South Africa – First Mathematical Report

Part of the idea of working with the CSIR – Centre for Scientific and Industrial Research – was gaining a better understanding of applied math, as the CSIR is a research institute containing about 50 different departments, all of which address different aspects of societal development, ranging all the way from learning to urban planning, mathematical modelling and development of more durable kinds of plastic .

Working here is very exiting as there is a tradition for as well as the opportunity of working across all professions, and because you meet new people with new approaches to things and new areas of knowledge. My closest neighbours in the housing complex of the CSIR count 2 game developers, a remote sensing expert, and 2 chemical engineers, and my department of the CSIR (Logistis and Quantitative Methods/Built Environment) is made up of statisticians, a theoretical physicist, a couple of operations researchers and some geographers, all working with each other in different combinations on different projects.

A lot is being done to secure the development of employees, both in terms of “people skills” courses on conflict management and intercultural tolerance, and in terms of support for education and in-service education, and once a week some employee presents the project he or she is currently working on. This way there is a fair chance of staying up to date with whatever is going on in the various departments and which projects people are currently working on. Last week the presentation was on how to minimise the risk of spreading airborne deceases through clever architecture and lighting, an important prospect for a developing country with limited means of paying for expensive chemical methods. This week it will be about complexity theory, which is what I’m working on, too.

I work on 2 different projects, one of which is about Humanitarian Logistics, i.e. quantitative methods used in humanitarian situations, natural or manmade disasters in which a lot of lives are at risk, and the other one is on complexity theory as already mentioned.

The first project is a literature search into which research and which quantitative methods are being used in humanitarian situations, and I was asked to proof read the mathematical part of the report. Most humanitarian organisation use heuristic methods, and they do not really seem to have much interest in or understanding of the importance of developing mathematical methods, as this often involves cooperation with companies that are traditionally regarded as some sort of “enemy” with conflicting interests to the NGO’s. The organisations that do use quantitative methods are usually part of the UN network, but certain research institutions around the world do research into using quantitative methods in humanitarian work, too.

Most methods used are heuristic or at most not very advanced statistics. Some research have been made into using operations research methods as there is some overlap between supply chain management , distribution and localising and problems such as placement of refugee camps and distribution of food packages and such basic aid items. Mostly, the kinds of models developed are models for the distribution of food and other basic necessities, migration of victims of disasters (e.g. to nearby hospitals), stockhouses for aid packages or the logistics of bringing out the aid packages to the affected people. In at least one study, fuzzy logic has been used to give an estimate of the total need for stockhouses and airplanes needed to deal with refugee situations all over the world.

The other project, complexity theory, is a relatively new area of research originating from observations of self-organising systems, originally from chemistry and physics, and which researchers attempt to develop into a theory for urban development. “Self-organising” refers to some property of a system that makes it develop more or less stable patterns out of seeming chaos, patterns which could not have been predicted just by observing the variables that went into the system. This is caused by non-linear dependencies which for differential equations leads to an infinity of solutions. The systems will not normally get into an equilibrium, though they can develop a balance in the sense that it will take a large (external) force to make it change state.

A very simple example of self-organising systems is a cellular automaton, which graphically described would mean dividing a surface into “squares” and equipping each square with a certain property, e.g. a predisposition for something or some other simple likelihood, and determining how each cell will develop depending on which properties the cells that form its neighbourhood have. Of course there are other possible neighbourhoods than the closest 8 cells (which all share a part of their border with the cell in question), but they do form the most generic one. For instance you could equip each cell with 2 states, one in which it prefers “wine”, and one in which it prefers “beer”, and a developmental rule stating that if 5 or more of the 9 cells in the neighbourhood (including the cell itself) have the opposite preference for alcohol than the cell itself, then it changes its preference in a very populist way.

Now, if you have a random distribution of wine drinking and beer drinking cells to begin with, and you colour the wine drinking cells black and the beer drinking cells white, the cellular automaton will after a some iterations take on a clear zebra pattern without any grey zones (areas in which beer drinkers and wine drinkers cohabit), although you wouldn’t have expected such strong division by this relatively vague criteria, which allow up to 4 out of 9 cells in the neighbourhood to have a different alcohol preference. This example is from Michael Batty: ”Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals”.

This project aims at making research into how to apply these methods into gaining a better understanding of self-organising systems and in the long run apply them to modelling urban development in South Africa, which is very different from urban development in e.g. Europe, where complexity theory successfully has been used to model various aspects of the development of cities.