Musical

In a recent weekend, I watched a musical with my younger daughter.

Don't be surprised. This is a musical for kids organized by my princess' kindergarten. Although she is a few months before 4 years of age, the performance was interesting enough to keep her sitting attentively for one and a half hour.

You may think I would be rather bored. Well, yes and no. If you consider the quality of the songs and singing, there is certainly a big room for improvement. (In this regard, I must say the only musical that I praise is Les Misérables. The Phantom of the Opera may be acceptable, and I never fancy Cats or Miss Saigon.) Nonetheless, the story is a remarkable one. In my opinion, it outshines most of the tales by Hans Christian Andersen or Brothers Grimm - and is closed to the level of Aesop's Fables.

It is about the race between a tortoise and a hare and a few other animals.

Itebana

My recent leisure reading is Itebana (凍花) by Kazu Saiki (斉木香津).

This is a crime fiction about three sisters. In short, the eldest sister killed the second one, and, as the story evolves, the youngest found out what happened and why. The element of detection is close to nothing and, to me, the story lacks the zest - or the twisty turn that makes it stands out. While thumbing through the pages, my mind kept thinking what plot Agatha Christie would use if she were telling the same story.

Nonetheless, the eldest sister does impress me, for she has the extraordinary habit of writing her blog as well as a private diary. As Ayako Miura (三浦綾子) said, a person who has continued to write diary (or blog, I dare say) for 5 years must be successful in some aspect of their life, and it certainly takes twice as much effort and determination to have both.

Such a person would never kill another one - at least not without careful planning.

Cooperation

What we are getting at is, there are two possible ways to subsist in a situation of this kind: Everyone works together and life is good and sustainable, or everyone looks out for themselves and life is good for a while but miserable in the long run.

The very question that we arrive at is, for a group of hunters, how to ensure cooperation?

Alas, this is the classical situation where free market doesn’t work and external governance is necessary.  In other words, we need laws and regulations so that favorable behaviour (that is, cooperation and compliance with the group strategy) is rewarded and, more usually the case, punishment would be given to those who work for their own short term benefit and breach the motto of cooperation.

Go read Dixit and Nalebuff’s The Art of Strategy.

Stag

Unfortunately, we are not living in a world of alternative physics. If all troops try to expand, the military system could not sustain.

Yes, some of you may recognize, this is a variant of prisoners’ dilemma in game theory. To go one step further, the situation is akin to the “stag hunt” game analyzed by the philosopher Jean-Jacques Rousseau.

For those who are not familiar with the science of choice and strategy, let me explain briefly: In the stag hunt, if everyone works together to capture the stag, they succeed and all eat well. However, if some hunters come across a hare and are sidetracked to chase after hares, there will not be enough hunters to catch the stag. In that case, everyone will do better chasing after hares. The best strategy of the hunters as a groups is to go after the stage if and only if they can be confident that everyone else is behaving similarly. In other words, a hunter would prefer chasing hares if he has no confidence in what the others would do.

Troop

When I first began my discussion, I mentioned that there are two aspects to consider when we talk about the number of officer in each rank. So far, I have outlined the macroscopic view with regard to the structure of an army for a country. The problem, however, would look very much different when we see it from a microscopic point of view.

I mean when you consider the strategy of each individual troop.

The difference in perspective is simple. Although continual expansion is not a valid strategy to maintain a healthy staff ratio when you consider the entire army, it is a workable method when applied microscopically. In other words, for each individual troop, there is no reason to encourage resignation of Generals or Majors. To the head of a troop, the team should grow. There are always reasons to improve and increase the scope of work provided, aren't there?

But, how could every individual troop expand but the size of the army as a whole remains static?

PS. In a certain universe with a different set of laws for physics, this mathematical paradox does exisit. There, you can have the GDP growth rate of a country lower than the rates of each and every of its province.

Need

Discerning visitors may notice I have neglected a critical consideration with regard to the military system.

I mean, while discussing the senior-to-junior ratio, I have not touched on the size of army that is actually needed for a country.

Em… no. The issue is not the size of the army as a whole. From what we have discussed, the question should be the number of front line soldiers that a country need.

And it is not all that difficult to calculate – because that depends on the provision of hardware, which is known and change easily anticipated. To go one step further, by knowing the size of front line soldiers needed and the average number of years that they would be in service (that is, before promoting to do a senior job or leaving the army), one could plan the size of military schools so that the number of graduate would meet the need.

PS. With the discussion so far, it is not difficult to predict what would happen if there is a sudden surge in the number of graduates from the military school - or I shall leave it to your imagination.

Supervisor

You may note that my discussion yesterday focused on the feeling of the Majors and Colonels. I must say the other side of the coin also worth considering.

I mean the feeling of the supervising Generals.

You see? Not all Generals like to supervise Majors or Colonels, and would prefer an obedient though mediocre soldier, because the middle grade often have their own idea and may not like to take advice. (It goes without saying that the less competent a General, the more likely they would turn away a middle grade subordinate. That's another story.)

And, at the same time, when you consider the inevitable happening of asking more middle grade to do junior duty, it becomes obvious that the battlefield is splitting into two halves: soldiers (and Captains and Lieutenants) led by Generals, and solo combat fought by the middle grade (hopefully with some advice from the higher rank every now and then).

All of a sudden, I find the old traditional system of the Royal College of Physicians illuminating: It used to take 3 or 4 years to become a member (that is, fairly independent to work under ordinary circumstances), but another 10 to 12 years to really become a fellow (when they are really senior and capable of supervising).