Today’s topic concerns exponential decay curves. This is what happens when “something” declines over time. A classic exponential decay curve is shown here:
Exponential decay curves are often found in nature. The classic one that is taught in classrooms concerns radioactive decay. For a given radioactive isotope of an element, the half-life of the isotope determines the shape of its decay curve. A half-life is defined as the amount of time for 1/2 of the radioactive decay for an isotope to have occurred. This can vary among isotopes from fractions of a second, up to 4 billion years in the case of Uranium 238. Half-lives are very important when calculating the potential radiation exposure to a radioactive isotope. Isotopes like Cobalt 60 are powerful radiation sources that are used industrially to examine welds and metals for defects. They provide plentiful gamma rays since the half life of this isotope is only 5.3 years. That is why there is concern about the use of this isotope in a dirty bomb, since the radiation from an explosive dispersal of Cobalt 60 would cause significant exposure to high powered gamma radiation.
Exponential decay curves may be found in other natural and also artificial systems. A new example of an artificial system that appears to be following an exponential decay curve is the Presidential tweet. The response to a Presidential tweet appears to be following a typical decay curve function. It is too early to get an accurate measurement of the half-life of tweet effectiveness, but a preliminary estimate is that the half-life of the response to a Presidential tweet is about two months.
Since this system of Presidential tweets is an artificial system (one not normally found in nature), it is uncertain as to what the response of the originator of the Presidential tweets will be to an ongoing decrease in tweet effectiveness. Most observers believe that the originator will greatly increase both the frequency and objects of tweets so as to continue to receive a total response to the tweets that approximates the effect of the first tweets.
However, it is nearly certain that since the effectiveness of any individual tweet will continue to decline, eventually the response to all Presidential tweeting may approach zero. There is a school of thought though, that maintains the belief that we may begin to see an inverse function develop for the tweet response. That is, instead of receiving a positive response to tweets, each subsequent tweet may result in a negative response. It is possible that the magnitude of the negative response may increase with additional tweets, so that Newton’s third law may be given a test in the political arena. For every action, there is an equal and opposite reaction. Observers of politics will be watching this process with rapt attention.