem here seems to be that complexity challenges classical rationality (else why would we have modern logic?), which people find difficult. On the other hand, with discovered complications one supposes that the ‘real’ logic of the situation is classical, and that one is working around the limitations of one’s ignorance. Thus one can cope ‘pragmatically’ without considering esoteric logics: complicated is, by definition, challenging in scale but not to logic. The danger, then, is of applying a ‘discovering complications’ approach to a complex problem, which may not work.

A simplistic pragmatic approach is to use a known model of the situation unless and until it is clearly broken. Under discovered complications, a complication might be hidden for a while until it is suddenly revealed. Thus, whereas in  a known complicated situation one works with what is known, under discovered complications one is always on the look-out for new complications, e.g. hypothesising them. Thus one has a variant of pragmatism in which one is looking for the full range of models that fit the observations so far, and making new observations to reduce the ambiguity. This is useful for complex situations too.

Under discovering complications one would expect that the more observations made the better one’s understanding, so that as long as one was making enough observations compared with the realisation of extra complications one would come to an adequate understanding of ‘the current situation’, and be able to take informed action, much as one can do for merely complicated situations, but taking account of the residual ambiguity. But in complex situations one expects continual novelty, and our activity (or even preparations for action) may provoke novel action.

In effect, an approach based on discovering complications can cope with routine responses but not ‘game-changing’ reactions.

## Example

For the small investor the stock market may seem complicated in the short term, but can occasionally change (as in 2007 and 2008) so that a ‘discovering complications’ approach is more appropriate in the medium term.  If the investor only considers concrete market news (within a fixed conception of markets), this might be reasonable, but if they pay attention to trends in economic thinking then they may realise that there is an evolving pragmatic relationship between theory and practice and hence the market is ‘really’ complex, and not tame. But a small investor may be powerless to exploit this insight, so perhaps may as well treat the market as ‘discovering complications’. On the other hand, a large investor (such as Soros) might affect the markets, and so is definitely in a complex situation. Even they may deal with the situation as complicated in the short term and with discovering complications in the medium term, but looking out for those situations (nexus) where long-term possibilities can actualise, so that the long-term become short term in calendar time, such as in a crisis. (Time crunches.)

Much of the above seems more generally true.

## Science

In practice science is often thought to be pragmatic in that one treats the current accepted theory as if it were true. That is, one treats the domain of science as if it were merely complicated, with science providing a handbook. Under a ‘discovering complications’ regime one would treat the current accepted theory as a possible theory, be looking for alternatives  that also fit the known facts, and looking for experiments that distinguish between possible theories. But this is what those ‘doing’ science do do, continually seeking to falsify the best available theories. The more pragmatic approach is what those applying science normally do.

The domain of any science could, in principle, be complex. It is generally supposed that the natural sciences are tame where they are complex, and one seeks theories that take views that minimise the impact of complexity (as in quantum mechanics). But in the social sciences, for example, complexity can matter. The publication of a theory of regularity can disturb the regularity. In general, it is challenging to find stable things to theorise about, but some applications may be quite tame, at least in the short term.

## Models

Some things can be modelled, such that the model ‘makes complete sense’ and for practical purposes the model can be treated as if it ‘corresponds to’ reality. A complicated situation will have complicated models, which we may only discover in stages. More complex situations can be modelled, but the model cannot be as effective. It may give bounds on reality but since a model cannot – in itself – be complex, a model cannot correspond to a complex reality. Thus in complicated situations one has a model, while under discovering complications one could have a model, but typically has an ambiguous model which one seeks to refine.  For more complex situations the model can only have a tenuous relationship to any reality, typically representing just some aspects of it. Whereas in complicated situations using a model is ideal, and under discovering complications modelling seems pragmatic, for more complex situations it may be better to work with what one actually knows directly, rather than attempt to encapsulate that knowledge in a model.

## Conclusion

The important distinction between complicated and complex is widely recognized. Here it has been argued that ‘discovering complications’ holds a significant intermediate position, and that such situations may admit more straightforward approaches than the more complex ones. When considering approaches to complex problems, it seems important to establish the type of complexity inherent in the problem and the type of complexity that can be dealt with using the approach. They may not match.

Dave Marsay