When you add constraints to a complex mathematical or engineering system, at first it does not change much. Then it begins to perform less well, but only gradually until suddenly, with the addition of an additional constraint that may itself be unimportant, the system collapses and either fails to produce a solution or produces one at a very much lower level of operating efficiency – mathematically, a “catastrophic” degradation.

In the real world, regulations operate very much in the same way. Initially, they detract little from the economy’s efficiency, while satisfying the egos of the regulators. Other constraints, environmental and geopolitical, may also have effects that are only modest. Then, with one often minor additional regulation or event, there is a “catastrophic” degradation in performance. We may now have reached that point.

Mathematical modelers in economics and the social sciences typically use equations that are either linear or exponential. Linear equations model many real-world factors perfectly adequately; those factors produce output results that are close to proportional to the input. To a first approximation, most mechanical forces are satisfactorily linear, and the science of mechanics indeed works well by making the assumption of linearity. Unexpected results also, such as the Pascal principle behind Joseph Bramah’s hydraulic press (which allows you to magnify a force by applying it over a larger area) turn out to be both linear and useful. The main advantage of linear modelling, if it is correctly applied to factors that are truly linear, is that nothing can go wrong; the model cannot be more than modestly inaccurate, if the equations are properly determined.

Modelling using exponential equations is less fool-proof. It appears appropriate for any kind of natural growth, for example in a human population or a disease virus. The difficulty is that such factors are not reliably exponential over long periods of time, though they may appear to be so for a few years. Over longer periods, adverse factors begin to explode in importance, preventing exponential growth from continuing ad infinitum. This is empirically sensible, if you think about it, because exponential growth infinitely prolonged takes over the universe; hence exponential growth cannot be infinitely prolonged.

The other factor making exponential modelling dangerous is that, because the models are calculated only to a finite number of decimal places, rounding errors creep in and, with the exponentiation, explode off the page if the forecast is carried on to several decades in the future. This was the problem with the original Club of Rome forecast in 1971, which predicted environmental disaster by 2010, whatever assumptions were made, even unrealistic ones, about improving technology, etc. The environmentalists of the Club of Rome used this result to claim that the world was doomed, and that only by adopting their extreme policies immediately could doom be prevented. In reality, of course, it merely proved that their computer model was flawed. Having worked on exponential models myself, I was able with the brashness of youth to point this out in a public meeting in the fall of 1971 to MIT Professor Dennis Meadowes, the inventor of the Club of Rome model. Not that he appeared grateful!

When you start adding to the complexity of models and adding constraints, all kinds of complexities appear. Economists do very little work with polynomial equations, because they are generally unable to solve anything beyond a quadratic (where the highest exponent is x^{2}). Solutions exist for cubic (x^{3}) and quartic (x^{4}) equations, but they are complex and difficult to work with; no general solution exists for quintic and higher-degree polynomials. Once you discover factors that can be multiplicative, polynomials quickly appear, and quickly get beyond the level that can easily be solved or modelled.

In general, realistic models of very complex systems such as the economy, the atmosphere and the weather involve many elements that form polynomial factors, either alone or in combination. Simplifying these systems to simple linear or exponential mathematical models is a category error. Just because economists or climate scientists can produce a model with equations they can solve does not mean that model is a remotely accurate representation of a complex reality.

The French mathematician Rene Thom, whose “Structural Stability and Morphogenesis” was published in 1972, identified one property of such polynomial systems: their tendency to produce discontinuities “catastrophes” where a very small change in one factor will suddenly produce an arbitrarily large change in another factor, making the overall system unstable. Since Thom’s work, a further property of such systems has been identified, initially by Edward Lorenz: their potential to produce “chaos” whereby the output can appear entirely random for certain input values, before reverting to “normal” behaviour as the values are varied further. A “catastrophe” then becomes a special case of “chaos” produced by the “butterfly effect” whereby in the almost infinitely complex system of the atmosphere a butterfly flapping its wings in Beijing can in principle cause a hurricane in Miami.

In modelling or in the real world, adding constraints to a system multiplies its complexity and its susceptibility to “catastrophes” and “chaos,” while introducing outside disturbances both increases the system’s complexity and may shift the output suddenly by an amount vastly exceeding in size the input of the disturbance.

This is clearly happening in the field of environmental regulation, and recent hiccups suggest we are reaching a critical point at which a large portion of the world’s power grids could fail to operate. The Russia-Ukraine war and the Western reaction to it have disrupted supplies of Russian natural gas and oil to the West, although in the case of oil, output appears to have been merely re-routed to other nations not sharing in NATO’s Ukrainian crusade.

That is a medium sized outside trigger to a systemic disruption mainly caused by regulation. The push for electric automobiles is beginning to put massively increased demand into an electric power grid that lacks capacity to handle it. That capacity has been lessened by refusing to build new nuclear power stations since the 1980s and taking existing nuclear power stations prematurely off-line, by closing coal-fired capacity that was still in excellent working order, by refusing to build or open natural gas pipelines that could provide lower-carbon alternatives in power generation, by irrationally preventing “fracking” of oil and gas to open massive new supplies and by devoting grossly excessive investment to solar and wind power technologies that are utterly unreliable. Any individual item of those policies and regulations is defensible, albeit often utterly irrational; their combination bids fair to push the electric power system over the edge into a chaotic or catastrophic state. The Ukraine war has worsened the problem, but only by bringing the internal contractions of “climate change”-driven energy policy into sharp relief.

A breakdown in the electric power grid would cause a catastrophic decline in global living standards, since much of our modern civilization is hugely dependent on reliable electric power. The global economy would not shut down altogether, but it would operate at much lower efficiency, with hugely expensive backup systems installed by the rich and mediaeval living standards suffered by the poor. That in turn would produce social and political turbulence that would doubtless make matters very much worse.

There is only one solution: a dramatic cut-back in regulations that frees the world’s energy system to adapt through the free market, producing a more or less optimal outcome with ample backup reserves and safety mechanisms in place to allow for sudden supply shocks like the Ukraine war. No longer should journalism majors be allowed to inject their politicized maunderings into the discussion of complex climate change or economic mathematical models that they are utterly un-equipped to understand. You would not trust a liberal arts major to run a nuclear reactor; it is equally absurd to allow such people to set regulatory policy for the global energy system.

Mathematics is hard. So is advanced industrial civilization. It must be left to the free market, with minimal regulation imposed only by intellectual grown-ups.

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*(The Bear’s Lair is a weekly column that is intended to appear each Monday, an appropriately gloomy day of the week. Its rationale is that the proportion of “sell” recommendations put out by Wall Street houses remains far below that of “buy” recommendations. Accordingly, investors have an excess of positive information and very little negative information. The column thus takes the ursine view of life and the market, in the hope that it may be usefully different from what investors see elsewhere.) *