A new astrophysics and astroinformatics study revisits one of the most famous ideas in the search for advanced civilizations – the Kardashev scale. Originally proposed in 1964, the scale classifies civilizations by the amount of energy they can use – from planetary-scale Type I civilizations to Type III civilization with energy on the scale of its own galaxy.

In the new article the author tests the standard Kardashev assumption that civilization energy production grows exponentially at a constant rate of 1% per year. Using global energy production data from 1965 to 2024, the study finds that this one-percent model does not match the observed historical record. Instead, statistical modelling suggests a higher average growth rate of about 2% per year.

However, the paper identifies a deeper problem. A simple linear model fits the historical energy data very well, but when extrapolated to the Kardashev Type II level, equivalent to the total energy output of the Sun, it predicts a timescale vastly longer than the age of the Universe. The author calls this contradiction “Kardashev’s Conundrum”: models based only on total energy production can either fit past data or remain physically meaningful, but not both.
To resolve this, the study argues that civilizational progress should not be measured by energy use alone. Instead, it should also reflect how efficiently a civilization converts energy into information and computation. The author proposes the Kardashev–Sagan–Nakamoto model, which divides global energy production by the Bitcoin network hashrate. This creates a new measure of energy per computational operation, expressed in Joules per hash, or the proposed KarNak unit.

The paper presents this as a bridge between the Kardashev scale, Carl Sagan’s emphasis on information richness, and the physical limits of computation described by Landauer’s principle. The result is a provocative new framework: advanced civilizations may be defined not simply by how much energy they command, but by how efficiently they use it to process information.

For more details, read the full paper here.