Friday, 7 October 2011

More time

This is a rather 'heavy' post, but two things have been fascinating me, both of which relate to the American Cybernetics Society conference. I should say at this point, for both these things, I'm not sure I understand them - particularly because there's a lot of maths; but I'm going to try to explain my fascination and my understanding (or lack of it) as things stand right now. But the main thing about this is that
a. learners and institutions (like all biological organisms) have hysteresis: their states are dependent on the history of what has happened to them.
b. The issue of 'memory', 'history' and 'anticipation' is dependent on 'time', but 'time' is problematic because it is an abstraction (Larry Richards has written a lot about this).

Time is a problem in cybernetics. I think it's a problem because 'time' is generally seen as 'one-headed', and I'm sure that it's 'many-headed' (see  However, critiquing time only gets us so far - I want to find a way through the distinctions to something that can unblock some of the blockages. Ultimately, the goal is a meaningful model of anticipation (but maybe, and paradoxically, one that doesn't depend on 'time' too much..!). We have to grapple with Kant's basic categories, because his categories are effectively one-headed categories, and we may need to rethink these as 'many-headed' categories.

One of the things which is exciting me is Faisal Kadri's work on hysteresis and multiplier feedback. Hysteresis is the key thing. In my model of communicating agents (see, none of my agents have any history or learning; they need hysteresis. But how to create it? One way is to look at the Volterra series. As Kadri explains, there is disagreement over whether the Volterra series can represent hysteresis (although it certainly has 'memory'), but it's sequence of different level integrals clearly means that the output is in some way dependent on the history of the input (it's unlike the Taylor series in this way).

Faisal explains that one way in which it might be able to demonstrate hysteresis is if we replace additive error-correction (i.e. adding direct corrective balances for errors detected) with multiplier error-correction (i.e. multiplying by a coefficient so as to adjust to errors detected). I wasn't sure if I was misunderstanding Faisal, but it struck me that this error-correcting multiplier (which he suggests is basically a decaying linear equation working with the nonlinear Volterra series) worked in a way where the emphasis was on achieving a balance between immediate error correction and some sort of anticipation of likely immediate patterns (does that make sense?).

More broadly, there seems to be something about harmony, symmetry and anticipation in all this. Faisal is particularly interested in how the multiplier feedback can model satiation. The symmetry connection is intriguing. In learning technology, I was fascinated to discover that Sugata Mitra has been thinking along these lines too.. the roots of his thinking can be seen here: In particular, symmetry places much more emphasis on performance.

It helps me to write this down, because I'm still only half-understanding it. When I was dealing with my communication model, the idea of applying a slow linear multiplier did occur to me as a way of giving my agents memory. But my idea was crude, and I hadn't thought about the properties of things like the Volterra series.

Hysteresis also features in the work that Leydesdorff draws attention to - particularly in the ways in which 'hypercycles' emerge. Particular states of a system trigger drastically different types of behaviour (for example, the starvation of Dictyostelium discoideum). Following Prigogine, Leydesdorff argues that there are different levels of chemical clock which trigger changes in this case. Leydesdorff sees the trigger for the change in state caused by a break in symmetry. But I'm not yet entirely clear on what this means, but it seems to resonate with Mitra's concerns. However, there is a fundamental question: can the hysteresis of dictyostelium discoideum and the emergence of the hypercycle be represented through Faisal's multiplier feedback in a Volterra series?

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