What Is the Curse of Dimensionality?

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What is the curse of dimensionality? Is it ever possible to predict the behavior of a complex system?

The curse of dimensionality is a mathematical principle that states that as a system grows, the rate at which it becomes complex accelerates. In his book Skin in the Game, Nassim Taleb argues that because of the curse of dimensionality, complex systems are impossible to reliably predict—any adjustment made to a large, complex system will cause an avalanche of unintended side effects. Without the true knowledge gained from failure, we would never know enough to navigate the infinitely complex world.

In this article, we’ll explore the concept of the curse of dimensionality.

Why Complex Systems Are Difficult to Predict

What is the curse of dimensionality? In simple terms, the curse of dimensionality is when a system is too complex (it has too many features or dimensions) to solve or reliably predict.

The trickiest thing about such systems is that they behave differently than their component parts.

Many theorists and analysts use the “mean-field approach” to study complex systems—they reduce a system down to one of its simple components, and use it to draw conclusions about the system as a whole. However, in the vast majority of cases, the mean-field approach proves nothing. Systems behave differently than their component parts—sometimes even in ways that appear to contradict them.

For example, large populations often adapt to the preferences of small minorities. If we were to use the mean-field approach, we would assume that in a country where 99.7% of people pay no attention to “kosher” dietary restrictions, kosher food would be incredibly difficult to find. Yet in the United States, 41% of all packaged food is kosher.

In his book Skin in the Game, Taleb examines how complex systems work in the exact opposite way from what a surface-level observer would expect.

The Nature of the Unknown

This idea of complex systems being impossible to predict because of the curse of dimensionality is one of the central themes uniting the books in Taleb’s Incerto series—in fact, Taleb derived the word “Incerto” from the Latin word for “uncertainty.”

In The Black Swan, Taleb argues that the majority of people entirely misunderstand “the unknown.” The unknown isn’t just the absence of knowledge, it’s the opposite of knowledge, a world where knowing more can mislead you. Applying previous knowledge in domains of uncertainty—that is, whenever systems are large enough to become opaque—can cause severe harmful consequences.

In The Black Swan, Taleb illustrates this idea by recounting a misunderstanding between Jews and Romans in the first century. The Romans put a statue of the emperor Caligula in the Jewish temple in exchange for a statue of Yahweh in their Roman temples. To the Jews, Yahweh wasn’t the same kind of god as the ones the Romans knew, and to diminish him to the status of a man like Caligula was disrespectful and profane. The Romans applied their existing understanding of “gods” in the wrong place, provoking the Jews to revolt.

In the same way, a modern intellectual could apply the mean-field approach to a complex field where it doesn’t belong, for example, economics, and come to conclusions that lead to massively harmful economic policy.

What Is the Curse of Dimensionality?

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Darya Sinusoid

Darya’s love for reading started with fantasy novels (The LOTR trilogy is still her all-time-favorite). Growing up, however, she found herself transitioning to non-fiction, psychological, and self-help books. She has a degree in Psychology and a deep passion for the subject. She likes reading research-informed books that distill the workings of the human brain/mind/consciousness and thinking of ways to apply the insights to her own life. Some of her favorites include Thinking, Fast and Slow, How We Decide, and The Wisdom of the Enneagram.

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