For What It’s
Worth
There's
something happening here
But what it is ain't exactly clear
There's a man with a gun over there
Telling me I got to beware
I think it's
time we stop
Children, what's that sound?
Everybody look, what's going down?
Isn’t it worth
figuring what is happening?
When something is happening,
it is generally obvious. In the world of
data analysis, pattern recognition, this is called a discontinuity, a phase change,
etc. Often when plotted as a curve, the data
will display a “Hockey Stick” shape, so much that I was tempted to use lyrics with
H-E- Double Hockey Sticks to begin the post.
The heel of that hockey stick most probably represents the beginning of a change from
one equilibrium to another. It can be expected that there will be two discontinuities,
one at each equilibrium. Knowing why
there is the first discontinuity might provide an understanding of the nature, the what, and
where, of that second equilibrium.
A plot of life expectancy shows a hockey stick shape, a discontinuity. The blue bars are the reported life expectancies for various period in history. The red line is a moving average of those life expectancies. A discontinuity happened in the 19th Century, …perhaps modern medicine and sanitation?…which is continuing today. However at some point this trend will be capped by the life span of a human and what we are seeing is a change from an life expectancy of ~30 years to one of ~100 years. Eventually it will be harder and harder to increase life expectancy and the curve will follow another downward facing hockey stick.
Source: analysis of data from https://en.wikipedia.org/wiki/Life_expectancy
Another famous instance of the
Hockey Stick shape may be global temperatures. Beginning at the start of the
industrial revolution and its accompanying burning of fossil fuel, this
increase will continue until it reaches a new equilibrium. That equilibrium can include humans that have
switched to non-fossil fuels for energy, or it can be without humans and their fossil
fuel burning. The first discontinuity has already happened. The debate is what and where will be that new equilibrium.
A third discontinuity is consumer prices. As I have blogged before, https://dbeagan.blogspot.com/2022/01/inflation.html,
there was a discontinuity that occurred with the Nixon Shock of 1971. It
is when the USD dollar continued to be the major international trading currency, but it was
no longer convertible into gold by foreign nations. It is suggested that this discontinuity has occurred and
the new trend will continue until an international trading currency which is separate from any national currency, is adopted. At that point there will be a second discontinuity.
Theses shapes are most probably the Cumulative Distribution Function of a logistic distribution, where ยต is the mean of the distribution, and note that the median, the 50% percentile value, occurs at this mean, and s is the the scale, an indication of the range over which the change occurs. The scale is a fixed factor of the variance of the distribution.
As shown in that distribution,
there will be a second change, discontinuity. Understanding the first can help make
decisions about the second. Stop. Everybody look what's going down.
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