People who think that I am on some sort of a crusade against the political “science” or what passes today for “history”, or rather what it becomes once some “historian” begins to offer “the range of interpretations”… they are absolutely right. These two fields of human “academic” activity–and this is not my definition, many other people used and continue to use it way before me–are the fields in which credentials are bestowed upon primarily interpretations and personal (however “justified” with sources) opinions. But in history, at least, there is some inherent knowable truth which could be found, once layer upon layer of “interpretations” will be peeled off, especially when it is done by professionals who know the subject which constitutes this layer. This is not the case with political “science” which for the last decades produced a dearth of BS and failed to predict just about anything.
It is not surprising. Just take a look at the political “science” courses, say in Columbia University, and you will find there a hodgepodge collection of mostly “current events” theoretical BS which anyone with IQ higher than room temperature can get from media. Here is one “unit” which has some relevance to real world: DATA ANALYSIS & STATS-POL RES.
This course examines the basic methods data analysis and statistics that political scientists use in quantitative research that attempts to make causal inferences about how the political world works. The same methods apply to other kinds of problems about cause and effect relationships more generally. The course will provide students with extensive experience in analyzing data and in writing (and thus reading) research papers about testable theories and hypotheses. It will cover basic data analysis and statistical methods, from univariate and bivariate descriptive and inferential statistics through multivariate regression analysis. Computer applications will be emphasized. The course will focus largely on observational data used in cross-sectional statistical analysis, but it will consider issues of research design more broadly as well. It will assume that students have no mathematical background beyond high school algebra and no experience using computers for data analysis.
As you can see yourself–they give them a very basic math, which later finds its other incidence, buried in the pile of purely story-telling topics such as “ISRAELI NATIONAL SECURITY STRATEGY, POLICY AND DECISION MAKING“, such as, and you have guessed it–Game Theory. Among all this disjoint collection of “stories” about politics the most remarkable is this: THEORIES OF WAR AND PEACE.
Salvo Equations’, unlike Osipov-Lanchester model, deal with discrete values. That is the things which you can actually count in exchange, they are not continuous, such as, for example an infantry battalion under the artillery barrage where it is possible but extremely difficult to model losses because not only the barrage could be continuous (for an hour with unknown number of shells) but depend dramatically on the design of defensive positions capable to take some degree of damage and thus save lives. In the end, even awareness and running skills of soldiers could be a factor in such an ordeal, which makes it extremely difficult to predict. Here is how Lanchester’s model looks like for combat:
This is not a nice looking set of differential equations where coefficients a and e define the rate of NON-combat losses, b and f define the rate of losses due to fire impact on areas, c and g define the rate of losses at the front line (immediate contact) and d and h are the numbers of arriving or withdrawing reserves. You see, a hot mess. And then, of course, you cannot shoot down every single artillery shell. Not so with missiles, which you can shoot down and which are discrete by their very nature, as are ships. If you have 5 ships in your task group–that is it. This is 5 ships and that is what gives Salvo Model an elegant and easily understood form. Not in embellished form, I underscore. Embellished Salvo Equations are a bit different animal and require a serious understanding of weapons, but I will touch upon those later. Here is basic Salvo Model for two hostile forces (fleets) A and B.
The beauty of this model is in the fact that it is not necessarily just a naval one. Missile exchange exists not only at the sea and between fleets. One can apply this model to exchange between defended base and combat air component attacking it. It is a classic missile exchange between discrete forces. We also will look into that, but for now it is clear that at this level of basic Salvo Equations one can easily “play” with them based on some assumptions and get a feel of how they work. Mathematically it is very simple and I did present some examples before elsewhere but let’s play a bit. But to cool down your enthusiasm a little bit because of a seemingly simple math in this model, the math behind it is actually quite complex and salvo model is basically a tip of the iceberg and its application requires a serious tactical and operational (and engineering) knowledge which, of course, is beyond the grasp of political “scientists”.
Here is a general solution for a salvo by a submarine:
So, this is just a minuscule part of what is needed to fully grasp what is this all about in Salvo Model, not to speak of Embellished Salvo Equations. So, don’t get cocky just yet. You will have the chance to get cocky once you will follow my blog and, of course, support (those well-off among you) me on Patreon.
As you can see yourself A doesn’t fare that well–it gets completely destroyed, and loses all 5 ships. But what about B. Plug in your numbers. As you can see, B didn’t fare much better and got its ass handed to it by A. So, two task groups basically sunk each-other. Of course, this is a completely unrealistic scenario but it showed that B having much less “resistance” to being taken out by enemy missiles (only one per each B ship) couldn’t capitalize on its advantage in a number of missiles it had over A. Force A ships simply could absorb more battle damage. If only B had better air defense or could absorb more damage. Should a1=2 and b1=2, that is being the same, force B could have won this exchange over A and would have retained 2.5 ships afloat. We round it and it is 3 ships–this is victory, a bloody one, but victory nonetheless. So, here we are, with some example of how simple this basic model is. But, of course, as you may have guessed it already, the devil is in those pesky details which define modern missile combat and that is a hell of a topic, which I intent on discussing…
P.S. If anyone notices some stupid mistakes in calculations, please inform–it is evening and even two monitors is not enough for navigating this mambo-jumbo. Do not forget to support me on Patreon.
To Be Continued…