Pauline Chen and The Red Chamber

Today's guest is my friend and author Pauline Chen.  Her recently released book The Red Chamber reimagines the provocative love triangle from the Chinese epic Dream of the Red Chamber.  Pauline is also the author of the children's novel Peiling and the Chicken-Fried Christmas.

Pauline's questions regard her new book:

At several points in my book characters travel to and from the south, either by barge on the Grand Canal or by horseback, and I've just very loosely estimated the time required by their journey. Could you do a more precise estimate of a journey from Beijing to Suzhou, taking into consideration possible routes and stops for the night?

...My other question concerns what it would have been like to live in Beijing at the time. Can you estimate what the approximate population would have been at that time, and what the population density would have been?

Google Maps lists the distance between Beijing and Suzhou as 1146 kilometers (712 miles).  Driving nonstop from one to the other would take the better half of a day, about 15 hours, but her 18th century characters certainly weren't using cars.  Let's consider the two modes of transportation Pauline lists.

1. Barge.  I have to confess, I'm not all that familiar with barges, so I'm going to guess a bit.  According to the Wikipedia entry for "water speed record," the fastest boat speed was about 42 kilometers per hours (26 mph) circa 1885.  However, Pauline's story takes place about 100 years before this and her characters wouldn't have had access to propeller or steam technology.  As such, I'm betting their barge moved appreciably slower.  I'll guess 10 kilometers per hour.  If the barge was much slower than this, walking would have been faster.  Assuming they remained on the barge for the entire trip, it would take about a week to travel from  Beijing to Suzhuo.  This assumes the distance is a bit longer than the straight line distance since the Grand Canal is about 1700 kilometers long.

2. Horse.  A horse's speed depends greatly on how much of a hurry it's in.  According to the Wikipedia entry for "horse gait," a walking horse travels about 6.4 kilometers per hour (4.0 mph) where as a galloping horse can move fast as 48 kilometers per hour (30 mph).  It's fair to assume the horse won't be sprinting at full tilt for a thousand kilometers in a row, so we should probably use its walking speed.  Assuming 10 walking hours per day, a horse would travel about 77 kilometers each day and would complete the trek in about two weeks.  This number is a bit misleading though because it assumes the horse is not carrying heavy cargo.  

With a wagon, a horse can't travel nearly as fast.

If the horse pulls a wagon, it will travel appreciably less quickly.  According to the Wikipedia entry for "Conestoga wagon," horses can travel about 25 kilometers (15 miles) each day, which would make the journey last about a month and a half.

Depending on the amount of time spent on the barge/horse and the amount of baggage brought along for the trip, the journey could take anywhere from one week to over a month.  (Though this assumes they're not distracted by various love triangles and such.)

For the second question, I'll need to be careful.  I tend to play fast and loose with numbers since I'm only going for order of magnitude accuracy, but I've gotten myself in trouble with populations before.  As one reader pointed out in my Pinker post, population growth can be more accurately described by a geometric series:

Let's assume the fertile population in 1900 is "p". Let's also assume that a given generation basically dies out after 75 years. This is a realistic life expectancy.
Then the generations of fertile (<25yr old) people looks as follows: 

(1850) : p / m^2
(1875) : p / m
(1900) : p
(1925) : p * m
(1950) : p * m * m
(1975) : p * m^3
(2000) : p * m^4

If we follow his trend line to the year 1775, we get a population given by

population in 1775 = p / m⁷ + p / m⁶ + p / m⁵.

Using my reader's values p = 0.782 and m = 1.565, we find that the world population in 1775 was roughly 170 million people.

As you can see from the chart above, the number is a bit off, but certainly within an order of magnitude.  A more accurate number would be about 800 million people.  At present, China is about 25% of the total world population. Assuming this percentage has remained roughly the same for the last few centuries, the population in China in the 18th century would be about 40 million people if you use my estimated number, though if you use the more accurate world population, you'll find it's closer to 200 million people.

If we want to find the population of Beijing specifically, we could assume the percentage of the Chinese population living there has remained fairly constant over the last few centuries.  This is not necessarily a safe assumption because cities are much smaller than countries. The smaller size makes them more prone to fluctuations in population, but I'm hoping the end result won't be too far off. Beijing is currently home to 20 million people or roughly 1.5% of China's population.  Using my 40 million people figure approximated above, we could estimate the Beijing population in the 1700s to be about 600,000 people.  Using the more realistic population figure would raise the number to about 3 million people.  According to the Wikipedia entry for "largest cities throughout history," Beijing grew from a population of 650,000 people in 1700 to 1.1 million in 1800, which would put my numbers very close to the actual value.  It would seem that an 18th century Beijing would look like a 20th century Indianapolis, at least in terms of population.

Thanks for great questions, Pauline!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.