Why I never took a history course in college.
Adam Gopnik, August 28, 2014 The New Yorker daily comment
But the best argument for reading history is not that it will show us the right thing to do in one case or the other, but rather that it will show us why even doing the right thing rarely works out.
... What history actually shows is that nothing works out as planned, and that everything has unintentional consequences. History doesn't show that we should never go to war -- sometimes there's no better alternative. But it does show that the results are entirely uncontrollable, and that we are far more likely to be made by history than to make it. History is past, and singular, and the same year never comes round twice.
In the summer after I graduated high school I read War and Peace. It was just after I had taken a calculus course and the analogies made by Tolstoy between history and calculus made a lasting impression on me. Adam Gopnik's blog posting reminded me of this and here are two links that give more details about Tolstoy's comments related to calculus in War and Peace.
The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history. But to arrive at these laws, resulting from the sum of all those human wills, man's mind postulates arbitrary and disconnected units. The first method of history is to take an arbitrarily selected series of continuous events and examine it apart from others, though there is and can be no beginning to any event, for one event always flows uninterruptedly from another. The second method is to consider the actions of some one man- a king or a commander- as equivalent to the sum of many individual wills; whereas the sum of individual wills is never expressed by the activity of a single historic personage. Historical science in its endeavor to draw nearer to truth continually takes smaller and smaller units for examination. But however small the units it takes, we feel that to take any unit disconnected from others, or to assume a beginning of any phenomenon, or to say that the will of many men is expressed by the actions of any one historic personage, is in itself false. It needs no critical exertion to reduce utterly to dust any deductions drawn from history. It is merely necessary to select some larger or smaller unit as the subject of observation- as criticism has every right to do, seeing that whatever unit history observes must always be arbitrarily selected. Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
"Absolute continuity of motion is not comprehensible to the human mind. Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements." "By adopting smaller and smaller elements we only approach a solution of the problem, but never reach it," Tolstoy declared. "Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach the solution of the problem." Building on this analogy, Tolstoy turned to the calculus as a model of how to apprehend history. "A modern branch of mathematics having achieved the art of dealing with the infinitely small can now yield solutions in other more complex problems of motion which used to appear insoluble," he wrote.