Rosenberg, Chaos and the Violin

In 1975 on a winter's day in Amsterdam, Rosenberg suddenly realised that he had been wrong. Very wrong. He had just finished a recording session at the Wimhuis and was in the process of being given a lift by the pianist Petrov Pindabrot. The violinist suddenly saw a tram which would take him directly to the house where he was staying. Pindabrot stopped the car and, after a hasty adieu  , Rosenberg sprang from the car in an attempt to reach the tram on the other side of the road, before the lights changed. Alas, a patch of black ice on the road between him and his objective prevented the intended union. He fell down flat on his face; his 1703 Tagliatelli violin - its neck broken. In short, a catastrophe.

In that accidental moment when the movie resorts to slow motion, Rosenberg realised that Chaos was not just the prerogative of Los Alamos and the Feigenbaums of this world. It could free-fall into anybody's lap - not just a Butterfly Effect  , more like a Banana Effect  . We could talk about the behaviour of complex systems such as the weather, water turbulence in pipes, smoke rising from a cigarette, the action inside a washing machine - but more significant for an area of activity such as violin playing was a science that looked for universal laws dealing with relationships between mistakes, errors, accidents or catastrophes. The everyday story and experience of violin-playing-man living in a contracting universe. Something useful at last. "That's all very well Holmes, but if one were to develop a theory based on the nature of error, it could expand into something beyond control - like shopping or religion for example." "Exactly Watson. The input could consist of data with barely measurable differences which, in even a comparatively short time, would become the huge, unacceptable differences in output that we associate with organised religion or politics. Violinists with brown eyes start not to trust those with blue eyes - it normally leads to war."

In the time it took for Rosenberg to go from the upright position to a state of horizontal entropy on that street in Amsterdam, a number of non-linear and quite aperiodic thoughts whizzed through his skull before the inevitable logic of impact.

Supposing there were just simply too many notes in the world? Not only your regular one-off, everyday kind of notes - but repeated notes. For God's sake, how many versions of Vivaldi's Four Seasons do we actually need?
In uncontrolled music proliferation, the linear growth function increases continually upwards. Rosenberg realised the necessity of an introduced noise variant. Useful noise would rise steeply only when the sonic environment became populated by too many notes. Past a certain point, the noise would peak out and masses of notes would then become mere casualty statistics. The note population would fall back to just below the projected level of equilibrium.

Using a logistic difference equation: x next = nx (1-x) the violinist started to feed in lots of notes, a mixture of the famous and not so well known - including an extra few sprinkles of his favourite note, B flat. Everything appeared just fine until the noise parameter was varied. Then Rosenberg saw that the final equilibrium (after rising, peaking out and the consequential high casualties) could never be predicted. He was left with extremely irregular oscillations, it looked very, very chaotic. The ramifications were wild, the whole future of music was on the line. Noise   (the amount not known) could cause a freak low dip in the periodicity curve, from which music would never recover. Rosenberg was looking at the possible extinction of whole species of music.
He checked his figures. Perhaps some other parameter could explain the discrepancy: for example, the sex of the notes, where they came from, how old they were (very significant in Western music), how long they were prepared to go on for, what fashion they belonged to, etc. No, there was no mistake. By turning up the noise, lines of gently oscillating notes would suddenly subdivide and drop straight to Hell.

If pitches and rhythms could determine different forms, could Noise   also determine these fundamentals (as we consider them) before the obligatory destruction? Another question. What happens when Noise   is introduced into a standard musical procedure like a fugue or even free counterpoint as is the basis of much heard improvisation? If it was minimal violin music? - no problem, the introduction of Noise   into such a system would bore the pants off anybody with ears, as it came around time and time again in ever changing sizes. No, we have to look for areas not so simplistic. Arbitrary Noise   does have the habit of suddenly blowing up into an arbitrarily large catastrophe.

I recall Rosenberg's concert on the cliffs of Cronulli, near Townsville in 1977. Quite a large-scale project involving two submarines from the Australian Navy, laser projection, movies projected onto giant screens floating on the sea and mystics who could walk on the water, etc. On the day of the performance a freak cyclonic storm, half an hour before the scheduled start of the proceedings, caused a cancellation until the next evening. The event required a high degree of split-second timing and after 24 hours that Noise   element had crept into the finely tuned system. Rosenberg arrived to find his specially constructed, multiple-violin apparatus had been moved from the precarious edge of, to a more protected place on, the cliffs. True, it was more protected but now he could no longer see the performers below him on the beach - communications were quickly set up with CB radio but it meant that after instructions had been relayed, he would always be a few seconds behind the action. From exactly the same starting point (8pm Eastern Time) a pattern emerged that saw the beach action and projected music grow further and further apart until all perceivable relevance between the two activities ceased to exist. (A computer analysis of the event shows a divergence graph almost identical to Lorenz's famous weather printout of 1961).

However, the fundamental problem was the tide - for the second attempt, nobody had taken into consideration that the sea level would be much lower. Consequently, one of the submarines hit a coral reef and sunk. Also the mystic water walkers proved themselves to be a very flakey bunch when their specially-built platform was revealed above the water line. Such is poetry! Just as people lost faith in weather forecasters, some of Rosenberg's colleagues thought it was time for him to give up on large scale outside events. The violinist saw it differently. If you could control the weather - make it do something different than what it actually did - then you would never know what it could do or what its effect could be. Like trying to find the answer to a question by proving that the answer itself could never exist.

Look Holmes, surely the accretion of knowledge through experimentation is fundamental to our being able to push back the frontiers of musical possibility. Wrong Watson, wrong my dear old pussy. Development of skills comes from the natural interspecies competition evident wherever music struggles to exist. These skills give one the ability to recognise the final coda, or last vodka when one reaches it. I don't see the point of standing there, knocking at this door of knowledge, winning awards because the hierarchy likes the sound of your knock. Better to recognise that dead end, then imagine another direction whether one believes in probability curves or not. Who would have thought that while going through your underwear last week, I would have come up with the new maxim `unpredictable locality equals global stability'. Yes Watson, a deterministic system can produce much more than just periodic behaviour and fashionable knickers.

Rosenberg realised that if you were going to use noise to create new structures in violin music, more exacting methods would first have to be found to measure the existing ones. By the mid 1970s Benoit Mandelbrot had shown that fractal measurements of standard violins caused the instruments to be pretty well infinitely large. However, we can disregard the ensuing panic by violin makers (and the radical increase in size of many violin cases) as rather missing the point. Measurement after all, rather like beauty, is in the ear as well as the eye of the beholder. The geometry of time would have to be measured. How long is a piece of music? According to Rosenberg, those people suffering severe leg cramps (rightly so) while waiting for the never-ending end of a Keith Jarret concert, have been asking the wrong question. The question should be - how wide is a piece of music? In his models, Rosenberg started laying out lines of music side by side - each new side derived through a scale-reduced self-symmetry of its neighbours. The reproductions started to produce more and more detail as the scale intensified. Then he noticed the Noise  . From previously unnoticed irregularities came the most incredible shapes - since they looked like parts of a violin, he decided to call them necks, strings, scrolls, f holes, pegs, etc. An extraordinary connection; the software of sound giving rise to structures resembling the instruments themselves.

Rosenberg thought he would check his findings by approaching the problem from the other end. Go from instrument to sonic structure. In an attempt to recreate the magnificent music, he utilised the creative power of turbulence by putting a couple of his violins in with the next home wash for a few hours. Again, he observed the effects of chaos. Blake had written `We see the world in a grain of sand'. Rosenberg noted in his diaries that he had witnessed the end of the universe through the fish eye window of his IBM washing machine.
Nonlinear systems develop bad habits, the bad habit eventually becomes the form of the system. But how could washing possibly be considered a bad habit? Simple. It wasn't a question of habit but one of occurrence - that was the little leap of faith required and it could all be mapped very simply by equations like V = V2 + C.
Take a violin, multiply it by itself, then add the original violin.

And could a bad habit reach a global audience?

There is now ample evidence to support Rosenberg's claim that the Earth has, from time to time, suddenly reversed its spin. The dinosaurs didn't die off from a meteor direct hit. Most of them were simply flung into space when the Earth came to an abrupt halt, before starting off again in opposite rotation. Those few who survived clearly had found a good sized solid rock to cling to. The Ice Ages are further proof of our planet hitting the brakes before going into reverse. It makes sense, the Earth keeps warm by its spin - like running on the spot. Stop doing that even for a cosmic second and you'll catch cold. That Rosenberg went on to build several whirling violins shows that he at least had faith in his own vision, even if we still must wait for the world's first whirling string orchestra. (The fact that ladies from the Montreal Symphony Orchestra   once played their violins, each with their head stuck in a rotating hairdrier, is not relevant to this debate.)
"All very well, Holmes. I understand that this helps in our appreciation of the unimaginably small or the mindbogglingly large, or even aiding a twit like myself to unravel the reasoning behind what I am supposed to say in this, like many of our meaningless conversations. But I thought this fractal stuff was to do with river eddies, spider webs, coastlines, the breakdown of compost, the frequency of wars, etc."
"Yes, yes Watson it has - but it is much more. Didn't you ever run your finger along the edge or belly of a 1683 Amati, a 1692 Stradivari or a 1625 Macaroni? This very sensuality can be measured, just like the scaling procedures associated with the Mandelbrot Set itself."

With cyclic behaviour and turbulence now up his sleeve, Rosenberg decided to take another look at linearity; basically he took the violin out of the washing machine and put it back on the road. In the triviality of his youth, he had dismissed chronological thought as a political plot. Now as he dragged one of his violins systematically (he used a map) around the streets of Sydney, he mumbled two words to himself - shape and form. As he went faster, he saw that the instrument split into two, four, eight then 16 parts. He noticed the oscillations; finally, when he had to negotiate the steps leading to the Opera House, the system broke up into chaos. In front of an excited crowd of music lovers, the violinist made the necessary measurements. Aren't you struck by the limited number of generic shapes in the Universe? he asked the exponentially expanding public. And Standard differential-calculus won't be able to take you where I'm going he shouted as two officials dressed in white coats, from the Social Services Department, helped Rosenberg into a nearby ambulance.

It was only a few years later that the concepts of `period-doubling' and `bifurcations' became standard nomenclature for scientists chasing The Chaos. While recovering his mental health, Rosenberg wrote another revised history of Western music under the title of `Polyphony and Chaotic Principles'. In the foreword he suggests that, in spite of much hopeful institutionalised pedagogy, the only idea in Western music has been the development of polyphonic process and that, seen in terms of chaos theory, it has led to confusion, reaction against complexity and an almost permanent anxiety about the future of music; that idea being kept afloat by people like me whose career is based on writing stuff like this. Needless to say, when considering his health again, we decided that it would be to the common good if he remained permanently under lock and key. He was clearly not well enough to take his place again as a useful member of society. Holmes had not said anything for the last three hours. Having given herself a quick `needle worth', she had retired to the study for some violin practise. I gazed out of the window into a familiar street. The light was fading as leaves were thrown randomly about by the invisible hand of autumn. Was there some universal law which would always predict the final resting place for each individual leaf? It did seem unlikely. Just then the door opened and, violin in hand, Holmes sprang into the centre of the room - a jump of about four metres!

"Watson," she announced, "consider that this room is a piece of music - it is not a finished composition. It is continuously in process, it is an improvisation without end. As I move around the room, I will play completely random pitches at different geographical points. A higher pitch than the previous one will mean one step to the left; a lower pitch will necessitate a step to the right. You, my dear Watson, will map the experiment."
For the next 19 days I made tiny marks on the floor of our flat at number 22B Baker Street. Holmes was indeed an obsessive personality. "Don't you see Watson, my darling, randomness is a red herring. It's important in obtaining the invariant images - the code of the fractional object. But the music itself does not depend on randomness. Chance is only a tool. It is like putting in the missing notes to a very long tune that you've heard somewhere before but you can't quite remember. Using simple probability, you always get the same pattern. The piece exists regardless of what I happen to play or where I play it. Watson, we are all playing the same tune!"

After a few years in the high security wing of the Wallabingi Psychiatric Hospital, Rosenberg was allowed to continue his research. A mass of computers, electrical devices (both analogue and digital) and violin technology soon filled his room. He started to investigate the interplay of different rhythms (as caused by bow pressure) in causing chaotic `attractors'. These were new and fantastic patterns of the used oscillations. No matter how hard the violinist dug his bow into the strings, the graphic and numerical measurements always came up showing the same stable and identifiable states. Rosenberg suspected that it was his playing that caused the always self-similar data, so he was allowed to invite other musicians to test the theory. Over a period of some months, violinists from all over the world visited the hospital to participate in the tests. All were skilled improvisers, so they used every trick in the book to cause some variation in the readings. There was, however, none. The laws of complexity seemed to hold universally and gave rise to simple systems which could, under certain circumstances, cause complex behaviour which could, in itself, cause simple systems which...

The same tune? I pressed the great man again for some sort of enlightened comment, I wanted - more, needed - some meaning - yes more, some purpose to my floundering career as music critic. Were we all really playing the same tune with only our restrictive listening practices preventing us from hearing this reality? If it were true, what should someone with my power and influence on the world of music do? Rosenberg's mouth moved - it was clearly an effort for him to communicate. I leaned closer to the maestro. What should I do? The all-encompassing smell of Rosenberg's day's Vodka intake caused me to reel unsteadily for a moment - I waited for the universal theme. The moment grew unsteadily longer. He belched - loudly. Then I heard it. It was the Theme from Dr. Zhivago . Oh no, I thought, there must be some mistake! It can't be this - of all tunes, not this monstrous pap! I felt I was drowning, like the brilliant man himself was, from the inside. His eyes suddenly focused on me and he said "Don't forget to do the shopping; it's the only thing left to do!"

Night fell. It was with a heavy heart that I made my preparations to leave the hospital. The violinist had spent the previous few hours in a desperately chaotic state. With great effort he had suddenly raised himself half off the functional hospital bed and sporadically blurted out what seemed to me to be the algorithm for the world's longest shopping list. Like a latter day Salieri I had taken down the dictation direct on my PC. Yes, I had a secret - if not THE secret - for Der Zeitalter Des Einkaufens   (The Age of Shopping). Or at the very least, when the program was up and running, I would know where the best place in town was to buy myself a new designer tie.

Yes, despite the fact that my old friend and colleague had spewed up all over my new Christian Tortu   shirt, this confrontation of intellects had surely been worthwhile. Yes, there was order and meaning in the music and ravings of this one-time virtuoso.

As I helped Dr. Rosenberg into his straight-jacket for the last time, I wondered if he had anything more to say to his fans out in the not-so-real world. "Yes", he said. "The only time you will reach equilibrium is when you're dead".