Simulations tree · what we have learned to simulate

Dreams (before records; measured since 1953 · In the mind)

The earliest recorded description of a mind making a world is in the Bṛhadāraṇyaka Upaniṣad (4.3.9–10, c. 7th–6th century BCE, with a wider scholarly range of about 900–600 BCE). In sleep, the self gathers material from the whole world and builds a dream by its own light. There are no chariots, horses or roads there, but it makes them for itself, “for he is the maker”. Aserinsky and Kleitman (1953) woke sleepers during rapid-eye-movement periods. They got detailed dream reports in 20 of 27 cases, against 4 of 23 when the eyes were still. Revonsuo (2000) argued that dreaming is a simulation of the world that rehearses spotting threats. That hypothesis is still debated.

Source: Aserinsky and Kleitman, ‘Regularly occurring periods of eye motility, and concomitant phenomena, during sleep’, Science 118 (1953) 273–274; Revonsuo, Behavioral and Brain Sciences 23 (2000) 877–901

Address: /trees/simulations?n=w-dreams

Children’s pretend play (before records; described 1945 · In the mind)

Piaget’s study of symbolic play (1945) described children treating an object or action as standing for another, inside an invented scene. Lillard and colleagues (2013) reviewed the evidence on what pretend play adds to development. They found it mixed, and too thin to show that it’s crucial for any one skill.

Led to: Glass Town

Source: Lillard et al., ‘The impact of pretend play on children’s development: a review of the evidence’, Psychological Bulletin 139(1) (2013) 1–34

Address: /trees/simulations?n=w-pretend

Greek tragedy (c. 534 BCE (traditional) · Run by people)

By the traditional date of 534 BCE, Thespis is said to have won the first tragedy competition at the City Dionysia. He is said to have been the first actor to play a character instead of speaking as himself. Staging a fiction for an audience, with performers living inside it, is the human-run form of a built world.

The sources leave this date or claim uncertain.

Source: Aristotle, Poetics 1449a (tragedy from the dithyramb; Aeschylus adds the second actor); Brill’s New Pauly, ‘Thespis’ (Parian Marble ep. 43 records him as tragedy’s first inventor)

Address: /trees/simulations?n=w-greek

Glass Town (1826–1831 · In the mind)

On 5 June 1826 their father gave Branwell Brontë twelve wooden soldiers. The Brontë children then invented the Glass Town confederacy and wrote its histories from December 1827. Later they split into the spin-off worlds Angria and Gondal. Scholars call such long-running invented worlds paracosms.

Built on: Children’s pretend play

Source: Glass Town, Wikipedia (citing Christine Alexander’s edition of the juvenilia)

Address: /trees/simulations?n=w-bronte

Alternate history (1836 (first novel); Livy c. 25 BCE · In the mind)

Livy (Ab Urbe Condita IX.17–19) already asked how Rome would have done if Alexander the Great had turned west. Louis Geoffroy’s Napoléon et la conquête du monde (1836) is the first novel built on a changed history, with a Napoleon who won in Russia in 1812. Nathaniel Hawthorne’s “P.’s Correspondence” (1845) is usually called the first complete alternate history in English. Each one runs a whole world forward in the reader’s mind from one changed event.

Led to: The Man in the High Castle; Counterfactual history as method

Source: Wikipedia, ‘Alternate history’

Address: /trees/simulations?n=w-althistory

Languages before the world (1915 onward · In the mind)

J. R. R. Tolkien began his first invented Elvish language, Qenya, in a notebook in March 1915. He said that Middle-earth was made largely to give his languages a world to live in. It’s the first invented world built from the language outward. Its histories, peoples and maps were worked out over five decades.

Led to: Lore worlds

Source: Tolkien Gateway, ‘Qenya Lexicon’

Address: /trees/simulations?n=w-tolkien

Link Trainer (1929–1934 · Analogue model)

Edwin Link filed a patent in April 1929, and it was granted in September 1931. It covered a pneumatic trainer that moved a mock cockpit in response to the controls, so pilots could practise flying on the ground. Early buyers were mainly amusement parks. The US Army bought six in 1934. By the end of the Second World War, 6,271 had gone to the Army and 1,045 to the Navy.

Source: Guinness World Records, ‘First flight simulator’

Address: /trees/simulations?n=w-linktrainer

The Man in the High Castle (October 1962 · In the mind)

Philip K. Dick’s novel imagines a United States split between Germany and Japan after an Axis victory. It won the 1963 Hugo Award. Dick named Ward Moore’s Bring the Jubilee (1953), in which the Confederacy wins, as his starting point. Inside the novel, a banned book imagines an Allied victory. So one counterfactual world contains another.

Built on: Alternate history

Led to: Counterfactual worlds

Source: Wikipedia, ‘The Man in the High Castle’

Address: /trees/simulations?n=w-highcastle

Dungeons and Dragons (1974 · Run by people)

Gygax and Arneson’s boxed set, published by Tactical Studies Rules in 1974, is described as the first role-playing game in print. Players speak as characters in a world kept by a referee. It joined tabletop wargaming to playing a character. Its dungeon-and-referee setup is the pattern that text and computer adventures later followed.

Built on: Kriegsspiel

Led to: Colossal Cave Adventure

Source: Dungeons & Dragons (1974), Wikipedia

Address: /trees/simulations?n=w-dnd

Colossal Cave Adventure (1975–1976 · Computer)

Will Crowther wrote a text game on a DEC PDP-10. The player types commands and reads descriptions of the rooms and objects of a cave system. Don Woods expanded it significantly in 1976. It was the first widely played adventure game. It made a described world a place one person could explore alone.

Built on: Electronic computer; Dungeons and Dragons

Led to: MUD1

Source: Raph Koster, ‘A Brief History’ of online worlds

Address: /trees/simulations?n=w-colossal

MUD1 (1978–1980 · Computer)

Roy Trubshaw began MUD at the University of Essex on a DEC PDP-10 in 1978, and Richard Bartle joined him. It let several players share one text world at the same time. It was named after Dungeon, a variant of Zork. It made a built world last and made it social.

Built on: Colossal Cave Adventure

Led to: A lore world with millions; Second Life

Source: Richard Bartle, ‘Early MUD history’

Address: /trees/simulations?n=w-mud1

Klingon (1985; institute 1992 · Run by people)

Marc Okrand built Klingon as a working language for Star Trek. It was published as The Klingon Dictionary in 1985, and Lawrence Schoen founded the Klingon Language Institute in 1992. Estimates of fluent speakers have stayed small: about a dozen in 1996, and 20 to 30 in 2009. But the language has a grammar, a literature and translated plays.

Led to: A child raised in Klingon; Lore worlds

Source: Wikipedia, ‘Klingon language’

Address: /trees/simulations?n=w-klingon

Counterfactual history as method (1991–1997 · Idea · Run by people)

Geoffrey Hawthorn’s Plausible Worlds (1991), Tetlock and Belkin’s Counterfactual Thought Experiments in World Politics (1996) and Niall Ferguson’s edited Virtual History (1997) brought “what if” into academic history and political science. They added criteria for which changed pasts are plausible. Richard Evans’s Altered Pasts (2014) argues that such histories always carry their authors’ beliefs from the present.

Built on: Alternate history

Led to: Counterfactual worlds

Source: Tetlock and Belkin (eds.), Counterfactual Thought Experiments in World Politics, Princeton University Press (1996)

Address: /trees/simulations?n=w-cfhistory

Civilization (1991; 73 million copies by 2025 · Computer)

Sid Meier’s Civilization (1991) lets a player run a civilisation from the first city to space flight, so every game is a history that never happened. When the seventh game launched in February 2025, the series had sold more than 73 million copies. That counts units shipped to retailers, not necessarily bought by players. Grand-strategy games such as Hearts of Iron, a Second World War with the outcome left open, sell in the millions.

Led to: Counterfactual worlds

Source: 2K press release, ‘Sid Meier’s Civilization VII now available worldwide’ (February 2025)

Address: /trees/simulations?n=w-civ

A child raised in Klingon (c. 1996–1999 · Stalled · Run by people)

The linguist d’Armond Speers spoke only Klingon to his infant son Alec for about the boy’s first three years. The boy’s mother spoke English. Speers wanted to see whether a child would pick up an invented language as a native one. Alec understood some and said a few words, but rarely answered in it.

Why it stalled: It stalled because a language alone is not a world. The boy had one Klingon speaker, no child speakers, and no stories or school in it. He began ignoring Klingon at about three, Speers stopped, and by thirteen Alec spoke none. To raise a native speaker of an invented language, you need the whole culture around the child.

Built on: Klingon

Led to: Lore worlds

Source: HuffPost UK, reporting Wired (1999)

Address: /trees/simulations?n=w-speers

Rome Reborn (1996 onward · Computer)

Rome Reborn began in 1996 at UCLA under Bernard Frischer. It models the whole city of Rome as it stood in AD 320. Version 1.0 was finished in 2007, and version 3.0 (2018) was rebuilt so you can walk through it in a headset. It’s a reconstructed world. Every building rests on archaeological evidence where there is some, and on inference where there isn’t.

Led to: Evidence or guess: the London Charter

Source: Wikipedia, ‘Rome Reborn’

Address: /trees/simulations?n=w-rome

Second Life (2003; peak 2009 · Computer)

Linden Lab’s Second Life (2003) is a world built by its residents, with land, an economy and a currency. It peaked at about 88,200 people online at once in early 2009. About 21 million accounts had been registered by late 2010. It’s the first large world that people treated as a second place to live, not as a game.

Built on: MUD1

Led to: Social worlds in headsets

Source: Engadget, ‘Linden Lab says Second Life is huge, shows numbers’ (22 September 2009)

Address: /trees/simulations?n=w-secondlife

A lore world with millions (2004; 12 million subscribers in 2010 · Computer)

World of Warcraft (2004) put millions of people inside one invented world, with its own races, histories and wars. It descends from the text worlds of MUDs. In October 2010 Blizzard announced that subscribers had passed 12 million, the game’s last headline figure. Players spend years in it, but the people in it who aren’t players are scripted.

Built on: MUD1

Led to: Lore worlds

Source: Activision Blizzard press release, 7 October 2010

Address: /trees/simulations?n=w-wow

Evidence or guess: the London Charter (2009 (term ‘virtual archaeology’ 1990) · Idea · Run by people)

Paul Reilly coined “virtual archaeology” in 1990. The London Charter (2009) set a rule: a visualisation must tell its viewer which parts show what survives, which are restorations based on evidence, and which are hypothesis. It’s the first standard for honesty inside a reconstructed world.

Built on: Rome Reborn

Led to: Reconstructed worlds

Source: Wikipedia, ‘Virtual archaeology’

Address: /trees/simulations?n=w-london

GameNGen (2024 · Computer)

Valevski and colleagues trained a diffusion model on recordings of an agent playing DOOM. With no conventional game engine, it generates each next frame from past frames and player actions, at about 20 frames per second on a single TPU. Human raters could tell short clips of the real game from simulated ones only slightly better than chance.

Built on: Learned surrogate models

Led to: Genie 3; Real-time photorealism

Source: Valevski, Leviathan, Arar and Fruchter, ‘Diffusion Models Are Real-Time Game Engines’, arXiv 2408.14837 (2024); ICLR 2025

Address: /trees/simulations?n=w-gamengen

Genie 3 (2025 · Computer)

DeepMind announced Genie 3 on 5 August 2025. It’s a world model that generates environments you can move around in, in real time, at 720p and 24 frames per second. Worlds stayed largely consistent for several minutes, and its visual memory reached back about a minute. It was released only as a limited research preview, for a small group of academics and creators.

Built on: GameNGen; Learned surrogate models

Led to: Ancestor simulation; Real-time photorealism; Reconstructed worlds; Lore worlds

Source: Google DeepMind, ‘Genie 3: A new frontier for world models’, 5 August 2025

Address: /trees/simulations?n=w-genie3

Social worlds in headsets (February 2026 · Computer)

VRChat set a record of 158,192 people online at once at a concert in February 2026. Ordinary weekend peaks are about 120,000. Roblox reported 151.5 million daily users in the third quarter of 2025, mostly on screens, not headsets. These are the biggest groups of people who live part of each day in built worlds.

Built on: Second Life

Led to: Immersive worlds in daily life

Source: Road to VR, ‘VRChat key stats’ (2026)

Address: /trees/simulations?n=w-vrchat

Real-time photorealism (2029–2034 · Forecast)

Home: the Technology tree.

Industry figures have forecast real-time images that look just like photographs. In 2024 one major vendor gave a window of 5 to 10 years. A 2013 forecast of ten years for the same milestone came due in 2023, with no claim that it had been met.

Built on: Genie 3; GameNGen

Led to: Full-immersion VR

Address: /trees/simulations?n=f-photoreal

Full-immersion VR (2029–2030s · Forecast)

Home: the Technology tree.

Only one named futurist has published dates for VR at the level of the nervous system. He puts it in the late 2020s to the 2030s, using nanobots in the brain. We found no expert survey or independent forecast of this milestone. No such system has been demonstrated.

Built on: Real-time photorealism; Whole-brain emulation

Address: /trees/simulations?n=f-fulldive

Immersive worlds in daily life (2026–2040 · Forecast)

These are forecasts that a large share of people would spend part of each day inside immersive worlds. Gartner’s date came due in 2026. VRChat’s record is about 158,000 people at once, and Roblox’s daily users are about 151 million, mostly on flat screens. That’s far from the quarter of all people that was forecast. A 2022 canvass of 624 experts split 54 to 46 on half a billion people by 2040.

Built on: Social worlds in headsets

Address: /trees/simulations?n=f-immersive

Reconstructed worlds (undated · Projection)

This is a lost civilisation, ours or another species’, rebuilt from what it left behind and run so that you can live in it. The evidence never covers a whole world. So every reconstruction is part record and part inference, and a long-dead alien civilisation would be mostly inference. The London Charter’s rule is to tell the visitor which is which. That becomes the ethics of the whole genre.

Built on: Evidence or guess: the London Charter; A face from DNA; Gene-edited ‘dire wolves’; Genie 3

Address: /trees/simulations?n=p-reconstructed

Counterfactual worlds (undated · Projection)

This is our own history run forward from a changed event, such as an Axis victory or a Mongol conquest of Europe. Novels have done it in the reader’s mind since 1836, and strategy games have done it in millions of copies. The projected step is running it with simulated people in it. That turns a thought experiment into a world with inhabitants.

Built on: The Man in the High Castle; Counterfactual history as method; Civilization; Simulated human society

Address: /trees/simulations?n=p-counterfactual

Lore worlds (undated · Projection)

This is a reality made entirely of lore, with orcs and elves, or the Klingons of Star Trek. Their languages, histories and religions are taken as true from the inside. A person could be born there and raised in it. Its own fiction could even feature a strange imagined race called humans.

Built on: Languages before the world; Klingon; A child raised in Klingon; A lore world with millions; Genie 3

Address: /trees/simulations?n=p-invented

Ancestor simulation (undated · Forecast)

Bostrom (2003) gives no date, and says the argument doesn’t depend on one. He estimates that simulating all human mental history takes about 10³³ to 10³⁶ operations. A planetary-mass computer could supply that in under a second of its capacity.

Built on: Whole-brain emulation; Genie 3; World3

Address: /trees/simulations?n=f-ancestor

Antikythera mechanism (c. 2nd century BCE · Analogue model)

A geared bronze device was recovered from a shipwreck off Antikythera. It showed the motions of the Sun, Moon and planets, and it predicted eclipses using Babylonian cycles. Its lunar gearing puts into metal a theory attributed to Hipparchos. Freeth and colleagues (2021) proposed a model of its front planetary display.

Source: Freeth et al., ‘Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism’, Nature 444 (2006) 587–591

Address: /trees/simulations?n=p-antikythera

Kelvin’s tide predictor (1872 · Analogue model)

Kelvin designed this machine with Edward Roberts for the British Association, and Alexander Lege built it. It added up ten harmonic tidal constituents mechanically to trace the tide at a port. More than thirty such machines were built between the 1870s and the 1960s. For about ninety years, a machine that embodied a system’s harmonic structure predicted its future.

Source: Science Museum Group, ‘William Thomson’s Tide Predicting Machine, 1872’

Address: /trees/simulations?n=p-tide

Richardson’s hand forecast (1922 · Run by people)

Lewis Fry Richardson worked out by hand the change in the weather for one morning in 1910. He used the finite-difference equations of the atmosphere. He wrote that drawing up the computing forms and working out the new distribution for two columns took the best part of six weeks. He pictured a hall of about 64,000 human computers working in step to keep pace with the real weather. It’s an early picture of a parallel computer.

Built on: Numerical integration

Led to: First computer forecast

Source: Lynch, ‘Richardson’s Forecast-factory: the $64,000 Question’, Meteorological Magazine / Weather

Address: /trees/simulations?n=p-richardson

Holmberg’s bulb galaxies (1941 · Analogue model)

Holmberg used light bulbs, 37 to a galaxy, with photocells to measure the brightness as a stand-in for gravity. Both fall off as the inverse square of distance. He moved the bulbs step by step to model two interacting disk galaxies. The experiment produced tidal tails and bridges, about thirty years before digital computers could check it.

Source: Holmberg’s analog computer (University of Oulu repository); Erik Holmberg, Uppsala University history pages

Address: /trees/simulations?n=p-holmberg

First computer forecast (1950 · Computer)

Charney, Fjortoft and von Neumann solved the barotropic vorticity equation on ENIAC. They covered a limited area, on a 19 by 16 grid with about 600 km between points, and produced four 24-hour forecasts. Each forecast took about 24 hours of computing, most of it handling cards by hand. So the machine was no faster than the weather.

Built on: Electronic computer; Finite differences; Richardson’s hand forecast

Led to: Phillips’s circulation run; Learned weather forecasts

Source: Charney, Fjortoft and von Neumann, ‘Numerical Integration of the Barotropic Vorticity Equation’, Tellus 2 (1950) 237–254

Address: /trees/simulations?n=p-eniac

Phillips’s circulation run (1955–1956 · Computer)

Phillips ran a numerical simulation of the atmosphere’s general circulation on the Institute for Advanced Study machine, for about a model month. It showed realistic monthly and seasonal patterns in the troposphere. It won the first Napier Shaw Memorial Prize. It’s commonly described as the first successful climate model.

Built on: First computer forecast; Finite differences

Led to: Coupled ocean-atmosphere; Global cloud-resolving model

Source: Phillips, ‘The general circulation of the atmosphere: a numerical experiment’, Quarterly Journal of the Royal Meteorological Society 82 (1956) 123–164; Norman A. Phillips, Wikipedia

Address: /trees/simulations?n=p-phillips

N-body star cluster (1960 · Computer)

Von Hoerner integrated the gravitational motion of 4 to 16 stars on a computer, with the time step set by the closest pair. In 1963 he extended it to 25. It’s the earliest documented N-body integration. The line from it runs through clusters of galaxies to simulations of the universe.

Built on: Electronic computer; Numerical integration

Led to: Millennium Simulation

Source: von Hoerner, ‘Die numerische Integration des n-Koerper-Problemes fuer Sternhaufen. I’, Zeitschrift fuer Astrophysik 50 (1960) 184–214

Address: /trees/simulations?n=p-vonhoerner

Lorenz’s chaotic convection (1961–1963 · Computer)

Lorenz ran a twelve-variable weather model on a Royal McBee LGP-30. When he restarted it from rounded printout values, the result drifted apart from the first run. In 1963 he published a convection model whose solutions are unstable and mostly nonperiodic. It showed that a deterministic simulation can be unpredictable past a limited time. That sets a limit on how far ahead any forecast can reach.

Built on: Electronic computer; Numerical integration

Source: Lorenz, ‘Deterministic nonperiodic flow’, Journal of the Atmospheric Sciences 20 (1963) 130–141

Address: /trees/simulations?n=p-lorenz

Coupled ocean-atmosphere (1969 · Computer)

Manabe and Bryan at the Geophysical Fluid Dynamics Laboratory coupled a model atmosphere to a model ocean. They used an idealised strip of ocean and continent, on the argument that the sea moves about as much heat as the atmosphere. It’s described as the first coupled ocean-atmosphere climate model.

Built on: Phillips’s circulation run; Finite differences

Led to: Global cloud-resolving model

Source: Manabe and Bryan, ‘Climate Calculations with a Combined Ocean-Atmosphere Model’, Journal of the Atmospheric Sciences 26 (1969) 786–789

Address: /trees/simulations?n=p-manabebryan

Millennium Simulation (2005 · Computer)

Springel and colleagues followed more than ten billion dark-matter particles as structure grew in a cubic region of the universe. They paired the run with models of galaxy and quasar formation, to compare simulated and observed large-scale structure. It showed baryonic features of the early universe turning up, distorted, in the galaxy distribution at low redshift.

Built on: N-body star cluster; Electronic computer

Source: Springel et al., ‘Simulating the joint evolution of quasars, galaxies and their large-scale distribution’, Nature 435 (2005) 629–636

Address: /trees/simulations?n=p-millennium

Global cloud-resolving model (2007 · Computer)

Miura and colleagues simulated a Madden-Julian oscillation event on the Earth Simulator. Their global model resolves clouds directly instead of approximating them. It reproduced the slow eastward drift of the event. The approach is the one later called global storm-resolving modelling.

Built on: Phillips’s circulation run; Coupled ocean-atmosphere

Led to: Destination Earth twins; Full Earth digital twin

Source: Miura, Satoh, Nasuno, Noda and Oouchi, ‘A Madden-Julian Oscillation Event Realistically Simulated by a Global Cloud-Resolving Model’, Science 318 (2007) 1763–1765

Address: /trees/simulations?n=p-miura

Learned weather forecasts (2023 · Computer)

GraphCast is a neural network trained on reanalysis data. It predicts hundreds of weather variables for the next 10 days at 0.25 degree resolution, in under a minute. It was more accurate than the European Centre’s operational deterministic system on 90% of 1,380 verification targets. It swaps step-by-step integration of the atmosphere’s equations for a learned map from one state to the next.

Built on: Learned surrogate models; First computer forecast

Led to: Destination Earth twins

Source: Lam et al., ‘Learning skillful medium-range global weather forecasting’, Science 382 (2023) 1416–1421

Address: /trees/simulations?n=p-graphcast

Destination Earth twins (2024 · Computer)

ECMWF built the first two Destination Earth digital twins, on climate change adaptation and weather-driven extremes. The second phase of the programme began on 10 June 2024. The programme states its aim as a digital replica of the Earth system by 2030.

Built on: Global cloud-resolving model; Learned weather forecasts; Electronic computer

Led to: Full Earth digital twin

Source: ECMWF, ‘Destination Earth system launched’, 10 June 2024

Address: /trees/simulations?n=p-destine

Full Earth digital twin (2030 (a stated programme aim, not an independent forecast) · Forecast)

The Destination Earth programme states an aim of a digital replica of the Earth system by 2030. Its first two twins went live in 2024. The only other source we found is a review of kilometre-scale climate models. It argues for a concerted effort and gives no date.

Built on: Destination Earth twins; Global cloud-resolving model

Address: /trees/simulations?n=f-earthtwin

Roman drill as rehearsal (c. 75 CE · Run by people)

In The Jewish War, Josephus wrote that every Roman soldier is exercised daily as if in war. He summed up the practice as exercises that are bloodless battles and battles that are bloody exercises. Rehearsing a battle with the same units and drills as the real one is an early documented form of simulating a war.

Source: Josephus, The Jewish War 3.5.1 (Whiston translation, sections 3.70–3.75)

Address: /trees/simulations?n=soc-josephus

Chaturanga, the army game (6th–7th century CE · Run by people)

Chaturanga means the four parts of an army: infantry, cavalry, elephants and chariots. It was played in India on an eight-by-eight board. The earliest Sanskrit mention of the name is in Bana’s Harshacharita, written in the 7th century. The game is the ancestor of chess, and it passed to Persia as chatrang about 600 CE. It boils an army and its terrain down to a few pieces and rules. It’s an early model of a war, run by humans.

Led to: Hellwig’s chess wargame

Source: Encyclopaedia Britannica, ‘chess’ (history section); see also Murray, A History of Chess (Oxford, 1913)

Address: /trees/simulations?n=soc-chaturanga

Hellwig’s chess wargame (1780 · Run by people)

In 1780 Johann Hellwig, a mathematics professor at the Collegium Carolinum in Braunschweig, published a tactical game built on chess. Two or more people played it on a board of about 49 by 33 squares, with mountains, swamps and water. The aim was to take an enemy fortress instead of capturing a king. It’s the earliest of the chess-based German wargames that came before Reisswitz’s Kriegsspiel.

Built on: Chaturanga, the army game

Led to: Kriegsspiel

Source: Hellwig, Versuch eines aufs Schachspiel gebaueten taktischen Spiels (Leipzig: Crusius, 1780), as described in Peterson, Playing at the World (Unreason Press, 2012) p. 213

Address: /trees/simulations?n=soc-hellwig

Kriegsspiel (1812–1824 · Run by people)

In 1811 the Prussian princes were shown a terrain table of damp sand and models. It was presented to the king in 1812. In 1824 the younger Reisswitz published rules that used topographical maps and put numbers on the effects of combat. Kriegsspiel is described as the first war-gaming system that a military adopted as a serious tool for training and research.

Built on: Hellwig’s chess wargame

Led to: Dungeons and Dragons

Source: Kriegsspiel, Wikipedia; Georg von Reisswitz, Wikipedia

Address: /trees/simulations?n=soc-kriegs

Phillips’s hydraulic economy (1949 · Analogue model)

Bill Phillips built the MONIAC, a hydraulic analogue computer. Water flowing through tanks and pipes stood for the flows of income and spending in the United Kingdom economy. He demonstrated it at the London School of Economics on 29 November 1949. At least twelve machines were built, and the original ran until 1992.

Led to: World3

Source: Computing History, ‘Professor Bill Phillips unveils MONIAC at the LSE’

Address: /trees/simulations?n=soc-moniac

The People Machine (1959–1960 · Computer)

Simulmatics was led by Ithiel de Sola Pool with Robert Abelson. It split the American electorate into 480 voter types and 52 issue clusters, built from past polls. Then it simulated how each type would respond to campaign choices. It worked first for the Democratic National Committee and then for the Kennedy campaign. Lepore counts three reports for the campaign and says its influence is unclear.

Built on: Electronic computer

Led to: Silicon samples

Source: Lepore, ‘Which category have they put you in?' (on Simulmatics), New York Review of Books, 8 October 2020

Address: /trees/simulations?n=soc-simulmatics

Schelling segregation (1969–1971 · Run by people)

In Schelling’s model, two kinds of agents move when fewer than a set share of their neighbours are like them. It showed that strong segregation in housing can come from only mild preferences. He worked it through by hand with coins on a checkerboard, so it was a simulation run by humans. It later became the standard first example of agent-based modelling.

Source: Schelling, ‘Dynamic Models of Segregation’, Journal of Mathematical Sociology 1 (1971) 143–186

Address: /trees/simulations?n=soc-schelling

World3 (1971–1972 · Computer)

Meadows and colleagues built World3 on top of Forrester’s World2 model. It links population, agriculture, industry, resources and pollution as feedback loops. Its standard run showed overshoot followed by collapse. It was published as The Limits to Growth in 1972, and it put a simulation of the whole human system in front of ordinary readers.

Built on: Electronic computer; Phillips’s hydraulic economy

Led to: Ancestor simulation

Source: World3, Wikipedia; Meadows, Meadows, Randers and Behrens, The Limits to Growth (1972)

Address: /trees/simulations?n=soc-world3

Simulating other minds (1978–1986 · Idea · In the mind)

In 1978 Premack and Woodruff asked whether a chimpanzee has a theory of mind. In 1986 Gordon and Heal, working separately, argued that people predict others by simulating them. They run their own decision process on the other person’s circumstances. On this account, understanding other people is a mental simulation of them.

Built on: Craik’s model in the head

Source: Gordon, ‘Folk Psychology as Simulation’, Mind and Language 1 (1986) 158–171; Heal, ‘Replication and Functionalism’ (1986)

Address: /trees/simulations?n=soc-gordon

Artificial stock market (1994 · Computer)

Palmer, Arthur, Holland, LeBaron and Tayler simulated a market in one stock. Adaptive trader programs held different strategies, and a specialist set the price, so prices came out of the traders’ interactions. The model didn’t necessarily settle at an equilibrium. It could show bubbles, crashes and persistently high trading volume.

Built on: Agent-based models

Source: Palmer, Arthur, Holland, LeBaron and Tayler, ‘Artificial economic life: a simple model of a stockmarket’, Physica D 75 (1994) 264–274

Address: /trees/simulations?n=soc-santafe

Sugarscape (1996 · Computer)

Epstein and Axtell put agents with different metabolisms and eyesight on a grid of sugar. Group formation, cultural transmission, combat and trade all arose from simple local rules. Their book described the method as growing a society from the bottom up.

Built on: Agent-based models

Led to: Artificial Anasazi

Source: Epstein and Axtell, Growing Artificial Societies: Social Science from the Bottom Up, Brookings Institution Press / MIT Press (1996)

Address: /trees/simulations?n=soc-sugarscape

Artificial Anasazi (2002 · Computer)

Axtell and colleagues modelled the Kayenta Anasazi in Long House Valley, with agents choosing where to farm and settle. The model reproduced the population swings and the shifting settlement pattern of a society from about 1800 BCE to 1300 CE. Its main mismatch is that the model valley could still have supported many people in 1300, when the real population left.

Built on: Sugarscape; Agent-based models

Led to: Simulated human society

Source: Axtell, Epstein, Dean, Gumerman et al., ‘Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley’, PNAS 99 (suppl. 3) (2002) 7275–7279

Address: /trees/simulations?n=soc-anasazi

Silicon samples (2022–2023 · Computer)

Argyle and colleagues gave a language model the socio-demographic backstories of thousands of real survey respondents. For US politics, they found its output could stand in for specific groups of people. They call this property algorithmic fidelity. They proposed these “silicon samples” for exploring hypotheses before doing costly work with human subjects.

Built on: Learned surrogate models; The People Machine

Led to: Simulated human society

Source: Argyle et al., ‘Out of One, Many: Using Language Models to Simulate Human Samples’, Political Analysis (2023), doi 10.1017/pan.2023.2

Address: /trees/simulations?n=soc-argyle

An agent civilisation (October 2024 · Computer)

Altera’s Project Sid ran from 10 to more than 1,000 language-model agents together in Minecraft. It reports that they took on specialised roles, changed their collective rules and passed on culture. The authors call the results preliminary. It’s the largest published attempt at a society of software people living in a game world.

Built on: Generative agents

Led to: Scripted inhabitants

Source: Altera, ‘Project Sid: many-agent simulations toward AI civilization’, arXiv:2411.00114 (2024)

Address: /trees/simulations?n=soc-sid

Simulated human society (No dated forecast; stated ambition only · Forecast)

The leading group building generative-agent simulations has stated an ambition of simulating eight billion people. It hasn’t given a timeline. Current published runs are far smaller: 25 agents in the 2023 paper and 1,052 individuals in the 2024 follow-up.

Built on: Generative agents; Silicon samples; Artificial Anasazi

Led to: Counterfactual worlds

The sources leave this date or claim uncertain.

Address: /trees/simulations?n=f-society

Craik’s model in the head (1943 · Idea · In the mind)

In The Nature of Explanation, Kenneth Craik proposed that an organism carries a small-scale model of the outside world and of its own possible actions. That lets it try alternatives before it acts. He compared this with testing a ship design on a model in a tank. That makes the nervous system a simulator, in the sense this tree uses.

Led to: Hippocampal replay; Imagining the future; Simulating other minds

Source: Craik, The Nature of Explanation, Cambridge University Press (1943), p. 61 (as quoted in Williams 2018)

Address: /trees/simulations?n=min-craik

Hodgkin–Huxley by hand (1952 · Run by people)

Huxley integrated the Hodgkin–Huxley equations for the squid giant axon on a hand-cranked mechanical calculator, because the Cambridge computer was out of service. One travelling action potential took about three weeks. The result matched the shape and speed of the nerve impulse. Later neuron simulation was built on this model.

Built on: Numerical integration; Differential equations

Led to: Cardiac cell model; Simulated neuron networks; Neocortical microcircuit; OpenWorm; Human Brain Project

Source: Physiological Society, ‘Hodgkin and Huxley’s modelling of the action potential’

Address: /trees/simulations?n=min-hh

Simulated neuron networks (1954–1956 · Computer)

Farley and Clark simulated a self-organising network on a digital computer at MIT (1954). In 1956 Rochester, Holland, Haibt and Duda used an IBM 704 to simulate a net of neurons and test Hebb’s cell-assembly theory. Cell assemblies formed out of an unorganised net, though they didn’t yet behave the way the theory needed.

Built on: Electronic computer; Hodgkin–Huxley by hand

Led to: Neocortical microcircuit; Human Brain Project

Source: Rochester, Holland, Haibt and Duda, ‘Tests on a Cell Assembly Theory of the Action of the Brain, Using a Large Digital Computer’, IRE Transactions on Information Theory 2(3) (1956) 80–93; Farley and Clark, IRE Trans. PGIT-4 (1954) 76–84

Address: /trees/simulations?n=min-rochester

ELIZA (1965–1966 · Computer)

Weizenbaum’s ELIZA ran on MIT’s time-sharing system. It answered typed sentences by matching keywords with breakdown rules, then rebuilding the input with reassembly rules. It was a scripted stand-in for one side of a conversation, with no model of meaning. It marks the start of programs that take a person’s place in a dialogue.

Built on: Electronic computer

Led to: Generative agents

Source: Weizenbaum, ‘ELIZA: A Computer Program for the Study of Natural Language Communication between Man and Machine’, Communications of the ACM 9(1) (1966) 36–45

Address: /trees/simulations?n=min-eliza

Hippocampal replay (1994 · In the mind)

Wilson and McNaughton recorded groups of hippocampal place cells in rats. Cells that fired together at one place during a task did so more often in the sleep that followed. It’s a widely cited demonstration that the brain re-runs earlier experience offline. It’s a mental simulation of events that have already happened.

Built on: Craik’s model in the head

Led to: Imagining the future

Source: Wilson and McNaughton, ‘Reactivation of hippocampal ensemble memories during sleep’, Science 265(5172) (1994) 676–679

Address: /trees/simulations?n=min-replay

Philosophical zombies (1996 · Idea · In the mind)

David Chalmers set out the zombie argument in The Conscious Mind (1996). A being could be identical to a person in every physical and behavioural way, yet have no experience at all. That’s conceivable. If it is, a simulated person could behave exactly like one of us with nobody there.

Led to: Shadow-people; Conscious inhabitants

Source: Stanford Encyclopedia of Philosophy, ‘Zombies’

Address: /trees/simulations?n=min-zombie

Shadow-people (2003 · Idea · In the mind)

Bostrom’s simulation argument estimates 10³³ to 10³⁶ operations to run all of human history in full. He notes the computing needed could be cut by simulating only some minds in full: ‘The rest of humanity would then be zombies or “shadow-people”’. It’s the first statement that a simulated world could hold both kinds of inhabitant.

Built on: Philosophical zombies

Led to: Scripted inhabitants

Source: Nick Bostrom, ‘Are You Living in a Computer Simulation?’, Philosophical Quarterly 53 (2003)

Address: /trees/simulations?n=min-shadow

Imagining the future (2007 · In the mind)

Schacter and Addis proposed that episodic memory partly exists to build imagined future events. It flexibly recombines pieces of past experience into simulations of possible futures. On this view, ordinary remembering and planning are a kind of simulation that the brain builds.

Built on: Hippocampal replay; Craik’s model in the head

Source: Schacter and Addis, ‘The cognitive neuroscience of constructive memory: remembering the past and imagining the future’, Phil. Trans. R. Soc. B 362 (2007) 773–786

Address: /trees/simulations?n=min-episodic

Human Brain Project (2009–2023 · Stalled · Computer)

In 2009 Markram promised to simulate the human brain within ten years. The European Human Brain Project followed. In July 2014 an open letter from more than 800 scientists objected to the bottom-up approach. After a mediation review, the project dropped complete brain simulation and refocused on computational tools for neuroscience. EBRAINS is its successor platform.

Why it stalled: The project didn’t achieve whole-brain simulation. It was restructured around tools for neuroscience.

Built on: Hodgkin–Huxley by hand; Simulated neuron networks

Source: Scientific American, ‘Scientists Tried to Re-create an Entire Human Brain in a Computer. What Happened?'

Address: /trees/simulations?n=min-hbp

OpenWorm (2011 onward · Idea · Computer)

OpenWorm is an open collaboration to simulate the nematode Caenorhabditis elegans, whose nervous system has 302 neurons. It works from the neurons and muscles up to body movement. Sarma and colleagues (2018) describe its sub-projects and results as partial. No report describes a complete simulation of a behaving worm.

Built on: Hodgkin–Huxley by hand

Led to: Whole-brain emulation

The sources leave this date or claim uncertain.

Source: Sarma et al., ‘OpenWorm: overview and recent advances in integrative biological simulation of Caenorhabditis elegans’, Phil. Trans. R. Soc. B 373 (2018) 20170382

Address: /trees/simulations?n=min-openworm

Neocortical microcircuit (2015 · Computer)

Markram and colleagues rebuilt and simulated about 0.29 cubic millimetres of juvenile rat somatosensory cortex. It had roughly 31,000 neurons and 37 million synapses. The simulation reproduced a range of experiments without tuning the parameters. It’s a detailed digital rebuild of a small piece of cortex, not of a whole brain.

Built on: Hodgkin–Huxley by hand; Simulated neuron networks

Led to: Whole-brain emulation

Source: Markram et al., ‘Reconstruction and simulation of neocortical microcircuitry’, Cell 163(2) (2015) 456–492

Address: /trees/simulations?n=min-markram

Generative agents (2023–2024 · Computer)

Park and colleagues put 25 language-model agents into a Sims-like town. Each had memory, reflection and planning, and each of those parts made the agents’ behaviour more believable. A 2024 follow-up built agents from two-hour interviews with 1,052 people. They matched the participants’ survey answers about 85% as often as the same people matched their own answers two weeks later. These agents stand in for individual people, the way ELIZA stood in for one side of a conversation.

Built on: Learned surrogate models; ELIZA

Led to: Simulated human society; An agent civilisation

Source: Park et al., ‘Generative Agents: Interactive Simulacra of Human Behavior’, UIST 2023; Park et al., ‘Generative Agent Simulations of 1,000 People’, arXiv 2411.10109 (2024)

Address: /trees/simulations?n=min-park

Scripted inhabitants (undated · Projection)

These are worlds whose people act convincingly with no one inside. They’re Bostrom’s shadow-people. They take far less computing, and nobody is harmed. But the world is closer to theatre, and a visitor can never be sure which kind they’re talking to.

Built on: Shadow-people; An agent civilisation

Address: /trees/simulations?n=p-scripted

Whole-brain emulation (2050–2075 · Bridge)

Also in the Technology tree and Becoming synthetic.

The 2008 FHI roadmap judged that emulation was possible before mid-century, but only if models at the electrophysiological level are enough. Finer detail would come later. A 2014 Monte Carlo model gives a median of 2064, if it happens at all. The Metaculus community median is about 2073.

Built on: Neocortical microcircuit; OpenWorm

Led to: Ancestor simulation; Full-immersion VR; Mind uploading; Conscious inhabitants

Address: /trees/simulations?n=f-wbe

Mind uploading (2060s–2100+ · Forecast)

Also in the Becoming synthetic.

Uploading is the step after emulation. You scan a particular person’s brain and run it. Forecasters place it after whole-brain emulation. Published dates run from the 2060s to about a century out, and some say it lies beyond the near-term AI horizon.

Built on: Whole-brain emulation

Address: /trees/simulations?n=f-upload

Conscious inhabitants (undated · Projection)

These are worlds whose people have experiences of their own. Each one needs the computational power of a full mind to run. Every one of them counts morally, and a dark world becomes real suffering. This is the branch where simulated worlds are societies, not stories.

Built on: Whole-brain emulation; Philosophical zombies

Address: /trees/simulations?n=p-conscious

Du Coudray’s birth mannequin (1756 · Analogue model)

Angelique du Coudray’s “machine” was a life-size model of the lower female body, made of fabric, leather and stuffing. Straps stood in for the stretching of the birth canal. She used it to teach midwives normal, breech and complicated births. The College of Surgery approved it on 1 December 1756, and it was taught across France.

Source: UCLA Center for the Study of Women, summary of research on eighteenth-century French midwifery

Address: /trees/simulations?n=life-coudray

Turing’s reaction-diffusion (1952 · Computer)

Turing showed that two chemicals that react and spread out can turn a uniform state into spots, stripes and waves. He used the Manchester University computer for some of the numbers. It was a computer model of how biological form begins, and it came before the molecular biology of development.

Built on: Electronic computer; Finite differences

Source: Turing, ‘The Chemical Basis of Morphogenesis’, Philosophical Transactions of the Royal Society B 237 (1952) 37–72

Address: /trees/simulations?n=life-turing

Evolution on the IAS machine (1953 · Computer)

In March 1953 Nils Barricelli filled the Institute for Advanced Study computer with random numbers. He followed numerical “organisms” that reproduced, mutated and formed symbiotic groups. He wanted to test whether evolution could happen in an artificial universe. It’s the earliest documented computer experiment on evolution. The first published account is a 1954 article in Italian.

Built on: Electronic computer; Cellular automata

Source: George Dyson, ‘An Artificially Created Universe’, Institute for Advanced Study; Barricelli, Acta Biotheoretica 16 (1962) 69–98

Address: /trees/simulations?n=life-barricelli

Cardiac cell model (1960 · Computer)

Noble adapted the Hodgkin–Huxley equations to reproduce, on a computer, the action and pacemaker potentials of a cardiac Purkinje fibre. It showed that a membrane model built for a squid axon could be re-tuned for another tissue. That was the first step toward computational models of the heart.

Built on: Electronic computer; Hodgkin–Huxley by hand

Source: Noble, ‘Cardiac Action and Pacemaker Potentials based on the Hodgkin–Huxley Equations’, Nature 188 (1960) 495–497

Address: /trees/simulations?n=life-noble

Life, played by hand (late 1960s–1970 · Run by people)

Conway and colleagues tried out candidate birth-and-death rules by hand on a Go board. They settled on the rules that Martin Gardner published in Scientific American in October 1970. Readers then ran Life by hand on graph paper, as well as on computers. That made a cellular automaton a pastime as well as a model of lifelike growth.

Built on: Cellular automata

Source: Conway’s Game of Life, Wikipedia (history section); Gardner, Scientific American, October 1970

Address: /trees/simulations?n=life-life

Protein dynamics (1977 · Computer)

McCammon, Gelin and Karplus simulated bovine pancreatic trypsin inhibitor, a small protein. They solved the equations of motion of its atoms under an empirical energy function. They found that the inside of the protein behaves like a fluid, with local motions that diffuse. That replaced the picture of a rigid, folded protein.

Built on: Molecular dynamics

Led to: Whole-cell models; Learned protein structure

Source: McCammon, Gelin and Karplus, ‘Dynamics of folded proteins’, Nature 267 (1977) 585–590

Address: /trees/simulations?n=life-protein

The Neandertal genome (May 2010 · Computer)

Green and colleagues published a draft Neandertal genome of more than 4 billion bases, from three individuals (Science 328, 710–722). They found that Neandertals had interbred with the ancestors of people outside Africa. It made an extinct human population readable from its DNA.

Led to: A face from DNA; Gene-edited ‘dire wolves’

Source: Green et al., ‘A draft sequence of the Neandertal genome’, Science 328 (2010)

Address: /trees/simulations?n=life-neandertal

Whole-cell models (2012–2022 · Computer)

Karr and colleagues combined 28 submodels into a model of Mycoplasma genitalium, a bacterium with 525 genes. They compared its predictions with many observed cell behaviours. Macklin and colleagues built a similar model of E. coli (2020). Thornburg and colleagues built a spatial kinetic model of JCVI-syn3A, a minimal cell with 493 genes (2022). The authors called the first version a first draft, and none yet covers a eukaryotic cell.

Built on: Protein dynamics; Numerical integration

Led to: Human whole-cell model

Source: Karr et al., ‘A Whole-Cell Computational Model Predicts Phenotype from Genotype’, Cell 150 (2012) 389–401; Macklin et al., Science 369 (2020) eaav3751; Thornburg et al., Cell 185 (2022) 345–360

Address: /trees/simulations?n=life-wholecell

A face from DNA (2019 · Computer)

Gokhman, Carmel and colleagues used patterns of DNA methylation to predict the anatomy of the Denisovans. They’re a human group known from one finger bone and a few teeth. The team drew a head and face that no fossil shows (Cell, 2019). It rebuilds a people’s bodies from their genome alone.

Built on: The Neandertal genome

Led to: Reconstructed worlds

Source: Gokhman et al., ‘Reconstructing Denisovan anatomy using DNA methylation maps’, Cell (2019)

Address: /trees/simulations?n=life-denisovan

Learned protein structure (2020–2021 · Computer)

AlphaFold is a neural network trained on known structures. In the CASP14 assessment (2020; Jumper et al., Nature, 2021) it predicted protein structures about as accurately as experiments, in most cases. It predicts the folded result directly. It doesn’t simulate the folding, so it’s a model of proteins, not a simulation of them.

Built on: Learned surrogate models; Protein dynamics

Led to: Human whole-cell model

Source: Jumper et al., ‘Highly accurate protein structure prediction with AlphaFold’, Nature 596 (2021) 583–589

Address: /trees/simulations?n=life-alphafold

Gene-edited ‘dire wolves’ (born 2024–2025; announced April 2025 · Analogue model)

Colossal Biosciences announced three grey wolves with about 20 edits in 14 genes, 15 of them based on dire wolf DNA. It presented them as revived dire wolves. The IUCN canid specialist group said they are neither dire wolves nor a step toward bringing them back. As a reconstruction, it’s part evidence and part substitution. It’s the honesty problem the London Charter set out for images, now in living animals.

Built on: The Neandertal genome

Led to: Reconstructed worlds

Source: Wikipedia, ‘Colossal Biosciences dire wolf project’

Address: /trees/simulations?n=life-direwolf

Human whole-cell model (No dated forecast · Forecast)

In 2018 Szigeti and colleagues argued that human whole-cell models are becoming feasible. They proposed a Human Whole-Cell Modeling Project, but gave no year. They note that the first bacterial model took more than ten person-years to build.

Built on: Whole-cell models; Learned protein structure

The sources leave this date or claim uncertain.

Address: /trees/simulations?n=f-humancell

Hooke’s hanging chain (1675 · Analogue model)

In 1675 Hooke published an anagram that was only solved after his death. It said that as a flexible line hangs, so, upside down, will a rigid arch stand. So a hanging model chain simulates a loaded arch, using gravity itself. Gaudi used hanging models to design the Colonia Guell crypt between 1888 and 1890.

Source: Funicular curve (with Heyman’s scholarship on Hooke’s anagram), Wikipedia

Address: /trees/simulations?n=mat-hooke

Froude’s towing tank (1871–1872 · Analogue model)

William Froude towed scale models of ships through a tank paid for by the Admiralty. He used scaling laws to predict the resistance of full-size hulls. One source dates the first test, on a model of HMS Greyhound, to 3 March 1872. The model was the simulation, and the scaling law was the rule for reading it.

Source: Royal Institution of Naval Architects, ‘William Froude: the father of hydrodynamics’

Address: /trees/simulations?n=mat-froude

Hand-computed implosion (1944 · Run by people)

In March 1944 Frankel, Nelson and Feynman ran an implosion calculation by hand. Each human computer passed the in-between results to the next on index cards, while the IBM punched-card machines were still on their way to Los Alamos. The trial showed that a chain of people following fixed rules could stand in for a machine. The punched-card operation then ran implosion hydrodynamics at scale.

Source: Trinity by the Numbers: The Computing Effort that Made Trinity Possible (arXiv 2103.06211)

Address: /trees/simulations?n=mat-losalamos

Hard-sphere fluids (1953–1957 · Computer)

In 1953 the MANIAC worked out the equation of state of hard disks by Monte Carlo. In 1957 Alder and Wainwright followed hard spheres through time and found a fluid-solid transition. The two methods disagreed at first. Wood and Jacobson repeated the Monte Carlo run in 1957 and found good agreement. It’s an early case of one simulation checking another.

Built on: Metropolis algorithm

Source: Alder and Wainwright, J. Chem. Phys. 27 (1957) 1208; Wood and Jacobson, J. Chem. Phys. 27 (1957) 1207

Address: /trees/simulations?n=mat-hard

Lattice gauge Monte Carlo (1979–1980 · Computer)

Creutz applied Metropolis-style Monte Carlo to gauge fields on a lattice of spacetime. He started with SU(2), a simplified strong-force theory with no quarks, in a 1979 Physical Review Letter, followed by a fuller 1980 paper. Computing the properties of hadrons from full QCD, with quarks, came later.

Built on: Metropolis algorithm

Source: Creutz, ‘Confinement and the Critical Dimensionality of Space-Time’, Phys. Rev. Lett. 43 (1979) 553; ‘Monte Carlo study of quantized SU(2) gauge theory’, Phys. Rev. D 21 (1980) 2308

Address: /trees/simulations?n=mat-lqcd

Feynman’s quantum simulator (1981–1982 · Idea · Computer)

Feynman argued that a classical computer can’t efficiently simulate quantum physics, because the work needed grows exponentially with the size of the system. He guessed that a computer built from quantum parts could simulate any physical system. The paper is where quantum simulation as a field begins.

Built on: Electronic computer; Metropolis algorithm

Led to: Cold-atom quantum simulator; Quantum chemistry simulation

Source: Feynman, ‘Simulating Physics with Computers’, International Journal of Theoretical Physics 21 (1982) 467

Address: /trees/simulations?n=mat-feynman

Ab initio molecular dynamics (1985 · Computer)

Car and Parrinello moved atoms under forces worked out on the fly from density-functional theory. That removed the need for a fitted model of the forces between atoms. Liquids, defects and chemical reactions could now be simulated from quantum mechanics, not from a tuned potential.

Built on: Molecular dynamics

Led to: Quantum chemistry simulation

Source: Car and Parrinello, ‘Unified Approach for Molecular Dynamics and Density-Functional Theory’, Phys. Rev. Lett. 55 (1985) 2471

Address: /trees/simulations?n=mat-abinitio

Cold-atom quantum simulator (2002 · Analogue model)

Greiner and colleagues loaded a Bose-Einstein condensate into an optical lattice. As they deepened the lattice, they saw a quantum phase transition from a superfluid to a Mott insulator. A system like this is a physical version of an interacting-particle model, so it computes by being that model. Later work treats such lattices as analogue quantum simulators.

Built on: Feynman’s quantum simulator

Led to: Quantum chemistry simulation

Source: Greiner, Mandel, Esslinger, Haensch and Bloch, ‘Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms’, Nature 415 (2002) 39–44

Address: /trees/simulations?n=mat-qanalog

Quantum chemistry simulation (No dated forecast; resource estimates only (about 4 million physical qubits and under 4 days in the 2021 estimate) · Forecast)

Published work gives resource estimates for simulating the iron-molybdenum cofactor of nitrogenase on a fault-tolerant quantum computer. It gives no date for when such a machine will exist. The only figures are estimates of the computing needed, and they fell by orders of magnitude between 2016 and 2021.

Built on: Feynman’s quantum simulator; Ab initio molecular dynamics; Cold-atom quantum simulator

The sources leave this date or claim uncertain.

Address: /trees/simulations?n=f-quantum

Differential equations (1684–1687)

Leibniz published the calculus in 1684. In 1687 Newton’s Principia wrote the motion of bodies as laws that link rates of change to forces. Every dynamic simulation on this tree is a way of solving equations like these when you can’t solve them on paper.

Led to: Numerical integration; Differential analyser; Finite differences; Hodgkin–Huxley by hand

Source: Newton, Philosophiae Naturalis Principia Mathematica (1687)

Address: /trees/simulations?n=m-calculus

Numerical integration (1768–1901)

Euler gave the step-by-step rule for moving a differential equation forward in Institutionum calculi integralis (1768–70). Runge (1895) and Kutta (1901) made the stepping accurate enough for real work. By hand or by machine, this is how nearly every simulation on the tree gets from one moment to the next.

Built on: Differential equations

Led to: Electronic computer; Molecular dynamics; Whole-cell models; Hodgkin–Huxley by hand; Richardson’s hand forecast; Lorenz’s chaotic convection; N-body star cluster

Source: Runge, ‘Ueber die numerische Aufloesung von Differentialgleichungen’, Mathematische Annalen 46 (1895) 167–178

Address: /trees/simulations?n=m-numint

Finite differences (1928)

Courant, Friedrichs and Lewy replaced partial differential equations with equations on a grid. They also showed the condition under which the stepping stays stable. Weather, ocean, fluid and wave simulations all rest on this trick. Richardson had already used it by hand in 1922, before the stability result was known.

Built on: Differential equations

Led to: Turing’s reaction-diffusion; First computer forecast; Phillips’s circulation run; Coupled ocean-atmosphere

Source: Courant, Friedrichs and Lewy, ‘Ueber die partiellen Differenzengleichungen der mathematischen Physik’, Mathematische Annalen 100 (1928) 32–74

Address: /trees/simulations?n=m-fd

Differential analyser (1931)

Bush’s differential analyser at MIT solved differential equations with turning shafts and wheel-and-disc integrators. Its parts behaved like the terms of the equation, so the machine did the simulating. Copies were built in the United Kingdom, United States, Canada, Norway and Japan, including one by Hartree at Manchester.

Built on: Differential equations

Led to: Electronic computer

Source: Bush, ‘The Differential Analyzer: A New Machine for Solving Differential Equations’, Journal of the Franklin Institute 212 (1931) 447–488

Address: /trees/simulations?n=m-diffan

Electronic computer (1945–1946)

Eckert and Mauchly built ENIAC to speed up the recalculation of artillery firing tables. It was finished by 1946, and Britannica calls it the first general-purpose electronic computer. The first large numerical simulations, including neutron diffusion and weather, ran on it or on machines of its generation.

Built on: Numerical integration; Differential analyser

Led to: Monte Carlo method; Metropolis algorithm; Molecular dynamics; Cellular automata; Agent-based models; Neural networks; Feynman’s quantum simulator; Evolution on the IAS machine; Turing’s reaction-diffusion; Cardiac cell model; Simulated neuron networks; ELIZA; The People Machine; World3; First computer forecast; Lorenz’s chaotic convection; N-body star cluster; Millennium Simulation; Destination Earth twins; Colossal Cave Adventure

Source: Encyclopaedia Britannica, ‘John Mauchly’ (ENIAC)

Address: /trees/simulations?n=m-computer

Monte Carlo method (1946–1949)

Ulam came up with the method in 1946 while thinking about the odds of winning solitaire. Von Neumann saw in March 1947 that it suited an electronic computer, and Metropolis and Ulam published it in 1949. It swaps a calculation you can’t do exactly for many random trials. That opened up neutron transport and, later, statistical mechanics to simulation.

Built on: Electronic computer

Led to: Metropolis algorithm

Source: Eckhardt, ‘Stan Ulam, John von Neumann, and the Monte Carlo Method’, Los Alamos Science 15 (1987) 131–141

Address: /trees/simulations?n=m-montecarlo

Cellular automata (1940s–1960s)

In the 1940s Ulam and von Neumann developed cellular automata: grids of simple cells updated by local rules. Von Neumann used one to show that a machine could, in principle, copy itself. Local rules on a grid became the standard minimal model of growth, pattern and self-organisation.

Built on: Electronic computer

Led to: Agent-based models; Evolution on the IAS machine; Life, played by hand

Source: Berto and Tagliabue, ‘Cellular Automata’, Stanford Encyclopedia of Philosophy

Address: /trees/simulations?n=m-ca

Metropolis algorithm (1953)

Metropolis, the Rosenbluths and the Tellers sampled the equilibrium states of interacting particles. They accepted or rejected random moves using a Boltzmann weight, and ran it on the MANIAC for two-dimensional hard disks. The method now underlies simulation across physics, statistics and biology.

Built on: Monte Carlo method; Electronic computer

Led to: Hard-sphere fluids; Lattice gauge Monte Carlo; Feynman’s quantum simulator

Source: Metropolis, Rosenbluth, Rosenbluth, Teller and Teller, ‘Equation of State Calculations by Fast Computing Machines’, J. Chem. Phys. 21 (1953) 1087

Address: /trees/simulations?n=m-mcmc

Molecular dynamics (1957–1959)

Alder and Wainwright used fast electronic computers at Livermore to integrate the classical equations of motion for several hundred hard spheres. They found evidence of a fluid-solid transition. Monte Carlo samples configurations. This followed the particles through time instead, which gave access to flow, diffusion and relaxation.

Built on: Electronic computer; Numerical integration

Led to: Learned surrogate models; Ab initio molecular dynamics; Protein dynamics

Source: Alder and Wainwright, ‘Phase Transition for a Hard Sphere System’, J. Chem. Phys. 27 (1957) 1208

Address: /trees/simulations?n=m-md

Agent-based models (1971–1996)

Schelling’s 1971 housing model gave each agent a local rule and let a pattern emerge. Reynolds’s boids (1987) and Epstein and Axtell’s Sugarscape (1996) did the same on a computer, with many different agents. The approach builds a whole from the decisions of its parts. That’s how crowds, markets and societies entered simulation.

Built on: Electronic computer; Cellular automata

Led to: Artificial stock market; Sugarscape; Artificial Anasazi

Source: Epstein and Axtell, Growing Artificial Societies: Social Science from the Bottom Up, Brookings Institution Press / MIT Press (1996)

Address: /trees/simulations?n=m-abm

Neural networks (1986)

Rumelhart, Hinton and Williams described backpropagation. It adjusts the connection weights of a network to shrink the gap between what it outputs and what you want, and it lets hidden units form their own features. That turned networks into function approximators that can be trained. They’re the basis of the learned simulators at the top of every band.

Built on: Electronic computer

Led to: Learned surrogate models

Source: Rumelhart, Hinton and Williams, ‘Learning representations by back-propagating errors’, Nature 323 (1986) 533–536

Address: /trees/simulations?n=m-neural

Learned surrogate models (2007)

Behler and Parrinello trained a neural network on density-functional energies. It then described the potential-energy surface of silicon several orders of magnitude faster than the quantum calculation it copied. Replacing an expensive simulation with a learned approximation is the step that later reached protein structure, weather and interactive worlds.

Built on: Neural networks; Molecular dynamics

Led to: Learned protein structure; Generative agents; Silicon samples; Learned weather forecasts; GameNGen; Genie 3

Source: Behler and Parrinello, ‘Generalized neural-network representation of high-dimensional potential-energy surfaces’, Phys. Rev. Lett. 98 (2007) 146401

Address: /trees/simulations?n=m-learned