https://www.google.com/books/edition/_/EclFh0oTx-8C?hl=en&gbpv=1
“Nonlinearity and Friction”
The sole outstanding item is the concept of nonlinearity as it has come to be understood in fields like mathematics and physics since the early 1960s. By revealing how small differences in inputs can make large differences in outcomes, nonlinear dynamics will not only complete the task begun in chapter 6 of building indirect arguments for friction 's undiminished persistence in future war, but furnish the conceptual elements needed to update and extend Clausewitz's original concept.
The idea that the subsequent motions and effects of physical phenomena could be completely predicted on the basis of their earlier states was first argued at length in the 1750s by the Jesuit priest Roger Boscovich (1711-1787). However, it was Laplace who … seemed to make good on this heady promise. At an early age, he set himself the task of tying up the loose ends of the Newtonian [universe].
Using the improved calculus developed by various colleagues, particularly Joseph-Louis Lagrange, Laplace was widely perceived to have "removed all the known errors from, and explained all known anomalies in, the Newtonian cosmology and Whereas Isaac Newton (1642-1727) had never been fully convinced of the stability Of the solar system, suggesting that it might require some divine correction now and again, Laplace eventually claimed to have proven "that every known … variation … was cyclic and that the system indeed entirely stable and required no divine maintenance."
On Laplace's understanding of reality, the operation of the universe, down to the most minute details and the smallest particles, is strictly determined by quantitative, predictive, mathematical laws. The world is quite literally a giant clockwork. [Therefore,] to Laplace's so-called "demon", (a sufficiently vast intelligence with … accurate and complete data about the universe) …, all past and future States are calculable.
During the drafting of the first edition of Newton's Principia Mathematica, … Newton ran into difficulties moving from the problem of two bodies mutually attracted to one another by gravitation, which he easily solved, to the problem of describing the dynamics of many such bodies (the many-body problem)."
In the summer of 1694 he returned to this problem in the form of [studying the motion of] the moon … about the Earth, which was in turn orbiting the sun (the three-body problem). Once again, though, Newton's achievements fell short of his aspirations. In retrospect, Newton's difficulties with the irregularities Of lunar motion are wholly understandable. As we now know, the three-body problem "does not admit a general analytic solution.” … The problem he intended to solve was literally an impossible one in the sense which Newton aspired to solve it
Authors note: What this means is that there is no equation that can accurately solve the three body problem.
The first individual to recognize that the three-body problem included unstable or nonperiodic behavior was Poincaré. In an 1890 essay he showed that a gravitational system involving only three bodies would not always give rise to predictable or periodic motion. Specifically, in the case of an idealized form of the three-body problem in which the third body is vastly smaller than the other two, Poincaré discovered motion so complex and irregular, “homoclinic tangles" to use the technical term, that he did not even attempt to draw the corresponding figure. This "chaotic" behavior is "fundamental" or built in; neither "gathering more information," nor processing it better, will eliminate the unpredictability.
Clausewitz wrote of war that no Other human activity "is so continuously or universally bound up with chance" suggested that war most resembles a game Of cards in its sensitivity to chance." He and Scharnhorst believed that chance (Zufall) could not be eliminated from military affairs. Clausewitz identified Chance events as an explicit source of general friction, although he did not (and could not) explain how small differences from what is expected or predicted could potentially turn success into failure and vice versa.
Laplace’s presumption is that human ignorance prevents us from completely eliminating tiny differences between our representations of phenomena and their actuality. If, however, these small differences cannot be eliminated, then nonlinear dynamics explain how global or macroscopic unpredictability can arise from the structural dynamics of iterated feedback when the feedback function exhibits, in at least some part of its domain, extreme sensitivity to initial or later conditions.
… there is increasingly persuasive evidence from a number of fields, especially mathematical logic and physics, that any coherent or formal system we develop "to represent or deal with large portions of reality will at best represent or deal with that reality incompletely or imperfectly," it appears that these differences and mismatches cannot be eliminated.
Consequently, the existence of nonlinear Systems confirms some of the deepest insights Clausewitz and Scharnhorst had into the nature of combat processes and the fundamental role of chance in those processes. It also suggests that unforeseen and unforeseeable differences in initial or later conditions, which, on present evidence, cannot be wholly eliminated even by Laplace's demon, allow us to subsume chance within the framework of nonlinearity.
Conclusions
The difficulty with this Laplacian outlook is not, of course, its plausibility or enduring appeal. By the beginning of the twentieth century the vast majority of working physicists accepted "Laplacian determinism", meaning causality plus long-term predictability, as a well-established scientific fact, and many people still do so today. The problem is that the universe we happen to inhabit is not [fully] deterministic …, not even [in] quantitative domains like physics and pure mathematics.
The first takeaway is that Laplacian determinism is a narrative that a large section of the world actually believes in, up to and including other scientists. For instance, such beliefs in this determinism is a critical part why the Allied armies of WWII were considered tactically inferior to their German counterparts. For centuries, the purpose of studies in leadership was teach officers to execute orders without friction; the closer a general could cure his army of this affliction, the better.
But what happened in WWI was the maturation of mission command (Auftragstaktik). Taking from Clausewitz’s understanding of friction, the idea was that friction cannot be cured, and therefore its only solution is by exploiting the enemy’s friction better than they can. In other words, it was better to solve friction by not making as few mistakes as possible, but by causing the enemy to make more.
However, the second takeaway is that, despite the success of this model, there are large portions of Western Society outside of the military which believe that friction is so easy to eliminate from an enterprise that its existence is proof of incompetence.
This narrative is a major cause for the growth of conspiracy theories today. Not only does this cause people to overestimate the power of large organizations, but such failures to reach their expectations often becomes proof that such failure was intended by some shadowy, more competent antagonist.
The fact of the matter is that if the chaos and uncertainty of friction cannot be eliminated from math and physics, it cannot be eliminated from human activity. Furthermore, the faster or further a human enterprise attempts to pursue a goal, the more resistance this friction will cause. All else being equal, large goals in a quick timeframe will cause the most failure.