In Chapter 17 of Life on the Mississippi, Twain writes the following:
"In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oölitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three quarters long."
This is an example of extrapolation in mathematics, or assuming that a statistic will stay at a steady rate forever and that by applying this statistic, one will reach a reasonable conclusion. Extrapolation involves reasoning beyond what is known to make other conclusions or predictions. Twain is clearly showing the ridiculous effect of applying extrapolation without thinking about other factors that could have caused the shortening of the Mississippi, such as human-made construction. His conclusions are patently ridiculous, as the Mississippi River would have reached far further than just into the Gulf of Mexico if it were over a million miles long. Twain is ridiculing people's tendency to be fatuously certain of certain facts and willing to apply them without using a modicum of common sense.
Twain begins his indication of frustration with those who tried to use extrapolation to predict anything about the river by citing statistics that showed the lower Mississippi River had "shortened itself two hundred and forty-two miles" over a period of one hundred seventy-six years. Twain creates an average rate of change based on this distance and time ("a trifle over a mile and a third per year"), then uses extrapolation to draw the ridiculous conclusion that
just a million years ago next November, the Lower Mississippi was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-pole.
First of all, this is an impossible distance - the river would circle the globe many times over if it were that long. Secondly, Twain is mocking those who claim to be capable of measuring a span of time so specifically as to be able to pinpoint it to the month. Finally, Twain spends a great deal of time detailing the numerous ways in which the Mississippi constantly changed. Extrapolation of any sort was pointless - the pilots needed to know the basic shape of the river intimately, but then had to be able to observe and alter their course in response to the continual changes of the river banks, bottoms, and obstacles.