Black holes are simpler than forests and science has its limits

Mandelbrot set (Wikipedia, https://en.wikipedia.org/wiki/Mandelbrot_set)Martin Rees (UK Astronomer Royal) takes on complexity and emergence. This is essentially a primer on why complex systems – as he says, accounting for 99% of what’s interesting about the world – are not susceptible to reductionist science despite being, at some level, reducible to physics. As he rightly puts it, “reductionism is true in a sense. But it’s seldom true in a useful sense.” Rees’s explanations are a bit clumsy in places – for instance, he confuses ‘complicated’ with ‘complex’ once or twice, which is a rooky mistake, and his example of the Mandelbrot Set as ‘incomprehensible’ is not convincing and rather misses the point about why emergent systems cannot be usefully explained by reductionism (it’s about different kinds of causality, not about complicated patterns) – but he generally provides a good introduction to the issues.

These are well-trodden themes that most complexity theorists have addressed in far more depth and detail, and that usually appear in the first chapter of any introductory book in the field, but it is good to see someone who, from his job title, might seem to be an archetypal reductive scientist (he’s an astrophysicist) challenging some of the basic tenets of his discipline.

Perhaps my favourite works on the subject are John Holland’s Signals and Boundaries, which is a brilliant, if incomplete, attempt to develop a rigorous theory to explain and describe complex adaptive systems, and Stuart Kauffman’s flawed but stunning Reinventing the Sacred, which (with very patchy success) attempts to bridge science and religious belief but that, in the process, brilliantly and repeatedly proves, from many different angles, the impossibility of reductive science explaining or predicting more than an infinitesimal fraction of what actually matters in the universe. Both books are very heavy reading, but very rewarding.

Address of the bookmark: https://aeon.co/ideas/black-holes-are-simpler-than-forests-and-science-has-its-limits

Originally posted at: https://landing.athabascau.ca/bookmarks/view/2874665/black-holes-are-simpler-than-forests-and-science-has-its-limits

From Representation to Emergence: Complexity's challenge to the epistemology of schooling – Osberg – 2008 – Educational Philosophy and Theory – Wiley Online Library

This is my second post for today on the subject of boundaries and complex systems (yes, I am writing a paper!), this time pointing to a paper by Osberg, Biesta and Cilliers from 2008 that applies the concepts to knowledge and education. It’s a fascinating paper, drawing a theory of knowledge out of complex systems that the authors rather deftly fit with Dewey’s transactional realism and (far less compellingly) a bit of deconstructionism.

I think this sits very firmly within the connectivist family of theories (Stephen Downes may disagree!) albeit from a slightly different perspective. The context is the realm of complex (mostly complex adaptive) systems but the notion of knowledge as an emergent and shifting phenomenon born of engagement – a process, not a product – and the significance of the connected whole in both enabling and embodying it all is firmly in the connectivist tradition. It’s a slightly different perspective but one that is well-grounded in theory and comes to quite a similar conclusion, aptly put:

education (becoming educated) is no longer about understanding a finished  universe, or even about participating in a finished and stable universe. It is the result, rather, of participating in the creation of an unfinished universe.

The authors begin by defining what they describe as a ‘representational’ or ‘spatial’ epistemology that underpins most education. This is not quite as simplistic as it sounds – they include models and theories in this, at least. Their point is that education takes people out of ‘real life’ and therefore must rely on a means to represent ‘real life’ to do its job properly. I think this is pushing it a bit: yes, that is true of a fair amount of intentional teaching but there is a lot that goes on in education systems that is unintentional, or emerges as a by-product of interaction, or that happens in playgrounds, cafes, or common rooms, that is very different and is not just an incidental to the process but quite critical to it. To pretend that educational systems are nothing but the explicit things we intentionally do to people is, I think deliberately, creating a bit of a straw man. They make much the same point: I guess it is done to distinguish this from their solution, which is an ’emergentist’ epistemology.

The really interesting stuff for me comes from Cillier’s contribution (I’m guessing) on boundaries, which makes the simple and obvious point that complex systems (as opposed to complicated ones) are inherently incompressible, so any model we make of them is inaccurate: in leaving out the tiniest thing we make it impossible to make deterministic predictions, save in that we can create boundaries to focus on particular aspects we might care about and come up with probabalistic inferences (e.g. predicting the weather). Those boundaries are thus, of necessity, created (or, more accurately, negotiated), not discovered. They are value-laden. Thus:

“…models and theories that reduce the world to a system of rules or laws cannot be understood as pure representations of a universe that exists independently, but should rather be understood as valuable but provisional and temporary tools by means of which we constantly re-negotiate our understanding of and being in the world

They go on…

We need boundaries around our regularities before we can model or theorise them, before we can find their rules of operation, because rules make sense only in terms of boundaries. The point is that the setting of the boundary creates the condition of possibility for a rule or a law to exist. When a boundary is not naturally given, as is the case with natural complex systems, the rules that we ‘discover’ also cannot be understood as naturally given. Rules and ‘laws’ are not ‘real’ features of the systems we theorise about. Theories that attempt to reduce complexity to a system of rules or laws, like our models which do precisely this, therefore cannot be understood as pictures of reality.

So, the rules that we find are pragmatic ones – they are tools, rather than pictures of reality, that help us to renegotiate our world and the meaning we make in and of it:

From this perspective, knowledge is not about ‘the world’ as such, it is not about truth; rather, it is about what we can do in the world, how we can change it.One could say ‘acquiring’ knowledge does not ‘solve’ problems for us: it creates problems for us to solve.”

At this point they come round to Dewey, whose transactional model is not about finding out about the world but leads to a constantly emerging and ever renegotiated state of being.

“…in acting, we create knowledge, and in creating knowledge, we learn to act in different ways and in acting in different ways we bring about new knowledge which changes our world, which causes us to act differently, and so on, unendingly. There is no final truth of the matter, only increasingly diverse ways of interacting in a world that is becoming increasingly complex.

One of the more significant aspects of this, that is not dwelt on anything like enough in this paper but that forms a consistent subtext, is that this is a fundamentally social pursuit. This is a complex system not just of individuals negotiating an active relationship with the world, but of people doing it together, as part of a complex system that drives its own adaptation, at every scale and within every (overlapping, interpenetrating) boundary.

They continue with an, I think, unsuccessful attempt to align this perspective with postmodernist/poststructuralist/deconstructionist theory, claiming that Dillon’s differentiation between the radical relationality of complexity and poststructuralist theorists is illusory, because a complex system is always in a state of becoming without being, so it is much the same kind of thing. Whether or not this is true, I don’t think it adds anything significant to the arguments.

The paper rushes to a rather unsatisfactory conclusion – at last hitting the promised topic of the title – about the role of this emergentist epistemology in schooling:

Acquisition is no longer the name of the game …. This means questions about what to present in the curriculum and whether these things should be directly presented or should be represented (such that children may acquire knowledge of these things most efficiently or effectively) are no longer relevant as curricular questions. While content is important, the curriculum is less concerned with what content is presented and how, and more with the idea that content is engaged with and responded to …. Here the content that is engaged is not pre-given, but emerges from the educative situation itself. With this conception of knowledge and the world, the curriculum becomes a tool for the emergence of new worlds rather than a tool for stabilisation and replication

This follows quite naturally and makes sense, but it diminishes the significance of a pretty obvious elephant in the room, which is that the educational institution itself is one of those boundaried systems that plays a huge role in and of itself, not to mention with other boundaried systems, regardless of the processes enacted within its boundaries. I think this is symptomatic of a big gap that the paper very much implies but barely attempts to address, which is that all of these complex systems involved processes, structures, rules, tools, objects, content (whatever that is!), media, and a host of other things are part of those complex systems. Knowledge is indeed a dynamic process, a state of becoming or of being, but it incorporates really a lot of things, only a limited number of which are in the minds of individuals. It’s not about people learning – it’s about that whole, massive, complex adaptive system itself.

Address of the bookmark: http://onlinelibrary.wiley.com/doi/10.1111/j.1469-5812.2007.00407.x/abstract;jsessionid=901674561113DC6F72BDE8756B165030.f04t03?systemMessage=Wiley+Online+Library+will+be+disrupted+on+11th+July+2015+at+10%3A00-16%3A00+BST+%2F+05%3A00-11%3A00+EDT+%2F+17%3A00-23%3A00++SGT++for+essential+maintenance.++Apologies+for+the+inconvenience&userIsAuthenticated=false&deniedAccessCustomisedMessage=

Boundaries and Hierarchies in Complex Systems

This rather elderly paper by Paul Cilliers peters off to an unsatisfyingly vague and obvious conclusion, but it does have some quite useful clarifications and observations about the nature of boundaries as they relate to hierarchies, networks and complex systems in general. I particularly like:

“We often fall into the trap of thinking of a boundary as something that separates one thing from another. We should rather think of a boundary as something that constitutes that which is bounded. “

This simple observation leads to further thoughts on how we choose those boundaries and the (necessary) ways we create models that make use of them. The thing is, we are the creators of those boundaries, at least in any complex system – Cilliers mentions neural networks as a good example – so what we choose to model is always determined by us and, like any model, it is and must be a partial representation, not an analogue, of the impossible complexities of the world it models. In a very real sense, we shape our understanding of the world through the boundaries that we choose to (or are hard-wired to) consider significant and there are always other places to draw those boundaries that change the meaning of what we are observing. It makes the analysis of complex systems quite hard, because we can seldom see beyond the boundaries we create that simplify the complexity in them and we have a tendency to over-simplify: as he points out, even apparently clear hierarchies shift and interpenetrate one another. This is more than, though related to, categories and metaphors of the sort examined by the likes of Hofstadter or Lakoff.

Since this paper was written, John Holland has done some mind-bending and deeply thought-provoking work on signals and boundaries in complex systems that delves far deeper and that begins to address the problem head-on, but which I have been struggling to understand properly for many months: I’m pretty certain that Holland is onto something of staggering importance, if I could only grasp precisely what that might be! He is not the clearest of writers and he tends to leave a lot unsaid and assumed, that the reader has to fill in. It’s also complicated stuff – suffice to say, stochastic urns play a significant role. This paper by Cilliers is a good stab at the issue from a high altitude philosophical perspective that makes a few of the wicked and profound issues quite clear.

Address of the bookmark: http://blogs.cim.warwick.ac.uk/complexity/wp-content/uploads/sites/11/2014/02/Cilliers-2001-Boundaries-Hierarchies-and-Networks.pdf