Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

The two competing technologies are fiber-optic cables and microwave relays. Light going down a fiber-optic cable travels at about 69 percent of the maximum speed of light in a vacuum, which is still blisteringly fast, covering about 128,000 miles every second. Microwaves move through the air at almost the full 186,282 miles per second maximum speed of light, but they have to be bounced from base station to base station to follow the curvature of the Earth. There are also problems about where microwave base stations can be built and where fiber-optic cable can be laid. So the path from DC to Chicago taken by the data will not be the shortest possible route. But to get a lower limit, we can assume that the data follows the shortest line between the Fed Building in DC to the Chicago Mercantile Exchange building (593.8 miles) at the full speed of light (new hollow-core fiber-optic cables can reach 99.7 percent of the speed of light) and calculate a time of 3.19 milliseconds. A similar calculation for the shorter DC–to–New York City journey gives 1.09 milliseconds. Those times assume that the data is racing down a fiber-optic cable following the curvature of the Earth. Straight-line travel would be slightly faster. There are already line-of-sight laser communication systems for financial data where the beginning and end points have nothing but air between them—for example, those that relay information between buildings in New York and buildings in New Jersey. To travel between ...