Friday 22 January 2021

Ashby on Reconstructability

The following quotes are taken from the introduction by George Klir to Roger Conant's "Mechanisms and Intelligence: Ashby's writings on Cybernetics", which can be downloaded here:

The balance between the reduction of complexity to a model and nature itself was a key point for Ashby. Datafying things "throws away information", as he puts it, but on the one hand, this is essential for science, whilst on the other hand, good science cannot lose sight of the ways in which a model might be used to reconstruct the complexity from which it is derived. 

In most data analytic work today, there is much reduction. And then it stops - and assumes that the reduction can be used to shape the reality - that is the mode of Facebook, Cambridge Analytica, etc. But reconstruction is essential, otherwise, how are we to know that it is these variables and not those that we should be attending to?

This also means that a "system" is not a thing-in-the-world, but rather an idea. As Ashby puts it, it is a "set of variables":

"At this point we must be clear about how a 'system' is to be defined. Our first impulse is to point at the pendulum and to say 'the system is that thing there.' This method, however, has a fundamental disadvan­tage: every material object contains no less than an infinity of vari­ables and therefore of possible systems. The real pendulum, for in­stance has not only length and position; it has also mass, temperature, electric conductivity, crystalline structure, chemical impurities, some radio-activity, velocity, reflecting power, tensile strength, a surface of moisture, bacterial contamination, an optical absorption, elas­ticity, shape, specific gravity, and so on and on. Any suggestion that we should study 'all' the facts is unrealistic, and actually the attempt is never made. What is necessary is that we should pick out and study the facts that are relevant to some main interest that is already given. ...The system now means, not a thing, but a list of variables."

And then here is the problem of reconstructability: 

"systems models which have recently been developed in many different areas are almost invariably constructed from subsystems. While the subsystems, each associated with a subset of the set of variables of the overall system, are often well validated models of the phenomena involved, the question of the ability to reconstruct the overall system from the given subsystems is almost never raised. It seems that there has been a tendency among many systems modellers to take the reconstructability for granted. It is clear that without an analysis by which the reconstruction ability of systems model is determined, the model is likely to be fundamentally incorrect and might be vastly misleading."

But I think this is the remarkable thing: the whole enterprise is not about "complexity", but "simplicity". Reflecting that the variety of the scientists will always be overwhelmed by the variety of nature, he suggests that the whole point of science is to find effective approaches to simplification:

"...system theory (is) the attempt to develop scientific principles to aid us in our struggles with dynamic systems with highly interacting parts, possibly exceeding 10^100 who faces problems and processes that go vastly beyond this size. What is he to do? At this point, it seems to me, he must make up his mind whether to accept this limit or not. If he does not, let him attack it and attempt to find a way of defeating it. If he does accept it, let him accept it wholeheartedly and con­sistently. My own opinion is that this limit is much less likely to yield than, say, the law of conservation of energy. The energy law is essentially empirical, and may vanish overnight, as the law of conserva­tion of mass did, but the restriction that prevents a man with resources of 10^100 from carrying out a process that genuinely calls for more than this quantity rests on our basic ways of thinking about cause and ef­fect, and is entirely independent of the particular material on which it shows itself. If this view is right, systems theory must become based on methods of simplification, and will be founded, essentially, on the science of simplification. ...The systems theorist of the future, I suggest, must be an expert in how to simplify."

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