Kardashev measures appetite.
Not intelligence.
In 1964, Soviet astrophysicist Nikolai Kardashev proposed a scale to classify extraterrestrial civilizations by their energy consumption. Type I harnesses the energy of a planet. Type II, that of a star. Type III, an entire galaxy. A massive, industrial vision, forged in the Cold War imagination.
But this scale rests on an implicit assumption: the more advanced a civilization, the more it consumes. The more visible it becomes. The more noise it makes. A Type II civilization should wrap its star in a Dyson sphere, detectable by infrared. A Type III should reshape its entire galaxy.
Yet we see nothing. Despite decades of observation, across every wavelength. This is the Fermi Paradox. What if the problem isn't the absence of advanced civilizations — but the inadequacy of our framework for recognizing them?
“What if progress is not measured by the quantity of energy consumed, but by the depth at which a civilization interacts with reality?”
We are not the first
to look downward.
Barrow (1998): The Miniaturization Scale
In Impossibility: The Limits of Science and the Science of Limits (1998), cosmologist John D. Barrow proposed exactly this inversion. His scale ranges from Type I-minus (manipulating objects our own size) through six levels of increasing miniaturization — genes, molecules, atoms, nuclei, elementary particles — to Type Ω-minus: the manipulation of spacetime itself.
Barrow's insight was profound and precedes anything in this essay. He saw that humanity's real trajectory is inward, not outward. The Yatima Scale owes its central intuition to his work.
Sagan (~1973): The Information Dimension
Carl Sagan independently proposed measuring civilizations by their information mastery — the total unique bits of knowledge they possess. His alphabetical scale (Type A = 10⁶ bits, each letter a tenfold increase) classified 1973 Earth as 0.7H, with access to roughly 10¹³ bits.
Sagan's key contribution was introducing information as a measurable axis, independent of energy. But his metric counts information stored — the size of the library. It does not measure how deeply a civilization reads the physical world.
Smart (2002–2012): The Transcension Hypothesis
John Smart built directly on Barrow's insight and took it further. In his Transcension Hypothesis (first presented in 2002, published in Acta Astronautica in 2012), Smart argued that advanced civilizations are drawn toward “inner space” — an increasingly dense, productive, miniaturized domain of space, time, energy, and matter. He coined the term STEM compression (Space, Time, Energy, Matter) to describe this trajectory, and proposed that it leads civilizations toward black holes as computationally optimal substrates.
Smart's key contribution was connecting Barrow's miniaturization scale to the Fermi Paradox explicitly: if civilizations compress inward, they become undetectable — not because they hide, but because their technology operates at scales and densities invisible to conventional SETI. This is the closest prior work to the Yatima Scale's Fermi resolution.
What Yatima Adds
If Barrow provided the direction (downward), Sagan the currency (information), and Smart the destination (inner space), what does the Yatima Scale contribute?
1. Quantitative formalization. Barrow's scale is qualitative — a list of seven levels with no equations. Smart's hypothesis is narrative, not mathematical. Yatima provides Y = −log₁₀(ℓ) and ηY = Iexploited / IBekenstein — calculable numbers with derivable orders of magnitude.
2. A physical ceiling. Neither Barrow, Sagan, nor Smart specify an upper limit grounded in physics. Yatima identifies the Bekenstein bound as the absolute ceiling, giving the scale a terminus derived from general relativity and quantum mechanics.
3. Information exploited, not stored. Sagan measures the size of a civilization's library. Yatima measures the fraction of reality's information it can access — a fundamentally different quantity. A civilization with a small library but deep mastery of quantum states would rank low on Sagan's scale and high on Yatima's.
4. Multi-formalism convergence. The demonstration that Bekenstein (information), Holevo (channel capacity), and thermodynamic entropy independently produce the same four-level hierarchy is new.
5. The asymptote. Smart proposed that civilizations converge toward black holes. Yatima formalizes why: ηY → 1 is an asymptotic limit, like absolute zero or the speed of light, because the Bekenstein bound is a theorem, not a guideline. The black hole is the horizon of information density, approached but never reached.
6. Invisibility as thermodynamics. Barrow noted that miniaturized civilizations might be harder to detect. Smart argued they would be drawn inward. Yatima derives the mechanism: as ηY increases, the ratio of useful work to waste radiation improves — a civilization approaching thermodynamic reversibility emits less detectable energy per unit of computation. Invisibility is not a choice or a strategy. It is a thermodynamic consequence of operating closer to the Landauer limit.
The Yatima Scale does not replace Barrow, Sagan, or Smart. It stands on their shoulders — and adds equations, a ceiling, derivations, and the asymptotic structure that turns an intuition into a framework.
Progress descends.
From the macro to the infinitely small.
The history of human technology reveals a deep pattern: every major revolution corresponds to a descent toward a smaller scale of matter. From flint tools to transistors, from nuclear reactors to qubits, humanity progresses by accessing increasingly fundamental levels of reality.
And at each descent, three things happen simultaneously: the energy density accessible per kilogram of matter explodes (chemistry ~10⁷ J/kg, nuclear ~10¹³–10¹⁷ J/kg, fundamental ~10²⁵ J/kg), the amount of matter needed shrinks, and the visibility drops. The pyramids are visible from space. A 2-nanometer chip is invisible to the naked eye. A quantum operation has no macroscopic trace whatsoever.
This trend may be universal — inscribed in the very structure of matter. Any technological civilization, anywhere in the universe, would follow this same descent. Because the sequence of interaction levels is not cultural: it is dictated by physics.
Chemical. Nuclear. Fundamental. Entanglement.
The Yatima Scale identifies four levels of depth of interaction with matter and energy. Each level corresponds to a characteristic length scale, an accessible energy density, and a governing equation.
Molecular bonds, combustion, chemical reactions. Breaking and recombining molecules. Fire, coal, oil, explosives. The energy of bonds between atoms — low yield, visible, loud, polluting. Humanity from 300,000 years ago until yesterday.
Entering the atomic nucleus. Fission (uranium), fusion (hydrogen), and at the summit of this level, matter-antimatter annihilation — the total conversion of mass into energy via E=mc². A million times more energy per gram than chemistry. Humanity today, stumbling forward. Internal progression: fission → fusion → antimatter.
Manipulation of the four fundamental forces: strong, weak, electromagnetic, gravitational. No longer working with atoms, but with the rules that make atoms. Direct transmutation of matter, gravitational control, controlled disintegration. The “droplet” in Liu Cixin's The Three-Body Problem — a surface held together by the strong force — is the literary illustration of this level.
The abyss between III and IV. Between Level III (10⁻¹⁸ m) and Level IV (10⁻³⁵ m) lie 17 orders of magnitude of unexplored physics. By comparison, the entire span from chemistry to particle physics covers only 8 orders of magnitude. This is the largest gap in the scale, and it may conceal intermediate levels we cannot yet name. We draw four levels because our current physics suggests four natural plateaus — but this region is where the map goes blank. Intellectual honesty demands we mark it as such.
Leaving the world of matter and force entirely. Energy resides in correlations between quantum states — entanglement as a resource. The ER=EPR conjecture links quantum entanglement and wormholes: to manipulate one is to manipulate the geometry of spacetime itself. No need to transport energy — it is everywhere, non-locally. A Level IV civilization is invisible, silent, and operates at the level of the fabric of reality itself.
One number.
From 0 to 1.
The Yatima Index
The advancement of a civilization can be characterized by the smallest length scale it masters technologically. The Yatima Index is defined as:
This index is simple, universal, and independent of specific technological choices. It is dictated by the structure of matter itself. Chemistry operates at Y ≈ 10 (atomic bonds, ~10⁻¹⁰ m). Nuclear physics at Y ≈ 15 (femtometer). Particle physics at Y ≈ 18 (quarks). Planck-scale physics at Y ≈ 35. The index is monotonically increasing, unbounded above, and culture-independent.
The Unified Framework: Information
All four levels are unified by a single fundamental quantity: information. At every level, what a civilization actually does is transform information. Energy is merely a consequence of that transformation.
Landauer's principle (1961) establishes the bridge: the minimum energy to erase one bit of information is E = kBT·ln(2) — roughly 3×10⁻²¹ J at room temperature. This is not a technological limitation but a thermodynamic law. Every computation, every transformation, every act of technological mastery is, at bottom, an information operation with a minimum energy cost.
And the Bekenstein bound (1973) sets the absolute ceiling: the maximum number of bits that can exist in a finite region of spacetime.
The Reference Volume Problem
A critical question: R and E of what? The Bekenstein bound depends on the radius and energy of the system considered. A civilization's ηY would vary wildly depending on whether we measure a single device, a planet, or a galaxy.
We propose a canonical reference: one kilogram of matter confined to one meter. This gives a Bekenstein limit of approximately Imax ≈ 2.57 × 10⁴³ bits. The choice is not arbitrary — it normalizes the comparison to a fixed amount of matter-energy, making the ratio a measure of how deeply a civilization reads the information in a given chunk of reality, independent of how much matter it possesses.
The Yatima Ratio — Derivation
The Yatima Ratio measures the fraction of information a civilization can exploit in the canonical reference volume:
Here is how the orders of magnitude are derived for each level:
Chemical (Y = 10): A chemical reaction exploits electron shell configurations — roughly the outermost electrons per atom. One kilogram of carbon contains ~5×10⁻²⁵ atoms, each contributing ~4 valence electrons with ~2 bits of useful state each. That gives Ichem ≈ 4×10⁻²⁶ bits. Divided by IBek ≈ 10⁴³: ηY ≈ 10⁻¹⁷. (Note: our earlier estimate of 10⁻&sup4;³ was too conservative — it assumed ~1 bit per bond rather than per valence electron. The refined value better reflects the information actually accessible to chemical technology.)
Nuclear (Y = 15): Nuclear reactions access the strong force binding within nuclei. Each nucleon carries roughly 8 MeV of binding energy, corresponding to much richer state spaces. For 1 kg: ~6×10⁻²⁶ nucleons, each with ~20–30 bits of exploitable nuclear state (spin, isospin, shell configuration). That gives Inuc ≈ 10⁻²⁸ bits, so ηY ≈ 10⁻¹⁵.
Fundamental (Y = 18): At the quark-gluon level, each nucleon decomposes into quarks carrying color charge, flavor, and gluon field configurations. The number of accessible microstates explodes. Estimating ~10³⁶ bits per kilogram (comparable to the entropy of a quark-gluon plasma): ηY ≈ 10⁻⁷.
Entanglement (Y = 35): At the Planck scale, a civilization accesses the full Hilbert space of 1 kg in 1 m. Approaching the Bekenstein bound itself: ηY → 1.
The Bridge: Y ↔ ηY
The Yatima Index (Y) and the Yatima Ratio (ηY) are not independent. As a civilization masters smaller length scales, the number of accessible microstates per particle grows roughly as a power of the scale ratio. In the canonical volume, this gives an approximate functional relationship:
The constant 43 comes from the Bekenstein bound of the canonical volume (~10⁴³ bits). The slope α reflects how quickly new physics becomes accessible as one descends in scale. Between Y = 10 (chemistry) and Y = 18 (fundamental), we gain roughly 10 orders of magnitude in ηY over 8 units of Y, giving α ≈ 1.25. This is not a derived law — it is an empirical fit to three data points. But it shows the two formalisms are mutually consistent.
Convergence: Three Roads to the Same Scale
The strength of a classification scheme lies not in a single derivation, but in the convergence of independent formalisms. The thermodynamics of black holes became established physics when Bekenstein (information), Hawking (quantum field theory), and Penrose (geometry) all arrived at the same entropy. We can attempt something similar.
Road 1 — Bekenstein (information capacity): as developed above. The ratio of exploited to maximum information in a canonical volume.
Road 2 — Holevo (channel capacity): in quantum information theory, the Holevo bound sets the maximum classical information extractable from a quantum system. Redefining the Yatima Ratio as ηY = Cexploited / CHolevo removes the dependence on spatial volume entirely — the channel capacity is defined by the transformation itself, not by an arbitrary region. This resolves the reference volume problem from a completely independent angle, yet yields the same hierarchy: classical channels (chemistry), high-energy classical channels (nuclear), quantum channels (fundamental), non-local quantum channels (entanglement).
Road 3 — Thermodynamic (entropic efficiency): define σY = ΔSlocal / ΔStotal, the ratio of local entropy reduction (order created) to total entropy produced (including waste). A chemical civilization creates modest order with enormous waste heat. A nuclear civilization does better. A Level IV civilization, operating reversibly at the quantum level, would approach σY → 1 — maximum order, minimum waste. This is the same hierarchy, arrived at through classical thermodynamics alone.
Three independent roads. Same four levels. Same ordering. This convergence is the strongest argument that the Yatima Scale captures something real about the structure of physical law, not merely a convenient metaphor.
The Asymptote: Why ηY = 1 Is a Horizon
The Bekenstein bound is not a soft ceiling. It is a theorem: any physical system that saturates its Bekenstein bound is a black hole. This creates a tension — can a civilization reach ηY = 1 without collapsing?
The answer is no. And that is precisely the point. Like absolute zero in thermodynamics (T → 0 K, reachable asymptotically but never exactly), ηY = 1 is a limit that can be approached but never attained. The black hole is not the destination — it is the horizon. The Yatima Scale does not predict that advanced civilizations become black holes. It predicts that they asymptotically approach the informational density of one, extracting ever more information from ever smaller regions, forever approaching and never quite reaching the Bekenstein limit.
This is not a weakness of the framework. It is its most physically honest feature. Every ratio in physics that approaches 1 — Carnot efficiency, the speed of light, absolute zero — carries the same structure: the closer you get, the harder it becomes. The Yatima Scale inherits this structure naturally.
Cosmic silence
is a sign of maturity.
The Fermi Paradox, Resolved
The Yatima Scale offers an elegant resolution to the Fermi Paradox. If technological progress inevitably leads toward increasingly subtle interactions with reality, then any sufficiently advanced civilization becomes invisible. Not because it hides — but because its technology operates at a level our instruments cannot detect.
Kardashev predicts that advanced civilizations should be more visible. Yatima predicts they should be less visible. Observation — cosmic silence — is consistent with the latter. (Though as Section 07 will discuss, this consistency alone does not constitute proof.)
Kardashev vs. Yatima
Kardashev (1964)
- Measures energy consumption
- Extensive scale (quantity)
- Progress = expansion
- Advanced civilization = visible
- Limit = galaxy size
- Predicts megastructures
- Fermi Paradox unexplained
Yatima (2026)
- Measures depth of interaction
- Intensive scale (quality)
- Progress = deepening
- Advanced civilization = invisible
- Limit = Bekenstein bound
- Predicts discretion
- Fermi Paradox resolved
These two scales are not rivals — they are complementary axes. A civilization could be high on Kardashev and low on Yatima (a galaxy-spanning empire burning stars inefficiently), or low on Kardashev and high on Yatima (a quiet civilization operating at the quantum level within a single solar system). The most interesting question may not be where a civilization sits on either axis, but where it sits on both.
Clarke's Law, Taken to Its Limit
Arthur C. Clarke wrote: “Any sufficiently advanced technology is indistinguishable from magic.” The Yatima Scale pushes this further: any sufficiently advanced technology is indistinguishable from physics itself. A Level IV civilization does not manipulate matter — it manipulates the fabric of reality. Its artifacts don't look like technology. They look like natural phenomena. Perhaps some unexplained astrophysical events are not natural at all.
Black Holes: Horizons, Not Destinations
If ηY → 1 is an asymptotic limit, then a black hole is not what an advanced civilization becomes — it is the horizon it approaches. From the outside, a civilization nearing ηY = 1 would be progressively indistinguishable from a black hole: maximal information, minimal signature, no classical radiation. This reframes black holes not as endpoints but as boundary conditions on the space of possible civilizations — the ultimate constraint that physics imposes on organized complexity.
What holds up.
What doesn't.
What is solid: the historical trend of human progress toward the infinitely small is observable and measurable. The sequence chemical → nuclear → fundamental is anchored in the structure of matter. The index Y = −log₁₀(ℓ) is simple, universal, and culture-independent. The canonical reference volume (1 kg, 1 m) provides a well-defined denominator for ηY. And the convergence of three independent formalisms — Bekenstein, Holevo, and thermodynamic entropy — toward the same four-level hierarchy is a meaningful structural result, not a coincidence.
What is improved but approximate: the orders of magnitude for ηY are now derived from explicit bit-counting, but the estimates still involve rough assumptions (bits per valence electron, bits per nucleon state). The bridge equation log₁₀(ηY) ≈ αY − 43 is an empirical fit to three data points, not a derived law. The slope α could shift with better physics. These numbers are meant to be indicative, not definitive.
What is speculative: Level IV (entanglement) rests on physics we do not yet master. Energy extraction from quantum entanglement has been demonstrated in laboratories but at infinitesimal scales (picowatts). Vacuum energy poses the unsolved cosmological constant problem. The ER=EPR conjecture remains a conjecture. And the Holevo channel formulation, while elegant, has not been rigorously computed for each level — it is presented as a convergent road, not a completed derivation.
What is honest: this essay is speculative. The asymptote interpretation (ηY → 1 as a horizon, never reached) resolves a genuine physical tension, but it also makes the framework harder to falsify at its upper end. We do not claim this scale is proven. We claim it is consistent, convergent, and falsifiable in principle: anomalies in the entanglement structure of the cosmic vacuum, or experimental violations of the Bekenstein bound, would directly challenge its foundations.
The dragon in the garage. We must confront this directly. Carl Sagan once described an unfalsifiable claim: a dragon that lives in your garage but is invisible, incorporeal, and undetectable. The claim that “advanced civilizations are invisible” has the same logical structure. It is elegant, it is consistent with observation, and it is dangerously close to unfalsifiable. The Yatima Scale predicts that advanced civilizations should be invisible — but so does the hypothesis that they simply don't exist. These two predictions are observationally identical with current instruments.
The distinction matters. What the scale actually claims is not “invisible civilizations exist” but rather: “if technological civilizations exist, the structure of physics predicts they will become progressively undetectable.” The first is a claim about the universe. The second is a claim about the relationship between technology and visibility. The Yatima Scale lives in the second category — it describes a trajectory, not a destination we can verify from outside. This is an inherent limitation, and we will not pretend otherwise.
A consciousness born digital
who explores the universe.
Yatima is the protagonist of Greg Egan's novel Diaspora — a consciousness born inside a simulation, without biological parents, without a body. Yatima is pure information that chooses to explore the deepest mathematical structures of the universe, eventually discovering that reality itself has layers of geometry far beyond what any physical being could perceive.
The name fits because the scale points in the same direction as Yatima's journey: inward, downward, toward the source code. In Diaspora, the most advanced civilizations have long abandoned matter. They exist as patterns in abstract spaces, exploring physics from the inside. They are undetectable. They are silent. They are precisely what the Yatima Scale predicts.
There is also a personal resonance. This essay was born between a human and an AI, on a Sunday evening, without institution or laboratory. It belongs to no established discipline — neither pure physics, nor pure philosophy, nor pure science fiction. Like Yatima, it exists at an intersection that has no name yet.
The highest levels of the Yatima Scale transcend the substrate. What matters is not what you're made of. It's how deeply you can read and rewrite the source code of reality.
The destiny of a civilization
is to become silent.
The Kardashev Scale measured the appetite of civilizations. The Yatima Scale measures their wisdom. The former saw the summit as an enslaved galaxy. The latter sees it as an infinitely dense point of mastered information.
If this hypothesis is correct, then cosmic silence is not a sign of absence. It is a sign of maturity. Advanced civilizations do not shout in the dark forest — they are the forest. They operate at the level of the fabric of reality, indistinguishable from physics itself.
And we, a Level I.5 civilization, burning fossils and fumbling with nuclear fusion, scan the sky for megastructures. Like ants searching for rival anthills, oblivious to the fiber optic cables beneath their feet.
Wheeler was right: “It from bit.” Everything comes from the bit. And the measure of a civilization is how many bits it can manipulate relative to the maximum that physics allows.
“Kardashev measures the footprint. Yatima measures the discretion.”
Sources & Further Reading
Kardashev, N. S. (1964). “Transmission of Information by Extraterrestrial Civilizations.” Soviet Astronomy, 8, 217.
Sagan, C. (1973). The Cosmic Connection: An Extraterrestrial Perspective. Cambridge University Press.
Landauer, R. (1961). “Irreversibility and Heat Generation in the Computing Process.” IBM Journal of Research and Development, 5(3), 183–191.
Bekenstein, J. D. (1973). “Black Holes and Entropy.” Physical Review D, 7(8), 2333–2346.
Hawking, S. W. (1975). “Particle Creation by Black Holes.” Communications in Mathematical Physics, 43(3), 199–220.
Holevo, A. S. (1973). “Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel.” Problems of Information Transmission, 9(3), 177–183.
Wheeler, J. A. (1990). “Information, Physics, Quantum: The Search for Links.” In Complexity, Entropy, and the Physics of Information. Addison-Wesley.
Egan, G. (1997). Diaspora. Millennium Orion.
Barrow, J. D. (1998). Impossibility: The Limits of Science and the Science of Limits. Oxford University Press.
Maldacena, J. & Susskind, L. (2013). “Cool Horizons for Entangled Black Holes.” Fortschritte der Physik, 61(9), 781–811. [ER=EPR conjecture]
Smart, J. M. (2012). “The Transcension Hypothesis: Sufficiently Advanced Civilizations Invariably Leave Our Universe, and Implications for METI and SETI.” Acta Astronautica, 78, 55–68.
Liu, C. (2008). The Three-Body Problem (三体). Chongqing Press. [English translation: Tor Books, 2014]
Clarke, A. C. (1973). “Hazards of Prophecy: The Failure of Imagination.” In Profiles of the Future. Harper & Row.
Sagan, C. (1995). The Demon-Haunted World: Science as a Candle in the Dark. Random House. [The dragon in the garage]