--- title: "Method · how the computing is counted · Simulation Hypothesis" url: https://simulation-hypothesis.com/method description: "The one formula behind every total on the site, the physical anchors it rests on (Lloyd, Landauer, Sandberg and Bostrom), and how far you can trust each input." license: https://creativecommons.org/licenses/by/4.0/ credit: "Ross Allan Dahl, Simulation Hypothesis (simulation-hypothesis.com)" --- # Method · how the computing is counted · version 2026.6 ## The formula Every total on the site comes from one formula. We work in log\_10 so that numbers as big as 10^150 and 10(10^80) still fit: FLOPS = units(scale, floor) × ops_per_unit(floor) / timestep(floor) × rendered_fraction + Σ minds × neurons × flops_per_neuron(model) (unless absorbed by the matter floor) × time_multiplier(time model) units mass / grain-mass, or atoms, or nucleons + electrons, or 2^(particles) for a full wavefunction rendered fraction of mass that gets the full floor; the rest runs as a "painted set" at 10^13 FLOPS per watcher absorbed at molecule-or-finer floors, brains are already matter, so the mind model adds nothing comparisons Lloyd's bound (5.4×10^50 ops/s/kg), Landauer's limit (kT ln 2 at 300 K), all Earth's hardware (~10^21 FLOPS) In words Count the units of matter at the floor you picked. Multiply by the operations each one needs per step, and by the steps per second. Then keep only the fraction of the world that gets rendered. Add the computing for one brain per inner life. The exception is a matter floor fine enough to include brains already. Then they add nothing. Multiply by the time model. Linear time is a single pass. Branching takes more, and many worlds takes the most. Tags show how much you can trust each input. measured is a published measurement. textbook is standard physics or a published estimate. rough is good to within an order of magnitude. wild guess is a placeholder with nothing empirical behind it, and we label it that way. These estimates are lower bounds on the operations of the model you pick. We leave out overhead, error correction, latency, memory and communication. A real run of that model would need more computing. One gap matters most for the cheap scenarios. A world rendered only where someone is looking has to stay consistent whenever anyone looks, at any level of detail. We don’t measure what it takes to guarantee that. The model’s own choices, like the grain, the timestep and the matter rendered per observer, aren’t bounds. They can move a total either way. ## Worked examples Four scenarios worked out by hand, so you can check the arithmetic without the site. Each line uses only constants from the table below. Every time the site is built, the engine runs the same scenarios. If any total here disagrees with it, the site won’t publish. ### [Earth atom by atom](https://simulation-hypothesis.com/builds/custom) Earth at the atom floor, everything computed all the time, every mind real. | Matter | 1.33×10⁵⁰ atoms × 1,000 operations per atom per step ÷ 10⁻¹⁵ s per step | 1.3 × 10^68 | | ------- | ----------------------------------------------------------------------- | ----------------- | | By hand | the lines above, added up | 1.3 × 10^68 FLOPS | | Engine | the site’s engine, same scenario | 1.3 × 10^68 FLOPS | Minds add nothing. At the atom floor a brain is already computed as the atoms it’s made of, so it’s inside the matter term. ### [Brain in a vat](https://simulation-hypothesis.com/builds/vat) One real brain outside the simulation. Everything it senses is a painted set, and everyone else is scripted. | Painted set | 10¹³ FLOPS per observer × 1 observer | 10^13 | | ------------------- | ------------------------------------- | ----------------- | | Scripted characters | 8,199,999,999 people × 10⁶ FLOPS each | 8.2 × 10^15 | | The brain itself | runs outside, so 0 | 0 | | By hand | the lines above, added up | 8.2 × 10^15 FLOPS | | Engine | the site’s engine, same scenario | 8.2 × 10^15 FLOPS | The scripted crowd takes over 800 times the computing the scenery does. In a world rendered for one person, the other people are most of the total. ### [Solipsism](https://simulation-hypothesis.com/builds/solipsism) Same as the vat, but the one real mind is simulated too, as a functional brain model. | Painted set | 10¹³ FLOPS × 1 observer | 10^13 | | ------------------- | --------------------------------- | ----------- | | The one real mind | 1 × 10¹⁸ FLOPS (functional model) | 10^18 | | Scripted characters | 8,199,999,999 × 10⁶ FLOPS | 8.2 × 10^15 | | By hand | the lines above, added up | 10^18 FLOPS | | Engine | the site’s engine, same scenario | 10^18 FLOPS | Simulating the one mind takes about 120 times the computing of the rest of the world put together. ### [The Matrix](https://simulation-hypothesis.com/builds/sleepers) A painted Earth with every person real and modelled at the biophysical level. | Painted set | 10¹³ FLOPS per observer × 8.2×10⁹ observers | 8.2 × 10^22 | | ----------- | ---------------------------------------------------- | ----------------- | | Minds | 8.2×10⁹ people × 10²² FLOPS each (biophysical model) | 8.2 × 10^31 | | By hand | the lines above, added up | 8.2 × 10^31 FLOPS | | Engine | the site’s engine, same scenario | 8.2 × 10^31 FLOPS | Minds outweigh the scenery a billion to one. The matter floor barely matters here. The mind model sets the total. ## Every constant, and where it comes from | Anchor | Value | Trust | Source | | ------------------------------- | --------------------------------------- | ---------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Lloyd’s bound | 5.4 × 10^50 ops · s⁻¹ · kg⁻¹ | textbook | Lloyd, “Ultimate physical limits to computation”, Nature 406 (2000). The ceiling for any lump of matter used as a computer. | | Landauer’s limit | 2.87 × 10^-21 J per bit erased at 300 K | textbook | Landauer, IBM Journal of Research and Development 5 (1961): kT ln 2 at room temperature. | | Mass of the observable universe | 1.5 × 10^53 kg | rough | Ordinary matter only, worked out from the critical density and a 46-billion-light-year radius. Dark matter and dark energy are left out on purpose. | | Age of the universe | 1.38 × 10^10 years | measured | Planck 2018 cosmological parameters. | | Nucleon mass | 1.6726 × 10^-27 kg | measured | CODATA proton mass; neutrons treated the same. | | Sun’s output | 3.83 × 10^26 W | measured | Solar luminosity, IAU 2015 nominal value. | | All computing on Earth | \~10^21 FLOPS | rough | A rough sum of data centres, PCs, phones and consoles in the mid-2020s. Could be off by 10× either way. | | Neurons in a human brain | 8.6 × 10^10 | measured | Azevedo et al., Journal of Comparative Neurology 513 (2009). | | Animals on Earth | \~4.5 × 10^20 individuals | wild guess | Mostly soil nematodes: van den Hoogen et al. (2019, Nature) estimate 4.4 × 10^20 in surface soils. Insects and other arthropods add about 10^19\. Marine nematodes and other small animals aren’t counted, so this is a minimum. A nematode has about 300 neurons, so the count barely changes the inner-life ladder, which starts at the fruit fly. | | Matter one mind is looking at | 10^7 kg | wild guess | The mass of the surroundings per observer, roughly a building. This sets how much of the world is computed at the full matter floor. | | Painted-set cost | 10^13 FLOPS per watcher | wild guess | Roughly one high-end real-time rendering engine per observer. The computing needed for a world held as a lookup table. | | Molecular-dynamics step | \~10^3 FLOPs per atom per step | rough | All-atom MD with a 1 nm cutoff: each atom feels a few hundred neighbours, at a few tens of FLOPs each. Real codes land within a factor of a few of this. | | One operation | 1 op = 1 FLOP = 1 bit erased | rough | Lloyd counts basic logic operations, Landauer counts bit erasures, and the total counts floating-point operations. The site treats them as one unit. A real 64-bit multiply is thousands of gate operations, so this makes the ceilings look better than they are and understates the heat by a factor of roughly 10^3 to 10^4. | | Mind-model costs | 10^6 to 10^49 FLOPS per human brain | rough | Sandberg & Bostrom, “Whole Brain Emulation: A Roadmap” (2008), levels 4, 5 and 10\. The scripted and quantum rungs are the site’s own placeholders, and they say so. | ## Scales | Scale | Mass | Atoms | Life-bearing worlds | | ------------------- | -------------- | ----------- | ------------------------- | | One brain | 1.4 × 10^0 kg | 1.2 × 10^26 | this one, if any measured | | One room | 10^4 kg | 3.0 × 10^29 | this one, if any rough | | Earth | 6.0 × 10^24 kg | 1.3 × 10^50 | 10^0 measured | | Solar system | 2.0 × 10^30 kg | 1.2 × 10^57 | 10^0 rough | | Milky Way | 1.2 × 10^41 kg | 7.0 × 10^67 | 10^6 wild guess | | Observable universe | 1.5 × 10^53 kg | 10^80 | 2.0 × 10^17 wild guess | ## Matter floor | Rung | Unit | Ops / unit / step | Timestep | Trust | | ------------------------ | ---------------------------------------- | ----------------- | ------------------------------------------- | ---------- | | Painted set | lookup table; 10¹³ per watcher | 1 | one frame at 60 Hz | wild guess | | Organ | mass / 1e-1 kg | 20 | 10 ms, so a heartbeat gets a hundred frames | wild guess | | Tissue | mass / 1e-3 kg | 50 | 1 ms | wild guess | | Cell | mass / 1e-12 kg | 100 | 1 ms, cell biology runs slow | rough | | Organelle | mass / 1e-16 kg | 100 | 1 µs | rough | | Protein | mass / 1e-22 kg | 1000 | 1 ns, folding timescales | rough | | Molecule | 0.5 × atoms | 1000 | 10 fs, coarse-grained MD | rough | | Atom | 1 × atoms | 1000 | 1 fs, standard all-atom MD step | rough | | Particle | 1 × nucleons + electrons | 100 | 1 as, electron dynamics | rough | | Quark | 3 × nucleons + electrons | 1000 | 1 ys, strong-force timescales | wild guess | | Quantum, mean field | (nucleons + electrons) × 1e+9 amplitudes | 10 | 1 as, time-dependent quantum step | rough | | Quantum, fully entangled | 2^(nucleons + electrons) amplitudes | 10 | 1 as | textbook | ## Minds Per-brain figures scale by neuron count from the human number. Where Sandberg & Bostrom’s 2008 whole-brain-emulation roadmap has a rung, that’s our source. | Model | FLOPS / human brain | Source | | ------------------- | ------------------- | ------------------------------------------------------------------------------ | | Scripted | 10^6 wild guess | about the cost of one scripted game character | | Functional | 10^18 rough | Sandberg & Bostrom 2008, level 4 | | Biophysical | 10^22 rough | Sandberg & Bostrom 2008, level 5 | | Molecular | 10^43 rough | Sandberg & Bostrom 2008, level 10 | | Quantum | 10^49 wild guess | no published estimate; Penrose & Hameroff for the idea | | Real brain, outside | none | none, by definition: the brain runs on its own neurons, outside the simulation | | Cutoff rung | Individuals on Earth, this rung and up | Neurons each | Trust | | ----------- | -------------------------------------- | ------------ | ---------- | | Fruit fly | 10^19 | 1.4 × 10^5 | wild guess | | Insect | 10^18 | 10^6 | wild guess | | Fish | 3.5 × 10^13 | 10^7 | wild guess | | Frog | 8.0 × 10^11 | 1.6 × 10^7 | wild guess | | Mouse | 2.2 × 10^11 | 7.1 × 10^7 | rough | | Bird | 1.3 × 10^11 | 10^9 | rough | | Pig | 1.5 × 10^10 | 2.2 × 10^9 | rough | | Dog | 1.2 × 10^10 | 2.3 × 10^9 | rough | | Dolphin | 8.3 × 10^9 | 1.5 × 10^10 | wild guess | | Human | 8.2 × 10^9 | 8.6 × 10^10 | measured | ## Reference points for the total | Machine | FLOPS | Note | | ------------------------------- | -------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | a phone | 10^12 measured | A current smartphone. | | a laptop | 10^13 measured | Runs a fruit fly nervous-system model faster than real time. | | one AI accelerator | 10^15 rough | One of today’s data-centre accelerators at low precision. Training a large language model takes thousands of them. | | the biggest supercomputer | 10^18 measured | Exascale class. It fills a building. | | every computer on Earth | 10^21 rough | Servers, personal computers, phones and consoles added together. | | a Dyson-swarm data centre | 2.8 × 10^37 rough | Every watt the Sun gives off, running chips at the best measured efficiency (about 7.4 × 10^10 operations per watt). | | a Sun of Landauer-limit chips | 1.3 × 10^47 textbook | The Sun’s whole output, at the thermodynamic floor of one bit erased per operation, at room temperature. | | an Earth-mass ultimate computer | 3.2 × 10^75 textbook | Every kilogram of the planet computing at Lloyd’s bound. | | a Jupiter brain | 10^78 textbook | A gas giant turned into a computer. | | a Sun-mass ultimate computer | 1.1 × 10^81 textbook | A star turned into a computer. | | a galaxy-mass ultimate computer | 6.5 × 10^91 textbook | The Milky Way as a single computer. | | one universe-computer | 8.1 × 10^103 rough | Every kilogram of ordinary matter in the observable universe computing at Lloyd’s bound. That’s the ceiling for ordinary matter. Counting dark matter would raise it about sixfold, but we couldn’t actually use any of it. | Existing simulations one uploaded fruit fly · FlyWire mapped \~139k neurons in 2024\. Runs on a laptop. 10^12 a large online game · A server cluster keeping a few thousand people at once in one shared virtual world. 10^15 a weather model · A data centre running a real weather forecast. 10^17 an Illustris-class cosmos · Thousands of supercomputer cores running for months, growing galaxies from the starting conditions. The resolution is coarse enough that stars are treated statistically. 10^15 ## Changelog 2026.6 · 2026-10-19 * After five outside reviews. Worked examples: four scenario bills done by hand on this page, checked against the engine on every build. No constant changed. * Affordability dates lead with their range (growth a fifth faster or slower), with the central year second. * The four schools now lean for, lean against or are divided, rather than endorsing or objecting; moral weights are shown in whole percents. Both are judgements, and the old wording claimed more than that. * The unpriced cost of keeping an on-demand world consistent under every observation is now stated beside the other omissions. 2026.5 · 2026-10-16 * After an outside review. Claims of impossibility now state their conditions: “never on one star’s power” holds for conventional logic that erases a bit per operation at room temperature; reversible computing and a colder heat sink would lower that floor, and the site does not price them. * Lloyd’s bound is described as a ceiling on operations for matter as hot as a plasma, not for a rocky body, and the mass it gives for Earth atom by atom counts operations only: storing that world’s state takes far more matter. * The universe-computer is the ceiling for ordinary matter (now tagged rough); dark matter would raise it about sixfold. * The 10^15 FLOPS comparison is one AI accelerator at low precision (was “a rack of GPUs”, tagged measured). * The quark rung is tagged wild guess: no known classical method follows quark dynamics in real time. The fully entangled rung notes that it counts amplitudes on a classical host. * All-atom molecular dynamics reproduces non-reactive chemistry only; bond-making needs quantum methods not priced at that rung. * Neuron counts on the inner-life ladder that have no published whole-brain measurement (fish, frog, dolphin) are tagged wild guess, and the human rung says it is a cutoff by species, not by neuron count. * Animals on Earth is about 4.5 × 10^20, mostly soil nematodes (was 2.5 × 10^19, “almost all insects”). It counts the animals left as scenery and does not change any bill. 2026.4 · 2026-10-07 * The inner-life ladder is ordered by neurons per individual: the mouse (7.1 × 10^7) now sits below the bird (10^9), and the pig (2.2 × 10^9) below the dog (2.3 × 10^9). Each rung keeps its own population; the counts “this rung and up” are re-summed. Sandbox links with a cutoff of 5 to 8 now name the reordered rungs. * Dial settings no longer carry confidence tags, since they are choices. A real brain outside the simulation costs nothing by definition and is no longer tagged “measured”. * The comparison machines from the Dyson swarm up are now computed from the constants above, not rounded to whole powers of ten. A Sun of Landauer-limit chips is 1.3 × 10^47 FLOPS (was 10^47) and an Earth-mass computer 3.2 × 10^75 (was 10^75), so 3.0 × 10^50 FLOPS now reads “2,200 ×”, not “3,000 ×”, matching the power tile beside it. * Feasibility no longer says “never, with known physics” for bills past the Sun’s line: a bill can pass one star’s power and still fit in matter computing at Lloyd’s bound. Earth atom by atom needs about 2.5 × 10^17 kg of such matter, not, as the Countdown said, about a planet. 2026.3 · 2026-10-06 * New mind model, “Real brain, outside”: the mind is a biological brain in the base reality, wired to the simulation. Its neurons do their own computing, so it adds nothing to the bill; only the world it senses is priced. * The Brain in a Vat preset now uses it. It used to simulate the brain itself at the biophysical level (10^22 FLOPS, about ten times every computer on Earth), which is an upload, not a vat. It now costs 8.2 × 10^15 FLOPS, almost all of it the scripted people around the brain. 2026.2 · 2026-10-04 * Feasibility now names the rung a bill passes, in one unit at a time: past every computer on Earth, past the Sun’s whole output at the Landauer floor (power), past an Earth-mass computer at Lloyd’s bound (mass), past the universe-computer. “Stellar-scale” and “galaxy-scale” mixed the two and are gone. * Computer size is written as a multiple of the rung at or below the bill (3.0 × 10^50 FLOPS reads “3,000 × a Sun of Landauer-limit chips”), not rounded to the nearest rung, which could hide a factor of 10^14. * One figure for how far chips sit above Landauer’s floor: the best measured machine, 1.36 × 10^-11 J per operation (Green500, November 2025), about five billion times the floor. The Dyson-swarm rung and the day bill use the same figure. * Infinite regress follows one rule: a simulated computer cannot out-compute the world it runs in, so each nested layer gets at most a share (1%) of its parent’s computation. The old panel divided headroom by an arbitrary factor. The stack can be built layer by layer on /nesting. * Every bill now carries a range. Each uncertain input is drawn from a log-normal spread set by its tag (one standard deviation: measured ±12%, textbook ±41%, rough ×3.2, wild guess ×10) and the engine is rerun 400 times; the Sandbox shows the 10th to 90th percentile and ranks the inputs by how far each alone moves the bill. Dial settings are choices and carry no spread. * Bills are also given in human terms: watts on the best measured chips against the world’s electricity, current AI accelerators (about 10^15 operations a second, about $30,000 each), a yearly electricity bill at $0.10 a kilowatt-hour, and Sagan’s Kardashev rating. Today’s-chip efficiency is now one constant site-wide (7.4 × 10^10 operations per watt, was 7 × 10^10 in two places), which moves the Countdown’s grid ceiling by 0.02 orders of magnitude. 2026.1 · 2026-09-28 * Dyson-swarm rung moved from 10^26 to 10^37 FLOPS. The old figure was the Sun’s watts, not what those watts buy at 50 GFLOPS per watt. * Molecular mind model re-sourced to level 10 of the Sandberg & Bostrom roadmap (it said level 9, which is 10^30, not 10^43). * Atom and molecule matter floors now cost 10^3 FLOPs per unit per step, up from 10^2, and are tagged rough. Bills at those floors rise tenfold. * Illustris-class cosmos moved from 10^18 to 10^15 FLOPS sustained. * New anchor saying out loud that an operation, a FLOP and a bit erasure are counted as the same unit. * α\_G on the former fine-tuning console described correctly: gravity against ħc, not against the electric force. * Real chips are about ten billion times above Landauer’s floor, not a million (2 × 10^-11 J per operation against 2.9 × 10^-21 J). ## What this is not This isn’t a verdict on whether we’re simulated, and it doesn’t judge what you believe. It can’t tell you who is real. The suffering dial and the inner-lives cutoff are settings for a hypothetical renderer. A hard life says nothing about the person living it. This is a computing model of a hypothetical, and it states its uncertainties. The site is written and maintained by [Ross Allan Dahl](https://rossdahl.com).