Iterations

Continuing my research in steam punk as a literary genre.

I've discovered that the chapters of The Difference Engine, apparently a critical work in establishing this genre, are called Iterations. As in "the first iteration," "the second iteration" and so forth. Why?

Iteration, which literally understood is just a fancy way of saying "repetition," is a term of art among computer programmers. It refers to the looping of a program. Typically, each trip around the loop, each iteration, is at least subtly different from the one before. For example, a "Monte Carlo" program -- one that incorporates an element of chance -- might call for an operation to be repeated 999 times, with some averaging at the end of that sequence. The 453d iteration is subtly different from the 452s -- not only will the calculation likely have a different result that time due to the stochastic element, but we are one step closer to the desired averaging.

Of much greater historical significance are the iterations of the Newton-Raphson method of solving general nonlinear equations. The gist of this is that you start your efforts at solution with a best guess. If the guess is right, the equation works, and you're done. If  your guess is wrong, as is a lot more likely, but certain conditions apply, all is still good: trying to work through the problem will tell you how far wrong you are, and what your next guess should be. Then you work through that second iteration, etc.

Iterations in this sense were crucial in Babbage's work, which in turn inspired the novel and much of steampunk.