Nation Reconciliation and Reconstruction

Resources for the Concerned Activist

Section
7

Military Science


    Overview: Martin Van Creveld, The Art of War: War and Military Thought. [External Reviews]

    James Holmes, Professor of Strategy, Naval War College, lists five "greatest military strategists" here.


Primary sources

How to think about warfare (more fundamental than strategy lessons, tactic lessons, etc.)

Master Sun's Art of War (Many translations)
   
Another source that talks about deception, a prominent element in the thought of Master Sun, is Joseph W. Caddell's Deception 101—Primer on Deception.

Carl von Clausewitz, On War, [online]. [External Reviews]

John Boyd's modern ideas  [Site 1] [Site 2] [Site 3]
   Note: Boyd did not write books, and there may be no permanent repository of the papers and "briefings" that he wrote.

Generals Robert H. Scales and Paul K. Van Riper
    Preparing for War in the 21st Century

General Robert H. Scales
    Future Warfare Anthology

Timothy Andrews Sayle
    Defining and Teaching Grand Strategy


Video Sources

General Paul K. Van Riper
    A Conversation with Paul van Riper

Ancillary readings

Center for Strategic and Budgetary Assessments
    Regaining Strategic Competence

Joint Force Quarterly
    Various articles on strategy

Inside (National Defense University)
    Strategists and Strategy

Discussion:

What does "chaos" mean? It means that a definitely calculable result at each iteration of an equation, the result of each iteration being fed into the next iteration, produces results that change greatly if the initials fed into the equation at the beginning are only slightly different. Here are two simulations that plot such successive values. Note how the dots are spaced out in the beginning but seem to be "attracted" to fill in a pattern.

If computers had not been available to evaluate a very great number of iterations of one of these so-called chaotic equations, it is unlikely that anyone would have noticed how a pattern is produced from many successive calculations, although the points so calculated are distant from each other. Some on-line devices that plot the successive answers obtained from the Henon Attractor equation or the Lorentz Attractor equation can be slowed down so that one can see the points as they are plotted one by one. The examples I have been able to include below are drawn so quickly that it is difficult to see how the figures are actually constructed on the screen.

Simulation from "free to copy" site
Henon Multifractal Map movie.gif [Info on Image]

Trajectory through Phase Space

A Trajectory Through Phase Space in a Lorenz Attractor [Info on Image]

Around and around and around she goes and where she'll land next nobody knows. 

One of the important observations made by Scales and Riper is that developments in warfare do not proceed in a linear way. They mean that, e.g., doubling the number of troops in an engagement does not necessarily double the effectiveness of the military movement because there are always other factors involved. What actually happens depends on other processes, and how they behave all may be sensitive to slight changes in initial conditions. The same kind of greatly varying changes in results depending on slight changes in initial conditions is demonstrated by a class of equations discovered in the course of research on mathematical weather prediction.  (See an exposition of one such equation, the Hénon attractor, here.) When such an equation is calculated through many iterations (a value calculated in one iteration becomes an input value in the next calculation) the answers do not plot close together. If the plotting of the graph immediately above is slowed down one can see that if a researcher were calculating values by hand, it would be a long time before any perceptible pattern would emerge. The sequentially calculated values are far separated and seem to be widely scattered. However, when many hundreds of values are calculated one can see that first a roughly circular pattern emerges and then it switches over to form the rest of a sort of figure-8 pattern, and over time it will go in circles in one half or the other half of the figure.




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This page was last revised 15 August 2016.