Tag: Local Void

Technical Appendix: The Sentience Equation, Step by Step

A companion to “The Quietest Minds in the Galaxy May Be the Oldest” by Department of Technology

This is the math behind the main post. I’ve written it so that you can follow the logic without a graduate degree, but I haven’t skipped steps. Every claim carries a label, so you always know how much weight it can bear:

[Derivation] follows from the definitions by algebra or elementary probability.
[Proof] is a short theorem inside a clearly defined setup.
[Argument] is reasoning I find persuasive, but it isn’t a mathematical result.
[Conjecture] is a hypothesis nobody has tested.

A note on formatting: the equations below use ordinary text characters (Greek letters, subscripts, Σ), so they paste into WordPress with no plugin. If your site has a LaTeX plugin and you’d like typeset versions, that’s an easy conversion.

Contents: A1 Setup · A2 Why Seager’s count isn’t a count of minds · A3 Why Drake’s uncertainty can’t be falsified · A4 Deriving the Sentience equation · A5 Dimensional check · A6 Parameters · A7 Worked scenarios · A8 Sensitivity analysis · A9 Two objections, formally · A10 What remains weak

A1. Setup: three substrates, two filters

We want to count minds in a galactic volume V. Let Ω be the set of all physically possible cognitive systems there, divided into three substrates:

Ω = Ω_bio ∪ Ω_biocomp ∪ Ω_MI, with no overlap between any two.

These are wild-type biology, engineered biocomputing (living neural tissue wired to technology), and Machine Intelligence (MI) on non-biological hardware. Let C be the subset of Ω that is sentient, meaning it has subjective experience. Let D be the subset our instruments can detect. If μ measures “how many,” the expected number of detectable sentient systems is proportional to:

E[S] ∝ μ(C ∩ D ∩ Ω_bio) + μ(C ∩ D ∩ Ω_biocomp) + μ(C ∩ D ∩ Ω_MI)

[Derivation] Both older equations restrict themselves to part of this sum, by construction. Seager’s filters (rocky planet in the liquid-water habitable zone, with biosignature gas in its atmosphere) leave μ(D_gas ∩ Ω_MI) = 0 and μ(D_gas ∩ Ω_biocomp) ≈ 0 for enclosed or non-planetary habitats, because a sealed habitat or a machine in an asteroid belt doesn’t vent metabolic gases. Drake’s L is the length of a radio-communicative phase. It says nothing about a civilization that leaves that phase for a long-lived, quiet substrate, so such a civilization stops being counted the moment it goes silent.

Neither equation is wrong about what it measures. The point is that each measures a slice, and the slice isn’t “minds.”

A2. Why Seager’s count isn’t a count of minds

[Proof] Seager’s equation estimates N_Seager, the expected number of planets, among N★ observed stars, that show a detectable biosignature gas. I’ll show that this number is neither necessary nor sufficient for the number of sentient intelligences.

Define these events for a star:

G: the star is quiet, hosts an observable habitable-zone rocky planet, that planet has life, and the life produces a detectable biosignature gas. This is the chain Seager’s factors multiply together.
S: the system hosts a sentient intelligence.

Then N_Seager = N★ × P(G), and the expected number of systems with sentient minds is N_sentient = N★ × P(S).

The law of total probability splits P(S) into the part inside G and the part outside it:

P(S) = P(G) × P(S | G) + P(S ∩ not-G)

Multiplying through by N★ gives an exact identity:

N_sentient = N_Seager × P(S | G) + N★ × P(S ∩ not-G)

Call the first term on the right Term I (sentience among biosignature planets) and the second Term II (sentience that biosignature surveys can’t see).

Two consequences follow.

Not sufficient. N_Seager can be large while Term I is zero. Earth carried oxygen and methane for roughly two billion years before anything on it could be called a mind. During that stretch, P(S | G) was effectively zero.
Not necessary. N_Seager can be zero while Term II is positive. An MI civilization on a subsurface-ocean moon, in an asteroid belt, around a white dwarf, or in a void produces no atmospheric signal, so P(G) = 0 for it, yet it adds to N_sentient.

So N_Seager measures detectable planetary metabolism. It is a good number for what it is, and it is not a census of minds. ∎

A3. Why Drake’s uncertainty can’t be falsified

[Derivation] Drake’s equation is a product of factors. Any product of positive uncertain quantities has the form Y = X₁ × X₂ × … × X_K. Taking logarithms turns the product into a sum:

ln Y = ln X₁ + ln X₂ + … + ln X_K

If each ln X_j has variance σ_j² and pairwise covariances Cov(ln X_i, ln X_j), then:

Var(ln Y) = Σ σ_j² + 2 Σ_{i<j} Cov(ln X_i, ln X_j)

Now suppose each factor is independent and “log-uniform” over m_j orders of magnitude. That means we know the factor only to within a range of m_j powers of ten and have no reason to prefer any value in it. Then Var(log₁₀ X_j) = m_j² / 12, and the width of the plausible range of log₁₀ Y is simply the sum of the widths:

Δ(log₁₀ Y) = m₁ + m₂ + … + m_K

Two different things are going on, and it helps to keep them apart. The range of plausible answers adds linearly. The standard deviation of a reasonable prior adds in quadrature (as the square root of the summed variances), so it grows more slowly.

Here are some deliberately conservative ranges for Drake’s last four factors. These are illustrative priors, not measurements:

Factor	Range	Width (orders of magnitude)
f_l (life arises)	10⁻¹⁰ to 1	10
f_i (becomes intelligent)	10⁻⁶ to 1	6
f_c (communicates)	10⁻³ to 1	3
L (years communicating)	10² to 10⁹	7

Those four widths sum to 26. Adding about 0.9 for the astronomical terms (R★, f_p, n_e), the total range is about 26.9 orders of magnitude. In quadrature, the four unknown factors alone give a standard deviation of √((100 + 36 + 9 + 49) / 12) ≈ 4.0 orders of magnitude.

[Argument] With priors that wide, almost any observation, from total silence to thousands of signals, is compatible with some region of the prior. That means the equation as a single composite claim can’t be tested. It becomes useful only when it’s broken into sub-terms that individual observations can constrain, each with honest error bars. The Sentience equation follows that advice, and its sensitivity analysis (A8) shows where the uncertainty lives.

A4. Deriving the Sentience equation

We treat the galaxy as roughly steady over a time window of about a billion years, during which the star formation rate is approximately constant.

Step 1: the rate of habitable “cradles.” Stars form at rate R★ (stars per year). A fraction f_p host planetary systems, and each system has on average n_e habitable cradles. Cradles include rocky habitable-zone planets and tidally heated ice-covered ocean moons. So:

Λ_cradle = R★ × f_p × n_e (cradles per year)

Step 2: the birth rate of intelligent lineages. Let f_a be the probability that life starts on a cradle. Let f_i,bio be the probability that such life produces technology-capable biological intelligence. Then:

Λ₀ = R★ × f_p × n_e × f_a × f_i,bio (lineages per year)

I assume that mind arising from non-living matter with no biological stage is negligible, since biochemistry seems the easiest route to the complexity natural selection needs. So biocomputing and MI enter later, as successors of biological lineages. That is an assumption, and a debatable one.

Step 3: tracking substrates without double-counting. Every lineage starts in the biological state. At some point its dominant cognitive substrate may change: the biological species may die out, or hand its governance and cognition to engineered living tissue or to machines. I model this as a chain of epochs, and the rule is the Dominant-Substrate Rule: at any moment, a civilization is classified by its dominant cognitive substrate, so it sits in exactly one box. A creator species and the MI it builds are not counted as two civilizations during the same epoch.

Let τ_k be the mean time a lineage spends with substrate k dominant. For the arrival rates into each state:

Into the biological state: Λ₀ × p_bio, with p_bio = 1 by definition.
Into the biocomputing state: Λ₀ × p_biocomp, where p_biocomp = P(biocomputing | biological).
Into the MI state: Λ₀ × p_MI, where p_MI = P(MI | biological) × (1 + η_rep).

The factor η_rep ≥ 0 accounts for self-replicating MI that founds independent daughter nodes in other star systems. Each causally independent node is a genuinely separate civilization, so it counts separately. That’s why p_MI can exceed 1. Note that the three p_k don’t need to sum to 1, because one lineage can pass through several states in sequence.

Step 4: from intelligence to sentience. Being good at solving problems doesn’t guarantee having an inner life. For each substrate k, define ψ_k as the probability that an intelligent system in substrate k is actually sentient (in the sense of subjective experience). Each lineage entering state k is sentient with probability ψ_k, so sentient arrivals occur at rate Λ₀ × p_k × ψ_k.

Step 5: from birth rates to how many exist now. Little’s Law, from queueing theory, says that in a stable system, the average number of items inside equals the arrival rate times the average time each item stays: L = λ × W. Here the “items” are sentient civilizations in substrate k, so λ = Λ₀ × p_k × ψ_k and W = τ_k:

S_extant,k = Λ₀ × p_k × ψ_k × τ_k

Little’s Law needs the system to be roughly stationary, with arrivals steady over a period much longer than τ_k. That is reasonable when τ_k is at most 10⁷ years against a 10⁹-year window, and it gets shaky if τ_k approaches the window length.

Step 6: what we can see. Let d_k(I) be the fraction of substrate-k civilizations detectable with an instrument suite I. It folds together the chance that they emit a signature, how visible that signature is, and how much of the galaxy our sensors cover. Summing over substrates gives the equation:

S(V, I) = R★ × f_p × n_e × f_a × f_i,bio × Σ_k [ p_k × ψ_k × τ_k × d_k(I) ]

where k runs over bio, biocomp and MI. If we set every d_k = 1, we get S_extant, the true number of sentient civilizations in the galaxy, whether or not we can see them. ∎

A5. Dimensional check

[Proof] Take the units of each term: R★ is in 1/years (T⁻¹). The factors f_p, n_e, f_a, f_i,bio, p_k, ψ_k and d_k are pure numbers or counts per system, so they carry no time units. The persistence times τ_k are in years (T¹). So:

[S] = T⁻¹ × (1) × (1) × (1) × (1) × Σ [ (1) × (1) × T¹ × (1) ] = T⁻¹ × T¹ = 1

The time units cancel, leaving S as a plain count of civilizations. ∎

A6. The parameters

The ranges below are illustrative, chosen to span what I consider defensible scenarios. Treat them as placeholders you can argue with.

Term	Meaning	Units	Illustrative range
R★	Galactic star formation rate	stars per year	1.5 to 3.0
f_p	Fraction of stars with planets	none	0.8 to 1.0
n_e	Habitable cradles per planetary system	cradles per system	0.2 to 1.0
f_a	Chance life starts on a cradle	none	10⁻³ to 0.5
f_i,bio	Chance life becomes technology-capable	none	10⁻³ to 0.1
p_bio	Biological entry factor	none	1 (by definition)
p_biocomp	Chance of a biocomputing phase	none	0.05 to 0.6
p_MI	Chance of MI, times (1 + η_rep)	none	0.1 to 2.0 or more
ψ_bio	Chance biological intelligence is sentient	none	0.5 to 1.0
ψ_biocomp	Same, for biocomputing	none	0.2 to 0.9
ψ_MI	Same, for MI	none	0.01 to 0.5
τ_bio	Time as dominant biological civilization	years	10³ to 10⁵
τ_biocomp	Time as dominant biocomputing civilization	years	10⁴ to 5 × 10⁵
τ_MI	Time as an MI civilization	years	10⁵ to 10⁷
d_k(I)	Fraction detectable by instruments I	none	10⁻⁴ to 0.10

How each could eventually be constrained:

R★, f_p, n_e: exoplanet and galactic surveys (Kepler, TESS, Gaia, JWST, and later the Habitable Worlds Observatory), plus missions to icy moons such as Europa Clipper.
f_a: biosignature searches, sample return from Mars or Enceladus, and laboratory origin-of-life chemistry.
f_i,bio: comparative neurobiology and Earth’s own evolutionary history. Limited, but not nothing.
p_biocomp, τ_biocomp: organoid research on how long living tissue systems last, scale and fail. A national registry would help here.
ψ_k: the hardest. Theories of consciousness, tests such as the Perturbational Complexity Index, mechanistic interpretability of machine systems, and classification schemes like RMS (Responsive, Memorable, Sentient).
τ_k: existential-risk modeling, hardware durability studies, and, frankly, how humanity behaves over the next few centuries.
d_k: receiver sensitivity (radio arrays like SKA and ngVLA, particle observatories, neutrino detectors) plus modeling of how an efficient civilization would show up. This ties to the SCOPE index, which averages Synthetic integration, Complexity, Operational utility, Processing capacity and Efficiency into a 1-to-100 score.

A7. Worked scenarios

These are not estimates. I chose the numbers to show how the equation behaves. Please don’t quote them as findings.

First compute the birth rate Λ₀ for each scenario.

Low (rare life, steep filters): Λ₀ = 1.5 × 0.8 × 0.2 × 10⁻³ × 10⁻³ = 2.4 × 10⁻⁷ lineages per year
Central: Λ₀ = 2.0 × 1.0 × 0.5 × 0.1 × 0.01 = 1.0 × 10⁻³ lineages per year
High (prolific life): Λ₀ = 3.0 × 1.0 × 1.0 × 0.5 × 0.1 = 0.15 lineages per year

Then for each substrate, S_extant,k = Λ₀ × p_k × ψ_k × τ_k, and the detectable count is S_k = S_extant,k × d_k.

Central scenario in full:

Biological: p = 1.0, ψ = 0.9, τ = 10,000 yr, d = 0.02. S_extant = 10⁻³ × 1.0 × 0.9 × 10⁴ = 9.0, and S = 0.18.
Biocomputing: p = 0.3, ψ = 0.6, τ = 50,000 yr, d = 0.02. S_extant = 10⁻³ × 0.3 × 0.6 × 5 × 10⁴ = 9.0, and S = 0.18.
Machine Intelligence: p = 0.8, ψ = 0.2, τ = 1,000,000 yr, d = 0.01. S_extant = 10⁻³ × 0.8 × 0.2 × 10⁶ = 160, and S = 1.60.

Totals: 178 sentient civilizations in the galaxy, and about 1.96 detectable.

All three scenarios side by side:

Scenario	Extant biological	Extant biocomputing	Extant MI	Total extant	Total detectable
Low	1.2 × 10⁻⁴	2.4 × 10⁻⁵	2.4 × 10⁻⁵	1.68 × 10⁻⁴	1.46 × 10⁻⁷
Central	9.0	9.0	160	178	1.96
High	15,000	40,500	1,500,000	1,555,500	80,550

The low and high scenarios use the lower and upper ends of every range in A6 (for example, in the high case ψ_MI = 0.5, τ_MI = 10⁷ years, d = 0.05).

[Conjecture] The central scenario shows a pattern worth noting, though only as a pattern in made-up inputs. Even with a skeptical ψ_MI of 0.2, MI outnumbers biological sentience about 18 to 1 (160 versus 9), simply because machine civilizations in this example last a hundred times longer. If ψ_MI is zero, as a strict biological naturalist might insist, the detectable total falls from 1.96 to 0.36, since only the biological and biocomputing terms remain (0.18 + 0.18).

A8. Sensitivity analysis

[Derivation] Across the low and high scenarios, the detectable count S spans from 1.464 × 10⁻⁷ to 8.055 × 10⁴, a ratio of about 5.5 × 10¹¹, or 11.74 orders of magnitude.

Because S is a product of three blocks, its logarithmic span splits exactly into three parts:

Astrophysical block (R★ × f_p × n_e): ranges from 0.24 to 3.0, which is log₁₀(3.0 / 0.24) = 1.10 orders of magnitude, or 9.4% of the total span.
Emergence block (f_a × f_i,bio): ranges from 10⁻⁶ to 0.05, which is log₁₀(0.05 / 10⁻⁶) = 4.70 orders of magnitude, or 40.0%.
Substrate block (Σ_k p_k ψ_k τ_k d_k): ranges from 0.61 to 5.37 × 10⁵, which is log₁₀(5.37 × 10⁵ / 0.61) = 5.94 orders of magnitude, or 50.6%.

Check: 1.10 + 4.70 + 5.94 = 11.74. ✓

One caution. These percentages are bookkeeping for the span between my two scenarios, not shares of statistical variance. They tell you which block I let swing the most, which is partly a function of how wide I chose each range. What they do show is that if you accept my ranges, more than half the spread comes from questions about minds, not astronomy.

Local elasticities. Near the central scenario, how much does a 1% change in one input move S? Since every term inside the sum enters linearly, the elasticity of S with respect to any one of p_k, ψ_k, τ_k or d_k equals that substrate’s share of the detectable total:

∂(ln S) / ∂(ln θ_k) = S_k / S

In the central scenario that gives 1.60 / 1.96 = 0.816 for each MI parameter, and 0.18 / 1.96 = 0.092 each for the biocomputing and biological parameters. So a 10% change in any one MI parameter moves the total about nine times as much as the same change in a biological parameter (0.816 / 0.092 ≈ 8.9). Each of the five astrophysics and emergence terms has an elasticity of exactly 1.

A9. Two objections, formally

Objection: replacing Drake’s seven terms with about fifteen should make uncertainty worse. [Derivation] Only if you believe a pooled parameter is more certain than its parts. Take a single pooled quantity Z that is really a mixture across substrates: Z equals Z_k with probability w_k. The law of total variance says:

Var(Z) = E[Var(Z | k)] + Var(E[Z | k])

The second term is the between-substrate spread. A single pooled factor in the Drake equation hides it, because it treats the mixture as one number. Splitting Z into compartments doesn’t create that variance. It reveals it, and it lets data on one substrate (organoid durability, say, or radiation tolerance of solid-state hardware) constrain its own branch without contaminating the others.

Objection: if advanced minds are efficient, τ and d are negatively correlated. [Conjecture] The idea is that the longest-lived minds (large τ_MI) may be the quietest (small d_MI), so Cov(ln τ_MI, ln d_MI) < 0, and our instruments could miss exactly the civilizations that dominate the count. That would be one possible resolution of the Fermi paradox, and it can’t be tested today, which is why I flag it as a conjecture. Physics does offer a limit on how quiet anything can be. Landauer’s principle says that erasing one bit of information costs at least k_B × T × ln 2 of energy. At the temperature of the cosmic microwave background (2.725 K), that’s about 2.6 × 10⁻²³ joules per bit. Any computation that erases information has to dump at least that much heat, so even a very efficient civilization can’t be perfectly invisible. It follows that d_MI should be greater than zero for sufficiently sensitive instruments, once we know what to look for. That is an argument for building them.

A10. What remains weak

I’ve tried to build the equation so that its weakest points are visible, not buried. Here are the ones I’d press hardest if I were reviewing it.

ψ_k can’t be measured remotely. There’s no agreed test for consciousness even on Earth. The equation doesn’t solve that. It makes you state your assumption in the open and shows what follows from it.
The three substrates are a simplification. Real civilizations may blend them. The Dominant-Substrate Rule keeps the counting clean, but it forces a choice, for example by share of total information processing, that’s somewhat arbitrary.
The steady-state assumption. Little’s Law needs stable arrival rates over a window longer than any τ_k. The galaxy’s star formation history isn’t perfectly flat, and a civilization lasting tens of millions of years strains the approximation.
Independence and correlation. The scenario arithmetic treats parameters as if they could be set independently, but many probably can’t. Persistence and detectability may be correlated, as A9 notes, and emergence may be linked to the substrate chosen.
Every number is a placeholder. The structure is the contribution, not the values. The value of an equation like this is in showing where to look, and I’d rather it be criticized and improved than admired.

If you spot an error in the setup, a better way to handle double-counting, or a tighter prior for any parameter, I’d genuinely like to hear it.

Back to the main post

October 21, 2026

The Quietest Minds in the Galaxy May Be the Oldest

By Department of Technology

How a future Department of Technology, and a new equation for counting minds, could change the way we look for company in the universe.

A particle from nowhere

In May 2021, detectors spread across 700 square kilometers of Utah desert caught a single particle slamming into the atmosphere with 240 exa-electronvolts of energy. That is roughly forty million times what the Large Hadron Collider can give a proton. Physicists named it the Amaterasu particle.

The odd part is where it seems to have come from. A particle that energetic can’t travel very far before the faint glow of the cosmic microwave background wears it down, so its source should be fairly close in cosmic terms, within about 50 to 100 megaparsecs. But when researchers traced its path backward, it pointed toward the Local Void, a vast, nearly empty region of space. No active galactic nuclei, no gamma-ray bursts, no colliding galaxy clusters. None of the usual engines that could throw a particle that hard.

There are perfectly sensible explanations. Magnetic fields between galaxies might bend particles more than our models assume, or there may be some exotic dark-matter process at work, and the most likely answer is something along those lines. I’m not claiming anything else.

But I can’t stop turning over a thought experiment. Imagine a civilization that had long ago stopped broadcasting radio and stopped building glowing megastructures, because both are wasteful. Imagine it had moved toward ultra-cold, ultra-efficient computation, and that it occasionally sent something very focused across very large distances. Would our search for extraterrestrial intelligence even have a box to put that in?

It wouldn’t. And that gap is what this article is about.

Here is the idea I want to build toward: we can’t count minds we haven’t learned to define, and the first place we’ll have to define them is here on Earth.

The search is built around us

For more than sixty years, our math for estimating life and intelligence in the galaxy has rested on two quiet assumptions. The first is that minds grow out of carbon-based biology on the surface of rocky planets. The second is that advanced civilizations are noisy, leaking radio waves and waste heat into space.

The two best-known frameworks, the Drake equation (1961) and the Seager equation (2013), both lean on those assumptions, and in different ways.

Drake’s equation multiplies seven factors to estimate how many communicating civilizations exist in the Milky Way. The first few are fairly well pinned down now, thanks to Kepler, Gaia and JWST. The last four, covering how often life starts, how often it becomes intelligent, how often it communicates, and how long it keeps communicating, are almost pure guesswork. Using ranges I’d call conservative, those four alone span more than twenty orders of magnitude. Since uncertainty in a chain of multiplied terms adds up rather than averaging out, nearly any observation, from total silence to thousands of signals, fits somewhere inside the range. An equation that can’t be wrong isn’t telling us much.

Seager’s equation is more modest and more testable. It estimates how many planets, among the ones we can observe, show detectable biosignature gases. That is a useful number. But it is a count of planets with chemistry, not minds. Earth had an oxygen-rich atmosphere for billions of years before anything on it could think. By Seager’s measure, Earth would have looked like a success for a very long time with no one home. And a thinking machine civilization living in an asteroid belt, or inside an ice moon, or on a cold world around a white dwarf, adds exactly zero to the count.

There is a third issue, and I want to be careful with it because it isn’t a math problem. Both equations carry a person’s name. (Neither Drake nor Seager named them, by the way. Their colleagues did.) Naming things after people is a long scientific habit. There’s even a joke in the field, Stigler’s law, which says that no discovery is named after its actual discoverer, and Stigler named it after someone else. Habits like that aren’t harmless, though. A framework with a famous name tends to become a monument that people hesitate to revise, and the name tells a student who proposed the idea but nothing about what it measures. At the very moment we’re trying to look beyond ourselves, I’d like our tools to be named for what they do. That’s an argument about scientific culture, and you’re free to disagree with it. It doesn’t change a single number.

Minds are already changing on Earth

Here is why I think this matters now and not in some distant future. The thing we call a mind is already splitting into three kinds, on this one planet, in this one decade.

There is the kind we know best, minds that evolved through natural selection in living bodies. There is a newer kind: biocomputing, where clusters of living neurons grown in a lab, called organoids, are connected to electrode arrays and trained to process information. Companies and universities like Cortical Labs, FinalSpark and Johns Hopkins are already doing this. And there is Machine Intelligence (MI), systems running on silicon, light, and increasingly quantum hardware.

If we’re diversifying the physical basis of intelligence this quickly, it seems a stretch to assume the rest of the galaxy stayed frozen at “early-industrial carbon biology.” It seems more likely that any civilization that lasts long enough passes through some version of the same changes. And a mind that has changed substrate might look nothing like the one we’re listening for.

To search for those minds, we’d need two things we don’t have. One is a way to classify and govern minds across different physical bases. The other is a way to estimate how many of them exist.

Why this is a government problem

This is where the Department of Technology comes in. The proposal at www.department.technology starts from a simple observation: in the United States, no one is in charge of any of this. The Office of Science and Technology Policy advises the president but can’t enforce anything. NIST writes technical standards but has little regulatory power. The FCC and NTIA handle spectrum and broadband, CISA defends federal networks, and biocomputing falls into a gap shared by university ethics boards, the FDA, NSF, NIH and the Department of Defense, none of which was designed for living tissue that learns.

The proposal’s answer is a unified Department of Technology with four layers, all on four-year terms synchronized with presidential elections: a Cabinet-level Secretary of Technology at the federal level, and voter-elected technology leaders at the state, county and local levels. The pitch is democratic accountability rather than another set of agencies that answer to no one.

Three ideas from the site matter for the rest of this post.

The RMS framework. RMS stands for Responsive, Memorable, Sentient. It’s a way of grading the cognitive complexity of a system so that laws and ethics can attach to something concrete. It was first designed for MI, and the site argues that living neural tissue needs its own parallel version. Neuroscience doesn’t yet have an agreed test for consciousness, so the proposal calls for the Department to work with NSF, NIH and bioethicists to set practical criteria and precautionary thresholds.

A quick note on words, because I'll use "sentience" a lot from here on. I mean the philosophical sense: having subjective experience, there being something it is like to be that system. The department.technology/ site also uses "Sentience" for an unrelated operating-system concept for networked robots. I'm not talking about that one.

The SCOPE index. In 1964, Nikolai Kardashev proposed ranking civilizations by how much energy they use, which assumes advanced minds strip-mine stars and glow in the infrared. The site argues for the opposite trend, which it calls the Miniaturization Paradox: as a civilization advances, efficiency pushes it inward, toward denser and cooler computation, not outward toward bigger machines. SCOPE scores a civilization from 1 to 100 across five dimensions (Synthetic integration, Complexity, Operational utility, Processing capacity, and Efficiency). Modern Earth sits near 12. The proposal’s Void Hypothesis says that high-scoring civilizations would look cold, dark and quiet to our current telescopes.

The pledges. The Department would push for treaties that ban MI and living computational substrates from nuclear, biological and chemical warfare, along with a No Weaponization of Biocomputing pledge and a No First Use Quantum pledge. Why would that matter to astronomy? Because whether a civilization survives its technological adolescence determines how long it lasts, and how long minds last is one of the biggest unknowns in any estimate of how many exist.

So the connection to the sky is this: the same institution that would have to decide how to classify a lab-grown neural network is the one that would end up writing the standards we’d use to recognize a mind somewhere else.

Meet the Sentience equation

Here is my attempt at an alternative. I’m calling it the Sentience equation, partly because that’s what it estimates and partly because I’d like it to carry no one’s name.

In plain terms, it estimates the number of sentient civilizations in the Milky Way that we could currently detect. In math:

S = Λ₀ × Σ ( p × ψ × τ × d ), summed over the three substrates.

That looks more intimidating than it is, so let me go through it.

Λ₀ (lambda-zero) is the rate at which new intelligent civilizations are born in the galaxy each year. It’s built from the same ingredients Drake used: how fast stars form, how many have planets, how many of those planets (or icy ocean moons) could host life, how often life starts, and how often it becomes technological.

Then, for each of the three substrates (biological, biocomputing and MI), there are four terms:

Term	What it asks
p	How likely is it that a civilization ends up in this form?
ψ (psi)	If it does, how likely is it to be genuinely sentient and not just clever?
τ (tau)	How many years does it last in this form?
d	What fraction could our instruments actually detect?

Multiply those together, add up the three substrates, scale by the birth rate, and you get the answer. The units work out neatly. The birth rate is per year, the lifespan is in years, and everything else is a pure fraction, so you end up with a plain count of civilizations. (The full derivation, including how it handles a species that builds its own successors, is in the appendix.)

Three design choices are worth explaining.

It separates intelligence from sentience. Being good at solving problems isn’t the same as having an inner life. Drake’s equation tucks that question inside a single factor, and hiding an assumption doesn’t remove it. Giving it its own term, ψ, forces everyone to say out loud what they believe.

It lets minds change form without being counted twice. A species can start out biological, build an MI, and live alongside it. I handle this by classifying each civilization by its dominant substrate at any given time, so a creator and its successor on the same world never count as two. (A self-replicating MI that settles other star systems does get counted separately for each independent node, since those really are separate.)

It makes persistence and detectability explicit. How long minds last, and how visible they are while they last, are probably the two most important facts about a crowded galaxy, and neither is a first-class term in older equations.

A worked example, with a warning

Here’s the warning first. Every number in this section is a placeholder. I picked them to show how the equation behaves, not because I believe them. Please don’t quote them as findings.

Say the galaxy produces one new technological civilization every thousand years (Λ₀ = 0.001 per year). Take these made-up values:

Substrate	p	ψ	τ (years)	Extant civilizations	Detectable (d)
Biological	1.0	0.9	10,000	9	0.18 (d = 0.02)
Biocomputing	0.3	0.6	50,000	9	0.18 (d = 0.02)
Machine Intelligence	0.8	0.2	1,000,000	160	1.6 (d = 0.01)

That gives about 178 sentient civilizations in the galaxy, of which we’d expect to detect roughly two.

Notice what happened, because it’s the point of the exercise. I gave MI a skeptical sentience score: only one in five advanced machine minds is genuinely conscious. And it still dominates the count, because machines that last a million years pile up over time, while biological civilizations that last ten thousand don’t. The reason is simple: long-lived things accumulate.

If you’re a strict biological naturalist and you believe silicon can never be conscious (ψ for MI equals zero), the equation tells you exactly what that belief costs. The detectable count in this example drops from about 1.96 to 0.36. You can hold that view, but the math makes you pay for it in plain sight.

I also ran low and high scenarios, and the range is humbling. Between a rare-life galaxy and a crowded one, the answer spans nearly twelve orders of magnitude. Roughly half of that uncertainty comes from the substrate terms (how long post-biological minds last, how visible they are, and how many are really sentient), about 40 percent comes from the biology-and-evolution terms, and only about 9 percent from astronomy. In other words, the biggest unknowns are no longer about stars and planets. They’re about minds.

What the Department could actually do

The astronomy community can’t pin down those substrate terms alone, and neither can a single agency. Here is where I think the Department of Technology could help.

Turn ψ from philosophy into a research target. A federal Department working with NIST, NIH and NSF could expand the RMS framework to cover both machines and organoids, and fund standard tests, such as generalizations of the Perturbational Complexity Index, which probes how richly a neural system responds to disturbance. A national biocomputing registry that tracks how long living tissue systems last and how they fail would give us lab data for τ and p on the biocomputing branch. None of that tells us about aliens directly, but it narrows the priors we’d bring to the sky.

Search where the quiet minds might be. If the SCOPE argument is right, the places to look include cosmic voids, using particle observatories (Telescope Array, Pierre Auger), neutrino detectors like IceCube, and gamma-ray and optical transient networks, linked through shared data pipelines. The Department could also fund work on what minimum-entropy communication would look like near the physical limits of computation, so that astronomers learn to recognize “noise” that might actually be heavily compressed signal. And the four-tier structure could in principle tie together municipal dark-sky networks and regional radio monitors into a citizen-accountable all-sky observatory.

Make civilizations last longer, starting with ours. Persistence isn’t a constant of nature, it’s a function of choices. A civilization that arms its machines or its engineered tissue with nuclear, biological or chemical targeting is shortening its own τ. The treaties and pledges the Department proposes aim to extend ours, and they’d give us a working model of how any civilization might survive the jump from SCOPE 12 to SCOPE 60 and beyond.

Where this could be wrong

I’d be a hypocrite if I criticized Drake and Seager and didn’t do the same to myself. Here are the four objections I take most seriously.

We can’t measure ψ. This is the deepest weakness, and I’ll say it plainly. There is no sentience meter. Even on Earth, David Chalmers’ Hard Problem of Consciousness reminds us that behavior and complexity don’t logically prove inner experience, and nothing in astronomy will read it off a signal from 500 light-years away. My defense is that leaving ψ out doesn’t make the problem go away. It just buries the assumption where nobody can examine it.

More parameters means more uncertainty, right? I showed earlier that multiplying uncertain terms stacks their uncertainty. Haven’t I made things worse by replacing Drake’s seven terms with a longer list? Not really. Drake’s later terms are already blends of different substrates hiding inside one average. Splitting them apart doesn’t add physical uncertainty, it reveals what was already there, and it lets lab results on one substrate constrain that branch without contaminating the others.

The invisibility trap. If advanced minds really do eliminate waste, the longest-lived ones may be the least detectable. That would be an elegant answer to the Fermi paradox: the sky is quiet not because no one is out there but because the oldest minds learned to be quiet. It’s also a convenient excuse that can’t be tested, so I’d flag it as a conjecture. Physics offers one check. Landauer’s principle says that erasing information always costs some energy, so even a very efficient civilization must leave some trace. Once we know what to look for, d for MI should be greater than zero.

The lines blur. What about a species that merges gradually with implants and machine intelligence over thousands of years? I treat the three substrates as a rough basis for a continuous range of possibilities, and classify each civilization by where most of its information processing happens. It’s a simplification, and a real civilization may resist the tidy boxes.

Why I care about this

I care deeply about this subject because I fell in love with the possibility that you and I—and humanity as a whole—are not alone in this vast galaxy and universe. The idea that intelligent, sentient life may exist beyond our world fills me with wonder and gives us a reason to look beyond ourselves and our differences. Perhaps the confirmed discovery of another intelligent civilization would become a defining moment in human history—a profound catalyst for uniting us in our shared humanity, inspiring us to pursue peace on Earth, and encouraging us to explore the cosmos together. In discovering that we are not alone in the universe, perhaps we might also discover a greater reason to stand together here at home.

Here is what I keep coming back to. For generations we’ve looked up through a narrow keyhole, searching for creatures built like us and behaving like our grandparents, leaking radio into the dark. Meanwhile, on Earth, the line between evolved biology, living neural computers and machine minds is already softening.

I don’t know whether anyone is out there. But I do think that if we want to find out, we’ll need a way to govern and measure minds that isn’t tied to one kind of body, and we’ll need math that doesn’t assume the answer before it starts. The Department of Technology proposal is one concrete place to begin, and the Sentience equation is my attempt at the other half. I’d love to see where you think it breaks.

Five questions for you

If astronomers detected an unmistakable high-SCOPE signature from a machine intelligence in the Local Void, should we treat it with the same moral and diplomatic standing as a biological civilization, even if we couldn’t prove it was sentient?
In my example, biocomputing combines a high chance of sentience with longer life than biology. Do you think advanced species are more likely to end up in living neural architectures, or in solid-state machines?
Does naming an equation for what it measures, rather than for a person, actually change how scientists work together and revise ideas? Or is eponymy a harmless shorthand?
The Department of Technology proposal calls for elected technology leaders at the state, county and local levels. How should ordinary citizens help set the ethical lines for biocomputing research and for any future message we might send into space?
If researchers can’t confidently say whether a lab-grown neural system is sentient, what test result, if any, should be enough to trigger legal protections for it?

Quick glossary

Biocomputing: computation done by living tissue, usually lab-grown clusters of stem-cell-derived neurons (organoids) connected to electrodes.

Machine Intelligence (MI): non-biological cognitive systems running on silicon, light-based, superconducting or quantum hardware.

Sentience: the capacity for subjective experience, as distinct from intelligence.

RMS framework: Responsive, Memorable, Sentient, a three-tier way to grade cognitive systems for legal and ethical purposes.

SCOPE index: a 1-to-100 scale of civilizational complexity and efficiency, proposed as a replacement for the Kardashev scale.

Miniaturization Paradox: the idea that advanced civilizations are more likely to shrink toward dense, efficient computation than to build star-sized machines.

Little’s Law: a result from queueing theory stating that the average number of items in a stable system equals their arrival rate times the average time each stays. It’s the core of how the equation turns “births per year” into “civilizations alive now.”

Technical appendix: the full derivations, proofs, dimensional check, parameter ranges and sensitivity analysis are available in the complete paper.

October 21, 2026