I like that he is using his physics background to find equations for cities, however, is it really a big surprise that if you know a cities area, country and population you can guess the average income to 85% accuracy? To me that seems rather obvious.

(population * (personal space)) / area = average income

solve for personal space:

((average income) * area) / population = personal space

..............

SF

Using wikipedia we can find the population of San Francisco and the area. We can now solve for how much personal space people like in the USA.

((average income) * area) / population = personal space

I can only find per capita income for counties...

City and County of San Francisco:

average per capita income: $34,556

area: 600.7 km²

population: 776,773

($34,556 * 600.7) / 776,773 = 26.7

So USA's personal space is 26.7 $km² per person

...............

LA

Lets try Los Angeles County:

average per capita income: $20,683

area: 10 517.9 km²

population: 9,802,800

remember our original equation:

(population * (personal space)) / area = average income

(9,802,800 * 26.7) / 10 517.9 = $24,884

$24,884 / $20,683 = 83%

Not the 85% goal we wanted but Im working with counties and not actual cities.

sources:

http://www.wordiq.com/definition/San_Francisco_County,_Calif...

http://www.wordiq.com/definition/California_locations_by_per...

http://www.wordiq.com/definition/Los_Angeles_County,_Califor...