Google and the U.S. government are in a complex dance around innovation, data and privacy.

At a Big Data conference at MIT’s Media Lab in Cambridge, Massachusetts, Google’s chief economist, Hal Varian, touted a GoogleNow application that can alert him to leave early for a distant meeting to avoid traffic congestion. How? By accessing and integrating personal calendar information, California highway traffic information and the location of his phone.

There is an incredible investment of dollars and human labor hours behind that app. Much of it not even Google’s.

However many technological and organizational hurdles Google had to overcome to develop it, Google’s app rests on the shoulders of the U.S. government, which built and maintains the global positioning satellite system that allows most GPS devices to work (not to mention the federal government’s role in the development of the California highway system and its stewardship of public airwaves through which mobile phones operate).

The U.S. Department of Defense took about 21 years — from 1974 to 1995 — to complete the initial NAVSTAR system of 24 satellites, which was originally conceived to provide more precise weapon delivery. The system now uses 30 satellites, six of which act as replacements or spare parts. Four satellites are used to pinpoint a location.

The slog to completion included budget setbacks, technical complications, schedule slips and the Challenger space shuttle catastrophe. Commercial use took off only after the military stopped deliberately fuzzing satellite transmission signals in 2000.

Cost estimates for the first 21 years of the GPS program start at $8 billion (1995 dollars). Current plans to modernize the current system and increase GPS location accuracy from meters to centimeters may cost upward of $22 billion. At the same time, Japan, India and Great Britain are planning to add their own systems to the GPS mix. Russia is the only other country with a comparable, functional system.

The global value of the industry for products and services tied specifically to GPS, according to one estimate, will reach $28.9 billion by 2015. Such estimates don’t incorporate the $30 billion drop in Apple’s market capitalization after the iPhone 5 launched with great expectations, but also with a flawed GPS-based maps functionality, AppleMaps.

Google’s dependence on GPS is just the beginning of its complex relationship with the U.S. government. Google’s innovations are changing the way people live, but that doesn’t mean the government is playing catch-up. Such a claim understates the nuanced dance that these very different types of organization practice with one another. It is also an error of historical reckoning. Each takes advantage of the other’s innovations, much like two dancers who use each other’s strength or grace for movements neither could generate alone.

A case in point is the collaboration between Google and the U.S. government to make self-driving cars viable for roadways. These new automobiles promise to reduce highway fatalities, conserve energy and improve commutes, saving time and money — a potential boon to both public interest and Google’s bottom line. The data self-driving cars may one day generate could deliver all kinds of insights (or privacy violations depending on your point of view) about where people go and when — a bounty of useful information for the government, Google and an unborn cottage industry of third parties.

To be sure, not every dance is graceful. Google and the government’s objectives do not always align. Toes get stepped on. Images get tarnished, especially around data use. For instance, over a six-month period in 2011, the government made close to 6,000 requests for private Google user data. At the same time, Google published a Transparency Report that tells how many disclosure requests they receive, and from whom. Which seems all very honest and forthright — until you remember that the government has also demanded regular, independent privacy compliance audits from Google for the next two decades, as part of a 2011 settlement regarding “deceptive” privacy practices the company was charged with during its effort to expand into social media.

It should come as no surprise that Google has become a leading corporate lobbyist to the U.S. government, spending more than $11 million a year on activities connected with 126 lobbyists (those registered as lobbyists for Google). Some of these lobbying efforts have been to protect the company from anti-trust accusations that come straight from Washington.

Google’s dance with the U.S. government can be more or less intimate, more or less at arm’s length. Whatever the distance between these organizations, three things are abundantly clear: these dance partners need each other; when they dance well together, the public can benefit in big ways; and, we all might be more comfortable if their dancing takes place on an open dance floor.