You smart? How about your children? The law of regression to the mean

Francis Galton -British scientist and cousin of Charles Darwin-, in the late 19th century cleverly coined the term "regression to (or towards) the mean," which means that if a variable shows an extreme value in the initial measurement, the subsequent observed values of that variable will tend to get closer to the average of its distribution. The classical example is height: a tall child will, on average, have parents who are shorter than themselves. Moreover, extremely short parents tend to have children who are smaller than average. However, in both cases, the children tend to be closer to the mean than their parents were (Senn, 2011).

In his book "El placer de decidir" (in Spanish), Rolf Tarrach, a former president of Luxemburg University, presents a different perspective on regression to the mean. Tarrach argues that this phenomenon is not limited to physical attributes like height but also applies to cognitive abilities. According to his rationale, intelligent parents are likely to have children who are not as smart as expected. Therefore, if you consider yourself intelligent and choose a partner who is also intelligent, Tarrach suggests that your children are unlikely to surpass the intelligence of both parents. This challenges the common expectation that children of intelligent parents should be even more intelligent. He points out that while there may be exceptional cases, such as the Bach or Bernoulli families known for their exceptional talents, they are deviations from the norm (outliers in the most classical statistical language).

Héctor Abad Gómez, colombian politician -murdered by his liberal and progressive perspectives- wrote an opinion article about the utopias of geniuses. Before reading it, take a look at this well-known figure:

Here it goes: hopefully, it will alleviate your desire to be a genius or for your children to be geniuses or influential people, or outliers in this somehow void world.

Genius is the painful self-discovery that one is different from others. And that comes with a price. Often, it leads to fame. [...] It is also experiencing the envy of the mediocre, who constitute the majority. Especially the mediocre who have been foolishly convinced by their upbringing and schooling that anyone can be a genius, that the only requirement to be a genius is effort, that anyone can be the best. And when one discovers that someone else is better, there is suffering, the futile suffering of the mediocre who envies the fertility of the genius.

This, which is an elementary and universal statistical law that states that the majority is average [...] seems to be unknown to or ignored by the educators of the world. They all vainly want a genius to emerge among their disciples. They choose one or a few for this sacrifice, forgetting the extraordinary scarcity of this rare natural product.

Here is the origin of so much useless suffering. If we had all been taught that the majority of us are inevitably mediocre -and that we should be content with our mediocrity- human life would be more peaceful and happier. The desire to be a hero, protagonist, leader, artist, without possessing the innate qualities for it, is the cause of a great deal of suffering, not only for the individual but also for others. We have all had to endure those who consider themselves geniuses without actually being one.

PS: If you want to reproduce the pretty normal distribution above, just copy and paste this code into R:

library(ggplot2

# Generate data
x <- seq(-3, 3, length.out = 1000)
y <- dnorm(x)

# Create a data frame
df <- data.frame(x, y)

# Plot the normal distribution
ggplot(df, aes(x = x, y = y)) +
? geom_line() +
? xlim(-3, 3) +
? ylab("Density") +
? xlab("Standard Deviations") +
? ggtitle("Normal Distribution - Geniuses appear beyond two and a half standard deviations") +
? theme_minimal() +
?
? # Add vertical lines at 2.5 standard deviations
? geom_vline(
??? xintercept = c(-2.5, 2.5),
??? linetype = "dashed",
??? color = "red"
? ) +
?
? # Adjust appearance of the lines
? theme(
??? panel.grid.major = element_blank(),
??? panel.grid.minor = element_blank(),
??? axis.text = element_text(size = 12),
??? axis.title = element_text(size = 14, face = "bold"),
??? plot.title = element_text(size = 16, face = "bold", hjust = 0.5)
? )

)