Features Australia

Whatever happened to the flapping butterfly?

20 April 2019

9:00 AM

20 April 2019

9:00 AM

The confluence of mathematics and science provides us with proof and certainty. It is also beautiful: think of Einstein’s theory of relativity, his seminal formula E = mc² or John Forbes Nash’s equilibrium theory, just two of multitudinous mathematical formulae that have changed our understanding of the world and universe around us.

So it is also with the science of chaos theory, a profound mathematical science that rarely receives the prominence it deserves. You may have heard of chaos theory in a simplistic and puzzling form – ‘if a butterfly flaps its wings in Brazil, does it cause a tornado in Texas?’. Indeed, the mathematical formulae underpinning chaos theory have been used to predict, within parameters of anticipated outcomes, chaotic or unpredictable systems, such as the weather and how plants grow for many decades – it forms the basis for worldwide meteorological weather predictions we see on the television news.

As Sardar and Abrams provide in their excellent reader and international bestseller Introducing Chaos: ‘It is the scientific discovery of randomness in apparently predictable systems and declares the universe to be far more unpredictable than we might have imagined.’

Consider a plant growing in your garden. You might think it grows in a random or unpredictable manner. However, mathematical scientists have developed formulae that predict, within certain parameters, how the plant grows. Exactly how the plant grows depends upon certain inputs into the formulae, such as the level of sun, water, wind, humidity and many other elements which the plant is exposed to. As you might imagine, even the slightest changes in these inputs can have considerable consequences.

This scientific methodology has developed exponentially with ever-increasing computer modelling power, known as General Circulation Models (GCMs). GCMs influence predictions in everything from financial markets to the outcomes of legal proceedings.


Paradoxically, the father of chaos theory, Edward Lorenz, chief mathematician and Director of the Department of Meteorology, Massachusetts Institute of Technology during the 1950s-‘60s, also invented GCMs, the very models he used to forecast the weather and which have now been used to deliberately manipulate totally different outcomes, but more of that later.

Lorenz first applied GCMs to predict weather in 1948. His first models used merely 12 inputs to predict weather outcomes. When computers became available, Lorenz modelled the earth’s atmosphere and oceans and studied the interrelationships between temperature, air pressure and wind speed. He found that very small changes in the input assumptions into his modelling could produce widely varying and unpredictable results. Lorenz concluded this behaviour was inherent in his modelling and in 1963 published his findings in ‘Deterministic Non-periodic Flow’ in the Journal of Atmospheric Sciences.

Lorenz’s discovery of chaos phenomena is best described in an interesting story. One day, Lorenz decided to take a short cut with his GCM. So, instead of restarting the model from the beginning, he started it halfway through. He entered the numbers into the computer from an earlier printout and went away to get some coffee. Upon his return, he was amazed by what he saw: the newly generated weather forecast was nowhere near the original, producing a totally different weather prediction. Then the penny dropped: he had entered the number 0.506 in the second run, instead of the original number – 0.506127 – stored in the computer’s memory. That minute difference – one change in 5,000 – was not inconsequential and Lorenz saw that the smallest difference in inputs could have dramatically different consequences.

Lorenz: ‘If, then, there is any error…in observing the present state – and in any real system, such errors are inevitable – an acceptable prediction… in the distant future may well be impossible.’

Since Lorenz’s work, meteorological GCMs now use millions of inputs yet, despite this, we all know that Bureaus of Meteorology the world over frequently do not exactly predict the weather for the next day or beyond because weather is the quintessential chaotic system, constantly changing, evolving and moving: consequently, long-term weather predictions are problematic, indeed impossible.

William Gray, an acknowledged hurricane expert: ‘GCM climate forecasts cannot compete with empirical climate forecast schemes. How can we trust GCM climate forecasts 50 and 100 years into the future (that cannot be verified in our lifetime) when these same models are not able to demonstrate short range forecast skill of a season or a year?’.

So how does this affect our understanding of ‘climate science’ that started out predicting ‘global warming’, morphed into ‘climate change’ and now predicts the world will end in 14 years?

The ‘climate science’ is predicated and promulgated by the Intergovernmental Panel on Climate Change (IPCC) primarily based upon GCMs. As identified by Lorenz, the smallest change in inputs to a GCM can have catastrophic consequences. Yet there is evidence the IPCC and, recently, even our own CSIRO and Australian Bureau of Meteorology, have been blaming anthropogenic CO2 emissions and deliberately manipulating their GCM input data (including conveniently ignoring the late medieval warming period), to produce the outcomes they seek, namely, global warming. It is telling that when such predictions prove inaccurate based upon raw data, including from Nasa satellites and undersea metering systems, that modelling is further manipulated and excuses are made. Indeed, the IPCC has admitted as long ago as 2001 in its third report (paragraph 4.2.2.2 page 774) that its own GCM data is unreliable: ‘In research and modeling of the climate, we should be aware that we are dealing with a chaotic, nonlinear coupled system, and that long-term predictions of future climate states is not possible.’

Bill Kininmonth, director of the Australian National Climate Centre (1986-‘98): ‘Despite the IPCC advocacy, it is not possible to isolate anthropogenic greenhouse gases as the cause… for the observed warming of the last two and a half decades of the 20th century.’

GCMs which are the basis for climate science, cannot and may never, be able to predict long-term weather forecasting or the effect of anthropogenic activity because weather is the quintessential chaotic system: the butterfly will flap its wings forever and we will likely never be able to anticipate the consequences.

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