• The test
• The result
• What linear growth implies
• A renormalisation: the KarNak unit
• Why this matters
• Paper and engagement

In 1964, Nikolai Kardashev classified hypothetical civilisations by their energy consumption: Type I harvests a planet’s incident stellar power, Type II commands a star’s full output, Type III taps a galaxy’s. Underlying the scale was a quiet but consequential assumption: civilisational energy use grows exponentially at roughly 1% per year. From that, Kardashev calculated humanity would reach Type II in about 3,200 years, Type III in about 5,800.

Sixty years later, that 1%/yr assumption still anchors most SETI detectability arguments, technosignature search priors, and Fermi paradox debates. I decided to test it against the data we actually have.

§The test

I used six decades of global primary energy production data (1965–2024) from the Our World in Data energy dataset. The methodology is standard: Markov Chain Monte Carlo (MCMC) inference for the exponential rate parameter, with linear ordinary least-squares as the natural alternative model.

§The result

The Kardashev 1%/yr exponential model fails.

The posterior growth rate is r = 2.01% ± 0.03% / yr (95% credible interval [1.94%, 2.08%]). Kardashev’s 1% sits well outside the credible interval — a clear statistical falsification.

But the more important finding is structural:

A linear model fits the data substantially better than any exponential.

The linear OLS fit has R² = 0.987 against the data, and is preferred over the free-rate exponential by ΔWAIC = 5.5 — strong evidence on conventional information-criterion scales.

This is a dual falsification:

• Kardashev’s original 1%/yr — too low (falsified at high credibility)

• Putnam’s (1948) GDP-extrapolation-derived 3–4%/yr that Kardashev cited as the high estimate — too high

• Exponential growth itself as the functional form — disfavoured vs linear

The year-over-year increments are also non-Gaussian (Shapiro-Wilk W = 0.925, p = 0.0014; skewness −0.664) with identifiable crisis outliers (2008, 2020). That rejects the independent-increment multiplicative structure required by Kardashev’s (1+x)^t geometric series.

§What linear growth implies

Extrapolating the linear model to the solar luminosity (L⊙ ≈ 3.828 × 10²⁶ W) yields a Type II civilisational timescale of approximately 1.6 × 10¹⁵ years.

For scale:

• Age of the universe: ~10¹⁰ yr (5 orders of magnitude shorter)

• Sun’s main-sequence lifetime: ~10¹⁰ yr (5 orders of magnitude shorter)

Long before any civilisation reaches Type II, its host star has evolved off the main sequence. Post-red-giant white dwarf luminosity drops 3–4 orders of magnitude over Gyr cooling timescales. The maximum extractable stellar power P(t) is no longer a civilisational variable — it’s set by stellar physics.

The Kardashev classification assumes a stable P(t) ceiling. Stellar evolution removes it.

This reframes the Fermi paradox: maybe nobody is exponential. Maybe the bottleneck is the functional form of growth itself, not the rate.

§A renormalisation: the KarNak unit

The paper proposes a new dimensionless ratio:

B(t) = P(t) / H(t)

where P(t) is civilisational power (watts) and H(t) is computational work rate (hashes/second). The unit is Joules per Hash — what I’m calling the KarNak unit.

Zero free parameters. It lets civilisational-energy scaling and computational-substrate scaling be compared on a single axis.

The Bitcoin connection isn’t decorative. Bitcoin’s hashrate is the only continuously-measured, globally-aggregated proof-of-work signal humanity has produced. It gives us a real, empirically observable H(t) curve to anchor the framework with.

Since 2009, B(t) spans 14 orders of magnitude, bounded below by Landauer’s bound (Landauer 1961; Bennett 1982): the minimum energy required to erase one bit of information at temperature T is kB T ln 2 ≈ 2.85 × 10⁻²¹ J at room temperature (T ≈ 300 K, where kB is Boltzmann’s constant).

This is, in part, recognition that Bitcoin’s proof-of-work infrastructure is the first planetary-scale, transparently-measured computational substrate, and that fact deserves to be in the physics, not just the economics.

I call the combined framework Kardashev–Sagan–Nakamoto (KSN):

• Kardashev — civilisational energy

• Sagan — information richness as the genuine intelligence signature (1973)

• Nakamoto — Bitcoin proof-of-work as the empirical computational substrate

Sagan’s information-richness requirement is finally formalised.

§Why this matters

If the functional form of civilisational growth is linear rather than exponential, every SETI timescale derived from the original Kardashev assumption needs revisiting. Waste-heat search priors shift more fundamentally than a rate revision alone would imply. The probability that any civilisation reaches Type II before its host star evolves drops sharply. The energetic invisibility of advanced civilisations may not be the Fermi paradox we think it is — it may be the natural consequence of linear-growth physics meeting stellar lifetimes.

§Paper and engagement

The paper is on arXiv and submitted to MNRAS Letters:

• arXiv: <https://arxiv.org/abs/2604.17516>

• ADS: <https://ui.adsabs.harvard.edu/abs/2026arXiv260417516G>

Dataset and notebook: <https://github.com/sebaguro/KSN_paper_I>

Sebastian Gurovich — astrophysicist, currently on unpaid leave from IATE-OAC-UNC-CONICET in Argentina, and based in Sydney. IVOA-exec Argentine representative 2015–2024.