Tuesday, January 6, 2009

Relative vs. Absolute Truth

In aircraft navigation, small deviations in course result in large errors over long distances. Since the beginning of aviation, the methods and tools for navigation have improved. Today, a common approach is to use the combination of GPS and INS. Most of us are familiar with GPS. An amazing technology that can pinpoint our location on the earth using signals from satellites. Unfortunately, GPS isn't sufficient for the sophisticated guidance systems of modern aircraft. These aircraft can make an entire flight from takeoff to landing without a pilot. This is accomplished with the use of computers that make hundreds of adjustments per second. The relative accuracy and the slow update rate (once per second) of GPS is insufficient for current needs.

The solution to this is the INS, or Inertial Navigation System. The INS has sensors that detect motion. The INS is mounted in the aircraft and as the aircraft rolls, pitches and flies, the INS detects these movements and reports them to the flight computer. The change in position can be reported 1000 times a second. The INS provides a much more precise position than the GPS and requires no external signal.

The INS only detects relative changes. It knows how much things have changed since the last measurement. From these changes it computes position, velocity, acceleration, roll rates, etc. Although the INS is very precise, it is not perfectly accurate. The small inaccuracy of the INS becomes a problem because each error gets added to a previous error. Over the long distances of aircraft flight, the accumulated error can be catastrophic.

Here is an example of 20 seconds where the INS inaccuracy is 1/1000th every 1/100th of a second. The circles show the GPS position.



A simple solution to this is to correct the INS to the correct GPS position for every GPS update. The actual solution is much more sophisticated. The result is below.



So what point am I trying to make? As time goes on, the norms of society are more like an INS. They use relative truths. We are not that much different than last few years. Taken over the last few decades, the differences become more noticeable. What used to be unacceptable at the margins has gradually made its way into the mainstream.

An example is marriage. Our society has drifted all over the map. It's been an arrangement. It's been all about romantic love. It's been a loose contract. What is the truth? I personally believe the Proclamation on the Family.

How about morality? I also believe there is an absolute truth.

How about our current financial crisis? Can we endlessly increase our debt? Is there a basic growth rate and standard of living that is sustainable? (See my blog on this)

In aviation, the acronym "CFIT" describes what happens when these small errors accumulate. CFIT stands for "Controlled Flight Into Terrain". You fly right into the side of the mountain or into the earth. Without some absolutes, what are the CFIT consequence for marriage, our economy, morality, etc?

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