Tag Archives: Cities

A City Is A Village Of Villages

There have been three major eras of human history: foraging, farming, and industry. During each era our economy has grown at a roughly steady exponential rate, and I’ve written before about some intriguing patterns in these growth eras: eras encompassed a similar number of doublings (~7-10), transitions between eras were much shorter than prior doubling times, and such transitions encompassed a similar number of growth rate doublings (~6-8). I’ve also noted that transition-induced inequality seems to have fallen over time.

I just noticed another intriguing pattern, this time in community sizes. Today in industrial societies roughly half of the population lives in metropolitan areas with between one hundred thousand and ten million people, with a mid size of about a million. While good data seems hard to find, during the farming era most people seem to have lived in communities (usually centered around a village) of between roughly three hundred and three thousand people, with a mid size of about a thousand. Foragers typically lived in mobile bands of size roughly twenty to fifty, with a best size of about thirty.

So community sizes went roughly from thirty to a thousand to a million. The pattern here is that each new era had a typical community size that was roughly the square of the size during the previous era. That is, a city is roughly a village of villages, and a village is roughly a band of bands. We could extend this patter further if we liked, saying that an extended family group has about four to eight members, with a mid size of six, so that a band is a family of families. (We might even go further and say that a family is a couple of couples, where a couple has two or so members.)

If previous growth patterns were to continue, I’ve written before that a new growth era might appear sometime in roughly the next century, and over a few years the economy would transition to a new growth rate of doubling every week to month. If this newly-noticed community size pattern were to continue, the new era would have communities of size roughly a trillion, perhaps ranging from ten billion to a hundred trillion.

Admittedly, after a year or two of this new era, things might change again, to yet another era. And the growth and community size trends couldn’t both continue to that next era, since a community size of a trillion trillion would require much more than twenty doublings of growth. So these trends clearly have to break down at some point.

I’ve been exploring a particular scenario for this new era: it might be enabled and dominated by brain emulations, or “ems.” Interestingly, I had already estimated an em community size of roughly a trillion based on other considerations. Ems could take up much less physical space than do humans, and since ems could visit each other in virtual reality without moving physically, em community sizes would be less limited by travel congestion costs.

So what should one call a city of cities of a trillion souls? A “world”?

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Are Firms Like Trees?

Trees are spectacularly successful, and have been for millions of years. They now cover ~30% of Earth’s land. So trees should be pretty well designed to do what they do. Yet the basic design of trees seems odd in many ways. Might this tell us something interesting about design?

A tree’s basic design problem is how to cheaply hold leaves as high as possible to see the sun, and not be blocked by other trees’ leaves. This leaf support system must be robust to the buffeting of winds and animals. Materials should resist being frozen, burned, and eaten by animals and disease. Oh, and the whole thing must keep functioning as it grows from a tiny seed.

Here are three odd features of tree design:

  1. Irregular-Shaped – Humans often design structures to lift large surface areas up high, and even to have them face the sun. But human designs are usually far more regular than trees. Our buildings and solar cell arrays tend to be regular, and usually rectangular. Trees, in contract, are higgledy-piggledy (see pict above). The regularity of most animal bodies shows that trees could have been regular, with each part in its intended place. Why aren’t tree bodies regular?
  2. Self-Blocking – Human-designed solar cells, and sets of windows that serve a similar function, manage to avoid overly blocking each other. Cell/window elements tend to be arranged along a common surface. In trees, in contrast, leaves often block each other from the sun. Yet animal design again shows that evolution could have put leaves along a regular surface – consider the design of skin or wings. Why aren’t tree leaves on a common surface?
  3. Single-Support – Human structures for lifting things high usually have at least three points of support on the ground. (As do most land animals.) This helps them deal with random weight imbalances and sideways forces like winds. Yet each tree usually only connects to the ground via a single trunk. It didn’t have to be this way. Some fig trees set down more roots when older branches sag down to the ground. And just as people trying to stand on a shifting platform might hold each other’s hands for balance, trees could be designed to have some branches interlock with branches from neighboring trees for support. Why is tree support singular?

Now it is noteworthy that large cities also tend to have weaker forms of these features. Cities are less regular than buildings, buildings often block sunlight to neighboring buildings, and while each building has at least three supports, neighboring buildings rarely attach to each other for balance. What distinguishes cities and trees from buildings?

One key difference is that buildings are made all at once on land that is calm and clear, while cities and trees grow slowly in a changing environment, while competing for resources. Since most small trees never live to be big trees, their choices must focus on current survival and local growth. A tree opportunistically adds its growth in whatever direction seems most open to sun at the moment, with less of a long term growth plan. Since this local growth end up committing the future shape of the tree, local opportunism tends toward an irregular structure.

I’m less clear on explanations for self-blocking and single-support. Sending branches sideways to create new supports might seem to distract from rising higher, but if multiple supports allow a higher peak it isn’t clear why this isn’t worth waiting for. Neighboring tree connections might try to grab more support than they offer, or pull one down when they die. But it isn’t clear why tree connections couldn’t be weak and breakable to deal with such issues, or why trees couldn’t connect preferentially with kin.

Firms also must grow from small seeds, and most small firms never make it to be big firms. Perhaps an analogy with trees could help us understand why successful firms seem irregular and varied in structure, why they are often work at cross-purposes internally, and why merging them with weakly related firms is usually a bad idea.

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Rising City Inequality

Barkley Rosser pointed to me to an ’05 meta-analysis of tail-power estimates for city distributions:

The estimated [power α] is on average not 1.0. If the regression is properly specified in the Pareto form, the pooled estimate of α is considerably larger than one, close to 1.1. … Point estimates of α are significantly smaller if the estimate is based on population data for metropolitan areas (instead of inner cities), the estimate is based on data for recent years, the estimate is for the US city size distribution, the sample comprises only a small number of observations, and the study reports only a single estimate.

So while this confirms that for US cities recently the tail-power is close to one (as I had cited before), it is higher in the rest of the world, and in the past. See this graph of power vs. year AD:

Inequality in cities has indeed been increasing over the last few centuries. And it may well increase more in the future.

So who bemoans increasing city inequality? Who wants to redistribute success from the 1% of cities, e.g., Tokyo and New York, to the many smaller cities? Few it seems, because while many dislike inequality in wealth or firm size, most seem to like city inequality.

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The Future Of Inequality

A few (3.6) years ago I wrote about the inequality over time induced by the big transitions, such as from primates to foragers to farmers to industry:

Advantages do accrue to early adopters of new growth modes, but these gains seem to have gotten smaller with each new [transition]. … 1. The number of generations per growth doubling time has decreased. … 2. … As we get better at sharing info in other ways, the first insight-holders displace others less. 3. Independent competitors can more easily displace each another than interdependent ones.

Earlier today I wrote about the inequality at each point in time, in the eras between transitions:

The number of species per genera and individuals per families has long declined with size as a tail power of two. After the farming revolution, cities and nations could have correlated internal successes and larger feasible sizes, giving a thicker tail of big items. In the industry era, firms could also get very large. Today, nations, cities, and firms are all distributed with a tail power of one, above threshold scales of (three) million, thousand, and one, thresholds that have been rising with time.

So, the unequal success that comes from some moving sooner in a big transition between growth eras has declined in more recent transitions. Yet the within-era inequality at a moment in time between groups like nations, cities, and firms has increased over time. As larger groups have become feasible, with more internal correlation in their success, the high tails of very large groups has gotten thicker, until they are now Zipf distributed evenly across many size scales. And in such Zipf distributions, typical group size increases with the both minimum efficient scale and total population, both of which have been increasing.

“But that is not all, no that is not all!” (Said the Cat in the Hat.) Continue reading "The Future Of Inequality" »

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The History of Inequality

I recently posted on how cities and firms are like distributed as a Zipf power law, with a power of one, where above some threshold each scale holds roughly the same number of people, until the size where the world holds less than one. Turns out, this also holds for nations:

Log Nation Size v Log Rank

The threshold below which there are few nations is roughly three million people. For towns/cities this threshold scale is about three thousand, and for firms it is about three. What were such things distributed like in the past?

I recall that the US today produces few new towns, though centuries ago they formed often. So the threshold scale for towns has risen, probably due to minimum scales needed for efficient town services like electricity, sewers, etc. I’m also pretty sure that early in the farming era lots of folks lived in nations of a million or less. So the threshold scale for nations has also risen.

Before the industrial revolution, there were very few firms of any substantial scale. So during the farming era firms existed but could not have been distributed by Zipf’s law. So if firms had a power law distribution then, it must have had a much steeper power.

If we look all the way back to the forager era, then cities and nations could also not plausibly have had a Zipf distribution — there just were none of any substantial scale. So surely their size distribution also fell off faster than Zipf, as individual income does today.

Looking further back, at biology, the number of individuals per species is distributed nearly log-normally. The number of species per genera:

and the number of individuals with a given family name or ancestor:

have long been distributed via a steeper tail, with number falling as nearly the square of size:

This lower inequality comes because fluctuations in the size of genera and family names are mainly due to uncorrelated fluctuations of their members, rather than to correlated shocks that help or hurt an entire firm, city, or nation together. While this distribution holds less inequality in the short run, still over very long runs it accumulates into vast inequality. For example, most species today descend from a tiny fraction of the species alive hundreds of millions of years ago.

Putting this all together, the number of species per genera and individuals per families has long declined with size as a tail power of two. After the farming revolution, cities and nations could have correlated internal successes and larger feasible sizes, giving a thicker tail of big items. In the industry era, firms could also get very large. Today, nations, cities, and firms are all distributed with a tail power of one, above threshold scales of (three) million, thousand, and one, thresholds that have been rising with time.

My next post will discuss what these historical trends suggest about the future.

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Why Hate Firms, Love Cities?

Families, clubs, professions, industries, firms, cities, and states are all important units of economic organization. That is, we coordinate to some extent via all of these units, to achieve mutual ends. But firms and cities make an especially interesting comparison.

First, firms and cities are similar in many ways. They both vary greatly in size, and can be costly for long-time associates to leave. Both tend to be “selfish” in avoiding and excluding those who do not benefit other associates, and thus tend to favor rich folks. People can relate to both kinds of units as investors, suppliers, leaders, and customers.

Second, people tend to like cities more than firms. For example, many movies are love songs to particular cities, yet few movies have cities as villains. Many movies have firms as villains, but few have firms as heroes. Sporting teams tied to cities play in huge stadiums, while teams tied to firms play in local parks.

While people tend to dislike bigger firms more than small ones, cities tend to be bigger than firms, and the biggest cities tend to be the most celebrated. People tend to resent firms more when it is more costly to leave them, yet it tends to be harder to leave cities than firms. So why are cities loved so much more?

One theory is that we related to cities less directly. If a city doesn’t hire you, you can say particular firms wouldn’t hire you. If a city won’t sell you a dress cheap, it is particular firms that wouldn’t sell it. So cities can more easily escape blame. However, a similar argument would suggest that we love shopping malls more than stores, or TV channels more than TV shows. Yet these seem weak effects, if they exist at all.

Another theory is that we often see firms as illicit dominators. We see the employer-employee relation as a dominance-submission relation, because firms give employees orders. Of course customers often give orders to firms, such as to waiters and cab drivers. But perhaps the joy of sometimes dominating does not outweigh the pain of at other times submitting. (And why are landlords seen as dominators, with renters submissives?)

Now cities do often seem to take a dominance relation to their citizens, such as via police, teachers, and rule-bound officials. But people seem to resent this dominance less. Is this because the major is democratically elected? CEOs are also usually elected, its just via one stock one vote, instead of one person one vote. Do people love cities less where local officials aren’t elected? Do people love non-profit firms as much as cities? Color me again confused.

Added 4p: Andrew Gelman says many firms are actually very popular. Alas he doesn’t have comparable data on cities.

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Em City By Combo Auction

Yesterday I outlined how combinatorial auctions could help our cities better coordinate their land use and utility capacity, without granting great discretion to a central power. But I ended with:

It would be very hard to get agreement to change to this system from today’s system of property rights and regulatory restrictions. I despair of it happening in our comfortable and change-averse cities. So we might have to wait until a big disruption creates lots of other change. (more)

Two years ago I pointed to a big-enough future disruption:

Rich stable nations … feel little inclination to consider big disruptive changes. … This frustrates rich-nation would-be-rebels like me who see our business, legal, political, etc. institutions as far from optimal. … If you long to say “come the revolution,” you might wait three to fifteen decades for the “em rev“, the whole brain emulation revolution. …

Rapid [em] growth will require huge rapid changes in economic organization, and supporting changes to business, legal, and political institutions. … Locations vying to be one of those [first em] centers may be open to big institutional change. … So if you have a favorite radical change you’d like the world to consider, you might give some thought to how your change could support a local em rev. (more)

The first em cities may be especially open to change regarding how cities are run. How might combinatorial auctions help them?

Here are my best guesses about (mid-em-era) em cities. City centers would mainly house computers, mostly running brains, and supporting infrastructure, e.g., power, cooling, structural support, part swapping paths, security, leakage containment, etc.

City centers would mostly house ems in virtual bodies doing office work, meeting often with other city workers. In most meetings, brains would stay put and just send signals; physical movement would be much rarer. Em minds would be sped-up relative to human minds as far as possible, until doubling an em’s mental speed much more than doubled its computing costs.

Outside of city centers there would be more ems in physical bodies, mostly small, helping with physical activities such as mining, harvesting, manufacturing, transportation, dumping, etc. Air cooling in the periphery would give way to water cooling closer in, and perhaps molten salt cooling very close.

All this would put a huge premium on inner city computer speed, density, and bandwidth. Cities would be very 3D, and city center computers would likely have very small physical structures generating lots of heat, making cooling crucial. Also important would be power sources, and physical paths for the replacement of devices and parts.

Today big computing centers are centrally planned, mostly with uniform parts and regular structures. But this level or coordination is may be infeasible for large cities, where diverse organizations make coordination expensive and change hodge-podge. In such a context, combinatorial auction might help improve coordination.

In am em city combinatorial auction, bids for locations could specify:

  1. spatial volume, shape, and orientation
  2. part swapping portal locations and sizes
  3. line of sight to outside, or to specific parties
  4. surface temperature and chemical corrosively limits
  5. amount and form of power and cooling, with price limits
  6. specific chemicals piped in, fluid garbage piped out
  7. communication distance from other particular residents
  8. time delay and expense to move hardware out and in
  9. support force tensors (including weight) get, support can give
  10. max stress-strain to support during earthquake
  11. limits on incoming, outgoing vibration distributions
  12. chances of incoming, limits on outgoing, leakage
  13. chance of explosive destruction, correlation with distant backups
  14. legal rules covering disputes with neighbors
  15. time commitments on each of these, and penalties for violations

As with cities today, winning allocations would say who gets what spaces with what supporting utilities, limits, etc. Competitive utility suppliers could also bid their prices to use particular spaces to supply particular utility amounts to particular locations. and futures markets about future winning bids might help estimate opportunity costs of commitment. Auction revenue could pay for utility fixed costs and repay city investors, and futarchy might choose the basic auction rules.

Yes, there’s a lot we don’t know about the future, and I could get some things wrong here. Even so, it seems worth thinking about what the future might be like, and when big institutional changes might be feasible.

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City By Combo Auction

I recently heard talks by Ryan Avent, author of “The Gated City”; and Matt Yglesias, author of “The Rent Is Too Damn High.” Both agreed that the inefficiency of urban land use has increased greatly in the last few decades, at least in the biggest US cities like New York. Most of the infrastructure that makes such cities great was made during the era of political machines, when a dominant party had great power to coordinate activities city wide.

We dismantled political machines out of revulsion for unchecked power. But now our cities fail to coordinate. Local zoning boards may often coordination to benefit local interests, but they also often fail to coordinate with distant boards to achieve city-wide gains. For example, when each area limits density to keep out poor folks, such as via lot size and height rules, the city fails to provide a place for needed poor workers. How can cities better coordinate, without the vast corruptible discretion of political machines?

Imagine for simplicity that we are starting a new city, or at least a new city area, from scratch. Some developers are thinking about building various types of housing, targeted at various types of residents. National chains are considering locating stores and food outlets. Employers and private schools are thinking of locating there as well. The question is: who will build where, and what utilities such as roads, power, water, sewer, internet will be built where to supply this new area?

One solution is to have a single developer initially own the entire area, and negotiate directly with all these parties. Political machines once filled a similar role. Today politicians and boards for zoning and utilities try to fill such roles. But there are other options. Yesterday I explained the concept of a combinatorial auction, using the example of assigning offices when moving to a new office building. Today I’d like to elaborate on how such a mechanism could be used to coordinate urban land use and utilities.

It would look a lot like the scenario I outlined yesterday for allocating offices. Just on a bigger scale. Each party would submit bids describing their willingness to pay for various combinations of land features. Bids could specify:

  1. Land area, soil type, topography.
  2. Views (or not) of mountains, ocean, factories, etc.
  3. Distance (meters or road time) from residents, shopping, jobs, schools, parks.
  4. Local limits on ambient sound, smells, light, etc.
  5. Limits on nearby resident demographics, and the “class” of shops.
  6. Limits you are willing to supply for own sound, smell, demographics, class.
  7. Utility services (e.g., power, water, internet, trash) required, at what prices.

A computer could then search for a max value set of mutually compatible bids. The winning assignment might specify:

  1. Which parties get what land for which uses.
  2. Local limits on building heights and appearances.
  3. What land is used for utilities such as roads, power generation, etc.
  4. What utility capacity is supplied at each place, and related price limits.
  5. Local policies limiting local behavior making sound, smell, light, etc.

Revenue from winning bids could help pay for city services. The cost of utility services could be included either via a cost model, or via bids from competing service suppliers. Adjustments might be made for an expected underbidding for shared resources. Bidding assistants and iterative bidding might keep bid elaboration efforts manageable. Calculation of max value bid sets might even be farmed out to competing calculators (who keep bids secret).

Now of course real cities are not usually built all at once, so we’d need to adapt the above process to incremental city change. Bids for each new time period could request options for similar future use at the same price, and specify a compensation due if that option is revoked. Futures markets estimating future winning bids might help determine the opportunity cost of awarding such commitments.

Yes there might still be opportunities for corruption and favoritism in this system, such as by leaking secret bids, and biasing the auction rules. But this still seems far less corruptible than today’s system. And we might use futarchy to take away even more opportunities for corruption.

Yes, it would be very hard to get agreement to change to this system from today’s system of property rights and regulatory restrictions. I despair of it happening in our comfortable and change-averse cities. So we might have to wait until a big disruption creates lots of other change. More about that tomorrow.

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The Future Of Cities

What sets city size? That is, what determines how many people all cluster together in an urban area? On the one hand, city size increases with feasible building height and with the gains to people and businesses from interacting closely with many others. On the other hand, city size decreases with how much space folks want, and with costs to transport people and goods within a city and from outlying regions. City size increases with more and cheaper nearby non-city economic activity.

Policy also matters; poor governance and positive externalities of density reduce city size, while being the center of government for a surrounding area increases city size. The size of big cities should be limited by the reluctance of nations to let their city activity be absorbed into big nearby foreign cities. And sunk costs and coordination failures can long delay the adaptation of city sizes and locations to changing circumstances.

In the farming era, cities held only a small fraction of the population, and so their size and locations were determined mainly by nearby farming activity. However, when most folks live in cities, then nearby non-city activity matters less, and decreasing transport costs make bigger cities more economical.

So how well have today’s city size and locations adapted to industry era tradeoffs? That is, how well do cities today trade the gains from more interaction in bigger cities for the added costs of transport and reduced personal space? While we expect optimal industry era cities to be more concentrated, i.e., fewer and larger, we also expect inertia, coordination failures, density externalities, and city mismanagement to slow the transition from an ideal farming era distribution of cities to an ideal industry era distribution. So cities today are probably too many and small. But how far off are they?

One clue – alas one that that is hard to interpret – is that today (log) city size follows a normal distribution, and (log) size changes follow a random walk. Another more informative clue is that in many large nations, a big (but not too big) fraction of the urban population is in the largest city. For example: South Korea 53%, Japan 44%, Egypt 43%, Argentina 37%, Bangladesh 34%, Philippines 28%, Mexico 24% (sources here, here). This weakly suggests that such cities might be running up against a political limit – the reluctance of neighboring nations to let these cities absorb their city activity.

How should we expect cities to change in a future em era, where trillions of human emulations live in virtual reality or in tiny android bodies? Since ems are easier to transport, require less space, and interact less with rural areas, optimal em cities should be even more concentrated than industry cities. Especially if ems learn to better subsidize density, to internalize today’s density externality. And since ems require quite different infrastructure from humans, and need large and rapid changes that most cities will initially be unwilling to allow, existing industry era cities may less constrain the size and location of em cities.

Together these suggest that em cities might be quite a bit more concentrated than our industry cities. Most ems might live within a half dozen or fewer really huge cities. Which would imply that only a half dozen nations would have substantial political power, allowing for easier global coordination.

If optimal em city concentration is really high, most ems might even live in just one biggest city. An analogy in the history of brains seems apt. Some of the first brains were spread out all over animal bodies, but then brains evolved to concentrate in one small region, to minimize signal delays within the brain.

Of course one big em city could be vulnerable to bad governance, so perhaps the biggest city would change as biggest cities became badly managed. Especially if ems had better ways (e.g. prediction markets) to coordinate their city switching activities. Creates an interesting picture of a competitive world government – at any one time most world economic activity might be under a single central city government, and yet cities might compete to offer the best world governance.

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A Galaxy On Earth

Our galaxy has about three hundred billion stars, and Earth today has about seven billion people. Assuming only half as many useable planets as stars, we could combine these two numbers into an initial crude guess for the size of a galactic civilization, and define a “galaxy of people” to be a thousand billion billion (or 1021) people. Now consider some famous galactic civilizations in science fiction.

One of the most popular science fiction stories ever was Issac Azimov’s Foundation series. It tells of the fall and rise of a galaxy-wide civilization, whose capital, Trantor, was a planet-wide city a kilometer deep into the ground. Trantor’s population was said to be forty billion, in a galaxy with millions of populated planets and a total population of a million billion (or one millionth of a “galaxy” as defined above).

Star War‘s Coruscant is also a planet-wide city and capital of a galaxy wide civilization, with planetary population of a thousand billion, in a galaxy also of millions of planets and a total population of a million billion. Some say Coruscant’s buildings averaged two kilometers tall. In Star Trek‘s Federation of 150 planets a few centuries hence, which controlled a few percent of the galaxy, each planet had no more than about our Earth’s seven billion, though some say the Federation held ten thousand billion people.

These all seem like dramatic underestimates to me. If Earth were paved over with a city the density of Manhattan today (1.6 million in 59 square kilometers), Earth would have a population of 14 thousand billion. Since Manhattan now has an average building height of 25 meters, a two kilometer deep version could hold a million billion people, and a two thousand kilometer deep version (Earth’s radius is 6400km) could hold a billion billion people.

There is roughly another thousand times as much useable material nearby, in other planets, comets, and the sun itself, allowing a solar-system population perhaps a thousand times larger. This brings us to a thousand billion billion, or a “galaxy” of people, the same as my initial crude population estimate for an entire galaxy above, and vastly larger than most science fiction galaxy estimates.

Furthermore, android ems (whole brain emulations in simulated bodies) could take up a lot less space than humans. I once somewhat conservatively estimated that an em might stand at 1% of human height (and run one hundred times faster). Since such an em would take up only one millionth of a human’s volume, a two kilometer deep Earth city could hold a “galaxy” (or thousand billion billion) of ems. And a solar system civilization might fit a billion billion billion ems, or a million “galaxies.”

Of course we have a long long way to go, not only to generate such huge populations, but also to develop the energy, manufacturing, heat-dumping, etc techs to allow us to support them. And yes, eventually we would run out of energy and material near our Sun, and need to go elsewhere to grow.

But we have strong economic reasons to stay close to one another as long as there is enough energy and material nearby, and especially as long as we continue to innovate. So most of our descendants’ economy should stay close to our sun until congestion here gets severe. We may well have a solar system population of a billion billion billion before the time comes when most of our descendants are closer to other stars.

Most science fiction seems to vastly underestimate the population that a single planet or star can hold, and the strength of the economic pressures to keep an economy close together, rather than spread across vast distances. Someday we will learn to tell stories that treat planets and stars as the vast spaces of possibilities that they really are.

Added 11a: Even an unmodified sun radiates enough energy to cover the calorie consumption of over a hundred “galaxies” of humans, and far more ems.

The timescale to grow from today’s population to a “galaxy” of descendants would be 600 years at an industry-style 15 year doubling time, 40 millennia at a farming-style thousand year doubling time, and four years at at next-singularity-style monthly doubling time.

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