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Non-linearity – ignore it at your peril.

In 1953 Enrico Fermi and his team at the US military research facility at Los Alamos made an interesting and unexpected discovery. A discovery which, I think, is worth noting in today’s global financial crisis.

They had been researching the behaviour of driven coupled oscillators. A simple oscillator is a weight being bounced up and down on a spring. Or a pulsing circuit or some of the internal dynamics of a nuclear explosion. Driven just means the system is being powered from the outside rather than left to damp down. Coupled oscillators are where the activity (the bouncing up and down) of one oscillator infects other oscillators it is connected to via lateral connections. They were researching these in computer simulation.

Fermi had expected that in a system of such oscillators any initial pattern of activity, or an initial shock, would soon be damped away and evened out. Much like the heat in a cup of tea evens away in a colder room. What he discovered, however, was that no matter how long they left their system the pattern did not disappear. It sometimes might seem to have gone but, to his astonishment, the pattern would re-appear. Eventually they proved mathematically that the system would revisit all its previous states. The shock would never go away it just moved around and morphed as it went.

Arcane nonsense? Actually no. For at its simplest an economy IS an oscillator. And a global economy, that has many lateral links between economies in different countries, is modelled rather well by coupled oscillators. In particular, the financial world, where shifts in cash flow are the driving force is very well modelled at a simple level by such a system.

OK Fine. So what?

The so what is that in a highly coupled world, especially in the frictionless world of electronic money and debt, shocks do not get damped away. They move around surfacing in one place after another. The debts from banks are still working in the system. Time and holding our breath are not going to make this go away.

Now before anyone jumps up and down and says its nothing to do with arcane mathematics there are real world event driving what is happening. I want to say I agree. All I am pointing out is that those real world events are happening not in a nicely damped linear world where economies effect each other weakly, through many inefficient and highly damped intermediary functions. The events in our world are transmitted efficiently through the system as Fermi discovered.

Today investors in the Shangahi composite index lost 5% of their invested wealth. The reasons given were problems and losses at Insurers, miners and property companies. Later the headline was altered to down-play the insurers an property and introduce continuing fears about the euro.

The truth is that the ‘experts’ don’t know why losses or gains happen. They make up a story after the fact that is plausible. What is the case is that events in Europe won’t get easily damped away. Nor will a five percent drop in Shanghai.

The more we integrate the oscillators the more bumpy and non-linear their behaviour will be. If we then constantly drive this system hard ( going for bubble levels of growth with high levels of leverage and debt exposure) we are virtually guaranteeing a chaotic outcome.

The solution of fast and vast growth to pay off debts is essentially to try to recover a set of oscillators that blew a gasket, by pumping new energy into the system and driving it even harder.

6 Responses to Non-linearity – ignore it at your peril.

  1. Britten123 May 17, 2010 at 2:52 pm #

    The Economy As An Evolving Complex System (Santa Fe Institute Studies in the Sciences of Complexity Proceedings)

    by Anderson/Arrow/Pines

    esp. the chapter titled "Do You Guys Really Believe That?"

  2. Golem XIV - Thoughts May 17, 2010 at 3:43 pm #

    Britten123

    Thanks. I have not read that. I

  3. Britten123 May 18, 2010 at 5:17 pm #

    that said, (speaking as an engineer/physicist)
    "physics envy" can also sometimes cost you money when dealing with humans ;->

  4. Golem XIV - Thoughts May 18, 2010 at 5:52 pm #

    I think some of the Santa Fe cheering squad have been known to make exaggerated claims for the direct applicability of their work to the real world.

    I see Non-linearity, complexity, evolving systems, self-organising system etc to be profoundly important but not necessarily at a surface level. They tell us the kind of world we live in, how it will change and some of the ways it will react to changes, but not what to do from moment to moment.

    David Ruelle is someone whose work I think is very good. Nice man too.

  5. Britten123 May 20, 2010 at 8:20 pm #

    I like to stick to the early people (as that book is) as well.

    As for applicability, in a sandpile cascade one can calculate the subsequent angle of repose, but not where us individual grains end up…

    What I do like is at least the recognition that there is more to it than people like to think, these are non-linear, open, non-equilibrium systems with sources, sinks, and drivers.

    I also find the concept of "fitness landscapes" useful, especially that the actions and decisions of the people around us change our "landscape", and how we are "fit" to it, hopefully with information as to how we should try to adapt. Whether we can pull it off is another thing.

    PS I believe hornets live in nests.

  6. Golem XIV - Thoughts May 20, 2010 at 8:26 pm #

    Britten123

    Fitness landscapes are a favourite of mine. I did quite a lot of thinking about them some years ago. The Red Queen Hypothesis was such a great idea when it first hit.

    Nests huh? No alliteration then – ah well.

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