Monday, August 02, 2010

Street Fighting Mathematics

Sanjoy Mahajan has written a book on practical mathematics. It sounds good and, even better, it's available for free download under a Creative Commons Edition, see Street Fighting Mathematics here.

Here's the first example
1.1 Economics: The power of multinational corporations
Critics of globalization often make the following comparison [25] to prove the excessive power of multinational corporations: In Nigeria, a relatively economically strong country, the GDP [gross domestic product] is $99 billion. The net worth of Exxon is $119 billion. “When multinationals have a net worth higher than the GDP of the country in which they operate, what kind of power relationship are we talking about?” asks Laura Morosini.
Before continuing, explore the following question:

What is the most egregious fault in the comparison between Exxon and Nigeria? The field is competitive, but one fault stands out. It becomes evident after unpacking the meaning of GDP. A GDP of $99 billion is shorthand for a monetary flow of $99 billion per year. A year, which is the time for the earth to travel around the sun, is an astronomical phenomenon that A dimensionally valid comparison would compare like with like: either Nigeria’s GDP with Exxon’s revenues, or Exxon’s net worth with Nigeria’s net worth. Because net worths of countries are not often tabulated, whereas corporate revenues are widely available, try comparing Exxon’s annual revenues with Nigeria’s GDP. By 2006, Exxon had become Exxon Mobil with annual revenues of roughly $350 billion—almost twice Nigeria’s 2006 GDP of $200 billion. This valid comparison is stronger than the flawed one, so retaining the flawed comparison was not even expedient!
That compared quantities must have identical dimensions is a necessary condition for making valid comparisons, but it is not sufficient.
Make sure to mind your dimensions and units.
Go and read it. Recommended.