In Praise of Advances Away from the Mean

Avi Loeb
5 min readMar 29, 2024

The late psychologist, Daniel Kahneman, noted during his Nobel Prize celebration in 2002: “there is regression to the mean, it is part of the human condition that we are statistically punished for rewarding others and rewarded for punishing them.” The experience he described is familiar from a visit to the beach. Sea shells are born with unique colors. But after they rub against each other as a result of being carried by transient ocean waves, the shells lose their unique colors and break into indistinguishable grains of sand. The loss of authentic colors is also what “regression to the mean” implies for heavy users of social media.

Through a similar attitude, some scientists find their life mission to step on any flower that rises above the grass level in their field of research. Others fight for equality of outcomes when they underperform. For those who spread toxicity in blog posts or journalistic reports about the frontiers of our scientific knowledge, I advise: “Be curious, not toxic!” Spreading misinformation about evidence-based, curiosity-driven research is misguided, because this train has already left the station and there is no way to stop it. And if these critics — some of whom are bloggers who were unable to secure an academic position and stopped writing scientific papers for over a decade but still call themselves “astrophysicists” — continue to be toxic, I ignore them and move on. Their toxicity would be a good conversation starter for their therapists. I have better things to do, given the large community of scientists and funders who support innovative research. These supporters are inspired by the scientific method, because they know that our imagination is more limited than the splendor of nature. If our “mean” conception of reality is off target, the only way to correct it is by exploring deviations away from the mean. To make discoveries, we must reward rather than punish those who take the risk of deviating from the crowd.

Large academic committees are also driven by the statistics of large numbers. Such committees tend to converge to the lowest common denominator of their members, with a deviation from the status-quo that scales inversely with the square-root of the number of committee members. If a university leadership prefers not to act on a controversial policy issue, all they need to do is establish an advisory committee with a large enough number of members such that its recommendation would maintain the status-quo and do nothing new.

Regression to the mean can also be studied through the evolution of artificial intelligence (AI) systems. In 2023, a research team from Stanford University and U.C. Berkeley wrote a paper suggesting that ChatGPT-3.5 and GPT4 got “substantially worse over time.” The study compared performance in March and June 2023 on the ability to solve math problems, answer sensitive questions, generate code and conduct visual reasoning. It found, for example, that the accuracy of ChatGPT4 in opinion response rate dropped from 97.6% in March to only 22.1% in June. These Large Language Models learn the biases fed into their training sets and generate content that could regress after many iterations to a disappointing mean, giving the impression that the models got dumber and less exploratory.

I often joke that “the best Harvard students are exceptional because they get an `A’-grade in all their classes, whereas the worst Harvard students get an `A’-grade in all their classes.” This state-of-affairs, where everyone is at the mean with no deviations, is obviously worthless, because the grading system was created to differentiate among students based on their performance.

Usain Bolt winning the 100-meter dash final in the 2008 Olympic Games. The audience focused on the deviations from the mean.
The 100-meters runners were well represented by their mean at the start of the race in the 2012 Olympics.

Imagine an Olympic Games in which the fast runners in the 100-meters-dash are slowed down by officials, so that they get to the finish line together with the slowest runner. This would be a wonderful gesture to the slowest runner but it hides the inherent diversity in athletic abilities. It misses the point that the Olympics is a celebration of an attitude opposite to our psychological tendency. Here, Kahneman’s statement should be paraphrased to the notion that “over the 100-meters track, a group of runners exhibits a progression away from the mean; as part of the Olympic spirit we celebrate those who run fastest rather than reward those who punish them.”

When I started my career as a scientist, the spirit of science resembled that of sport. The underlying system was based on the understanding that breakthrough discoveries in science represent departures from the mean. To foster these discoveries, the academic culture resisted the natural psychological tendencies of regression to the mean. Even today, some funding agencies still recognize that spirit. For example, over the past year I received grants from the Brinson Foundation and the Richard King Mellon Foundation, specifically dedicated to fostering innovative research within the Galileo Project which breaks away from the beaten path of past academic research. Similarly, the upcoming annual TED Conference in Vancouver on April 15–19, 2024 will celebrate “The Brave and the Brilliant” by featuring a list of speakers who represent advances away from the mean.

Since deviations from the mean generate friction with the mainstream, such excursions are rare. Most people prefer not to rock the boat even if the boat is headed in the wrong direction. But just because deviations are rare, any successful advance away from the mean is remembered long after it pioneered a new path of exploration. We remember Galileo Galilei because the “mean view” before him was represented by the notion that the Earth is at the physical center of the Universe. And people might remember the Galileo Project in the future if its research team will identify evidence that the Earth is not at the intellectual center of the Universe.

Those who seek the comfort of not rocking the boat and prefer not to worry about the direction it takes, deserve to miss the most exciting destinations in the intellectual journey of humanity.


Image credit: Chris Michel (October 2023)

Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, was published in August 2023.



Avi Loeb

Avi Loeb is the Baird Professor of Science and Institute director at Harvard University and the bestselling author of “Extraterrestrial” and "Interstellar".