EXTRAPOLATION is the process of using a given set of points, numbers, or other data to establish a regression line to predict and project a trend within those numbers forward or backward or both, i.e. to attempt to predict outcomes for hypothetical cases. Decades ago, Algebra students were taught to look up logarithms in a table and then to attempt to go "beyond” (the significant figures of) the table. The extrapolation was based upon ratios and was thus a linear projection i.e. as if the logarithmic values followed a straight line formula. Instead, they are expressions of a curvilinear function. In the straight line method, one might assume that 23 and 28 would follow 8. 13 and 18. Little did these students know that these nu been rounded off and the entire logarithmic values was based upon the curvilinear nature of the progression.
But, to show how foolish extrapolation can be, we might consider an example. Suppose one is in the midst of a snow storm i.e. a blizzard. One shovels particular areas and within 45 minutes there is an 2-1/4 inches of new snow on top. To summarize, the snow is quoted to be falling at 3" an hour. So one may assumes by extrapolation, that rate the snow would accumulate to 72 inches in a day and 2,190 feet in a year. WHAT NONSENSE! (Snow fall is not generated by a man made machine with fixed rate of production.) As clouds vary, so snow varies —over time and over varying locations and terrains. It never snows for a year straight at a given rate. The rate of 3 inches per hour was special, ideo geographic, limited to just that hour at that location. There might have been a 4 minute period when a half inch in accumulated which, if projected, would be 15 inches an hour. But this was very short lived and the projection and extrapolation totally removes it from its context. Snow fall is not uniform and does not submit to and obey our prognostications.
One of the reasons as to why Extrapolation fails is that those who extrapolate are naive to the notion that change changes change and that what we put into the world makes the world operate differently. Sometimes reactions are self-catalyzing and sometimes they are self extinguishing and in a sense, all reactions develop lives of their own much like no two raindrops are ever exactly the same a that has ever existed, has not existed before (with those very same molecules).
Extrapolation is a mindless application of straight line projections to data. It is as naive as considering any particular endeavor without weighing in the tradeoffs, costs, resistance, etc. It sounds like politicians reciting what they will undertake when winning office and forgetting that there is resistance, tradeoffs, budgetary problems, process, egos to dealt with and legislative "gamesmanship.)
Be on the lookout for EXTRAPOLATIONS. Back in the 1960's naive commentators asserted that the crime rate was increasing 3 times faster than the population was growing. But which crime rate. For what portion of what city? And what ever makes us think that the rate was constant as if being orchestrated and choreographed by a “crime master.” All “rates” are guesses and based upon biased samples, which are changing both as we measure them and to, in part, because we measure them. Like cops, if we put them on film doing bad things and they know it, they will “lighten up” and try to look better for the camera. We sometimes forget that measuring anything feeds back in and can cause changes in the system. If there is too much crime, we can under report it. We forget that everything we do changes the world a bit so that the new change does not affect the world like the old change. Again, Change changes change.