The difference of differences

“There is an ecology of bad ideas, just as there is an ecology of weeds, and it is characteristics of the system that basic error propagates itself.”(Felxi Guattari, les trios ecologies, 1989)

The idea that an ecological system is driven by some kind of dynamic has been around for a long time. It is a cliché that he growth of a population, in the absence of any restraint, is exponential. The earliest mathematical model of population growth can be found in the work of Leonard of Pisa, in 1220. His model was about the reproductive behaviour of rabbits, not in its biological sense, but numerological. He assumed that in the beginning there was one pair of rabbits. Every season after, the mature rabbits beget one immature pair, which in turn matures for a season, and all newly mature pairs beget one immature pair per season as well. The series of numbers, each being the sum of the previous two is a discrete dynamical system for which the time interval is a season; the state of the system is the pair of numbers. The growth law is the dynamic. If nothing happened then after 114 generations the total volume of rabbits would exceed that of the known universe. This is of course absurd. In practice, some external influence will come into play to limit the population to more sensible numbers. The availability of oxygen for example, but more likely, lack of space or lack of food, or both. The simplest models of population growth are iterative, just like Leonardo’s, but enormous variety of mappings have been proposed each attempting to capture some alleged facet of the reproductive process. If you approach then in a classical spirit, you will begin with the impression that each mapping should lead to highly distinctive dynamics. It must be realized the experimental ecology it is hard to get really good data. So there are serious problems. it is probably best to accept that the experimental evidence, such as its, detects a whole class of models rather than individual one. The upshot of this is that even the simplest models of population growth in a restricted environment can generate periodicity and chaos. Periodicity is common in real populations. So is random fluctuation, which poses a real problem: how much of it is due to external influences, and how much is genuine deterministic chaos?

Robert May offered his though to why it took so long for chaos to move to centre stage. His answer was that wide spread appreciation of the significance of chaos had to wait until it was found by people looking at systems simple enough for generalities to be perceived in contexts with practical applications in mind, and in a time when computers made numerical studies easy.

It requires a combination of circumstances- time, place, person, culture – for a new idea to take root. In fact general population biologists were in some sense aware of chaos in the 1950s. For example Moran studied insects in 1950 and found stable solutions, periodicity, and even chaos. But by 1970, the necessary “combination factors” had come together, which made it impossible not to notice chaos occurring in numerical simulations. Anyone who has played around iterating mappings on a computer – a very easy problem to programs- will find that the difficulty is avoiding chaos, rather than finding it.

Bacteria are everywhere, but without a microscope, you will never see them. Galaxies are everywhere, but without a telescope, they look like slightly blurred stars. Subatomic particles are not only every where, but everything. The invention of new instruments has always led to immediate progress in science, but instruments alone are not enough. It takes the wit of a scientist to recognize that revealings are important.

Chaotic dynamics raises entirely new, and difficult, problems for the interpretation and analysis of data. But it’s better to have a clear problem, than to live forever in a foul’s paradise. To analyse some system it is important to do the dynamics first, and then average the results, rather than take averages first and then do the dynamics. Consider a car travelling a distance of 30 Km at a speed of 20 Km/h, and returning at 60 Km/h. what is its average speed? If you just add the speeds and halve you get 40 Km/h. but that is wrong. It takes the care 1/5 hours to go out, half an hour to comeback, a total of two hours, so the average speed is 60/2=30 Km/h. The reason that adding and halving does not give the right average is that speed is proportional to the reciprocal of time, this is a non linear relation. In other words, you have to average in the right place.

The spread of HIV being related to factors such as sexual behaviour, is also very patchy as studies based upon average incubation periods and average sexual behaviour may prove misleading. This is a question that deserves looking into because control of the diseases depends on having good models of how it is transmitted.

The interrelation between thermodynamics and information theory can be assumed largely responsible for explaining the functioning of life, no longer as “essence” but as “differences” continuously transmitted – information is a techne, a writing of sorts that makes life possible. These are no boundaries, no limits in a traditional sense that work along lines of inclusion and exclusion of the thinking system. What thinks is the total system, that is , human being plus environment.

“Living systems consist of networks of pathways. Along them move differences – rather than impulses – that are transmitted on neurons. These notions give a different conception of the world and new ways of thinking about mind. Bateson conceives the mind as a system with written programs in which differences are transmitted (Bateson 1972: 478-87).”

For Bateson, exploring relations between nature and the living, ecology is not understood primarily in its derivative sense of “defense of nature”. Humans are no longer independent agents who act on nature, or impose order as they would like. They are a priori in exchange with their environment. Rejecting physical metaphors like that of energy, Bateson articulates models of behavioursm from materials in biology and information theory. Physics is commented by biology or the logic of life. Energy stored in the body makes possible the flow of information.

“Man” against nature. We end up with polluted lakes and rivers, deforestations, extinction of species , drought, and famine. Breakdown of natural ecosystems is paralleled or followed by breakdown in social eco-systems.

As a complex system, nature inscribes what is global in all things local because of the new proximity of the world at large in every perceptible phenomenon.