Errors of Addition

Let us examine the two most common types of thinking errors that occur within the human mind, as I have witnessed and experienced as a writer, critic, philosopher, and political commentator. These are errors not of argument (though they can cause poor argumentation), but in understanding.

The first is the error of Addition, which is where one adds information to a set of data or facts. The second is the error of Ignorance¸ in which one ignores or down-plays information that is relevant to a subject or judgment.

Of these two errors, ignorance is the one that has over the past century received the most attention and is the most easily identified in others as a form of undue discrimination or prejudice. Addition errors, by contrast, are often unrecognized, and are in fact rampant in academia as well as “science journalism.”


The Error of  Addition


Consider this factoid:


The total income of women in the united states is approximately 70% of the total income of men.


This statement regards what is commonly called the gender wage gap. Here is a permutation of that statistic:


Women earn 70 cents on the dollar for what men earn for the same work.


The words in bold indicate an error of addition. The information being added is that women and men are engaging in the same work, when the original data comparison (all earnings by men compared to all earnings by women) contains no information about the type of work being engaged in by the two groups. It created a very appealing statement for inciting resentment or piquing peoples’ sense of justice, but one cannot say it is representative of reality.

Thomas Sowell, in his book Economic Facts and Fallacies, takes down with a more diverse collection of information what has come to be known on the right as the “myth of the gender wage gap.” This is also a strategic use of language, since “myth” can be both true and untrue, depending on context. The gender wage gap is a real thing; the problem is that a very simple and very general data comparison does not reflect the nuance of reality. Sowell communicates the problem as “comparing incomparable individuals.” The nuanced reality is that men and women tend to choose different work with different benefits and costs that appeal to their gender roles in different ways. When you compare comparable individuals, like men and women who have never been married (and thus are less tied into their reproductive gender roles), the wage gap virtually disappears. Not just that, but the comparison in general falls apart when you actually take into account gender roles, and that women’s unique production, that of children, doesn’t show up in GDP or any economic metric, even though it is the most important future investment that exists.

In the case of the wage gap, more specific information eliminates the error of addition. We can see with increased information that the second statement above, that women are paid less for the same work, is false. Without that specific information, we can say that it is unproven, and therefore should be considered at best hypothetical. All of this is from just one example, but if you scrutinize other beliefs constructed on data, especially large sets of data containing limited variables, you are likely to find many, many, more.


The Narrative

So why is the error of addition so common? It has to do with the way people remember and use information. Facts by themselves, without context or a clear path to make use of them, are meaningless and easily forgotten. Thus, the first thing that happens when a person is presented with information is to ask himself, “What does this mean, and how is it useful?” If the context is missing or inadequate for meaning, we tend to add enough information to make it meaningful, as the above example illustrates.

This addition often takes the form of what I call “the narrative.” It’s no coincidence that news stories are called “stories.” Memories take the form of a logical series of events, just as stories do, even if the events in question weren’t logical. This is why memory is often unreliable – we make memories, not record them. In the same way, we tend to place facts in an arrangement that tells a story.

Women face discrimination by men that results in men paying them only 70% of what they deserve.

In a single sentence you have a story, complete with villain (men), a conflict (equality), an action (discrimination), and an outcome that elicits pathos (the wage gap). There are numerous other examples (many of which I have seen in comments on my channel):

People with college degrees make more on average than those who don’t have one. You need to get a college degree so you can make more money.

Women file 69% of divorces. The majority of women get bored and divorce men when they feel like it.

Blacks are imprisoned at a higher rate than whites. Blacks go to prison while whites receive a free pass because the system is inherently biased.

The gap between rich and poor has widened. The rich are getting richer and the poor are getting poorer.

When you understand our ancestry, it’s easy to understand why our minds work like this. Our ancestors were presented with experiences that had to be quickly extrapolated into predictable phenomena. If your ancestor came upon the fishing hole, but there was no fish, he had to quickly determine why and what the solution was – he didn’t conduct a study to determine how depleted the fish population was; he simply tried to solve the problem by moving to a new area, finding other food, or stepping up his religious sacraments. If a man in the village got sick to his stomach, you immediately looked at what he ate and avoided it yourself. Deeper understanding wouldn’t, in these situations, be useful, but would eat up precious time. If the fish were dead because of an increase in fry predation, so what? You need to find living fish quickly. If the sick man was dying of cancer, not a poison food, so what? You suffer no negative effects by avoiding the same food as him, especially for a short time.

Filling in the information likely helped your ancestors, especially when recognizing that precaution has potentially massive upsides with usually minimal downsides.

For the most part, this is still the most effective way to live life, but as a methodology of contextualizing modern statistics it creates a distortion of reality, rather than a flawed but efficient model of it, simply because data is not presented in a way that can be contextualized as useful information in most cases. It takes much more information than a gross comparison, and the more information you receive, the more incomprehensible the subject becomes until predictive models break down.

The modern media is particularly adept at utilizing this common thought flaw to manipulate peoples’ understanding of current events. In 2017 I analyzed a news cycle involving a man being forcibly removed from an airplane ( In most reports the events were described in a quick and simple sequence – the airline overbooked a flight, needed somebody to leave, a passenger was picked at random, he refused to leave, he was removed by force, and he was injured in the process.

Unsurprisingly, important information was left out of the story, and most people contextualized the event sequence using the error of addition. In fact, if you bring this event up to most people, they will still tell the story with the addition error in place – they will say that the airline forcibly removed the passenger. If you notice from the event sequence I gave, the who was completely absent. He “was removed” – a placement in the passive voice that media uses frequently when they want the reader to commit the error of addition. Only when I brought up the local papers (the Chicago Tribune and the Chicago Sun-Times) was there a mention of who, since the who was particularly relevant to local politics. It was a special police force, a controversial police force, that was attached specifically to the airport and was embroiled in local scandal.

The airline called the police when the passenger refused to leave the plane, and the police injured him while forcibly removing him from his seat.

This is the final part of the event sequence without the error of addition (and without the switch to the passive voice). However, there is more. Most people assume that the passenger was removed because the flight was overbooked, but it was actually to make room for pilots that were needed on a flight at the next destination. Most people have had a bad experience with airlines, and it begs attention when some story pops up that damns the airlines as violent crooks. But of course, reality is far more nuanced than a headline can allow.

Why the media does this is a subject for an entirely different book.

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