Peterson is known to be extremely critical of Marxism and certain approaches to the reduction of inequality. In the aforementioned video, he tries to make his case by referencing the Pareto distribution. This caught my attention because this is a specific, well-defined concept in mathematics and statistics. Let us break down his words.

He starts by making the following statements.

Let’s go back to the idea that Marx had something to say. We can clarify that a little bit. This is the problem that seems to emerge as a function of a fundamental force that we don’t really quite understand, and that’s this phenomena (sic) that I’ve been referring to as the Pareto distribution. If you look at any creative endeavor that human beings engage in […] where there is variability in individual production , it doesn’t matter what it is […] almost everybody produces zero, a small minority are a tiny bit successful and a hyperminority are insanely successful.

First of all, to say that the distribution of productivity in every human creative endeavor follows a Pareto distribution is a rather bold claim to make, especially without citing any sources. It makes one wonder what Peterson actually understands by this term. His next statements are quite revealing in this regard.

The Pareto distribution is the geometric graph representation of that phenomena (sic).

I think that any competent scientist will agree that this is a rather exotic — to say the least — way to define the Pareto distribution. It is definitely not a “geometric graph representation” of imbalance in human productivity. We can nevertheless give him the benefit of the doubt and assume he was just trying to avoid technical terms in order to convey his point to the general public, and messed it up a little bit in the process.

His next statement completely gives him away, though.

The rule is, the square root of the number of people in consideration have half of whatever it is that is under consideration. This works everywhere.

This is just laughably wrong. Anyone with a basic understanding of mathematics can easily check this. To clarify why, we just need to analyze the expression for the proportion of output of a Pareto variable accounted for by a portion of the population, derived from the Lorenz curve. Given an instance of the Pareto distribution, it is a constant factor of the population size. Saying that this square root rule applies to the Pareto distribution is just ludicrous.

A detailed derivation illustrating exactly why this is wrong is included as an appendix to this article — I thought I would spare those less appreciative of the beauty of mathematics. Scroll down if you’re interested.

So where did Peterson get this ridiculous idea from? A quick inspection of the Wikipedia page for the Pareto distribution reveals a link to Price’s law, which is essentially the notion that he describes. Specifically, Derek John de Solla Price hypothesized that half of the material published in a field of science will be authored by approximately the square root of the total number of existing authors. This is the only reason I can think of why Peterson might have mixed these two concepts up. Interestingly, Price’s law has been shown to carry little weight empirically. For a thorough discussion see the work of Nichols.

Despite the irrelevance of the square root law, Peterson feels entitled to give a detailed example, in his habitual authoritative tone, of how this applies to classical composers and how much their music is played. There is empirical evidence that some forms of measuring success in music are well described by an inverse power function, that is, the family of functions that the Pareto distribution belongs to — this paper by M. E. J. Newman contains a more serious discussion of the topic. However, this is categorically not what Peterson describes. He just does not understand the very concept upon which he seems to have built his argument.

A scientist worth listening to is one that has a thorough understanding of the concepts he or she works with, and on top of that has the ability to communicate them to the general public without the need for overly technical terms. The man we see on this video is instead throwing around a bunch of somewhat related notions that he does not seem to be able to grasp. He simply does not know what he is talking about.

We could adopt an extremely indulgent stance and assume that even if he might be stumbling on a few technicalities, he still manages to convey a compelling message about inequality. However, in that case his exposition essentially reduces to “the rich get richer” or “productivity is unequally distributed”, and this is precisely where my problem with Peterson lies. What is so compelling about this? He is just stating the obvious, but invoking technical terms and adopting an arrogant tone to make it sound like the insightful revelations of a profound intellectual.

Even if we get past his glaring flaws, the rest of his discourse is very weak. Apparently, he is trying to discredit Marxism, and more generally any form of enforced equality, by accusing their proponents of ignoring this “fundamental law of nature we don’t quite understand” that is the Pareto distribution, or of misinterpreting it as an exclusive problem of capitalism. This is a blatant example of the straw man fallacy. I do not think that any advocate of policies to increase equality actually ignores that imbalance in productivity or accumulation of wealth arises naturally.

This is not the only example of Peterson dressing up nonsense by the use of sophisticated vocabulary. He famously invoked Gödel’s incompleteness theorems as evidence for the existence of God. His preposterous but unbacked claims seem common as well, as shown by his statements about ancient depictions of DNA. A Reddit user was kind enough to compile a series of examples of Peterson’s blunders. Make sure to check it out.