How often does Jordan Peterson not know what he is talking about?
Since Jordan Peterson stepped into the spotlight after the Bill C-16 controversy, he has attracted the attention of numerous journalists attempting to discredit him. And many have failed.
The most notorious one of these failures is probably the interview by Cathy Newman, where she repeatedly tried to characterize his claims as misogynistic alt-right rhetoric. This display of seemingly deliberate misrepresentation did little more than pep up his fans, and in all likelihood contributed to the incorporation of more acolytes to his already prosperous cause.
My main concern about Peterson’s popularity is not that he might be a misogynist or a bigot. It is that, very often, what he says seems to me of little intellectual value. He appears to be a well-read scholar and sometimes discusses interesting philosophical issues with competence, but I rarely have the feeling that he is saying something particularly insightful or profound. Rather, I believe he conceals the shallowness of his claims behind nebulous grandiloquence, the misuse of technical terms or the misrepresentation of scientific concepts.
An example of his lack of depth and rigor can be found in this clip, where he discusses why Marxism is hopelessly wrong. To put it bluntly, what this video shows is simply a carnival of nonsensical rambling. Here I argue why.
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.
So how is it possible that a man so prone to uttering hogwash has become one of the most influential intellectuals in the western world? There are certainly many aspects to this, but here I would like to focus on one: there seems to be something wrong with the way we understand intellectuality these days.
Intellectual inquiry is largely a collective endeavor. The amount of knowledge amassed by philosophy and science up to these days is so vast and complex that real progress is almost exclusively made in the form of specialized research. In the literature reporting those advances, at least the ones that are really valuable, we will most often find conclusions in the form of very nuanced and cautious claims. Blanket statements about complex issues such as economic inequality are thus unlikely to be of any value. Findings that do constitute worthy contributions to our understanding of a particular field are most commonly very specific and small steps resulting from months or years of work. It is unlikely that a single person will be able to cover ground on a wide variety of topics and make valuable, let alone groundbreaking, contributions.
But despite this, nowadays many people seem to long for a guru that gives them the answer to all questions, if possible as a collection of snappy one-liners. This is illustrated by the success of the many YouTube videos that claim to show how Peterson “UTTERLY DESTROYS FEMINISM”, often in less than ten minutes.
In addition to this, there seems to be a tendency to conflate vagueness with sophistication. Our understanding of the world is an application of our ability to reason, and as such is bound to the rules of logic. Thus, any claim we want to make is valuable only to the extent that its constituents are well defined. Wise statements are often difficult to understand not because they are vague, but because they tend to involve numerous complex concepts which must be understood first. Once these are mastered, the most sophisticated observations are not difficult to comprehend. By being vague, one can get away with anything, because the actual meaning of one’s words can be altered post hoc to dispel unforeseen challenges. If you are not entirely convinced that Peterson can be extremely vague, see this ten-minute-long speech on the source of meaning.
Alas, in the clip discussed above Peterson did make a specific claim, and it turned to be just wrong.
This is the only time I have tried to rigorously break down something Jordan Peterson was saying, and the conclusion was that he simply did not know what he was talking about. However, he talked in an arrogant and authoritative tone, making it sound carefully thought out and convincing. If we start taking apart more of his interventions, I wonder how often we will reach the same verdict.
Appendix
Consider a population of size n and a random variable X representing the productivity of an individual, with Pareto density f and cumulative distribution function F. We can interpret F(x) as the probability that a person picked at random produces at most x units. To examine Peterson’s claim, we need to figure out the fraction of the population that produces half of the output. According to him, it should be the square root of n.
Given a density function f(x), the Lorenz curve L gives the proportion of output generated by the least productive fraction of a population. It is defined as
The denominator is the expected value of the distribution, while the numerator is now shown to be an elementary integral. Defining
where m is the minimum productivity we consider (the scale parameter of the distribution) and p=F(y), we have
where z=F(x) and we have substituted u=1-z.
For the output of the most productive portion of the population we need to compute
Using the above results it is straightforward to see that
If we want to know the proportion of the population that produces half of the outcome, we need to solve the following equation for q=1-p.
And we easily see that
That is, for a Pareto distribution with fixed shape α, half of the output is produced by a constant factor of the population. In other words, it is not, in general, the square root of the total population.
In other words, Peterson’s claim is nonsense.
