The Date of Change.
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In the figure above the case of changing from a history where the shoreline is growing seaward to a time when the coast is eroding landward. The red dots represent the measurements taken, i.e. the data. Mathematics and fine computers permit us to fit a line to the data that most closely passes through the data. It doesn't hit all the points. It just the smoothest, simplest line we can draw through the data. We now have an equation and we can find the year that the change happened. We all this the critical point. The best estimate of when the change happened.