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.