{"id":53593,"date":"2021-11-14T16:04:00","date_gmt":"2021-11-14T20:04:00","guid":{"rendered":"https:\/\/www.shortform.com\/blog\/?p=53593"},"modified":"2021-11-22T10:02:02","modified_gmt":"2021-11-22T14:02:02","slug":"what-is-the-curse-of-dimensionality","status":"publish","type":"post","link":"https:\/\/www.shortform.com\/blog\/what-is-the-curse-of-dimensionality\/","title":{"rendered":"What Is the Curse of Dimensionality?"},"content":{"rendered":"\n

What is the curse of dimensionality? Is it ever possible to predict the behavior of a complex system?<\/p>\n\n\n\n

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<\/em>, Nassim Taleb<\/a> argues that because of the curse of dimensionality, complex systems<\/a> are impossible to reliably predict\u2014any 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.<\/p>\n\n\n\n

In this article, we’ll explore the concept of the curse of dimensionality.<\/p>\n\n\n\n\n\n\n\n

Why Complex Systems Are Difficult to Predict<\/h2>\n\n\n\n

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.<\/p>\n\n\n\n

The trickiest thing about such systems is that <\/strong>they behave differently than their component parts.<\/p>\n\n\n\n

Many theorists and analysts use the \u201cmean-field approach\u201d to study complex systems\u2014they 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\u2014sometimes even in ways that appear to contradict them.<\/p>\n\n\n\n

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 \u201ckosher\u201d dietary restrictions, kosher food would be incredibly difficult to find. Yet in the United States, 41% of all packaged food is kosher<\/a>.<\/p>\n\n\n\n

In his book Skin in the Game<\/em>, Taleb examines how complex systems work in the exact opposite way from what a surface-level observer would expect.<\/p>\n\n\n\n

The Nature of the Unknown<\/h3>\n\n\n\n

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\u2019s Incerto<\/em> series\u2014in fact, Taleb derived the word \u201cIncerto\u201d from the Latin word for \u201cuncertainty.\u201d<\/p>\n\n\n\n

In The Black Swan<\/em><\/a>, Taleb argues that the majority of people entirely misunderstand \u201cthe unknown.\u201d The unknown isn\u2019t just the absence of knowledge, it\u2019s the opposite of knowledge<\/em>, a world where knowing more can mislead you. Applying previous knowledge in domains of uncertainty\u2014that is, whenever systems are large enough to become opaque\u2014can cause severe harmful consequences.<\/p>\n\n\n\n

In The Black Swan<\/a>, <\/em>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\u2019t 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 \u201cgods\u201d in the wrong place, provoking the Jews to revolt.<\/p>\n\n\n\n

In the same way, a modern intellectual could apply the mean-field approach to a complex field where it doesn\u2019t belong, for example, economics, and come to conclusions that lead to massively harmful economic policy.<\/p>\n","protected":false},"excerpt":{"rendered":"

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\u2014any 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<\/p>\n","protected":false},"author":7,"featured_media":4206,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[21,160,25],"tags":[529],"class_list":["post-53593","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-philosophy","category-science","category-statistics","tag-skin-in-the-game","","tg-column-two"],"yoast_head":"\nWhat Is the Curse of Dimensionality? - Shortform Books<\/title>\n<meta name=\"description\" content=\"What is the curse of dimensionality? 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