Intelligence Means Exponential Growth

Avi Loeb
4 min readDec 16, 2023


Discussion on quantum electrodynamics at the Shelter Island conference in 1947, featuring (left to right): W. Lamb, Abraham Pais, John Wheeler (holding paper), Richard P. Feynman (holding pen), Herman Feschbach and Julian Schwinger.

What is the mark of a genius? The ability to reach a solution through an unforeseen shortcut instead of a random walk or an elaborate effort.

In the late 1940s, the brilliant physicists Shin’ichirō Tomonaga and Julian Schwinger offered an operator method for calculating quantum electrodynamics, which was entirely different from Richard Feynman’s diagrammatic method. The two approaches appeared very different, until a 25-year old physicist, Freeman Dyson, had a eureka moment and demonstrated in a 1949 paper that they are equivalent. The circumstances were unexpected.

In spring 1948, Dyson took a cross-country road trip with Feynman. Upon his return, Dyson went to Ann Arbor to spend six weeks with Schwinger. Subsequently, he left Michigan for another cross-country bus trip. Dyson referred to a “flash of illumination on the Greyhound bus,” where everything fell into place and he saw the equivalence of the two competing formulations that had evaded both Feynman and Schwinger.

I often tell my students and postdocs that scientific insights are not necessarily the product of hard work. Take a vacation … go to the movies … enjoy music. If at the end of it all, you’ll return with a brilliant solution to a problem that others were struggling with, your contribution is invaluable. Your intelligence is measured by the originality of your intellectual discoveries and not by the number of likes you get on social media.

What makes human intelligence so unique relative to animals? It is its ability to promote knowledge exponentially fast. Natural selection is often set up through gradual zero-sum games in an environment that offers limited resources. Animals with better motor skills maintain territorial control more effectively than their competitors. This perspective changed drastically over the past century of human history. Modern science and technology now offer an infinite-sum game with unlimited resources. Whereas natural evolution was limited to Earth, humans launched spacecraft towards new domains of real estate within the solar system and beyond.

Human intelligence allows exponential growth in technological capabilities. Moore’s Law for the miniaturization of semiconductors applies to a broader range of technological capabilities, including 3D printing, drones, robotics, artificial intelligence and synthetic biology.

Without intelligence, unplanned progress is limited to random walks. For example, mutations sample by chance alternative designs of biological systems. Science is made efficient by design through cooperation, as summarized in a 1675 letter by Isaac Newton to Robert Hooke: “if I have seen further, it is by standing on the shoulders of giants.” Sharing scientific and technological knowledge among individuals and groups makes the growth rate of knowledge proportional to the amount of existing knowledge. When the rate scales with the amount, growth is exponential.

Communication via a language and mathematics is key for the exponential evolution of science and technology. Sharing information promotes its growth at a rate that is proportional to what is already known by the community.

It is reasonable to imagine that these traits are universal and likely to apply also to alien species on exoplanets. If extraterrestrial gadgets reach Earth, then the senders probably communicated with each other through a language. In other words: technological aliens communicate!

And if their technological growth is exponential as is ours, they could be far more superior if their technological age exceeds ours. When we encounter their gadgets we might be filled with religious awe, like Moses witnessing the burning bush which was never consumed and concluding that it was manufactured by a superhuman entity.

Humans exceeded the evolutionary level of chimpanzees not by developing better motor skills, but by developing rockets that can reach the Moon and Mars. Given this perspective, it is surprising that some of my colleagues insist that interstellar meteors must be stones. I refer to this perspective as “the stone age of science.”

Imagining what might lie beyond the solar system is a mark of intelligence. We know that 83% of the cosmic matter is not stones but an unknown substance labeled as “dark matter”. Our ability to consider alternatives to the familiar, enables growth in our scientific knowledge. Those who insist on past knowledge will remain ignorant, in the same way that chimpanzees never imagined landing on the Moon and non-avian dinosaurs never looked through telescopes in anticipation of a looming catastrophe from an asteroid impact.

Extending our ventures to interstellar space beyond the boundary of the Solar system would be the next mark of human intelligence and ingenuity. Enrico Fermi asked: “where is everybody?” The answer may arrive as soon as we exit the Oort Cloud to interstellar space: “Welcome to the club of intelligent civilizations whose knowledge grows exponentially.”


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 chairs the advisory board for the Breakthrough Starshot project, and 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".