The Apex Fallacy, The Exponential Function, And The Pareto Distribution


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Albert Bartlett spent over sixty years in the University of Colorado at Boulder, during which time he delivered his classic lecture on arithmetic, population and energy over seventeen hundred times, a lecture that may be summed up in one sentence: “The greatest shortcoming of the human race is our inability to understand the exponential function”.

Although the apex fallacy and the Pareto distribution are nowhere near as important, the failure of politicians and especially left wing activists to understand them, often wilfully, is a major cause of social and world unrest. So what are they?

The apex fallacy is the easiest to understand. Men occupy most of the positions of power in our society, therefore men are a privileged group, and women the victims of systemic “oppression”. That is the feminist version.

The full version of the Pareto distribution requires a knowledge of higher mathematics, but it is usually simplified to the 80/20 rule, eg, 20% of the people produce 80% of society’s output.

Although it involves the transcendental e, the exponential function is relatively easy to understand; it is the limit to growth. Approximately 2.71828, e is related to that even more famous transcendental pi by an amazing equation, and like pi can also be expressed as the sum of a series.

Normally though, when we hear the word exponentially, we think of something changing or growing extremely fast. We will return to e shortly, but first the other two. They are both abused when it comes to promoting what is often alluded to as a better, more equitable, more just society, but what do these claims actually mean? Usually, they mean removing men, or perhaps only white men, from positions of power and replacing them with…Alexandria Ocasio-Cortez and Lori Lightfoot – seriously?

The reality is that the people in positions of power are, or should be, our servants rather than our masters, and in any case, people are distributed among the professions irregularly. The phenomenon of the Asian shopkeeper or the black basketball player are surely proof positive of that. If American blacks are among the highest earners in American sports and music, does it make sense to suggest they should also excel in politics or the hard sciences?

Most of us are familiar with the bell curve, the so-called normal distribution, this applies to many populations – women, trees, pebbles on a beach…if you arrange them by height, size, or any other characteristic, you will find a very small number at the bottom of the distribution, a very small number at the top, and the vast majority in the middle – eg, midgets and dwarves at one end, giants at the other, and the majority of us sandwiched between the two. Bell curves can overlap, thus men are taller than women, so will be further along to the right of the graph.

The Pareto distribution doesn’t work like that, including with wealth, and in that instance we are not talking about an 80/20 distribution but at times of extreme “inequalities”. The socialist “solution” to this “problem” is to tax the ultra-wealthy and give their money to the poor. Look how well that has turned out. Not.

The problem of exponential growth is a lot more serious. The population of the world at the turn of the Fifteenth Century was perhaps 400 million (estimates vary). By 1700. it was around 600 million, in other words, it increased by fifty percent in three hundred years.  By contrast, in 1960, it was around 3 billion, by 1999/2000, it was over 6 billion, in other words it had doubled in a mere forty years. If it doubled again in the next forty years, we would be looking at 12 billion in 2040. That would mean a massive increase in food production, and without some revolutionary source of alternative energy, there would be no more oil or coal left. Check out Professor Bartlett’s lecture for the reality rather than the fantasy peddled about oil pipelines, shale, and drilling for gas.

In other words, a child born today will grow up in a world that will be in deep trouble. In order to at least tackle the problems the yet unborn will inherit, we have to stop playing stupid games with the apex fallacy and the Pareto distribution so we can concentrate on the real dangers we face, and which are growing exponentially.

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The statements, views and opinions expressed in this column are solely those of the author and do not necessarily represent those of The Duran.

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