It appears that the industrial revolution in the UK was sparked by rising literacy, which was in turn the product of rising population density:

Tim de Chent via Per Square Mile

The Industrial Revolution was fostered by a surge in literacy rates. Improvements in reading and writing were nurtured by the spread of schools. And the founding of schools was aided by rising population density.

Unlike violent revolutions where monarchs lost their heads, the Industrial Revolution had no specific powder-keg. Though if you had to trace it to one event, James Hargreaves’ invention of the spinning jenny would be as good as any. Hargreaves, a weaver from Lancashire, England, devised a machine that allowed spinners to produce more and better yarn. Spinners loathed the contraption, fearing that they would be replaced by machines. But the cat was out of the bag, and subsequent inventions like the steam engine and better blast furnaces used in iron production would only hasten the pace of change.

This wave of ideas that drove the Industrial Revolution didn’t fall out of the ether. Literacy in England had been steadily rising since the 16^th century when between the 1720s and 1740s, it skyrocketed. In just two decades, literacy rose from 58 percent to 70 percent among men and from 26 percent to 32 percent among women. The three economists combed through historical documents searching for an explanation and discovered a startling rise in school establishments starting in 1700 and extending through 1740. In just 40 years, 988 schools were founded in Britain, nearly as many as had been established in previous centuries.

The reason behind the remarkable flurry of school establishments, the economists suspected, was a rise in population density in Great Britain. To test this theory, they developed a mathematical model that simulated how demographic, technological, and productivity changes influenced school establishments. The model’s most significant variable was population density, which the authors’ claim can explain at least one-third of the rise in literacy between 1530 and 1850. No other variable came close to explaining as much.

Logistically, it makes sense. Aside from cost, one of the big hurdles preventing children from attending school was proximity. The authors’ recount statistics and anecdotes from the report of the Schools Inquiry Commission of 1868, which said boys would travel up to an hour or more each way to get to school. One 11 year old girl walked ten miles a day for her schooling.

14 November 2011 20 underpaidgenius Permalink

Investigating the likelihood of lightning strikes causing damage to telecommunications systems, NTT researchers stumble upon the 3/4 exponent — the same exponent underneath the relationship of placenames and population density (see The curious relationship between place names and population density) and other density-related phenomena:

Tim De Chent via Per Square Mile

Using past data on lightning strikes, telecom equipment failures due to lightning strikes, and the 2005 Japanese census, they [NTT researchers] developed a model to describe how telecom equipment failures due to lightning correlate with population density. At first blush, I expected urban areas to receive the brunt of the impact—after all, they have loads more equipment than rural areas—but the results were just the opposite. Expensive circuitry and antennas were safer in urban Tokyo than they were in rural Gunma, even when the discrepancy in lightning strikes between the two regions was taken into account.

The authors offer two explanations for why telecom equipment is safer in urban areas. First, many of the copper lines that feed base stations and boxes run underground in cities, which lowers the induced voltage during a strike. Second, the equipment itself tends to be exposed to the elements in the country, either on the ground or perched atop telephone poles. In the city, most of it in encased in apartment buildings.

But there is another possible explanation they missed—the design of telecom networks and their relationship to population density. The evidence lies in their calculated coefficient that describes how population density can predict equipment failures due to lightning strikes. The coefficient is ¾, and if you’ve been reading this blog for a while, you’ll no doubt recognize that number. As an exponent, ¾ is powerful descriptor, explaining a variety of phenomenon ranging from how plant sizes influences population density to how human population density affects the density of place names.

In this case, ¾ seems to say less about the pattern of lightning strikes than it does about telecom network design and the differences between rural and urban infrastructure. Denser populations require more equipment, but not at a fixed rate. Cellular networks provide a good example. In rural areas, cell sizes are limited by area, not the number of users. It’s the opposite in the city—the more users, the smaller cells become. Therefore, phone companies can rely on fewer cells and less equipment per person in the city than in the country.

The relationship between infrastructure demands and population density could go a long way to explaining why there is a lower rate of equipment failure in denser areas—there’s simply less equipment per person in the city than in the country. But the fact that telecom infrastructure—and damage to it—appears to scale at the same power that describes an range of phenomena related to density and metabolism, well, that’s just too good to be a coincidence.

11 October 2011 13 Permalink