Civilizations' energy growth isn't what we thought ⚡ экспресс
Using Bayesian inference (MCMC) on global energy production data from 1965–2024, Kardashev's hypothesis of 1% annual growth was tested. The rate is robustly estimated at 2.01% ± 0.03% per year; linear and exponential models are statistically indistinguishable. Extrapolating to the Type II civilization threshold (solar luminosity) shows: a linear trend implies a transition time of order 10⁵ Hubble times, while an exponential trend is ruled out by heat dissipation limits and carrying capacity constraints. Thus, coherent achievement of Type II scale on realistic trajectories is impossible—the 'Kardashev paradox.' This explains the null results in Dyson sphere searches and supports logistic solutions to the Fermi paradox. The root cause is the dimensional incompleteness of power as a single variable. A renormalization is proposed: the Carnac unit (J/hash) — dividing power by global hashrate, which introduces an information dimension and preserves the Type II concept.
Humanity is a pot on a stove. Sixty years of data show: the heat is being turned up faster than astrophysicist Nikolai Kardashev expected — about 2% per year, not 1%. But even so, the pot will never hold an ocean: to harness all the energy of the Sun with even heating would take a time comparable to the age of the Universe. And accelerated heating over a thousand years would heat the planet to the temperature of the solar corona — the civilization would melt. This is the paradox: supercivilizations are doomed to overheat to stellar scale.
The solution is to evaluate not just power, but steam control. A new index 'CarNac' (joule per hash) links energy to computation, such as mining. Taking into account the entropy of data processing, it explains why photometry — precise measurements of stellar brightness — doesn't find Dyson spheres: advanced civilizations prefer to compute, not burn.
🎯 If energy consumption growth were linear, humanity would need about 100,000 ages of the Universe to reach a Type II civilization level.
🎬 The Dyson sphere, described by Larry Niven in 'Ringworld', is a favorite construct of science fiction.