Precisely because it has been proven that long-run climate prediction is not possible, it is inappropriate to attempt to state that there is a “consensus” that “global warming” caused by increased greenhouse-gas concentrations will be dangerous if it continues. Scientific dissent on the question of climate is and will always be legitimate, because it is settled, proven science that long-run prediction of the behavior of mathematical objects such as climate is not possible unless the initial climatic state at any chosen moment is known to a fineness of detail that is in practice impossible to attain, and unless the processes for the subsequent evolution of the object are also known in detail, which they are not.

It is the proven characteristic of mathematically-chaotic objects such as climate that neither the magnitude nor the timing of their phase-transitions (in environmentalist jargon, “tipping points”) can be predicted (Lorenz, 1963; IPCC, 2001), because there is simply too little information about the state of the climate in the present to allow us to look as far as 100 years into the future and say with any degree of confidence how little or how much the world will warm.

As Lorenz (1963) put it in the landmark paper with which he founded chaos theory –

“When our results concerning the instability of non-periodic flow are applied to the atmosphere, which is ostensibly non-periodic, they indicate that prediction of the sufficiently distant future is impossible by any method, unless the present conditions are known exactly. In view of the inevitable inaccuracy and incompleteness of weather observations, precise, very-long-range weather forecasting would seem to be non-existent.”

> And climate, of course, is very-long-range weather. Recently another scientist has considered the limitations upon climatic prediction with some care. Giorgi (2005) defines two types of prediction:

> “In the late 1960s and mid 1970s the chaotic nature of the climate system was first recognized. Lorenz defined two types of predictability problems:

> 1) Predictability of the first kind, which is essentially the prediction of the evolution of the atmosphere, or more generally the climate system, given some knowledge of its initial state. Predictability of the first kind is therefore primarily an initial-value problem, and numerical weather prediction is a typical example of it.

> 2) Predictability of the second kind, in which the objective is to predict the evolution of the statistical properties of the climate system in response to changes in external forcings. Predictability of the second kind is thus essentially a boundary-value problem.”

> Giorgi explains:

> “… Because of the long time scales involved in ocean, cryosphere and biosphere processes a first-kind predictability component also arises. The slower components of the climate system (e.g. the ocean and biosphere) affect the statistics of climate variables (e.g. precipitation) and since they may feel the influence of their initial state at multi-decadal time scales, it is possible that climate changes also depend on the initial state of the climate system … For example, the evolution of the thermohaline circulation in response to greenhouse-gas forcing can depend on the initial state of the thermohaline circulation, and this evolution will in general affect the full climate system. As a result, the climate change prediction problem has components of both first and second kind which are deeply intertwined. … The relevance of the first-kind predictability aspect of climate change is that we do not know what the initial conditions of the climate system were at the beginning of the ‘industrialization experiment’ and this adds an element of uncertainty to the climate prediction.”

> Giorgi also points out that the predictability of a mathematical object such as climate is adversely affected by non-linearity:

> “A system that responds linearly to forcings is highly predictable, i.e. doubling of the forcing results in a doubling of the response. Non-linear behaviors are much less predictable and several factors increase the non-linearity of the climate system as a whole, thereby decreasing its predictability.”

> Climatic prediction is, as Lorenz said it was, an initial-state problem. It is also a boundary-value problem, whose degrees of freedom – the quantity of independent variables that define it – are approximately equal to the molecular density of air at room temperature, an intractably large number. It is also a non-linearity problem. It is also a problem whose evolutionary processes are insufficiently understood. When studying the climate we are in the same predicament as Christopher Columbus. When he set out for the Americas, he did not know where he was going; on the way there, he did not know what route he was following; when he got there he did not know where he was; when he returned he did not know where he had been; and, like very nearly every climate scientist worldwide, he did the whole thing on taxpayers’ money.

> A thought-experiment

> To illustrate the difficulty further, let us conduct a thought-experiment, examining the proven mathematical impossibility of predicting the future state of a complex, non-linear object. For our little experiment we shall use the Mandelbrot fractal, which is defined using the simple, iterative function f(z)= z² + c. Compare the extreme simplicity of this function with the complications inherent in the million-variable computer models upon which the UN so heavily relies in attempting to predict the future evolution of the climate.

> In the function that generates the Mandelbrot fractal, the real part a of the complex number c = a + bi lies on the x axis of the Argand plane; the imaginary part b lies on the y axis. Let z = 0. Compare this certainty and clarity with the uncertainty and confusion of the climate object, where, as Lorenz proved, accurate long-term projection into the future cannot be made unless an exceptionally precise knowledge of the initial state of every one of the million-plus variables at any chosen starting point is known to a very great degree of precision. The UN presumes to make predictions a millennium into the future. This, as our thought-experiment will convincingly demonstrate, it cannot possibly do.

With the Mandelbrot fractal, then, there is no initial-state problem, for we can specify the initial state to any chosen level of precision. However, with the climate object, there is a formidable and in practice unsolvable initial-state problem. Likewise, we know the process by which  the Mandelbrot fractal will evolve, namely the simple iterative function f(z)= z² + c. However, our understanding of evolutionary processes of the climate object, though growing, is insufficient, and the computer models which try to project future climatic states continue to be caught by surprise as events unfold. The computers did not predict the severity of the El Nino event in 1998; they did not predict the cooling of the oceans from 2003 onwards; and the operators of one of the UN’s leading computer models have recently admitted that the model makes errors that are orders of magnitude greater than the rather small phenomena which they are trying to predict.