Plotting the Future

Creating a plausible future history is such a daunting task that most SF authors don't even bother to try. The future history page suggests many rules-of-thumb and shortcuts, but it is still a lot of work. Wouldn't it be nice if one could automate the process?

This is an area which has not been explored in any detail, but is not totally without any trailblazers. Who knows? You might be the one to make a real contribution in this field. A computer spread-sheet that calculates graphs plotting historical trends would be a major help. But the ultimate tool would be some sort of computer program that is an SF Future History Generator.

I gave a very simplistic example of modeling future history on this page.


There is a more complicated but more entertaining way to create a future history: Simulation. This is not strictly automation, but it is easier to just making everything up.

Role Play

There was a (sadly defunct) game company called Game Designer's Workshop. For their hard-SF role playing game 2300 AD, they needed a future history. So they simulated it with a game, the so-called "Great Game." A team of expert players was each assigned one nation and the game was played until the time reached 2300 AD. The events that occurred were recorded, and became the future history.

An overview of the rules and the game map can be found here. The actual rules to the game can be found here.

The same simulation technique is being used to create the future history behind the game Attack Vector: Tactical using a starmap.

A more cinematic but powerful method is to use the role-playing game Microscope to create your future history time line. With this game, the players generate their history fractally. It is an innovative and surprisingly effective technique. You can read more about how to use it to generate your future history here.

Reviews are here and here. The game is played with index cards on a table, but there is an iOS app Microscope Journal.


More recently, a gentleman named Steve Walmsley has created a computer based game called Aurora. On the surface it is just another game where players vie to create the largest interstellar empire. But the game's purpose is to provide an environment in which the players can build detailed interstellar empires and write associated fiction.

If you are interested, go to the Aurora forum, register, and you will be allowed into the download forum.


John Barnes Model

The best guide to calculating history that I've managed to find is John Barnes' How to Build a Future. Dr. Barnes stated in the essay that his imagination is not up to creating an entire future history from scratch, so he uses spreadsheets to plot trends for inspiration. He goes into great detail about the theory behind the forecasts, but leaves the gathering of hard data to feed into the forecasts as an exercise for the reader. After all, Dr. Barnes does not want to make it easy for any other authors to compete with him.


…Assuming that interstellar colonization would be a relatively low priority for future civilization (important for prestige or PR, perhaps, but not truly vital), how long before colony ships would be cheap enough to represent little or no strain on the global budget? That would mark the beginning of a plausible colonization era.

Where physical worldbuilding uses equations, social worldbuilding generally must use models. A model, technically, is a “system state vector” (a set of numbers, like population, growth rate, GNP, economic growth, and per capita income, that characterizes the system at one moment in time [say 1989]) plus a “transformation rule” for calculating a next vector in the same format (“multiply the growth rate by the population and add it to population to get new population,” “divide GNP by population to get per capita income,” etc.). By applying the transformation rule over and over, you can project a set of values indefinitely into the future.

To do modeling, I usually set up a spreadsheet (a columnar pad, for the rare Analog reader not yet computer-initiated). Each row is a system state vector, the values for one time period; each column is a social variable of interest. The cell formulas are the transformation rule. The values of social variables are calculated partly from present-day, and partly from lagged (previous period, next row up) values of other social variables. You simply record the initial state of the world in the first row, set up the cell formulas to calculate the next row, and then generate more rows until you reach the desired year.

Initially I just wanted a quick-and-dirty estimate of the earliest quarter century in which a colony starship might reasonably depart Earth, so I set up my spreadsheet with one row equal to twenty-five years.

I started forward from 1985 with the following assumptions:

1. The fully loaded ship, exclusive of fuel, masses about 330 million kg. (60 percent of the size of the biggest present-day oil tankers). Dividing by 25 percent gives 1.33 billion kg of mass at launch, so 1 billion kg of fuel are required (regardless of destination because the ship travels ballistic most of the time).

2. GWP (gross world product, the annual total value of all production and services worldwide) grows at a conservative 2.5 percent indefinitely. (This and other unattributed specific numbers are either found, or calculated from values found, in the 1989 World Almanac. There are better and more esoteric sources of numbers, but you can do just fine with that one simple source.) Working in increments of twenty-five years, that’s about 85 percent per iteration.

3. The starship is a government venture. As Earth continues to industrialize, the public/ private mix, and the growth of the public sector, will tend to approximate those of the Westem democracies of today.

(If you think that’s a whopper of an assumption, you’re right. Feel free to play around with drastically different values.)

Right now the average size of total government budget among Western democracies is about 37.9 percent of GDP (gross domestic product—GNP without foreign trade, to more accurately reflect the actual size of a national economy) and the public sector claims an additional 7 percent per twenty-five years (Heidenheimer, Heclo, and Adams, page 173). We might simply figure a future date at which the government budget becomes 100 percent of GWP, but I chose to assume that the private sector is actually losing 10 percent share per twenty-five years. Thus the private sector dwindles but does not disappear (in fact it continues to grow in absolute terms—just more slowly than government.)

4. The first colonizing starships will be built when one of them represents one half of one percent of five years of global government budgets. Modern nations rarely pursue non-vital projects of more than five years’ duration, and one half of one percent of total government budget is about two-thirds the proportion of all federal, state, and local outlays going to NASA, and thus a conservative estimate of what the future civilization might find a sustainable funding level.

5. Fuel is the cost bottleneck. (A century or more of unmanned or small-crew exploration has developed the necessary technology.) This seems especially credible because the fuel converts to five million times present American annual energy production.

6. The price of energy remains constant. Energy price automatically sets a boundary on fuel price because the price of any fuel must lie between the price of the energy it will yield, and the price of the energy it takes to obtain it—below that range, none will be made; above, it will be too valuable to burn. I assumed starship fuel (antimatter or balonium) could be produced from electricity with perfect conversion, so it cost exactly what electricity did—good enough for the one-digit-or-so accuracy needed. For greater precision, I’d have had to specify a fuel-to-energy conversion efficiency and an energy consumption per unit fuel made, and calculated prices based on those.

Given a starship budget and a price of fuel, I just put a column for "starships per year” (annual starship budget divided by the price of one billion kg of fuel) on the modeling spreadsheet, and scanned down the sheet to see where it exceeded .2; that date plus five years would be a good figure for the first launch.

Unfortunately, with energy prices at present levels, launch year came to 3165. From past experience, that’s much too far into the future to model at all, not to mention being extremely discouraging.

To get out of that situation, I added more balonium to the technology mix. I came up with the “Von Neumann powersat” of “VNP”—a space-borne electric power plant that puts out fifty trillion watts and reproduces itself every eight years. Whether VNPs are solar, nuclear, antimatter generators, or balonium transformers didn’t matter to me any more than it usually matters to a mainstream author whether the electric power in his fictional house comes from hydro or coal. If it were relevant to the story, I’d simply work up some specific physical rationale to fit those economic parameters.

So this gave me a new Assumption 6, to replace the one above:

6. Sometimes in the early 2000s the first VNP is constructed; within a few decades, their rapidly growing population is virtually the whole electric production for the solar system.

VNPS increase about eightfold every quarter century. GWP increases 1.85-fold in the same time. Demand for electricity is roughly a function of the square of national GDP, so presumably that means demand is going up (1.85)2 = 3.24 fold per quarter century at the same time supply is increasing eightfold.

In the very long run—and in twenty-five years you can modify machines, homes, practically anything—you can use an almost infinite amount of electricity if it’s cheap enough. Assuming society holds growth in its electric bill at the same proportion of total expenditures, then, every twenty-five years the planet is buying 8 times as much electricity for 3.24 times as much money. Or, to the one digit of accuracy we needed, the VNP causes price of electricity to halve every twenty-five years.

Under the new assumptions 2285 began the quarter century in which launching was feasible. Humankind’s first interstellar colony would be launched in 2290.

Three centuries is still a very long way into the future—think back to 1690—and that’s just the beginning of the colonization era. Since the idea I started out to work on pretty much demands that other solar systems have been colonized for some centuries, it takes a while to build and launch hundreds of starships, and it might take as much as eighty-five years travel time to some of the colonies, the date of the story is still further away from the present than any reasonable ability to extrapolate. (My experienced-based general rule is that five hundred years is the absolute maximum.)

I didn’t want the world to get utterly unrecognizable (though that might make another good story), but clearly I would need a reason why it wasn't unrecognizable. I decided to add an event to the background: at or around the time the colony ships are leaving, for some reason or other, the global human culture decides change in general is bad, and begins the Inward Turn (a period like the Enlightenment or Renaissance). There will be much refinement but little new development after A.D. 2300.

Such things have happened. The familiar case is Tokugawa Japan, but China, Persia, and India have done similar things at times, and the tendency was clearly there in other cultures (e. g., Dark Ages Ireland, fourth century Rome). So it’s a reasonable human possibility.


…What triggers the Inward Turn? We need to have some major event happen three hundred years from now, give or take fifty. What could it be?

If I already had a clear picture of the society of 2285, I might simply make up a shock to impose. Since I don’t, I’ll develop the society first. Because good social models tend to be unstable, there may be a big enough shock occurring “naturally” near the desired date.

For this projection, I calculated annual values of the social variables, giving a more elaborate fine structure, because the social event I was looking for would lie somewhere in the rich detail of history. I’ll discuss only the seven variables that gave me a result I would use for the story, but I actually modeled more than forty variables. (Like photographers, modelers have to shoot a lot more pictures than they keep.)

We’ll start with the economy, taking Woodward and Bernstein’s advice—as good in the social sciences as it is in investigative journalism—to “follow the money.” It also happens to be a good example of cyclic phenomena.

Economic Cycles
Hansen 1
(Juglar cycle)
Hansen 2
(Kitchin cycle)
Cycle Length45–60 yrs15–25 yrs7–11 yrs3–5 yrs
Cycle Length
54 yrs18.3 yrs8.3 yrs3.5 yrs
Quarter Cycle
13.5 yrs4.575 yrs2.075 yrs0.875 yr
Cycle Start
+¼ cycle
1930 to 1939
+¼ cycle
1930 to 1939
+¼ cycle
1930 to 1939
+¼ cycle
Cycle Start
+¼ cycle
+¼ cycle
+¼ cycle
Making own
+¼ cycle

The major cycles in economic growth rate are the Kondratiev (54 years), Kuznets (18.3 years), Hansen 1 (Juglar cycle) (8.3 years), and Hansen 2 (Kitchin cycle) (3.5 years). The error bars on those times are so wide that you can arbitrarily flex values plus or minus 10 percent. (Kondratiev: 45–60 years, Kuznets: 15–25 years, Hansen 1: 7–11 years, Hansen 2: 3–5 years)

There are cycles in the rate of growth, not in the actual size of the economy itself. You can take growth of GWP as varying from 1 percent to about 6 percent annually (postwar values for industrial nations except for peculiar cases like japan and Germany during postwar reconstruction) with the average at around 3.8 percent; or, taking data going much further back in history, you can assume annual economic growth can fluctuate between -3 percent and +9 percent, with an average of around 2.7 percent. I chose the smaller range.

The effect of each cycle is about 1.8 times as large as the effect of the next shortest—thus the Hansen 1 is 1.8 times as big, the Kuzents 1.82 =3.24 times as big, and the Kondratiev 1.83 = 5.83 times as big as the Hansen 2. (these are called "coefficients")

I usually just use a sine wave with a period equal to the length of the cycle.

First pick a year when the cycle “troughed”—went through a minimum. The year 1795 seems to have been the last four-cycle trough, but all cycles except the Kondratiev seem” to “reset” during very deep depressions, so you might arbitrarily pick three years during the 1930s for the Kuznets and Hansen troughs.

The trough will be one quarter cycle before the start of a new cycle, so you add one quarter of the period to that year, and now you have the zero year for that cycle (e.g., Kondratiev trough at 1795, period is 54 yrs, so zero year is 1795 + (54/4) = 1808.5).

For the economic cycles (of a newly colonized planet, not Terra), I suggest (instead) starting the Kondratiev wave with its minimum value on the landing date, the Kuznets cycle whenever you think they’d start putting up buildings, the Hansen 1 cycle at the point where they’d be setting up factories, and the Hansen 2 cycle whenever they’d start making their own goods rather than living on what came in the ship, because the three shorter cycles are traditionally identified with building (infrastructural investment), physical capital (fixed investment), and inventory investment (inventory, e.g. pork cycle). (Kondratiev wave is identified with technological basis) (don't forget to add a quarter of a cycle)

For the value of each of the four cycles at all future dates, then:

Cycle_value = sin ((Current_date - zero_year) / (Period / 2π))

(ed note: Basically the equation is generating a sine wave with a cycle time equal to Period. So Period is 54 years for Kondratiev, 18.3 for Kuznets and so on. zero_year is the year zero for that cycle: 1808.5 for Kondratiev, etc.

A sin(x) function creates one cycle per full circle for reasons I'm not going to try and explain, but are taught in Trigonometry 101 class.

Here the sin(x) function is expecting "x" to be in radians, as most spreadsheets and computer programming languages do. That's why the period is divided by 2π, the number of radians in a circle. If your sin(x) uses degrees, you'd divide by 360 which is the number of degrees in a circle.)

Total_cycle_value = sum of all four cycle_values times their respective coefficient (those powers of 1.8) (e.g., mutiply Kondratiev cycle_value by 5.83, Kuznets cycle_value by 3.24, etc.)

Growth = average_growth + k(total_cycle_value), where k is a normalizing constant, a simple fudge factor to make the results come out within the range of growth you’ve selected.

The value of GWP in year Y is then simply:

GWPY = GWPY-1 * (1 + growth_rate)

(ed note: where GWPY is value of GWP in year Y and GWPY-1 is value of GWP in previous year)

As you can see in figure 1, in the next three centuries the growth rate flexes all over the place, but in the long run of history what we see is simply the same explosive growth that has characterized the last century or so. By the time of the Inward Turn, everyone is a lot richer. But what is available for them to buy?


I need not tell an SF audience that technological advance has dramatic effects. There are a lot of different ways to model it; this time I used the “shopping list” approach—gadgets are invented at a steady rate, but they are economically deployed (that is, come into actual widespread use) in bursts. Schumpeter suggested deployment might correlate with the upswing in the Kondratiev wave; it’s also a truism that war brings rapid technical development.

To express this, I simply assume significant new inventions go onto a “shopping list” or “technological backlog” of potential technology, and move off the list and into real deployment at a rate that varies between 0 and 100 percent, depending on the Kondratiev cycle value and the values of warfare indicators (see below).

As you can see in figure 2, this gives a fairly credible situation: technology sometimes stagnates as nothing new is deployed for a long time, and at other times skyrockets, especially after a long hiatus. This gave me as much information as I really wanted: eight major surges of technological innovation between now and the beginning of interstellar colonization. (A “major surge” is something on the order of the highly innovative periods 1900-20 or 1940-65.)

To envision the surges, I use a general rule that has no justification other than gut feeling. Each new surge is 90 percent what you might have expected from the last one, plus 10 percent magic (in its Clarke’s Law sense). So from the viewpoint of 1920, 90 percent of the gadgets of the (roughly) Manhattan Project through Apollo Project boom would be imaginable (indeed, some, like TV, were abortively available in the previous boom). But 10 percent (lasers, nuclear power, transistors) would be absolutely incomprehensible—magic.

I further arbitrarily assume that the major discoveries for the next surge have all been made as of today.

The graph shows a major surge in the 2000s and 2010s, Surge Zero, which should deploy everything in SF that seems pretty likely right now. Everything.

Does that feel like a real explosion in the brain, like Bruce Sterling or William Gibson at their dazzling best? All the same it’s only the start.

Surge One must be an immense extension of everything in Surge Zero, plus a 10 percent addition of things that work according to as-yet-undiscovered principles. Surge Two must be extensions on everything in Surge One (including the 10 percent of magic) plus 10 percent new magic. From our viewpoint it’s now 19 percent magic.

And Surge Three … well, you see where this gets to. Since the Inward Turn starts at the end of Surge Seven, 52 percent of significant new technology in the culture we’re imagining must be stuff we currently would not find comprehensible.

Realistically, the world should be half magic. Who’d have thought calculations, the lifeblood of hard SF, could drive us that far into fantasy?

Magic Percentage
% Magic010192734414752576165697275


Since we’ve already been through the business of setting up cycles, I’ll just mention that there are four prominent cycles in the (Wheeler) Index of International Battles, of lengths 142, 57, 22, and 11 years, in battles per year. (Any separable clash of armed forces between competing sovereignties is a “battle.”)

57 year cycle
Use horizontal scroll bar to pan the graph. Yes, I know there is a gap in the center, sorry about that.
22.2 year cycle
Use horizontal scroll bar to pan the graph. Yes, I know there is a gap in the center, sorry about that.

The same cycles apply to “battle days per year.” Each day contains as many “battle days ” as it does battles—so that, for example, if ten distinct battles go on for ten days duration, that’s a hundred battle days.

Like the economic cycles, the longer the cycle the bigger its effect, but it’s not quite so pronounced, and one-digit accuracy is about as far as I can comfortably go, so I suggest coefficients of 3, 2, 2, and 1 for those cycles.

Estimates on actual numbers of battle days per year vary wildly; all sorts of international, defense, and peace organizations publish estimates, and no two are even remotely close to each other. (The problems include defining when a battle starts and stops, which incidents are big enough to be battles, and how separated things must be to be separate battles.) Thus there’s no good guidance on what the numbers actually should be.

Once again flying by the seat of my pants, I simply estimated a range. In all of human history, I doubt there’s been a day of peace—somewhere on the Earth, two military forces were probably fighting each other on every day of history. So an absolute minimum would be four hundred battle days per year (one-digit accuracy, again).

On the maximum side, the most battles probably occurred either during the nineteenth-century European colonial conquests or during World War II. There were eight major European colonial powers, and most of them were fighting one insurrection or another most of the time. Add in the American Indian wars, and assume the larger British and French empires were usually fighting two insurrections at once, and you get eleven battle days/day.

In World War II, counting four Allied fronts against Japan and five against Germany/Italy, plus partisan activities in occupied areas, and counting each front as a battle day every day, we get eleven battle days/day.

Either way it comes to about four thousand battle days per year, which is obligingly one order of magnitude greater.

After about 1900, the percentage of global population killed in war per annum is an exponential function of the number of battle days. (This is just something I’ve found in playing with UN and various other statistics. It’s purely do-it-yourself social science and comes with no institutional pedigrees, so if you don’t like it please feel free to cook up your own.)

Again, I set this up as a function that would flex between a minimum and a maximum. According to UN figures, in a very good year only about 1 in 100,000 people worldwide die of something directly war-related.

About the highest figure I can conceive (excluding genuine nuclear wars of annihilation so that there will be a future to write about) is that a twenty-year war might kill half the global population. That’s about an order of magnitude worse than World War II, which, if you extend to include the Sino-Japanese, Ethiopian, Spanish, and Russo-Finnish wars leading into it and the many aftershock wars (Greece, Malaya, Korea, China, Ukraine, Palestine, etc.), killed around 5 percent of the global population between 1931 and 1952. So the global fatality rate varies between .00001 percent and 3.4 percent per annum, as an exponential function of battle days.

Wars are allegedly about something or other. We aren’t interested in every little brushfire conflict, of course, and neither will our descendants be—when was the last time you heard anyone refer to the War of the Pacific, Queen Anne’s War, or Prussian-Danish War in passing, and expect you to follow the reference? But the two really heavy periods of fighting that appear in the three hundred years should have some global significance.

In the theory of international competition, the classification “great power” comes up frequently. I like a modified version of Kennedy’s definition: a great power is, first, a nation that can, if it has the will, militarily enforce its wishes on any other nation not classified as a great power, and on credible alliances of non-great powers; and second, a nation that is able to make conquest by any other great power too painful for the aggressor to contemplate.

If you apply those rules the way I do, there are five great powers in the world today: the United States, Japan, the Soviet Union, China, and the European part of the NATO alliance.

Great powers come into being from sustained periods of economic growth. Major wars against other great powers produce very high death tolls and economically ruin great powers, busting them back to secondary status, sometimes permanently and often for decades.

The great powers normally get and consume the bulk of the world’s wealth, so an ambitious secondary power needs a generation—twenty-five years—of fast world growth to rise to great-power status. Success for one rising power precludes anyone else’s success. There are finitely many resources, power vacuums, and unclaimed turf in the world, and the secondary power that gets all or most of them is the one that becomes a great power---while shutting out everyone else, so I also allowed only one new great power to emerge per decade.

To express the way wars between great powers quickly knock them down the scale, I assumed that if annual global war deaths exceed 1 percent, twice their WWII value, all the great powers must be involved. I expressed this as a simple fraction--every time war deaths went over 1 percent, I busted three-eighths of the great powers (to the nearest integer) to secondary status. Thus a three- or four-year war at those historically unprecedented levels is enough to break all the great powers in the world.

The numbers of great powers, along with war deaths, are shown in figure 3. There are two truly big wars in this future—World War III and IV, let us cleverly call them—and the starship launches come right when a second power manages to lurch up to great powerhood again. Normally that would be time for another war … so why not this time?

Let’s look at population statistics. (This stage of the creative process approaches sex, like violence, in terms of its quantitative results, rather than its messy particulars.)

How many people are there in 2290, and where do they live?

The results of the model can be seen in figure 4.

Virtually all the growth of population in the long run comes from rural populations. This is caused by something that always startles elitists: people are not stupid. Agriculture is labor-intensive, and as long as an additional person can produce food in excess of its consumption, it pays to have another baby. (Famines are generally caused by a drastic change from the expected future—war, drought, or land confiscation changes the value of children after they’re born.) In most parts of the world, the expected value of children doesn’t reach zero right out to the limit of human fertility.

By contrast, life in cities is expensive, and work children can do there is less valuable, so having kids really doesn’t pay. Thus over the long run (it takes time to alter perceptions, and peasants who move to the city don’t suddenly de-acquire children), city dwellers will have children at or below a replacement rate and rural people will have all they can. “All they can” globally currently corresponds to a global rural population increase of about 2.3 percent per year.

Luckily, practically everyone would rather live in the city. (The American back-to-the-land fetish is an extreme minority taste.) Currently a bit under half of one percent of global population moves from country to city per year. If that continues, by 2056, the growth of rural areas has reversed, and as they decline in population the rate of population growth slows. In fact, World War IV is so big that global population actually peaks at around fifteen billion in 2237 and declines to just under eleven billion by the beginning of the colonization era. Global population is then more than 95 percent urban (as opposed to 22 percent today).

For a quick extrapolation of spaceborne populations, assume a VNP makes work for 100 people and the percentage of spaceborne population that would be working in the energy industry declines steadily by 10 percent every twenty-five years. That gives a population growth rate of 6 percent (most of it supplied by immigration at first).

By the beginnings of interstellar colonization, there are 1.256 billion people living permanently in space. Go ahead and gasp—but it’s a slower rate than the European population increase in Australia 1788 to 1900, and Australia effectively cost more to get to…


…In A.D. 2290, global population is steady at eleven billion, down 27 percent after World War IV, forty-one years ago. Practically everyone lives in town, and about 17 percent of the population lives in giant high-density towns—the equivalent of twentieth century LA or bigger. Half the technology is, by twentieth-century standards, magic. Global per capita income is about 110 times 1985 American per capita income. World War IV reduced transpoli (freaking huge cities) from seven to five, and hyperpoli (merely huge cities) from twenty-three to seventeen, well within living memory. There are many veterans, former refugees, and survivors around, and the ruins of the destroyed hyperpoli and transpoli are still in existence, raw scars visible even from the cities on the moon, visited by grieving pilgrims as Auschwitz is today. In the last few years, the hegemony of one super-power has been challenged by the rise of another, and the fear of another war is in the air.

And that seems to me enough to explain the Inward Turn. At such a moment a charismatic leader might successfully move for an effective global sovereignty. The Earth becomes a loose federation, committed to develop internally, refining and integrating its culture, bringing technical, social, and political change to a near stop, letting humanity find time to knit together. (Again, that sounds unattractive to us—but we don’t have four billion dead in a landscape of ruins, and a recent scare that it might happen again. People whose world was shattered only forty years ago might feel very differently.)

From HOW TO BUILD A FUTURE by John Barnes (1990)


This is from Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies (2014)

The paper is about making mathematical models of human societies that predict sustainability or collapse. The latter is of interest to science fiction writers using the popular Decline And Fall Of The Roman Galactic Empire background.

First off, the paper examined numerous civilizations in both the old and the new world which collapsed.

Other studies had proposed explanations for each specific case of collapse, including one or more of the following: volcanoes, earthquakes, droughts, floods, changes in the courses of rivers, soil degradation (erosion, exhaustion, salinization, etc.), deforestation, climate change, tribalmigrations, foreign invasions, changes in technology (such as the introduction of ironworking), changes in the methods or weapons of warfare (such as the introduction of horse cavalry, armored infantry, or long swords), changes in trade patterns, depletion of particular mineral resources (e.g., silver mines), cultural decline and social decadence, popular uprisings, and civil wars. The paper found these to be a distraction because A) each were specific to a particular case of collapse instead of general causes common to all collapses, and B) many of the civilizations had previously experienced the phenomenon identified as the collapse cause WITHOUT collapsing.

For instance, the Minoan civilization had suffered many earthquakes but simply rebuilt their cities even more splendidly. What was so special about the final earthquake that destroyed their civilization?

Additionally since civilization collapse in prior cultures is so universal, the causes must be similarly universal. The cause must not be specific to a particular time period, culture, technology, or natural disaster. So they based it on the classic predator-prey model.


They call their model HANDY (Human And Nature DYnamics).

The study authors are not saying this is a highly accurate model. What they are saying is this is a simple model or general framework that allows scientist to carry out thought experiments of collapse, and to test changes that would avoid it.

The key parameters are:

  1. the stretching of resources due to the strain placed on the ecological carrying capacity
  2. the economic stratification of society into Elites and Masses (or “Commoners”)

They cite quite a few other papers to justify these two parameters, refer to the actual paper for details.

While based on the predator-prey model, the inclusion of two societal classes allows a richer set of dynamic solutions, including cycles of societal and ecological collapse, as well as the possibility of smoothly reaching equilibrium (the ecological carrying capacity). Carrying Capacity is defined by the study authors as the population level that the resources of a particular environment can sustain over the long term. They call the environment resources “Nature”.


  • xC = population of commoners
  • xE = population of elites
  • φ = xE/xC = starting ratio of elites to commoners, at beginning of scenario.
  • s = subsistence salary per captia
  • κ = factor that elite's salary per capita is bigger than subsistence
  • y = natural resources or Nature
  • w = accumulated wealth (surplus resources stored for a rainy day, mostly in the hands of the elites)
  • ρ = minimum required consumption per capita, below which is starvation
  • wth = ρxC + κρxE = threshold value for wealth below which famine starts.
  • CC = min(1, w/wth)sxC = consumption of the commoners
  • CE = min(1, w/wth)κsxC = consumption of the elites
  • βC = birth rate of commoners
  • βE = birth rate of elites
  • αm = normal (healthy) death rate
  • αM = maximum (famine) death rate
  • αC = αm + max(0, 1-(CC/sxC))(αM - αm) = death rate of commoners
  • αE = αm + max(0, 1-(CE/sxE))(αM - αm) = death rate of elites
  • γ = regeneration factor of Nature
  • λ = capacity of Nature, maximum size of Nature in absence of depletion
  • δ = rate of depletion per worker, who are all commoners. Only commoners produce

So the HANDY model differential equations are:

C = βCxC - αCxC
E = βExE - αExE
ẏ = γy(λ - y) - δxCy
ẇ = δxCy - CC - CE

Note that αC, αE, CC, and CE are all functions of w, xC, and xE.

In the HANDY model, population is in units of people, nature/wealth are in units of "eco-Dollars", and time is in units of years. "Eco-dollars" are a combination unit created due to the fact that the structure of the model requires nature and wealth to be measured in the same units.

Model Description

The total population is divided between xC and xE, the population of commoners and elites. The population grows through birth rate β and decreases through death rate α. While β is the same for both populations, but α is different since it depends upon wealth. No surprises there.

The equation for the natural resources of nature ẏ = γy(λ - y) - δxCy has a regeneration term γy(λ - y) and a depletion term -δxCy.

The bit (λ - y) in the regeneration term means the regrowth is exponentially huge when y is a tiny fraction of &lambda, but regrowth rapidly slows down as y approaches λ. The maximum rate of regeneration is when y = λ/2.

The depletion term models the reduction in natural resources due to pollution as well as consumption. δ is the rate of depletion per worker, xC is because all workers are commoners. The elites are all in executive, management, and supervisory jobs; they don't actually produce anything. Heaven forfend that they get their hands dirty.

The equation for wealth ẇ = δxCy - CC - CE has wealth increasing with production δxCy, and decreases with the consumption of the commoners and the elites CC and CE.

Note that the consumption of the commoners equation CC = min(1, w/wth)sxC means that they are all being paid a bare minimum subsistence salary per capita s. And that is only if there is enough wealth to pay them, that's the min(1, w/wth) part.

The elites pay themselves min(1, w/wth)κsxC, that is, their salary is κ times larger than the subsistence salary the commoners have to make do with. The rich get richer while the poor get poorer, which again is no surprise.

However this does mean that when the wealth becomes too small to support this consumption (w < wth), the elites will suffer a higher rate of death than the commoners. Offsetting that is the fact that even after the commoners start experiencing famine, the priviledged elites will still be consuming at the higher rate κ.

Actually κ represents the factors that determine the division of the output of the total production of society between elites and masses, such as the balance of class power between elites and masses, and the capacity of each group to organize and pursue their economic interests. The HANDY model currently has κ as a constant in each scenario. The study authors are going to explore having it determined exdogenously by other factors in the model.

The death rates αC = αm + max(0, 1-(C/sx))(αM - αm) vary between a normal heathy value of αm when there is plenty of food, and a maximum famine value of αM when everybody is starving to death. Note that by "famine" the model also means such things as emigration, increased disease susceptibility, breakdowns in social order, banditry, riots, rebellions, revolutions, and wars. Also note that an increase in death rates might actually be a decrease in birth rates. In any event, "famine" means "a reduction in population when it exceeds the environmental carry capacity."


The report studied several scenarios in different types of societies. The society types were:

  • EGALITARIAN SOCIETY: no elites. xE = 0, κ is not used
  • EQUITABLE SOCIETY: there are both elites and commoners. However, the pay is equal. xE ≥ 0 but κ = 1
  • UNEQUAL SOCIETY: the sadly common kind. There are elites, and they get more pay. xE ≥ 0, κ > 1

The report found two types of collapses:

TYPE-L (Disappearance of Labor) collapse due to a scarcity of labor following an inequality-induced famine.

In this type of collapse, the growth of elite population strains the availability of resources for the commoners. This causes a decline of the commoner population. Since the commoners do all the labor and creates all the wealth, there is a decline of wealth. Eventually the wealth declines to the point where the elite population plumets as well.

Example: the disappearance of the Mayan civilization in the Yucatan.

This type of collapse can only occur in an Unequal Society because the root cause is inequality.

TYPE-N (Exhaustion of Nature) collapse due to a scarcity of Nature, depletion of natural resources.

In this type of collapse, it all starts with an exhaustion of Nature, followed by a decline of Wealth, which causes a decline of the commoner population, and eventually the decline of the elites.

Depending upon the depletion rate, a Type-N can be "reversible" or "irreversible." In the former case, regrowth of nature can trigger another cycle of prosperity. In the latter case, if the depletion is pushed beyond a certain limit, Nature fully collapses and the entire society follows. The paper calls an irreversible Type-N collapse a "full" collapse.

Examples: reversible Type-N, the Greek and Roman collapses. irrevrsible Type-N, Easter Island.

Egalitarian Society

Equitable Society

Unequal Society

Michael Flynn Model

“We have to be prepared to be surprised by the future, but we don’t have to be dumbfounded."
Kenneth Boulding

Has the Great West African War already started‘? How many race riots will the U.S. experience during the outbreak of 2010 A.D.? How many orbital factories will go bankrupt during the Recession of 2033? Is the imminent breakup of everything together; but researchers in fields ranging from ecology to differential topology have already laid the "Foundations. ”

“But the curves, if they meant anything at all, included free will . . . Every morning three million ‘free wills’ flowed toward the center of the New York megapolis; every evening they flowed out again—all by ‘free will,’ and on a smooth and predictable curve."

Robert A. Heinlein (“The Year of the Jackpot”)

Psychohistory is an attempt to understand the forces driving human history and to express them in useful mathematical terms. ln short, to replace anecdote with analysis. Specifically, we want to formulate laws regarding: 1) the internal structures of different societies; 2) their geographical relationships; and 3) their dynamics over time. (Books purporting to psychoanalyze historical figures have been dubbed “psychohistory” by the literati, but this is not the science we mean here. Psychoanalysis is a religion, not a science. That is, its premises cannot be proved false by any objective evidence and must be accepted on faith.)

This bare statement is enough to trigger cries of outrage. Science is dehunanizing! We need less of it, not more! Laws of history are impossible because people have free will! Besides, human societies are too complex for scientific analysis!

But are these objections valid? Science is the process of discovering the material causes of measurable phenomena. As such, it is de-mystifying rather than de-humanizing. If conditions like war and poverty have material causes, they can only be corrected by attacking those causes, not by “wishing them away” with good thoughts. At any rate, as anthropologist Marvin Harris observes, the study of culture is not currently suffering from an overdose of the scientific method.

As for free will, freedom is the opposite of compulsion, not of causality. A free choice is not an unreasonable one. That is, it has reasons—or causes —that could be summarized in the form of a law. A scientific law is a description, not a cause, of phenomena. A law of history could no more compel you to behave a particular way than an actuarial table compels you to die.

The complexity of human society only means that laws of history could be hard to find, not that they don’t exist. Certainly, many of the examples cited in this article are simplistic; but “simplistic” needn’t mean “wrong.” Even a simplified analysis can be illuminating. At this stage, no one expects to write down a single, all-encompassing system of differential equations describing every facet of society. After all, the physicists have yet to solve the general three-body problem. A mathematical, scientific approach to culture is just beginning.

Psychohistory is a broad subject, and we can’t cover it in depth here; but we can take a look at some of the highlights of this emerging science.

Scientific laws are statistical laws. They deal with the overall tendencies of large groups. Nuclear physics does not predict the fate of every neutron; nor organic chemistry“ that of every molecule. In the same way, predicting an individual’s behavior is a practical impossibility, meaning it is impossible as a practical matter to identify and measure all the factors that influence it. However, in large groups individual variations can cancel out, producing regularities or patterns. Thus, the average behavior of a group may be predictable, even though that of the individuals in the group is not. That’s what keeps casinos and insurance companies solvent.

Let’s look at a few examples of pattems and regularity:

1. U.S. Slave Revolts/Race Riots have been plotted in five-year increments on a Shewhait quality control chart (Figure 1). A Shewhart chart is a statistical tool that distinguishes between random fluctuations, inherent in the system, and non-random fluctuations, caused by disturbances to the sys- tem. The dotted line is the upper probability limit for a stable Poisson process. This is the same process used to model the emission of radioactive particles. We see that the U.S. has “emitted” riots/slave revolts at the rate of λ = 0.29 riots/year for the last 170 years. This average is “built into" the U.S. cultural system. Peaks occur every other generation. The regularity of these peaks indicates a second structural cause. (Of course, it's easier to blame the riots on the rioters. But that's like blaming the thunderstorm on the thunder!)

The persistence of the pattern shows that Emancipation did not fundamentally alter the position of blacks in American society; and (unless the Civil Rights Movement did change the system) that we can expect the next peak around 2010 A. D.

2. U.S. Birth Rates have declined linearly since at least 1820, with Boom and Bust cycles snaking their way around the trendline (Figure 2). The recent “Baby Bust" and the new Baby Boomlet, signaled by the chart in 1979, are only a continuation of this trend. (By the way, notice that the “post war” Baby Boom started before the war.) The usual reasons given for declining birth rates (The Pill, legalized abortion, women’s lib) cannot explain this pattern. What natural force is at work here?

3. U.S. Homicide Rates have only recently returned to the peaks achieved in the 1930s, when executions were common (Figure 3). Do executions (or the lack of them) cause the homicide rate to change? Or do changes in the homicide rate cause people to demand executions? Which is the cause; which, the effect?

4. U.S. Economic Cycles, plotted by Dewey and Dakin in 1945, accurately forecast the recent recession, back on an S-shaped growth curve (Figure 4b). Seemingly chaotic patterns can often be decomposed into several of these simpler ones, each being the reflection of a basic law. (The 54-year Kondratieff cycle has been traced, in British wheat prices, back to 1240 A.D. Obviously, the root cause cannot be the policies of particular presidents. Yet every time the economic indicators jump up and down, so do the Economists as they “explain” The Cause or, more importantly, Fix the Blame.)

5. Half-life of Ideas. There is often a lag of five generations (ca. 137 years) between the establishment of an idea in a society and the reaction to it (Figure 5). For example, Toynbee noted that the intelligentsia (created by Peter the Great in 1689 in imitation of the Western bourgeoisie) rose up against the Tsar in the Decembrist revolt of 1825. Similarly, the westernized Committee of Union and Progress overthrew Sultan ‘Abd-al-Hamid ll in 1908, 134 years after the Porte began Westernizing Turkey in 1774. The 1629 Charter of the Massachussets Bay Company established American colonies for the exploitation of the mother country; an idea that was rejected in the Stamp Act riots of 1765. The establishment of Orthodox Christianity as the official church of the Greek (a.k.a. Roman) Empire in 313 was repudiated in 451, when the Empire’s Syriac-speaking, Monophysite subjects rejected the Council of Chalcedon.

6. Lifetimes of Unitary States are shown plotted on Extreme Value probability paper (Figure 6). Extreme value distributions are used to model the breakdown of complex systems where failure is of the “weakest link” or “peak overload” type. Evidently, it doesn’t matter if the complex system is electrical, mechanical, or cultural. Empires have a Mean Time Before Failure (MTBF) of 160 years for the first failure. lt takes an average of 70 years to “repair” the system (MTTR), which then survives for an additional MTBF of 185 years. Of course, there is also random variation around these averages. What structural factors account for the characteristic life? For variation around that life‘?

As these examples indicate, cultural processes do exhibit “lawful” behavior. The problem, of course, is to discover the law!

History being a branch of the biological sciences, its ultimate expression must be mathematical.
Colin McEvedy

One approach is to devise mathematical equations linking various factors in the social system. We can validate such models by “postdicting”. past events. lf the model simulates Real World behavior. that is strong evidence in its favor. For example, political scientist Robert Jackman developed a model for coups d’état that correlated 92% with the actual coup frequencies among Black African states (Figure 7). The model was based on structural factors internal to each country, such as the literacy rate and the percentage of the population engaged in non-agricultural work. Similarly, Jay Forrester’s computer model of the U.S. economy produced 50+ year “Kondratieff cycles,” just like the Real World, despite the fact that Forrester and his team were unaware of the existence of such cycles when they constructed the model. The cycles resulted from the linkages between different economic sectors in the model.

Mathematical modeling lets us understand how history works, by turning our attention away from the symptoms of individual events and toward the process that produces them. One early example was Lewis Fry Richardson’s model of arms races:

Let X and Y be the belligerent behaviors of two coalitions. Each will increase in “defensive reaction” to the other. But increases will also be “damped” by economic and other constraints; so that:

dX/dt = axY - bxX + cx

dY/dt = ayX - byY + cy

Using “expenditures on arms” as a first approximation to X and Y, Richardson reported a good fit to the arms races that preceded World Wars I and II (Figure 8). The stability point of this system (if it exists) is dX/dt = dY/dt = 0, a bilateral freeze. But notice that such a freeze cannot be imposed on the system at any arbitrarily-chosen point (X,Y). Rather, it occurs naturally at a particular point determined by the values of the a, b, and c parameters. (Unfortunately, there is no guarantee that war will not break out before the stability point is achieved. In fact, if anyone knows of an arms race that did not end in war, I would be glad to hear of it!)

In his book, Looking at History through Mathematics, pioneer psycho-historian Nicholas Rashevsky showed how the mathematical techniques of the hard sciences could be applied in principle to such historical processes as village and class formation or the “kinematics of social behavior.” Transformations: Mathematical Approaches to Cultural Change, edited by archeologist Colin Renfrew and mathematician Kenneth Cooke, gives many further examples, including the uses of topological catastrophe theory, a subject to which we will return shortly.

Let’s look at some further examples of modeling:

1) Ecozones. Historian Colin McEvedy has developed a graphical technique for identifying ecozones, regions that are “attractive” to certain ways of life. He defined the “littoral ecozone” in the Mediterranean as follows: First lay a fine grid over the map and define coastal squares as those which contain a segment of coastline. Then color those land squares, a majority of whose neighbors are coastal. This identifies sites whose coastal connections outweigh their inland connections and will, therefore, be attractive to sea-going societies, such as the Greeks, Carthaginians, Venetians, or Byzantines. The ecozone concept may explain why lifestyles and customs stop spreading even when no obvious geographical barrier stands in their way. For example, the distribution of continental monasteries founded by lrish monks during the Dark Ages almost exactly matches that of the ancient Celtic Hallstatt culture. Coincidence or ecozone?

2) Settlement Formation. ls there a general process that explains how settlements are sited? If there is, it may tell us something about the success of projected lunar or orbital colonies. Robert Rosen has studied this problem. Starting with an abstract landscape and a function, α, defining the population density at each coordinate, he postulated two “forces” at work: 1) a preference for sites of lower population density, and 2) an affinity (ρ) for sites providing positive reinforcement (such as access to fertile soil, Broadway theatres, or interstellar wormholes.) McEvedy’s ecozones are examples of affinity functions. Both of these forces define gradients on the landscape: one tending to clump the population around “attractive” sites, the other tending to disperse the population uniformly, in a kind of cultural “heat death. ” When combined with the birth-death process, these assumptions produce the same formula that describes a chemical diffusion-reaction process, namely:

(Sorry! I promise not to do that too often. But this is the main reason "soft" scientists resist the very notion of a science of history!)

Isn’t it intriguing how often the same—or similar—equations appear in widely different contexts?

3. Topological Networks. The settlements generated bythe above processes form the nodes of a topological network. The nodes with the highest connectivity are likely candidates for capital cities. Georgrapher Forrest R. Pitts studied the connectivity of medieval Russian towns (which lie, of course, in the riparian ecozone). Moscow ranked second; nearby Kolumna, first. The older capital, Vladimir, was also in this region. Topologically, Petrograd was an unnatural, “un-Russian” aberration. Similarly, all the major capitals of Mesopotamia (Kish, Agade. Babylon, Ctesiphon, Seleucia, and Baghdad) are closely clustered. Only briefly was Iraq ruled from outside this small region. (Usually from Iran, and even the Achaemenid Shahs preferred Babylon to Persepolis.) A topological analysis of intemal commodity movements reveals the startling fact that there are four (or possibly five) Indias (cf. Ekistics, by C. A. Doxiadis). These are regions of relatively high population density and industrialization separated by areas of subsistence agriculture, and may represent the future political boundaries of the subcontinent.

4. Cultural Interaction. Geographers have found through empirical studies that the amount of traffic (and other forms of communication) flowing between two sites is best described by:

which they blandly call a “gravity model.” Mass is a function of population and wealth, while distance is the time and energy needed to travel between the two sites. (This concept of “cultural distance" explains why High Earth Orbit is "halfway to anywhere" in the solar system. Half the ΔV is neededjust to get that far!)

Using “nearest neighbor” analysis of Aztec-era settlements in the Valley of Mexico and the known political boundaries, archeologist John Alden derived an empirical value of k = 1.9. (Close enough to the inverse square law to cause some serious head-scratching among you physicists out there!)

He then used the model to “postdict" the unknown political boundaries of Toltec-era states. We can use the same model to determine cultural “potential fields,” including “natural” political and economic boundaries.

Applied to New York City, for example, we find that the “cultural boundaries” with Boston and Philadelphia lie just short of Providence and Trenton, respectively. At Easton, PA, New York City is nearly-three times more “attractive” than Philadelphia. (Some of you may be puzzled by the use of "attractive" and "New York City" in the same sentence. But, then, a black hole is attractive, too.)

5. Central Place Theory. Villages cannot supply every possible service. Goods offered for sale have minimum and maximum ranges, based on the distances people are willing to travel to buy (or sell) them. This gives rise to a hierarchy of central places (market towns) that, on an idealized landscape, forms a lattice of inter-penetrating hexagons called Christaller grids (Figure 9). Central Place Theory, first proposed by the German geographer Walter Christaller in the 1930s and further elaborated by August Lésch, predicts the geographic distribution of central places and the hierarchical relationships among them. It may also explain the placement of services within modern cities: Why some are scattered about (eg. gas stations), while others are concentrated (e.g. Wall Street), and still others are handled by itinerant “circuit-riders” (e.g. visiting consultants) or periodic markets (eg. Tupperware(r) parties). Many centrally-planned economic reforms fail because they unwittingly work against these natural forces. This has profound implications for Third World development.

“These things are so bizarre that I cannot bear to contemplate them.”
Henri Poincaré

There are three fundamental axioms of psychohistory:

a) Human societies are homeostatic systems. They are subject to general system laws, of which the laws of physical, biological, and cultural systems are localizations.
b) Human societies are biological populations. They are subject to ecological laws regarding production and reproduction." especially the production of food and other forms of energy.
c) The causes cultural institutions are material, not mystical.

These are modern restatements derived from what these three gentlemen originally wrote. lt may seem odd to list Adam Smith, Thomas Malthus, and Karl Marx as co-founders of anything. Ma‘rx, for example, called Malthus a “baboon in parson’s clothing” and the level of debate in the social sciences has changed very little since then. (Neither has the mutual animosity among capitalists, environmentalists, and socialists.) But, despite their respective shortcomings, all three did try to use the scientific method. ln fact, Marx’s pronouncement that cultural phenomena have material causes amounts to a simple statement that cultures can be analyzed scientifically! A scientist cannot “explain” a custom like Hindu cow love by calling it a religious duty. He must discover natural, material reasons why it became a religious duty in the first place.

A homeostatic system is one that “seeks” an equilibrium. Mathematically, we say that the system is “governed by a potential function.” A society is attracted so strongly toward its equilibrium that, even when it is disturbed, it will return to its former trajectory once the disturbance is removed (Figure 10). The set of equilibrium points is called the attractor of the system. Some attractors are fixed points, like the rest point of a pendulum; others are simple orbits, like the business cycle. However, in complex systems, we must deal with so-called “strange attractors" whose topology is not so simple. The climate, for example, is the strange attractor of the weather. (Strange attractors have nothing to do with the people you meet in singles bars.)

Rashevsky developed a mathematical model for the “kinematics of social behavior,” based upon psychological stimulus-response theory (making him truly a psycho-historian). The model predicts the number, location, and stability of the equilibrium levels; that is, the fraction of the population that will ultimately “exhibit the behavior.”

When we see (hear or read about) a new behavior we are stimulated to imitate it. The strength of the stimulus depends upon three factors: X, the number of doers (“Mom! Everyone is doing itl"), Ax the persuasive (or coercive) resources of the doers (“C’mon! What are ya, chicken‘?”), and A, the population’s innate willingness to imitate. (We won’t worry for now how to measure those last two!)

Imagine a behavior B advocated by Xo, a group of “partisans.” Another group, Yo, advocates not-B. The remainder choose either B or not-B as the spirit moves them. According to Rashevsky’s model, the equilibrium level is determined by the “coercion/imitation” ratio (AxXo - AyYo)/A. When this ratio exceeds a critical value, C*, a majority of the society will eventually adopt B. lf it is less than -C*, a majority will adopt not-B. lf it falls in between ±C*, then B and not-B are both potential equilibria. That is, the society would be attracted toward both levels; and identical conditions could cause different behavior in different societies!

Theoretically, given the number of partisans for each candidate, plus some measure of their ability to reach and persuade voters, Rashevsky’s model could forecast the outcomes of elections. Provided, that is, that the elections were free and were always held after the equilibrium was reached! Unfortunately, the latter isn’t always the case. The equilibrium level itself can change before the system reaches it! The equilibrium is determined by the parameters of the system; and the parameters themselves are variables.

Imagine a ball bearing drawn toward a magnet. Very simple laws will describe its trajectory and predict its resting place. But what if the magnet itself is moving‘? The ball’s trajectory is no longer so simple. Cultural dynamics is like that. Imagine the dynamics of a solar system in which the gravitational constant and planetary masses were changing! (Hmmmm.)

Usually, small parametric changes result in small changes in the equilibrium; but not always. Sometimes a small parametric change can cause a large, sudden change in behavior. For exam- ple, as a rubber band is stretched, it grows incrementally longer—until it passes through a singularity and snaps, a behavior utterly unpredictable by extrapolating its past growth. Societies can snap, too. Revolutions, coups, fads, economic booms & busts, technological breakthroughs. Sudden change often interrupts the path toward equilibrium (Figure ll).

Perhaps the most dramatic such changes have been the collapse of certain state-level societies, whose complex structures simplified rapidly into chiefdoms or even tribes. The collapses of the Mayan and Aegean societies were the most complete of such collapses; but the Egyptian society after the Vl Dynasty or the Graeco-Roman society in Westem Europe are also well-known examples. Could it happen here? There are also cases of equally-sudden complexification: e.g. the formation of the Saxon and Zulu kingdoms or of the Iroquois Confederacy. A smaller scale example is the collapse of passenger railroads in the U.S. Passenger miles increased and decreased in sudden “exponential epochs." What are the causes of sudden change?

We usually blame sudden change on exogenous factors: barbarian invaders, communist subversives, outside agitators, the CIA, and the like. The change is “forced” on the society by external forces. However, topological catastrophe theory, developed by René Thom, has shown that sudden change can result from endogenous factors, internal to the society (cf. Ian Stewart, “What Shape is a Catastrophe?” Analog, June, 1978).

The roots of sudden change lie in the fact that, as in Rashevsky’s model of social behavior, there are sometimes two (or more!) equilibrium levels for the same parameter values. We can visualize this situation by means of a “catastrophe surface.”

For simplicity, imagine that there are two parameters (the “control variables”). These define a plane called the parameter space. (Even in very complex situations, a relatively few control variables determine the bulk of the actual behavior.) Also suppose that there is one state variable, represented by a potential function, and express this as vertical distance above the parameter plane. For each point in parameter space there is one (or more) equilibrium state. The set of all equilibrium points forms a manifold that sits over the parameter space. This is the “catastrophe surface.” Thom’s theory states that there are only seven “elementary” surfaces. For two control variables and one state variable, that surface is called the Cusp, a sheet with a pleat, or fold, in it. Let’s look at two simple examples.

1. Collapse of State-level Societies: Archaeologist Colin Renfrew developed a cusp surface to describe the sudden collapse of early agricultural societies. The two control variables were E, the energy assigned to cultural devices used to promote adherence to the central authority; and M, the margin between productivity and taxes. The state variable is C, the “degree of centrality,” which is some measure of the information carrying capacity of the society ( No, the model is not E = MC2. That would have been cute, though ). Archaeologically, C is indicated by a Christaller grid of central places, the maintenance of bureaucratic records, flags and insignia, and so on. Let’s follow the trajectory of a typical society in Figure l2.

An egalitarian, tribal society (1), intensifies production through the urgings of so-called “big men,” and invests the surplus in the trappings of central au- thority (2). “Big men” become “chiefs,” then “kings.” Complexity increases until the State appears (3). However, population growth eventually compresses production. lt is no longer so easy to increase the per capita yield enough to support the central authority. The society is under stress (4). As E decreases slightly, the society enters a region of the parameter space called the “bifurcation set” (5). ln this region, there are two equilibrium levels for which social efficiency is maximized. However, inertia (caused by the time lags or “viscosity” of the system) keeps the society on the upper fold of the pleat (6a). Then, as the society leaves the bifurcation set, the local maximum van- ishes, and it is now attracted only by the lower sheet (6b). The society “falls” off the‘ edge of the fold. The drop will not, of course, be instantaneous, but it will be exponential.

Renfrew went on to add two more control variables (kinship and extemal threat), producing the multi-dimensional Butterfly Catastrophe, whose hypersuiface contains a pocket. The pocket in this example corresponds to stable chiefdoms, a level of social complexity partway between tribal and state organizations.)

2. Political Ideologies: E. C. Zeeman developed a cusp model of political ideologies. The two parameters, A and B, were economic (opportunity versus equality) and political (the rights of the individuals versus the rights of the group). The state space was a “cloud of points” representing the opinions of the individuals in the society. (These are measurable, at least in theory, by opinion polling.) The cloud was embedded topologically in a one-dimensional space, Y, which turned out to be the traditional left-to-right political spectrum. Zeeman‘s catastrophe surface shows why this simple line really has a complex “anatomy” (Figure 13).

Projecting the surface onto the AY and BY planes reveals why dictatorships of the left and the right resemble each other so closely, and why right-wing populists often sound like left-wingers. It also shows why some social changes must be revolutionary; and why one-party states frequently develop left and right wings within the Party.

We have seen that cultural processes are, at least in principle, susceptible to mathematical analysis and modeling. Far from being inappropriate, the tools of the hard sciences can have great util- ity here. Not the least benefit would be the translation of cultural theories into rigorous testable format, something now usually lacking in the “soft” sciences.

However, even the most sophisticated mathematics is sterile. We must also have a theory to support it. That brings us to the other two Basic Axioms, the subject of Part II.


“How many hours till nightfall?” he asked.

“About twenty." Yamashita pointed to the clock on the board, it was calibrated to Venus’ seventy-two hour day. “It's around one hundred thirty kilometers to the camp, so we should just about make it by sunset."

“That isn’t very fast," said Hollister. “Why not fly, or at least build roads?’

“The aircraft are all needed for speed travel and impassable terrain, and the roads will come later," said Yamashita. “These tanks can go it all right—most of the time."

“But why have the camp so far from the city?”

“It’s the best location from a supply standpoint. We get most of our food from Little Moscow, and water from Hellfire, and chemicals from New America and Roger’s Landing. The cities more or less specialize, you know. They have to: there isn’t enough iron ore and whatnot handy to any one spot to build a city big enough to do everything by itself. So the air camps are set up at points which minimize the total distance over which supplies have to be hauled."

You mean action distance, don't you? The product of the energy and time required for hauling.("time required for hauling" goes up as the ground becomes more rugged. It takes less time to haul along a road than it does across a swamp.)

Yamashita nodded, with a new respect in his eyes. “You’ll do," he said.

From THE BIG RAIN by Poul Anderson (1954)


I have an unhelpful note I wrote in the early 1980's that shows a tiny bit of a macroeconomic model created by Dr. Barnes using an ancient icon-based software package called STELLA (Systems Thinking Experiential Learning Laboratory) for the early Apple Macintosh. (STELLA is from Isee Systems, formerly High Performance Systems. It is quite expensive.) The note is unhelpful since I appear to have neglected to write down the magazine it was published in. The diagram shows a "Macroeconomic model long-wave generator, used as a driver for other models", and includes cryptic icons with names like Merchant Balances, Seller Deposits, Production, Consumption, Inventory, Depreciation, and other things. If anybody knows where this magazine article came from, please send me an email. (William Seney suggests that it was an issue of MacWorld, and that does ring a bell. Now to find what issue it was.)


The way I'd create a history generator is to develop a computer program that was some species of 4X computer game. These games have the primary goals of eXplore, eXpand, eXploit and eXterminate. The best known example is Sid Meier's Civilization.

So you would start with a star map of your SF universe, set up mathematical models for population growth, types of government and mechanisms for governmental change, technological advancement, interstellar transit times, colonization techniques, interstellar war and conquest, revolutionary colonies splitting from the parent empire, and interrelations between these factors. Begin with an initial population on planet Earth with however many nations you care to track, start the program, then relax with your favorite beverage as you watch it crank out your future history.

Obviously much easier said than done.


Before you can start making mathematical models, you have to settle on metrics to quantify the various factors. Here are some examples:

For nations, the state of the citizen's well-being can be measured by the Human Development Index. This factors in life expectancy, literacy, education, and standard of living into one number. Among other things it can indicate whether a country is a developed, developing, or underdeveloped country.

The economic Misery index is found by adding the unemployment rate to the inflation rate. This tends to predict the relative crime rate of one year in the future.

The Gini coefficient is a measure of inequality of a distribution of income. If the difference in income between the rich and the poor becomes too absurdly large, the society becomes increasingly unstable. Historians often point to a large Gini coefficient and the disappearance of the middle class as two of the warning signs of the downfall of the Roman empire.

The above three metrics were suggested by Stephen Rider.

Jerry Pournelle's Political Axis and the Inglehart-Welzel Cultural Map of the World have possibilities. Each nation would have a ranting in the two values used in each graph, and as the values changed so would the nation's classification. For instance, on the Pournelle chart, if the government of Zeta Reticuli II had a Rationalism rating of 4' and a Statism rating of 3.5, it would be in the Socialist classification and would make decisions using whatever you programmed for that classification. If for whatever reason its Rationalism rating dropped to 3.5', it would change to Welfare Liberal classification with corresponding changes in its decision making process.

You might want to experiment with Oswald Spengler's cultural life-cycle. And Psychohistory.

There are some equations for modeling interstellar colonization here.

There are tons of equations for modeling interstellar trade in the classic book GURPS Traveller: Far Trader.

A book over-flowing with useful equations for modeling geopolitical situations is Chris Crawford's BALANCE OF POWER International Politics as the Ultimate Global Game (Microsoft Press 1986, ISBN 0-914845-97-7, do NOT make the mistake of ordering the game manual as it has no equations). In the book, Mr. Crawford discusses the mechanisms inside his eponymous award-winning computer game. The book is out of print but copies can be found at

Stephen Rider is mulling over the factors involved with such a program:

After looking at a few generation systems/empire modeling games, I know that I need to at least look at the following: I know it's a lot of points that more research is needed on all of them, but please let me know if any of them are truly whacked.

1) the movement of populations between systems. emigration and immigration normally are determined randomly, but if I have the computational power to actually figure out how people will move, then we should do that as...

2) political allegiance is something that needs to be at least looked at, at the moment I'm thinking of a system that'd start with the major planet (say Earth) and then create a hierarchy of settled planets, much like a tree structure, but if population flows got mixed in, it could create strange balances.

3) economic loyalty - this 'theoretically' would allow worlds that were growing fast economically to become the center of their own mini empire economically, if too many worlds became economic power houses, then it wouldn't work. If you saw a map of trade density, it would look like mountain peaks with the peaks being the major economic players that swept allow smaller worlds. When the simulation end period came along, this could be one of the major ways that the factions were determined.

4) Political priorities - life path problems. Kinda getting back to the idea that each colony will need to come up with their own character, colonies would start with an archetype (not sure how to do this, but it'd be a function of looking at the initial reason for building the colony, money input and world climate/world traits) and then within that framework have random events that could happen based on planet and who colonized it. This would generate a set of planetary traits, such as idealism, pragmatism, greed, environmentalism et al that would effect the options available to the government when problems turned up. For example, a Three Generations Rule problem might be very easy for a highly pragmatic colony to deal with, while one that was high in idealism might run into problems. Yes, in a sense this is trying to ascribe in a half dozen variables a political/social culture...maybe impossible.

5) Political groups - no planet will have just one political faction, this should also help complicate problem solving because not everyone will see a problem as a problem per see.

6) economic investments - infrastructure has to grow and the simplest way to determine how to choose what to invest in is by being able to calculate the cash flows. Assuming that a nominal risk free interest rate can be set, it does become possible to discount cash flows and determine if building that super big star port is really a good idea at the time, or if it's not such a hot idea, which brings us to...

[assuming that investment outside of the planet's solar system is also being looked at the process each turn would be to calculate all the investment opportunities for each planet, combine them, rank them by ROI and then allocate resources to the best one and work your way down the list until you ran out of investment money]

7) what is the rest of the economy doing? you're not going to be investing 100% of a worlds income, so what will the rest of it be doing? More research needed

8) random fluctuations and results are going to be common, a new star port terminal or whatever may have an expected to reduce the planetary movement cost by $50 or so such, but it will be more variable than that, sometimes engineers get things wrong and sometimes they get things really right. This is another dynamic designed to prevent the cookie cutter feel of planets from such things as Masters of Orion II where past a certain point you just knew you wanted to build everything.

9) Transfer costs, this is an assessment of how hard it is to get into the solar system from a planet/economic point (asteroids will have basically zero while heavy gravity worlds will have very high costs), this also applies between systems. This put together with manufacturing costs will set the minim price for off world goods, and yes if I could figure out how to run a supply and demand economy, that's the first thing I'll try to set up.

10) tech level - this will be a sliding scale that will set the availability and constructability of planetary assets and define part of the manufacturing costs of a given sector. Looking at how 2300's Great Game II set it up, it'll be a function of literacy, college education and urbanization, it doesn't have to be a nice number (meaning 13.451 is a valid tech level). It's all evolutionary technology so there won't be any major break troughs, just making it better.

11) Human Development Index/Misery Index will also be part of what makes a planet, if for no other reason than to generate a push for immigration/emigration. I almost get the feeling that you could model population movement between to planets by looking at the indexes and trying to balance them out as a physics problem with gases under pressure.

Stephen Rider

Balance of Power

Here are some of the equations from Chris Crawford's BALANCE OF POWER International Politics as the Ultimate Global Game (Microsoft Press 1986, ISBN 0-914845-97-7). You should read the book for the theory behind the equations. The game pits the USA player vs the Soviet player in a geopolitical fight for world domination.

Please note that the equations were for a game, not a simulation. Also note that due to game development constraints, many factors were left out of the game. These include the influence of trade (trade restrictions, trade barriers, trade boycotts, trade embargoes), multipolarity (in the game there is a bipolar situation between the US and the Soviet Union, and all other nations are allied with one or the other. Things get more complicated if there are more than two superpowers), warfare between two minor powers (in the game all wars have at least one and sometimes two superpowers involved), arms control, and human rights.

Due to technical details of computer programming, the equations use values of 0 to 255 instead of 0 to 100, and values of -127 to +127 instead of values of -100 to +100. For arcane reasons any programmer can explain to you, this gives better accuracy in the calculations. And due to the limits of the computer (Apple Macintosh), he used 16-bit signed integers, which means all the numbers range between -32,767 and +32,767. Any calculations that yield a result outside of this range will make the equations act crazy. For similar reasons some of the equations need odd numbers like 256 and 2048, they too are due to the limits of the computer.

Governments vs. Internal Insurgencies

An insurgency is an armed attempt by native elements acting outside the government to overthrow the government or repudiate its control over a region. It is characterized by a protracted campaign between the armed forces of the state and those of the insurgency. An insurgency is differentiated from a coup d’etat by the facts that a coup is a very sudden event and one that often involves persons working from within the machinery of the government.

Three primary ingredients are necessary to cook up an insurgency. First, you must have a government or other legitimate authority against whom the insurgency is directed. After all, you can’t have a rebellion against no one! Second, you must have the insurgents themselves: the people who rebel against the government. Third, the insurgents must be willing to use armed force against the government. The element of armed force is not necessary to ensure success (witness Mohandas Gandhi), but without it you have civil disobedience or a coup d’état, not an insurgency.

Balance of Power must calculate the behavior of the insurgency in each country of the world. This means that it must first calculate the strength of the insurgency and the strength of the government forces. It must then determine how these two forces fare in combat with each other. Then it must determine the significance of this outcome, such as whether the insurgency has graduated to the status of a civil war. Finally, the program must compute the consequences of an insurgency victory on the makeup of the government and its relationships with the superpowers.

TotalWeapons = Weapons + MilitaryAid

GovernmentPower = ( (2 * Soldiers * TotalWeapons) / (Soldiers + TotalWeapons) ) + InterventionPower


  • Soldiers = number of solders the government has in its army
  • Weapons = amount of government money spent on weapons
  • MilitaryAid = amount of money for weapons a government receives from a superpower
  • GovernmentPower = net military power resulting from soldiers and weapons
  • InterventionPower = military power provided to government by any intervening superpower troops

Note the balance between soldiers and weapons. If, for instance, you have vastly more soldiers than weapons, adding more soldiers does little to increase government power. Adding more weapons has a much stronger effect.

Chris Crawford's national maturity ratings for 1980
Saudi Arabia40

InsurgentSuccess = sqrt(6400 * LastYearInsurgencyPower) / LastYearGovernmentPower

Fighters = ((256 - Maturity) * Population * Success) / 20480


  • InsurgentSuccess = how successful the insurgents were last year when battling the government
  • sqrt(x) = square root of x
  • LastYearInsurgencyPower = the value for InsurgencyPower last year
  • LastYearGovernmentPower = the value for GovernmentPower last year
  • Fighters = number of fighters in the insurgency "army"
  • Maturity = 0-255, a measure of the stability of a nation's cultural and governmental institutions. As an example, sub-Saharan African nations have low maturity metrics, and tend to be caught in endless cycles of violence. In the game these were constants, but in a longer term simulation they will be variable. The longer the period of stability, the higher the maturity value will grow.
  • The constants 6400, 256, and 20480 are intended to scale things to the 0-255 metric of Maturity.

In the game, Chris Crawford "intuitively selected" the following sample maturity values for the various nations in the year 1980. These appear in the table to the right. In 2014 he noted that given his now 30 years of hindsight, he'd make quite a few changes in those maturity values.

InsurgencyWeapons = 2 * WeaponsShipmentsFromSuperpowers

IF (InsurgencyWeapons < (Fighters/8)+1) THEN InsurgencyWeapons = (Fighters/8)+1

InsurgencyPower = ((2 * Fighters * InsurgencyWeapons) / (Fighters + InsurgencyWeapons)) + InterventionPower


  • WeaponsShipmentsFromSuperpowers = amount of money for weapons an insurgency receives from a superpower
  • 2* = Insurgents tend to use their weapons more effectively than government troops
  • IF x THEN y = if the expression "x" is true, then perform equation "y"
  • InterventionPower = military power provided to insurgents by any intervening superpower troops
Governments and Insurgents Inflict Casualties On Each Other for One Year
> 512Peace
512 to 33Terrorism
32 to 2Guerrilla War
2 to 1Civil War
< 1Government falls
Insurgents take over

GovernmentPower = GovernmentPower - (InsurgencyPower/4)

InsurgencyPower = InsurgencyPower - (GovernmentPower/4)

The above is an exceedingly simplistic method of combat resolution, feel free to substitute something more complicated. Mr. Crawford was writing a game about geopolitics, not a war game. The equations basically say that each side can inflict damage on their opponent's power equal to one quarter of their strength.

InsurgencyRatio = GovernmentPower / InsurgencyPower

InsurgencyRatio is calculated, and the new state of affairs in that country is looked up in the table on the right

In the game, the two players take the parts of superpowers The United States and The Soviet Union. The players give aid to key nations, giving to either the government or insurgents of a nation trying to influence the outcome. The players give (if anything) for MilitaryAid, WeaponsShipmentsFromSuperpowers, and/or InterventionPower for each nation's government or insurgency.

In the game, one player is a human being while the other is a simplistic program algorithm trying to give the human a run for their money. For our history generator the program will have to somehow make the decisions for both sides. The program influenced by the current ideology of the superpower in question.

If The Insurgents Win

The insurgents become the new government. If they had help from a superpower (i.e., any MilitaryAid, WeaponsShipmentsFromSuperpowers, and/or InterventionPower) the new government (former insurgents) will modify their left-wing/right-wing stance to be more like the helper superpower.

GovernmentWing = (GovermentWing + HelperSuperpowerGovernmentWing) / 2

Popularity = 10 + ((128 - abs(GovernmentWing)) / 2)


  • GovernmentWing = Political leaning of the government. -128 = extreme left-wing. +128 = extreme right-wing. 0 = moderates. Note: it would be interesting to somehow replace this one-dimensional metric with a two-dimensional one like Jerry Pournelle's Political Axis or the Inglehart-Welzel Cultural Map
    HelperSuperpowerGovernmentWing = Political leaning of the superpower that helped the insurgency. USA = +20. Soviet Union = -80.
  • abs(x) = Absolute value of x (i.e., make any negative values into positive)
  • Popularity = popularity of the government. This is used in figuring the likelihood of a coup d'etat (see below). The equation above gives a new "blank slate" popularity for a new government.

The new government's diplomatic relation with the two superpowers are calculated. The following equations are calculated for both superpowers in turn.

PoliticalCompatibility = abs(GovernmentWing - SuperpowerWing) - abs(FormerGovernmentWing - SuperpowerWing)

GoodAid = WeaponShipmentToFormerInsurgents + (2 * InterventionForFormerInsurgents)

BadAid = WeaponShipmentToFormerGovernment + (2 * InterventionForFormerGovernment)

DiplomaticAffinity = (PoliticalCompatibility / 2) + (8 * (GoodAid - BadAid))

  • PoliticalCompatibility = used in the DiplomaticAffinity equation
  • GovernmentWing = Political leaning of the new government/former insurgents
  • FormerGovernmentWing = Political leaning of the deposed former government
  • SuperpowerWing = Political leaning of the superpower in question
  • WeaponShipmentToFormerInsurgents = total WeaponsShipmentsFromSuperpowers to the former insurgents from the superpower in question
  • InterventionForFormerInsurgents = total InterventionPower to the former insurgents from the superpower in question
  • WeaponShipmentToFormerGovernment = total WeaponsShipmentsFromSuperpowers to the deposed former government from the superpower in question
  • InterventionForFormerInsurgents = total InterventionPower to the deposed former government from the superpower in question

As previously mentioned, the above equations are calculated for both superpowers. Naturally if a superpower gave lots of help to the deposed former government, the former insurgents/new government will hate that superpower (i.e., have a low DiplomaticAffinity). In the game, changes in DiplomaticAffinity add to or subtract from each superpower's Prestige Points, which help determine which superpower "wins" the game. This is probably worthless in our history generator. There are some elements of insurgencies that the above equations fail to take into account, for details read the book.

Coup d'etat

A Coup d'etat, unlike an insurgency, only changes the executive. The rest of the government remains intact. Coups also tend to be much less violent than a revolution. In some cases a coup might be an integral part of a government system, for example an election. Since economics plays such a large role in a coup, the economic equation from BALANCE OF POWER will also be presented here.

ConsumerPressure = (20 - GovernmentPopularity) * 10

IF ConsumerPressure < 1 THEN ConsumerPressure = 1

InvestmentPressure = (80 - InvestmentFraction) * 2

IF InvestmentPressure < 1 THEN InvestmentPressure = 1

InsurgencyStrengthRatio = InsurgencyPower / GovernmentPower

MilitaryPressure = sqrt(InsurgencyStrengthRatio) + USA_FinlandizationProb + SovietFindlandizationProb

IF MilitaryPressure < 1 THEN MilitaryPressure = 1


  • ConsumerPressure = pressure the government feels to increase consumer spending at the expense of investment spending and military spending.
  • InvestmentPressure = pressure the government feels to increase investment spending at the expense of consumer spending and military spending.
  • MilitaryPressure = pressure the government feels to increase military spending at the expense of consumer spending and investment spending.
  • GovernmentPopularity = measure of the popularity of the government, generally between 1 and 20
  • InvestmentFraction = fraction of the total GNP that was spend on investment (new roads, schools, factories, etc). Range is 0 to 255 where 0 = 0% and 255 = 100%
  • InsurgencyStrengthRatio = ratio of insurgency strength to government strength.
  • USA_FinlandizationProb, SovietFindlandizationProb = degree to which the government feels vulnerable to and threatened by the two superpowers.

TotalPressure = ConsumerPressure + InvestmentPressure + MilitaryPressure

FractionalPot = 0

IF ConsumerFraction < 16 THEN ConsumerFraction = ConsumerFraction - 8 AND FractionalPot = FractionalPot + 8

IF InvestmentFraction < 16 THEN InvestmentFraction = InvestmentFraction - 8 AND FractionalPot = FractionalPot + 8

IF MilitaryFraction < 16 THEN MilitaryFraction = MilitaryFraction - 8 AND FractionalPot = FractionalPot + 8

Again FractionalPot, ConsumerFraction, InvestmentFraction, and MilitaryFraction are all on a 0 to 256 scale, so 16 = 6.25% and 8 = 3.125%

InvestmentFraction = InvestmentFraction + ((InvestmentPressure + FractionalPot) / TotalPressure)

MilitaryFraction = MilitaryFraction + ((MilitaryPressure + FractionalPot) / TotalPressure)

ConsumerFraction = 255 - (MilitaryFraction + InvestmentFraction)

OldConsumerSpendingPerCapita = (255 * ConsumerSpending) / Population

The 255 scales it to the 0-255 range of the various fractions.

VirtualGNP = GNP + EconomicAidFromSuperpowers

GNP = GNP + ((VirtualGNP * 2 * (InvestmentFraction - 30)) / 1000)

This assumes that if you spend less than about 30 (12%) on investments, your GNP will suffer negative growth.

NewConsumerSpendingPerCapita = (ConsumerFraction * VirtualGNP) / Population

Improvement = (100 * (NewConsumerSpendingPerCapita - OldConsumerSpendingPerCapita)) / OldConsumerSpendingPerCapita

GovernmentPopularity = GovernmentPopularity + Improvement + (abs(GovernmentWing) / 64) - 3

GovernmentPopularity term on the right represents the loyalty of the masses.

Improvement term is how much the masses life situation has improved due to government action

GovernmentWing term assumes that radical governments (both left and right wing) have an advantage over centrist governments. This is due to how radical governments suppress dissent, and the divisiveness that often cripples centrist governments.

-3 term assumes that the masses expect a 3% consumer spending growth rate

IF GovernmentPopularity < (USA_Destabilzation + SovietDestabilization) THEN Trigger a Coup

USA_Destabilzation, SovietDestabilization = level of superpower attempts to trigger a coup, ranges from 0 to 5
Generally the superpower destabilization will be zero, so it reduces to a coup being triggered if the GovernmentPopularity becomes negative.

If A Coup Is Triggered

GovernmentWing = GovernmentWing * -1

Right Wing becomes Left Wing, and vice versa

GovernmentPopularity = a randomly selected positive number

People have an optimistic expectation of the new government

Soldiers = Soldiers * (a randomly selected percentage)

TotalWeapons = TotalWeapons * (a randomly selected percentage)

Soldiers do not fight as well when they do not know who they are fighting for.

Atomic Rockets notices

This week's featured addition is SPIN POLARIZATION FOR FUSION PROPULSION

This week's featured addition is INsTAR

This week's featured addition is NTR ALTERNATIVES TO LIQUID HYDROGEN

Atomic Rockets

Support Atomic Rockets

Support Atomic Rockets on Patreon