Time and Again

"Those who cannot remember the past are condemned to repeat it" - George Santayana

     Time is tricky business. That much is certain. It is also a very nice orchestral piece by Hans Zimmer from Inception, and just about as tricky for me to figure out on the piano. But when humankind gets in the way of time, it does some interesting things.

     Time is often modeled as a linear, eternal progression. Timelines, for example, are obviously lines. Not squares or parabolas. Viewing time as a line is convenient and logical. I think however, that approaching time, but more importantly history, with a linear viewpoint can obscure some interesting facts about how time interacts with the world. For example, I think we could all attest to the fact that history has a tendency to repeat itself. Why does history repeat? Simply because those in the present do not learn from the past. Until humanity as a whole returns to the failures of the past (an impossibly idealistic assumption), the events of time will continue to loop around in circles. Imagine a cog rolling down a slightly inclined board. Humanity is this cog, and the board is time. The cog is going somewhere, but it continues repeating and repeating until it falls off the board, or it hits a wall, or is struck by a meteor. Imagine that the present is a single spoke on the cog. Perhaps you might think that this spoke would simply move in a uniform circle around the center of the cog, and you would be right. But that would be a rather hopeless situation if that spoke turns and turns forever without any linear progression. That is why the board is important. It creates opportunity for a new pattern for the spoke on the cog to trace. Now, that spoke, when viewed relative to the board, neither goes in a circle or a straight line. It moves in a pattern of cycloids. I just found out about cycloids when studying pendulums, and it further proves that there is a word for everything. A cycloid is the arch that is traced by a point on the diameter of a rolling circle. It looks like this:

     Imagine a whole bunch of these arches lined up, and you can picture how I think the timeline of history should be drawn. This model has its low points and its high points, but it is a consistent pattern that I think could be fitted to the history of the world in a suitable fashion. Only when we learn and study this repetition of history can we begin to foresee the tell-tale signs of the low points and the high points of the future.