Why Mathematical Models Break Down. And Why Our Life Depends On That-1.

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It is in human nature to quantify things—nothing is wrong with that. Quantification allows us to see some order in otherwise seemingly chaotic things, it also allows to predict the outcomes based on those quantifications. Sometimes predictions pan out but often they do not. As the events of the last 20 or so years showed us, no mathematical model, no matter how sophisticated, can properly predict global strategic balance, even despite availability of what became known as a “Big Data”. Two things do not allow to trust such a modeling fully:
1. It matters WHAT data and WHO counts it. A famous meme of GIGO—Garbage In, Garbage Out did not appear out of nowhere—recall a complete trash all US pollster were providing prior to the latest US Presidential Elections. This example alone is a good illustration of a dreadful influence biases provide even in something as large politically as electing POTUS. Then, of course, comes WW II and how it was “interpreted” in the West. 
2. Anything related to strategy and military is inherently human at the very foundation, and as such it is stochastic in nature, that is susceptible to the introduction of random variables and those variables sometimes become this proverbial monkey wrench which screws up all, even perfect, plans. In the end, the data itself MUST be full and reliable—otherwise one gets Wall Street reports on the state of economy, which are as reliable and are as connected to the actual reality as I am a NASA astronaut. 
For a former military professional who had to deal with some operational issues and who survived the collapse of the USSR, it was always fascinating for me how the outcomes may be influenced by accumulation of sometimes really insignificant disruptors which literally change the state of the affairs almost instantaneously and dramatically—in global matters a decade or two is not that long, really. In historic terms it is altogether—an instant. Dmitry Orlov is very good in describing some of the factors which, in particular, influence collapse on a societal level. But my point here is simpler—it is to give some insight on how things go haywire in military-political field and how they lead to a gigantic outcomes. 
I am aware–people do not like math. But hear me out here, the math presented herein is not really that difficult. At least, I tried to exclude any kinds of even remote references to differentiation (and integration) which necessarily accompany all kinds of models—it will all be within very basic algebra of a middle school level, at least I tried to keep it there. So, here it is: The Global Status of the Nation. One of the methods (models), which is based on the body of works by all kinds of geopolitical thinkers from Mahan, Morgenthau and, eventually, RAND Corporation. Some notable Russian thinkers also contributed to it. It is, indeed, natural for people to have a number on anything. So, many thought for more than a century about how to put “a number” on the might of the nation. In my book I gave a brief review of the CINC (Composite Index of National Capability) and reviewed some of the predictors for military victory as well as the components of the status of nations. 
So, here is the (Nation’s) Status Model developed within the framework of the massive project titled Complex System Analysis and Modelling of Global Dynamics, which was done on the base of the world-renown Keldysh Institute of Applied Mathematics of Russian Academy of Sciences. A lot in this model also was taken from RAND’s estimates of national might. Well, here is this general formula. 
Don’t despair—this formula is as simple as a toilet. To get to the value of Status at any given time you have to merely multiply the values. In it, S(t) is a measure of a nations global status. S(t) merely stands (as a function of time) for Status of the nation in given time. In this formula FA(t) is a value (again—time dependent, hence (t)) of a function of “influence” which is not related to geopolitical factors and accounts for the product of values obtained for quality of governance, economic and military independence, plus additional factor of being in coalition etc. The formula for this is not difficult, albeit long, and with a calculation of a factor of governance based on expertise. We will omit reviewing this factor and go directly for G(t)—a geopolitical potential of the nation. Here, we go for the formula and this is how it looks:
In this formula all Xs with subscript stand for shares of the nation in global indices of: T-territory, D-demography, E-economics, M-military. Numbers above are exponents or the power to which those indices must be raised. These ARE very easy indices to find since all of this data is in the open. That is with a huge exception of the Military index. But let’s do some simple math exercise—let us compare G(t)s of say US and China, accepting FA(t) for both of them as equal and thus easily disposed of in our basic analysis. Let’s see how the United States looks in its main Xs in G(t) formula. For that we go to Internet and get data there, let’s count things for the US and China:
T–territory for the US will be almost the same as China’s, both have about the same size of territory, but let us be anal about it and go for 9.147 million square km for the US (and, consequently—9.326 for China). Consequently the SHARES in the global scheme of things are as follows: US—6.13% of global land mass (I use round number of 149 million for the World’s total land mass) and China’s-6.26%. 
D–demography, easy. The United States’ population is 322 million, China’s—1,404 million. Consequently the SHARES in the global population are as follows: US—4.31% of total population (I use round number of 7,467 million for the World’s total population) and China’s-18.8%.
E—economy. Easy again, we go for PPP as normal people do and here it is: US GDP is (per CIA)—19.36 trillion, China’s—23.12. Consequently the SHARES in the global GDP are as follows: US—15.24% of total GDP (I use CIA’s round number of 127 trillion for the World’s total GDP) and China’s-18.2%.
M—military. Before I announce a train wreck here, ask yourself a question when looking at the formula of G(t) why XM, that is military component not only has the largest exponent (0.43) of them all, beating even Economy and why Military needs its own formula for calculation? Here is the formula: 
Where M1 is a Share of the nation in global military expenditures (I need to hear warning bells and sirens going off like crazy now) M2 is a military potential of the nation’s Army, M3 is a military potential of nation’s Navy and, finally, M4 is a potential of a strategic nuclear forces. The immediate question which arises here is HOW do one calculate PROPERLY all those indices. Let us calculate comparative G(t)s and, as a consequence, S(t)s for the US and China based on assumed military parity, that is American XM=Chinese XM=1. Just an example, not real indices. So, G(t) for the US will be, using basic scientific calculator: 
0.5*(1+1^0.43)*6.13^0.11*4.31^0.19*15.24^0.27 = 
0.5*(1+1)*1.22*1.32*2.09=3.366  
For China this will look like this:   
0.5*(1+1^0.43)*6.26^0.11*18.8^0.19*18.2^0.27 = 
0.5*(1+1)*1.22*1.75*2.19=4.676
As you can see here, China squarely beats the United States for a title of the nation with the most geopolitical status, granted that we initially assumed that both nations have the same value of function of influence FA(t) and that their  XMs are equal–but they are not and the main REAL, tangible, component which will define most of those status bids is precisely this very XM and how it is interpreted correctly by serious analysts. That I will review in the next post. Needless to say, however, any calculation of national power and status without serious review of doctrinal, strategic and operational issues is a complete baloney–but that is what Western so called “expertdom” was doing for the last few decades. We all know the (catastrophic) results…
To Be Continued…
      

from http://smoothiex12.blogspot.com/2018/06/why-mathematical-models-break-down-and.html

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