Tuesday, September 7, 2010

Deviation from Trend

A Non-Random Disturbance in the Force

Lots of things that grow, grow "exponentially." That means they double in size at regular intervals. It is a natural phenomenon. For some reason, one of the things that tends to grow exponentially is debt. The graph of total debt looks very similar to an exponential trend-line:

Graph #1: Total Debt and the Exponential Pattern

That closeness fascinates me. But the graph above is an old one, from my Google Site. I want to take another look, using debt numbers from the sources I found recently. You know: three sources, but one of'em doesn't line up...

It didn't make me happy, but I set the "mismatch" data aside. That left me with the 1956-1995 numbers and the 1975-2009 numbers. The numbers in the two sets are close. So I just took the 1956-1974 numbers from the one set and stuck them in front of the 1975-2009 data. And then added the exponential curve:

Graph #2: Total Debt and the Exponential Pattern

Pretty similar to the old graph. But then I started wondering about those little gaps between the red and blue trend-lines. I wanted to see the difference between debt and the exponential trend-line. I wanted to graph the difference. I got thinking, Suppose I use the exponential curve as a base line...

So I divided the actual debt number by the exponential trend number, subtracted 1 from the ratio, and showed the result as a percentage. The result amazed me. It is far less random than I expected. There is a pattern to it. It looks like a sine wave:

Graph #3: A Sine of the Times

We take the actual numbers for total debt in America. We figure out how much these numbers differ from a purely mathematical pattern -- the exponential curve. And amazingly, the difference looks very much like another purely mathematical pattern -- the sine wave. Except of course for that collapse, there at the end.

Clearly, there is more at work here than politics. The graph tells me that debt growth is more a function of mathematics than politics.

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