Saturday 11 August 2018

Does cybernetics understand complexity?

I'm writing a paper about music at the moment and questioning my understanding of the word "complex". That's a bit embarrassing for someone who considers themselves a cybernetician - a subject which is fundamentally concerned with complexity. This is a moment where I have to ask myself if I really understand what "complex" means.

This is the definition of complexity that I have believed up until this point, in a beautifully argued explanation by Ross Ashby:
"The word ‘complex’, as it may be applied to systems, has many possible meanings, and I must first make my use of it clear. There is no obvious or preeminent meaning, for although all would agree that the brain is complex and a bicycle simple, one has also to remember that to a butcher the brain of a sheep is simple while a bicycle, if studied exhaustively (as the only clue to a crime) may present a very great quantity of significant detail. Without further justification, I shall follow, in this paper, an interpretation of ‘complexity’ that I have used and found suitable for about ten years. I shall measure the degree of ‘complexity’ by the quantity of information required to describe the vital system. To the neurophysiologist the brain, as a feltwork of fibers and a soup of enzymes, is certainly complex; and equally the transmission of a detailed description of it would require much time. To a butcher the brain is simple, for he has to distinguish it from only about thirty other ‘meats’, so not more than log2 30, i.e., about five bits, are involved. This method admittedly makes a system’s complexity purely relative to a given observer; it rejects the attempt to measure an absolute, or intrinsic, complexity; but this acceptance of complexity as something in the eye of the beholder is, in my opinion, the only workable way of measuring complexity." (Ashby, 1973 - "Some peculiarities of Complex Systems", Cybernetic Medicine, Vol 9, no. 1) 
On the face of it, this is perfectly sensible. But there are things in life which are not like bicycles or brains, butchers or detectives.

If I was to point to three problems with Ashby's view, they are:

  1. The problem of reference and meaning: Ashby sees information as being about something - the brain to the butcher is information about something, just as it is to the brain surgeon.
  2. The problem of ergodicity - Ashby's examples are inanimate and static in the information they present - but nothing in life is really like this, and neither are observers (or what a friend of mine calls "systems of reference"). Whatever information is conveyed and how we think about information is not ergodic. That means that the features of its "alphabet" are different from one moment to the next. 
  3. The problem of the non-arbitrariness of the diachronic emergence of understanding. This is the really tricky one, but basically the fact that human agree on distinctions, that we are capable of love, that somehow we resonate with each other in the face of phenomena is not the product of a kind of random search for coherence in the manner of Ashby's "homeostat". There seems to be some underlying principle which guides it. 

Music and education are where these problems become most apparent. Bach's music, for example, is often called "complex" because of its counterpoint. But if you examine it closely, all Bach's music is simply an elaboration of chords which are rather like a hymn. And what Bach does with the chords is not to add entropy (or disorder); instead, he adds and overlays new patterns, or redundancies! His complexity arises from the interaction of redundancy. If he added entropy, the music would never have any coherence. But there's something else. These emergent patterns are not random. Each of them appears to be a re-articulation of some fundamental symmetry which is expressed through the whole thing - even when they appear to be initially "surprising". The music is holographic in the way that Bohm describes. Its aesthetic closure appears to be arrived at when sufficient redundant descriptions are overlaid and coordinate rather like different colours of the spectrum combine to make white light.

Cybernetics has no understanding of how this might happen as far as I can see. We need something else. 


Paul Hollins said...

As ever Mark a thought provoking post. although on this occasion I'm not sure that I agree with your conclusion from a cybernetic perspective.

Ashby's position on complexity was a useful starting point in cybernetics but Beer took Ashby's position much further and I would argue Beer's positions that did not assume ergodic states in information, quite the contrary, Beer suggested regulation , amplification or attenuation to achieve a homeostatic system state surely if the assumption was ergodic little or no regulation would be required. Beer talks in his example of humans and rope tension of the unpredictability, randomness of the complex system and how this is amplified the larger (more complex humans contributing) it becomes. I like the concept of not random emergent patterns you present in the musical context which is broadly form my perspective is evident in most ecological systems.

Thanks Mark and a re -read of Beer !

Mark Johnson said...

Ok, Paul... let me introduce the problem in a different way!

Take your favourite definitions of:
1. variety
2. attenuation
3. amplification (that's the really tricky one - it could hold the key to the problem!)
4. error

Now apply them to describe:

1. A real hospital (with crisis, medical accidents, etc)
2. A real university (lets take Bolton!)
3. Picasso's "Woman in a fish hat"
4. Captain Beefheart's "Trout Mask Replica"
5. You

You can go to as many levels of recursion as you like (both Beer and Ashby have this concept - see Ashby's Design for a Brain, and Ashby and Conant's "Every good regulator" rule; also they both assume countability of variety, so non-ergodicity is ignored - Beer uses Shannon throughout)

Now take your description and use it to re-generate the things you described.

Now ask yourself, If the world was really as Beer or Ashby describe, what would be different to the world we know? What does the model predict which doesn't actually happen? What happens which isn't in the model? Can the difference be generated by amending the models?

Very importantly, Ashby argued that the cybernetician should "observe what might have happened but did not".

That's what we should do now. And our current thinking isn't right. I think it's got to do with counting - a problem which Ashby and Beer were well aware of!

Mark Johnson said...

I should add that some might object to my question in that "it is only a model" and that "somewhere we have to draw a distinction"...

But what guides us to make our distinction? Some arbitrary process? Why do I doubt that? Is my doubt arbitrary too???

Paul Hollins said...

As you say "It is only a model?" and as such there are deficiencies (as there are with any model) . I've done as you suggested and found the process interesting and revealing and if anything found endorsement of my view. (ignoring three and four as I'm not sure cybernetic modelling "art" is something I would recognise (as being helpful or indeed possible not thinking of art being a system) and still retain my view that complexity is recognised at all levels of recursion . Can we predict or model everything ? of course no that would be the word we live in. Enjoying the discussion.

Mark Johnson said...

So what are the deficiencies? How does the system know that they are deficiencies? How does it choose how to respond? How does it know what parameters to shift? Does it run a search routine for a new "better" set of parameters?

Shang said...

where can i find the full text of the Ashby article ? I have searched online for hours but no success