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.

I see these as Watkins main mistakes:

1. Overestimating coordination capacities. Watkins said we’d cut underused letters like C,X,Q from our alphabet, eliminate mosquitoes and house-flies by ending their breeding grounds, put all city traffic below or above ground, and accept many American republics into the USA union. All of these require far more coordination than we seem capable of.
2. Underestimating wealth indulgence and signaling. Watkins said we’d adopt an engineer’s efficiency attitude toward food preparation and personal fitness. People unable to walk ten miles at a stretch would be weaklings, and we’d use central cooking instead of personal kitchens. But rich folks don’t want to work that hard, and humans have long asserted wealth and autonomy via personalized vs. communal dining. Institutional communal food, such as in dorms, ships, military bases, boarding-house, etc., has long been avoided a sign of low status.

Added 10a: The institutional food that is cheapest, and lowest in status, makes you eat where they say, when they say, and what they say. Yes of course a restaurant is “institutional” in some ways, but it costs more because it offers customers more flexibility in time, location, and food.

In our society, “sympathy” by high status folks for low status folks usually functions similarly — it affirms their high status while giving little net benefit to the low status. For example, the latest New Yorker reviews several books on the Roman empire, including one on the lives of ordinary Romans:

Much of what we know about the Roman emperors is based on myth and misunderstanding. But even that much can’t be said for the vast majority of their subjects, whose way of life has barely left a trace in the historical record. …

[It is] an overwhelmingly dark picture. “Invisible Romans” is full of anecdotes and quotations that speak volumes about Roman attitudes toward women, slaves, and the cheapness of life in general. … In general the lot of the ordinary Roman was no different from that of the vast majority of human beings before the modern age: powerlessness, bitterly hard work, and the constant presence of death. The thing that strikes Knapp most about Roman popular wisdom is its deep passivity in the face of these afflictions, which feels so alien to moderns and especially to Americans. The Romans, he writes, had no concept of progress … A slave might dream of manumission but hardly of abolition. For women, “there were no alternative lifestyles and aspirations either offered or considered … Even the amenities of the ‘Roman world, like the famous public baths, lose their lustre … “baths offered not only social interaction but a lack of hygiene schooling even to contemplate.” (more)

It almost seems as if this author feels it would have been better if these pathetic creatures had never existed, if not for their eventually giving rise to worthy creatures like him. So sad, he muses, that they didn’t bother to even imagine the future changes that could justify their miserable existence. He probably thinks it only a coincidence that his disgust affirms his lofty status among all the humans who have ever lived.

Sigh. The lives of ordinary folks in the Roman empire might not have been as nice as this author’s, nor as nice as yours. Yes they sometimes had pain, hunger, and sickness, but even so they were mostly lives worth living, with much love, laughter, engagement, and satisfaction. Poor folk do smile.

As I’ve enjoy some science fiction by John C.Wright, I found it interesting to read the nostalgia that energizes him:

High Fantasy rests for its paramount appeal on nostalgia: the longing for a world once known, now lost. An Uzi is a more efficient killing machine than the great sword Excalibur, but the Uzi is never to be described in words [as poetic as] these: … The sewers and streets of New York are cleaner than the crooked lanes of Athens, but New York is famed neither for her acropolis nor her philosophers. … Anyone who does not sense or suspect that modernity is missing something, something important, has no heart and no taste for High Fantasy.

The difference between a culture that respected and reveres the virginity of the maiden fair and the bravery of the warrior prince, and the cult that reveres the bravery of the transgendered community and protects the crooked penis of a presidential adulterer with comically ferocious self-righteousness, is not merely a difference between an ape and a man, a savage and a savant. … The Middle Ages may have been evil and cruel and dirty in many things, but they were never held Mutually Assured Destruction by thermonuclear annihilation to be a work of wise political policy. …

The only tales ever told in the history of the world without any element of magical or the supernatural were those told in the modern age. … There is a common thread linking speculative fiction with romances and epics and fairy tales of old. That thread is an acknowledgement that the world is wider and wilder and weirder than we suspect, and that there are fields beyond the fields we know where elves might dance in moonlight or demons rage in flame or angels clothed in brightness soar at their lord’s command on errantry to deeds immense of which we mortal men hear no slightest fame. …

The current world in which we live, the current age of darkness, rests on certain assumptions which High Fantasy undermines: the assumption that might makes right, the assumption that man is the master of his own fate, the assumption that the universe is a machine and everything in it (including man) is merely a raw material to be exploited in the restless search for pelf and pleasure. … The assumptions of the modern world, … Low Fantasy undermines them by showing the reader a glimpse of a world where the strength of a man’s arm decided the triumph or downfall of cities, and the honor of his word and the courage of his heart decided the strength of that arm. (more; HT David Brin)

Wright’s skill with words shows me the depth of his feelings, even though such feelings fail to resonate with me – his nostalgia still seems to me mostly wishful thinking. Yes, modernity is missing something, and stories of other eras can highlight what we lack. But some of what we lack is impossible, and so is missing everywhere. And every time and place is missing something; there are so many tradeoffs.

But let me make a prediction. In the future, stories will be told that are set in forager worlds, in farming worlds (where most of our fantasy is set), in industry worlds (like our world), in em worlds, perhaps in further worlds we can now only dimly imagine, and finally in worlds of a vast stable future lasting for trillions of years. My prediction is that in that vast stable future, when they tell nostalgic stories about other eras, they’ll tell more stories set in industry worlds than in farming or forager worlds.

John C. Wright can’t see the romance of our era, compared to farming era romance, but I doubt the first farmers could see much romance in their world, compared to forager worlds. But eventually story tellers will find many fine ways to see our dream-time era conflicts as engaging. For a cosmologically brief time, everything changed rapidly, anything seemed possible, and its mostly rich residents indulged in a great many real-life fantasies.

It is sometimes supposed … that rich people have always lived healthier and longer lives than poor people. That this supposition is generally false is vividly shown by Harris who compares the life expectancies at birth of the general population in England with that of [rich] ducal families. From the middle of the 16th to the middle of the 19th century, there was little obvious trend in general life expectancy. For the ducal families up to 1750, life expectancy was no higher than, and sometimes lower than, the life expectancy of the general population. However, during the century after 1750, the life prospects of the aristocrats pulled away from those of the general population, and by 1850–74, they had an advantage of about 20 years. After 1850, the modern increase in life expectancy became established in the general population. Johansson tells a similar story for the British royals compared to the general population, though the royals began with an even lower life expectancy at birth. …

Men die at higher rates than women at all ages after conception. Although women around the world report higher morbidity [= sickness] than men, their mortality [= death] rates are usually around half of those of men. … Women get sick and men get dead. … Biology cannot be the whole explanation. The female advantage in life expectancy in the US is now smaller than for many years, 5.3 years in 2008 compared with 7.8 years in 1979, and it has been argued that there was little or no differential in the preindustrial world. The contemporary decline in female advantage is largely driven by cigarette smoking; women were slower to start smoking than men, and have been slower to quit. (more)

This is a provocative hypothesis, but I don’t believe it. That is, I don’t believe that in general status and gender were unrelated to mortality until the industrial revolution. Chimp females live longer than chimp males, and I’ll bet that holds for foragers too. I’ll also bet that in both chimps and foragers high status tends to correlate with lower mortality.

Mortality decline doesn’t work as an explanation for fertility declines:

Fertility in the United States declined for decades before any noticeable decline in mortality.

Nor does new contraception tech:

Throughout the nineteenth and early twentieth century, withdrawal and abstinence remained the primary approaches used by married couples. Since these technologies had been available, essentially, throughout human history, it is unlikely that the condom and similar new methods played a strong role in the fertility transition. … Methods available even prior to the fertility transition were sufficient to produce voluntary reductions of the magnitude we observe in the nineteenth and early twentieth centuries.

Nor do child labor laws:

Most [child-labor] measures either did not apply to agricultural work, or did so in a more relaxed way. … German restrictions did not successfully limit the role of children in production at home, which remained important throughout the nineteenth century. And in every case, the restrictions’ impact would depend both on enforcement measures and parents’ desire to evade them. Finally, if child-labor restrictions were introduced when they were mostly irrelevant, …

Nor do new social insurance programs:

Economic ties between parents and children varied dramatically across the societies in question before the fertility transition. … At the other extreme, rural laborers’ children in England would, from at least the early-modern period, leave home for good in their early to mid teens. … social-insurance systems introduced at the end of the nineteenth and early twentieth century were usually replacing earlier schemes. Thus there is no clear “before.” … The broad patterns also do not make it likely that social insurance alone is central to the story. The two forerunners, France and the United States, were laggards in developing social insurance.

Still in the running, he thinks, are increases in urbanization, female employment, and gains to schooling:

Several studies document the existence of fertility control among small groups as early as the seventeenth century. These “forerunners” were usually urban elites or members of minority groups such as Jews. More generally, research based on either sub-national aggregates or micro data often find earlier fertility declines than in national data. The Princeton studies report earlier fertility declines in cities, for example. … Most studies find that urban fertility was lower than rural fertility in the nineteenth century, … Once the fertility transition began, fertility usually fell first in urban areas, with rural areas then catching up. …

Cross-sectional regressions for U.S. states in 1840 show that fertility is negatively correlated with measures of nonfarm labor-market opportunities. Once such proxies are introduced, land prices have no influence on fertility. … Crafts … finds a consistent, negative correlation between women’s [1911] local labor-force opportunities and marital fertility. …

Goldin and … Katz … find that the return to an additional year of [1915 Iowa] high school or college then was, for males, on the order of 11–12 percent. Mitch estimates the present value of acquiring literacy in Victorian Britain for a representative child. The present value of the cost of acquiring literacy would be about £4. At a wage premium of 5 shillings per week for literacy, the present value of the higher wages for a 35-year work life would be over £200.

English common law made livestock owners responsible for damages by roaming livestock, assigning the responsibility to fence in livestock. In contrast, the American colonies adopted legal codes that required farmers to fence out others’ livestock. Without a “lawful fence,” farmers had no formal entitlement to compensation for damages by others’ livestock. …

From 1880 to 1900, the introduction and near-universal adoption of barbed wire [in the US west] greatly reduced the cost of fences, relative to the predominant wooden fences, especially in counties with the least woodland. Over that period, … average crop productivity increased relatively by 23% in counties with the least woodland, controlling for crop-specific differences among counties and crop-specific statewide shocks. The increased productivity was entirely among crops more susceptible to damage from roaming livestock. … This increase in agricultural development appears partly to reflect farmers’ increased ability to protect their land from encroachment. (more)

Before the invention of barbed wire, it just didn’t make sense to build fences around farms in areas with little wood. Thus, it didn’t make as much sense to farm, near where others raised livestock. If you farmed, nearby livestock might just come and eat or trample your crops. In such times and places, many ranchers probably thought that “natural law” favored ranching, not farming, and favored property in animals more than property in land.

But the kinds of property and activity that makes sense depends on the available institutions and technology. Before barbed wire, it make less sense to farm, or to enforce property rights in land against roaming animals. But after barbed wire, farming and land property rights made a lot more sense.

Similarly, the kinds of innovation activities and intellectual property rights that make sense depend on available institutions and technologies. I’m happy to admit that today intellectual property (IP) is not obviously a good idea. Such property can create large “anti-commons” transaction and enforcement costs that greatly raise the cost of combining old ideas into valuable new ideas. Such costs often outweigh the social benefits of the incentives to create IP, in order to sell it. Today, it is often better to rely on other social incentives to innovate, incentives that don’t require such expensive support.

But if true, this is a sad fact about our limited abilities, not a fundamental natural law or right. You have no fundamental right to enjoy the innovations produced by others without compensating them. You owe them, at least your gratitude. Yes for now it may be best to let you take innovations freely without paying, since the alternative seems too expensive. But you have no right to expect that situation to last forever, any more than ranchers had a right to expect they could forever let their animals trample nearby farms.

Just as farmers developed barbed-wire, someday I expect IP advocates will develop better forms of intellectual property, and better technologies for marking, sharing, and enforcing such property. Using such innovations, I expect we will allow more and stronger intellectual property, and more of the world economy will focus on developing such property. Which, like barbed-wire, will mostly be a good thing.

I went looking for clues and found:

The core thing about fantasy tales is that, after the adventure is done and the bad guys are defeated… the social order stays the same. It may be the natural genre … but should we be proud of that? Science fiction, in sharp contrast, considers the possibility of learning and change. (more)

Rowling thus uses magic as a means to remove the reader from the modern technological world, through which she shows the [usual] dehumanized reality and entices the reader to reflection about the alternative possibilities to shape our world. … Magic in the world of Harry Potter is a connecting force among people, not something that makes them lonely; it presupposes the continuation and deepening of man’s connection with nature, the connection that appears to have been lost in our modern reality. (more)

Habits of so-called magical thinking — the belief, for instance, that wishing harm on a loathed colleague or relative might make him sick — are far more common than people acknowledge. These habits have little to do with religious faith. … Magical thinking underlies a vast, often unseen universe of small rituals that accompany people through every waking hour of a day. … For people who are generally uncertain of their own abilities, or slow to act because of feelings of inadequacy, this kind of thinking can be an antidote, a needed activator. … Magical thinking is most evident precisely when people feel most helpless. [Researchers] … sent questionnaires to 174 Israelis after the Iraqi Scud missile attacks of the 1991 gulf war. Those who reported the highest level of stress were also the most likely to endorse magical beliefs. … “Persons who hold magical beliefs or engage in magical rituals are often aware that their thoughts, actions or both are unreasonable and irrational.” … “With most people, if you were to confront them about their magical beliefs, they would back down.” (more)

Nostalgia is a predominantly positive, self-relevant, and social emotion serving key psychological functions. Nostalgic narratives reflect more positive than negative affect, feature the self as the protagonist, and are embedded in a social context. Nostalgia is triggered by … negative mood and loneliness. Finally, nostalgia generates positive affect, increases self-esteem, fosters social connectedness, and alleviates existential threat. … Nostalgia is found cross-culturally, and among well-functioning adults, children. … Although homesickness refers to one’s place of origin, nostalgia can refer to a variety of objects (e.g., persons, events, places). … Participants in the negative-mood condition were more nostalgic. … Participants in the high-loneliness condition were more nostalgic than those in the low-loneliness condition. … [Researchers] proposed that nostalgia imbues life with meaning, which facilitates coping with existential threat. … According to terror management theory, one can mitigate existential anxiety through shared beliefs about the nature of reality that imbue life with meaning. … after reminders of mortality … participants who were more prone to nostalgia. (more)

Both magic and nostalgia are common, arise more when we feel threatened, and comfort us in such situations. If questioned, we admit these styles of thought are biased, but away from such criticism we’ll easily slip back. Both magic and nostalgia rely especially heavily on wishful thinking – magic presumes we are especially able to influence events important to us, while nostalgia presumes that our previous social orders were especially functional, moral, good to people like us, etc. The fact that fantasy tends to combine both magic and nostalgia suggests that some readers have an especially strong tolerance for wishful thinking, and/or demand for comfort, and fantasy targets that audience.

As science fiction is often lumped with fantasy, does that suggest science fiction fans also have an unusual tolerance for wishful thinking and demand for comfort? To some extent yes – relative to reality, science fiction tends to presume tech changes fast, that it is very influential on society, and that small tech teams are very influential on such tech. And science fiction usually presumes that good guys tend to win and society basically works out ok.

Is the main difference between fantasy and science fiction that fantasy orients more to the past, while science fiction orients more to the future? While we think more far about both the distant past and future, we think more far about the future:

Since the distant past is also further away in time, we also expect past folk to live further away and travel longer distances, but the many concrete details we know about the past reduces this effect. (more)

Do the many specific details we know about the past give us a clearer anchor for our wishful thinking – so we can wish that those particular social orders are functional, moral, etc.?

Not so long ago, the average American man in his 20s had achieved most of the milestones of adulthood: a high-school diploma, financial independence, marriage and children. Today, most men in their 20s hang out in a novel sort of limbo, a hybrid state of semi-hormonal adolescence and responsible self-reliance. …

What has become obvious to legions of frustrated young women: It doesn’t bring out the best in men. … “A guy’s idea of a perfect night is a hang around the PlayStation with his bandmates, or a trip to Vegas with his college friends. … They are more like the kids we babysat than the dads who drove us home.” …

Large numbers of single young men and women living independently, while also having enough disposable income to avoid ever messing up their kitchens, is something entirely new in human experience. … We often hear about the miseries of women confined to the domestic sphere. … But it seems that men didn’t much like the arrangement either. … They turned to hobbies and adventures, like hunting and fishing. … What explains this puerile shallowness? … The qualities of character men once needed to play their roles—fortitude, stoicism, courage, fidelity—are obsolete. … Relatively affluent, free of family responsibilities, and entertained by an array of media devoted to his every pleasure, the single young man can live in pig heaven.

This makes sense, except that Hymowitz seems to unfairly exempt women from criticism:

Among pre-adults, women are the first sex. They graduate from college in greater numbers, and they have higher GPAs. As most professors tell it, they also have more confidence and drive. … They are more likely than men to be in grad school. … In a number of cities, they are even out-earning their brothers and boyfriends.

And why exactly should society celebrate women’s college GPAs more than men’s high PlayStation scores? After all, college is mostly a wasteful signaling game. And men still out-earn women on average at all ages, mostly because women tend to choose self-fulfilling majors and careers over high paying ones. So those higher fem GPAs are more a sign of self-indulgence than social contribution, at least if we measure contribution by income.

And even if women did earn more, are folks devoted to working to pay for high fashion or travel really any less self-indulgent than those who hone guitar skills? Let’s not forget that our vast fall in fertility seems due more to the changing preferences of women (vs. men) for a fun life unencumbered by kids.

This needn’t be a gender issue. Can’t we just all admit that we’ve all become more self-indulgent as we’ve grown rich, and that, like our icky odors, our own self-indulgence smells better than that of others?

A lot has changed in the past six years. The economies of the developing world have expanded 50 percent in real terms, despite the Great Recession. Moreover, growth has been particularly high in countries with large numbers of poor people. India and China, of course, but also Bangladesh, Tanzania, Ethiopia, Vietnam, Uganda, Mozambique and Uzbekistan – nine countries that were collectively home to nearly two-thirds of the world’s poor in 2005 – are all experiencing phenomenal economic advances. ..

We updated the World Bank’s official $1.25-a-day figures to reveal how the global poverty landscape has changed. … We estimate that between 2005 and 2010, nearly half a billion people escaped extreme hardship, as the total number of the world’s poor fell to 878 million people. Never before in history have so many people been lifted out of poverty in such a short period. …. The emerging markets of Asia are recording the greatest successes; the two regional giants, China and India, are likely to account for three-quarters of the global reduction between 2005 and 2015. … With few exceptions, however, those who care about global development have been slow to catch on to this story. We hear far more about the 64 million people held back in poverty because of the Great Recession than we do about the hundreds of millions who escaped impoverishment over the past six years. (more)

The greatest surprise, however, is the one taking place in Sub-Saharan Africa. Between 1980 and 2005, the region’s poverty rate had consistently hovered above 50 percent. Given the continent’s high population growth, its number of poor rose steadily. The current period is different. For the first time, Sub-Saharan Africa’s poverty rate has fallen below 50 percent. The total number of poor people in the region is falling too. (more)

Doesn’t sound much like stagnation to me.