One of the most familiar axioms of Euclidean geometry states that a straight line is the shortest distance between two points. This is true for plane geometry, but it does not hold true for curved surfaces. Longitudinal lines on a globe of the earth appear to be straight and even parallel over short distances, but they actually are curved and intersect at both poles. Even latitude lines are not necessarily the shortest east-west distance between two points. Planes flying from San Francisco to Europe, instead of heading east along latitude lines, frequently follow a great circle route over the North Pole. This could be called "the path of least time."
In 1983 the National Geographic magazine published an article on "The Wonderful Brooklyn Bridge," and the author described the suspension cables as "having a lazy catenary curve." A cable that evenly supports a weight such as a bridge, forms a parabolic arc. A catenary curve on the other hand is one that is formed by a flexible rope or cord that hangs by its own weight alone, such as a jump rope or an electric wire between two poles. The National Geographic has an impeccable reputation for scientific accuracy, so I was quite shocked by this error. I wrote to them and received a reply which apologetically acknowledged the mistake by the curator of civil and mechanical engineering at the Smithsonian Institute. I mention this episode to introduce the concept and attributes of the catenary curve. It has been used to construct some of the most beautiful arches in churches and in California missions. It also has the unique property of being "the path of least time" for objects sliding down an incline. This means that an object descending along a catenary trajectory would reach the bottom before one following a straight line or any other curve.
There is a clock in the Naval Observatory in Washington D.C. that sets the standard for all the clocks in th US and probably the whole of North America. This clock keeps time with an accuracy measured in milliseconds. However, it is no match for the cosmic clock in heaven. That clock has been ticking off in nano-seconds this earth's history so that the plan of salvation has transpired on schedule according to a divine timetable. The last great time prophecy of the Bible, the 2300-day prophecy of Daniel 8, ended in 1844, and at that time an angel stood and declared that time should be no more (Rev. 10:5,6). So time has run out, the cosmic clock has stopped, and we are in a holding pattern. We are told that the final movements will be rapid ones. Satan is going about as a roaring lion, knowing that his time is short (Rev. 12:12). The unfallen universe eagerly awaits the culmination of the drama of the ages. The whole wicked world is sliding ever faster toward the ultimate pit of final destruction along "the path of least time."
