Complex complexity

I’ve only just had the good fortune to read Warren Weaver’s mission statement for the sciences (original paper; transcription), published in American Scientist in 1948, but I’m glad I did. Since I entered academia, I’ve felt that the standard of writing in research papers is really rather mediocre – not poor (writers do generally try to be precise and explanatory) but mediocre as in overlong, over-reliant on previous results (jargon, shorthand and techniques – and this makes very few papers “self-contained” in any meaningful sense), and a bit dull*. No-one expects a technical article to be a page-turner, but there are limits…

Reading Warren Weaver’s publication in American Scientist was like a breath of fresh air, not least because of the tone of postwar optimism but mainly because of it’s readability and accessibility. American Scientist (unlike the symmetrically titled Scientific American) is not aimed at “the general publics” but scientists, so although its audience is not as specialised as a typical journal article (even in Science or Nature), it’s not as broad as mainstream journalism would be. And it is a speculative paper, all of which afford him freedoms not present in normal academic paper-writing.

The paper focusses on what Weaver perceived as the future challenges of science, and separated scientific problems into three broad categories:

Class 1: simple problems (ones which have few constituent elements, even if their description is complicated e.g. the billiard ball on a smooth table),

Class 2: problems of disorganised complexity (many, many elements which may be treated statistically or probabilistically as a result – e.g. the atoms in a gas) and

Class 3: problems of organised complexity (systems composed of a large number of elements, but less than the second category; where these elements’ interaction does not appear to be “random”).

Weaver’s contention is that traditionally physics has done very well with class 1 (the planets, the hydrogen atom, the earth’s gravity) and latterly class 2 (statistical mechanics, kinetic theory) and at the time he was writing, class 3 very much belonged to biologists, sociologists and so on – the messy sciences (my words, not his).

This is a fascinating way in which we can think about categorising scientific problems, but I confess that I’m not clear where many lie. His contention seemed to be that class 2 problems are tractable – you can rely on statistical properties of your system and neglect the influence of an individual; class 1 problems are clearly all about the individual (or small collections thereof), and so class 3 problems are ones where there are many individuals, but the behaviour of each must be considered.

(This recalls to me the realm of mesoscopic physics – on an individual atoms level, we can make reasonable observations and predictions; likewise for a big block of metal or a canister of gas; but what about an intermediate number of atoms – a protein, a buckyball, a DNA strand?)

Are Class 3 problems defined by interactivity? If a single atom in a small canister of gas behaves unexpectedly (i.e. contrary to statistical predictions), it will not have much effect on its neighbours, at least compared to a liquid, or a grain of sand in a sand dune; it will just be an outlier. But this distinction does not seem significant: in fluid dynamics, researchers use techniques to treat liquids as continuous rather than as made up of discrete atoms and molecules; its strong interaction can be regarded as a strength. As in crystalline solids and statistical gases, scientists have found ways of finding parameters that describe macroscopic order which also relate to molecular and/or microscopic quantities. Perhaps, in time, many more of these complex systems will be describable in terms of a small number of variables.

How does one classify these systems? One imagines human beings to be “organized”, as in co-ordinated and with individual behaviours; at the opposite extreme we don’t imagine a canister of gas to have “complex” behaviour. But where is the distinction? Is a liquid a complex system? If we succeed in simplifying our model of a system does it become less complex? Is Complexity, like Entropy, another name for our ignorance?

*really, I’m not claiming my scientific writing is gripping either.