Necessary and Sufficient: Issues of Complexity

Necessary and Sufficient: Issues of Complexity 

Looking to the Oxford English Dictionary, we see our terms of interest are defined in the following ways:

Necessary: "Needed to be done, achieved, or present; essential."

Sufficient: "Enough; adequate."

Necessary and sufficient in practice, especially within however, are a bit more nebulous. 

Looking from the point of view of formal logic, we know that if a condition is necessary, it makes a conditional statement true, such that if we have the statement: if N then S, or N is implied by S, N<--S. For example, it is necessary to be exist in order to be alive; E<--A. We can also say that S cannot occur without N; as A cannot occur without E. On the other hand, a sufficient condition goes in the other direction, tying the truth value to the consequent (N) rather than the antecedent (S). We can say then: if S, then N or S --> N, or that S guarantees N. For example, being alive (A) suffices for existence (E). In order to have both, we would need to say S if and only if N, or S <--> N.  (Betz, 2010). 

We say "this is a necessary condition for my model" but we don't always think of what that means. There can be many necessary conditions and many sufficient conditions which operate on different scales and levels. For example, if I want to travel from Boston, MA to New York, NY - there are many ways I can get there - plane, train, bike, on foot - all are sufficient. In order to choose one, I need to know the enabling conditions (and restricting constraints) along with the context (why I am I traveling? cost?).

Given in the above example, it’s harder to relate these to complex problems. For example, we know what is necessary and sufficient to have a rectangle in geometry – but what is the necessary and sufficient conditions for a water treaty to be signed? What is the necessary and sufficient conditions for the rise of a fascist regime in societies? It’s extremely to reach an objective, general solution to these problems that is constant through time and space.

Is it even possible to enumerate all the possible solutions to necessary and sufficient conditions? In fact, I suggest we can’t enumerate them – so we need to understand the enabling conditions (Islam and Susskind, 2012) for a complex problem. We can’t use the framework of necessary and sufficient conditions since these problems are interconnected and dynamic. In epidemiology, the more recent focus on contributing (component) causes rather than sufficient causes shows the issues with this simplistic view of problems.

Figure 1 Two views of causal mechanisms of disease – note that A the necessary cause must be present, while some of the component causes are B, C and D (Gerstman, 2013). 

For example, in order to develop AIDS, you must be exposed to HIV (necessary) but it’s not clear what the specific sufficient conditions are – even we need a certain viral load of exposure to develop an infection. In this way, even this traditional example in epidemiology is contingent on our knowledge - there is a limit to the application of the necessary and sufficient framework within complex systems (Figure 1).  However, we suggest that the contributing causes of a problem are flexible – many things can cause and outcome, and seem to be more realistic to problems. 

I suggest that in order to do this, I must map the feasible space of a complex problem. In order to do this, we can go through four steps:

1. Define the problem: What is the actionable goal or outcome for your research? E.g. providing clean water (as defined by WHO)
2. Constraints search: Enumerate the initial conditions (temporally-focused) and boundary conditions (spatially-focused) for the problem E.g. initial conditions there is limited piped water and income, and many people use chlorine, but use has decreased due to poor supply chain; boundary conditions we are located in Sub-Saharan Africa where there is limited electric power, road infrastructure, technology.
3. Enabling search: Enumeration the conditions which can lead to the adoption of your goal E.g. what point-of-use technologies do people use which provide clean water within the constraints of your initial and boundary problems – what has worked in the past.
4. Adapt: We can re-enumerate the concepts in steps 1 through 3, thinking about the system and contingencies. 

 I would welcome comments and questions on the above, feel free to post below. 

Sources

Betz, Frederick. Managing Science: Methodology and Organization of Research. Springer Science & Business Media, 2010. [link, pg 248]

Gerstman, B. Burt. Epidemiology kept simple: an introduction to traditional and modern epidemiology. John Wiley & Sons, 2013. [link]

Islam, Shafiqul and Lawrence Susskind. Water diplomacy: a negotiated approach to managing complex water networks. Routledge, 2012. [link]