I sometimes say, with a smile and a wince, that it only takes three data-points for economists to start building a theory — and that in pinch, we can make due with less data. But of course, anyone who develops a theory based on limited data is prone to false extrapolations. Mark Twain offered one vivid example in his 1883 memoir Life on the Mississippi. This passage describes how there are places where the river loops back and forth in the shape of horseshoe curves. At some point, there is a cut-through (often caused by nature, but sometimes with an assist from those who saw the value of riverfront property). The river charges through the cut-through instead, and thus becomes shorter.
\”They give me an opportunity of introducing one of the Mississippi\’s oddest peculiarities,—that of shortening its length from time to time. … The water cuts the alluvial banks of the \’lower\’ river into deep horseshoe curves; so deep, indeed, that in some places if you were to get ashore at one extremity of the horseshoe and walk across the neck, half or three quarters of a mile, you could sit down and rest a couple of hours while your steamer was coming around the long elbow, at a speed of ten miles an hour, to take you aboard again. …
\”Pray observe some of the effects of this ditching business. Once there was a neck opposite Port Hudson, Louisiana, which was only half a mile across, in its narrowest place. You could walk across there in fifteen minutes; but if you made the journey around the cape on a raft, you traveled thirty-five miles to accomplish the same thing. In 1722 the river darted through that neck, deserted its old bed, and thus shortened itself thirty-five miles. In the same way it shortened itself twenty-five miles at Black Hawk Point in 1699. Below Red River Landing, Raccourci cut-off was made (forty or fifty years ago, I think). This shortened the river twenty-eight miles. In our day, if you travel by river from the southernmost of these three cut-offs to the northernmost, you go only seventy miles. To do the same thing a hundred and seventy-six years ago, one had to go a hundred and fifty-eight miles!—shortening of eighty-eight miles in that trifling distance. At some forgotten time in the past, cut-offs were made above Vidalia, Louisiana; at island 92; at island 84; and at Hale\’s Point. These shortened the river, in the aggregate, seventy-seven miles.
\”Since my own day on the Mississippi, cut-offs have been made at Hurricane Island; at island 100; at Napoleon, Arkansas; at Walnut Bend; and at Council Bend. These shortened the river, in the aggregate, sixty-seven miles. In my own time a cut-off was made at American Bend, which shortened the river ten miles or more.
\”Therefore, the Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago. It was eleven hundred and eighty after the cut-off of 1722. It was one thousand and forty after the American Bend cut-off. It has lost sixty-seven miles since. Consequently its length is only nine hundred and seventy-three miles at present.
\”Now, if I wanted to be one of those ponderous scientific people, and \’let on\’ to prove what had occurred in the remote past by what had occurred in a given time in the recent past, or what will occur in the far future by what has occurred in late years, what an opportunity is here! Geology never had such a chance, nor such exact data to argue from! Nor \’development of species,\’ either! Glacial epochs are great things, but they are vague—vague. Please observe:—
\”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 Oolitic 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, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.\”