KOW links to a fascinating post about Israeli strategy in Gaza. I haven’t had time to wade through the original post yet, but just reading the KOW post I’m struck by the jump from inanimate complicated networks to dynamic human-based networks.

In general, the underlying idea is: each system has its own critical point. If I know where it is, I hit this point and destroy the whole system. If I do not know this, I will have to go on hitting different components of the system until I accidentally hit the critical point. The more components I damage, even without hitting the critical point, the closer is the moment when the system disintegrates.

And there is a certain connection between “q” - which is the percentage of component interconnection - and “Q” which describes the probability of the whole system collapse.

When the rate of component failure q is 11%, the probability Q(q) for total system collapse is 50% When q=25%, Q=81% When q=50%, Q=100%

Fig. 4. The Probability of System Collapse

So what does this formula tell us? In case the damage level of the components (q) within the system is 50%, the system will definitely stop functioning. There are simply no systems capable to withstand the malfunctioning of half of its components. In case q is 25%, there is still an 80% probability of its falling apart.

I’ll buy that one could make this sort of assessment of an electrical network or a water distribution system or an oil pipeline network. But a dynamic network of organizational authorities, human relationships and commands? I think we’d have to generalize away all the interesting content to make such a comparison.

Also, there are obviously assumptions about the underlying the network topology behind the above calculations. I’d be fascinated to learn what they are. Maybe when I read the whole thing I’ll find out.

While I admire the impulse, I have trouble seeing this Sim Afghanistan project ever contributing any real insights.

Same goes for the Sim Iraq idea.

Put simply, if we had adequate mathematical models for human and societal behavior, then we could apply them at home to figure out who will win an election before it happens. Actually, that would be an easier challenge because it wouldn’t confront any language or culture barriers.

I’ve got a quant background, so I deeply identify with the desire to rationalize decision making through the use of models (so that we can do substantive what-if analysis). But these problems are so poorly defined and the content so staggeringly broad that I’m skeptical that we have the adequate knowledge to start building a useful tool.

I just read a powerhouse book review by Freeman Dyson discussing global warming.

The entire article deserves to be read in full. For the moment, I’ll just comment on his conclusion:

All the books that I have seen about the science and economics of global warming, including the two books under review, miss the main point. The main point is religious rather than scientific. There is a worldwide secular religion which we may call environmentalism, holding that we are stewards of the earth, that despoiling the planet with waste products of our luxurious living is a sin, and that the path of righteousness is to live as frugally as possible. The ethics of environmentalism are being taught to children in kindergartens, schools, and colleges all over the world.

This is the most succinct assessment of the state of the debate that I’ve read. Before any adherents to this secular religion start commenting, let me point out that Dyson doesn’t think this secular religion is necessarily a bad thing at all:

Environmentalism has replaced socialism as the leading secular religion. And the ethics of environmentalism are fundamentally sound. Scientists and economists can agree with Buddhist monks and Christian activists that ruthless destruction of natural habitats is evil and careful preservation of birds and butterflies is good. The worldwide community of environmentalists—most of whom are not scientists—holds the moral high ground, and is guiding human societies toward a hopeful future.

Be that as it may, successful policy requires more than good intentions and wishes. On this front, Dyson points out the issues created by the distorted discourse:

Much of the public has come to believe that anyone who is skeptical about the dangers of global warming is an enemy of the environment. The skeptics now have the difficult task of convincing the public that the opposite is true. Many of the skeptics are passionate environmentalists. They are horrified to see the obsession with global warming distracting public attention from what they see as more serious and more immediate dangers to the planet, including problems of nuclear weaponry, environmental degradation, and social injustice. Whether they turn out to be right or wrong, their arguments on these issues deserve to be heard.

I would add that there are also plenty of moral people who are horrified to see the obsession with global warming distracting public attention from more serious and immediate threats to the well-being of humanity, but that’s a discussion for another time.

Ultimately, we need to see clearly if we are to have the best chances of crafting successful policy. Hopefully, with the efforts of thinkers like Dyson, we are improving the precision of our collective sight.

For any who have been enjoying the war gaming discussions, there is a treat for you over at Argghh! John brought his extensive professional experience to bear in an excellent post discussing the role of Lanchester in military modeling.

…Lanchester can be useful, at it’s most macro and most micro levels, when you are comparing forces which can be generally assumed to be at parity on the issues in contention. Oddly enough, that’s pretty much all that Lanchester was proposing.

Such as modeling force-on-force from a hardware perspective, to examine the effects of the hardware. It can also be useful for examining organizational structure and doctrine - again, essentially positing a peer opponent. If your hardware wins, and your doctrine wins, and your hardware *and* doctrine wins in a Lanchester world, you are going to probably fare well, within the confines of entropic events and effects.

Of course, that’s a very narrow set of bounds. And the consequences of bad assumptions about parity (and *your* basic competence and morale) are huge.

Read the whole thing.

Argghhh! was kind enough to link me a few days ago with some comments and I left the following on their thread.
—
Thanks much for the link.

I was being a bit harsh, so let me clarify myself.

Mathematical laws of chemistry describe immutable dynamics of the physical world. I question whether combat has any similar immutable dynamics that are waiting to be mathematically modeled. The difference lies in the thinking adversary inherent in war, as opposed to the stable relationships of chemistry.

Maybe the mathematics of dynamical systems offers a way to account for this - I think this is why chaos and complexity theory get folks so excited - but I haven’t encountered it yet.

My second post didn’t claim Lanchester wasn’t useful; it argued that it was being used in situations where it wasn’t appropriate. The question wasn’t ‘is Lanchester useful,’ it was how often is it useful and in what cases? I was voicing my concern that Lanchester is rarely useful and sometimes used inappropriately. Not because it helps, but because it’s something concrete we can work with.

… of course it would have helped my argument if I had, I dunno, had an actual example to back that up…

To refine my earlier critique of Lanchester, his model applies to combat situations where the limiting factors to one’s destructive firepower are mass and weapon efficiency. Such situations do arise in war, and therefore Lanchester’s model is an appropriate tool for this narrow subset of military engagements.

Iwo Jima offers a classic example of a battle that fit the assumptions of Lanchester’s model. The small size of the island led to concentrated, firepower-based combat. J.H. Engel studied the recorded casualty rates to demonstrate that attrition during the battle for Iwo Jima closely followed the rates predicted by a Lanchester-style model [1].

Other historical studies show varying results, some demonstrating support of Lanchester’s linear law, others finding inconclusive results.

While the coefficients of attrition rates can be modified to account for training, terrain, moral and the host of other factors Lanchester does not explicitly consider, these modifications do not change the fact that Lanchester chose to make these factors exogenous to his model. This says a great deal about his assumptions regarding what dynamics would be interesting to study, and the implicit assumptions accepted by subsequent analyses using his models. My concern is that while it accurately describes a relatively rare type of military engagement, Lanchester’s model became the de facto standard for all combat.

[1] Engel, J. H. “A Verification of Lanchester’s Law,” Operations Research, 2, 163-171 (1954).

Perhaps I’m the last one to the party on this, but Penny Arcade of all places clued me into a subculture of flight sim enthusiasts who’ve built their own online air traffic control net to manage a virtual airspace of fight sim pilots.

I hope that the FAA already has people looking at SquawkBox; I doubt they could build a better test environment for candidate airspace modernization ideas, and here is one already sitting out there.

During the 20th Century, cryptographers repeatedly found the precise mathematical tools they needed already perfectly formed (having been developed by number theorists for completely different reasons). It was like the guys building the Saturn V rocket wandering into a hardware store and finding precisely the part they need already sitting on a shelf in the corner. “How’d this thing get here? Why’d somebody build it?” “That? Oh, some guy just made it because he thought it was interesting. Wrote a paper about it, you know.” The 21st Century may witness a similar phenomenon in the realm of hyper-realistic online environments for scenario gaming and analysis of alternatives.

Lanchester’s models of attrition, though originally published in the early 20th Century [1], still represent the deepest foundation of much of American military modeling.

The assumptions of Lanchester’s original model include the following:

• in combat, the primary form of self-defense is to kill the enemy before he kills you (p47)
• combat is essentially collective (p47)
• each side enjoys equal benefits from cover, morale and training (p49)
• battles are fought to conclusion until one side is annihilated (implicitly assumed throughout)

Each side’s relative rate of attrition, then, depends on the number of opposing forces, their rate of fire and the accuracy of their weapons.

A consequence of this model is that:

a small force attacking or attacked by one of overwhelming magnitude is wiped out of existence without being able to extract a tool even comparable to its own numerical value; it is necessary to say in the open since, under other circumstances, the larger force is unable to bring its weapons to bear, and this is an essential portion of the basic hypothesis. (p63)

In short, Lanchester model applies to the very narrow range of situations where two forces mechanically pound each other until one collapses. There is no defense; only a faster rate of fire, more forces or more accurate weapons. The entire modern system, as Biddle calls it, developed in order to avoid this situation. Thus, if one were to find one’s self in a situation where Lanchester’s model applies, then one already knows that he is facing an enemy not using the modern system.

Also note that if these assumptions ever do hold, victory requires a mathematically illiterate opponent.

Therefore, the accuracy of a Lanchester-based analysis depends in large part upon an ill-trained and incompetent enemy. This seems to be the least interesting scenario to explore, not to mention the least important.

[1] F. W. Lanchester. Aircraft in Warfare. Sunnydale, CA: Lanchester Press. 1995 (originally published: 1916).