It really amazes me how so many subjects we study in schools and colleges are so interconnected. The clear-cut precise borders that were demarcated for us by our teachers become extremely blurred and sometimes even get decimated as one studies higher and higher levels. I do believe someone once made a comment about how knowledge is essentially a bunch of different rivers emptying into a single ocean. I couldn't agree more. Science may be the Ganga and humanities the Brahmaputra but they both end up reaching the Bay of Bengal. Taken in another sense, people may try and classify the world's waters into four or five different oceans (to say nothing of several hundred seas) but one just needs to glance at an atlas to realize that all the oceans are essentially just one big body of water. The same can be said of knowledge.
Those who don't agree can sample the following argument. What's the connection between a pair of birds with ticks on their heads and the scene in The Dark Knight where the Joker threatens to blow up two boats (one carrying immured criminals and the other ferrying common citizens)? Moreover, how does one connect both of these, somehow, to the oil crisis that nearly crippled America in the 1970s? The answer can be summed up in two words – Prisoner's Dilemma. Prisoner's Dilemma is a concept in Game Theory (a statistical subject with applications in various fields) which I think was conceived in the 1950s (not too sure) and later substantially improved by Robert Axelrod, a political scientist. The basic premise of the concept is fairly simple. Assume that you're a prisoner about to be incarcerated by the police for a crime that you committed in collaboration with another person. Now, let us suppose the police have enough evidence to immure both of you but in order to strengthen their case in court, they need an open confession from one of you. They come up with a clever strategy where they place you in one room and your partner in another. Then both of you are offered the same deal: If one of you confesses the crime (and in the process, implicating both collaborators), the informer will be let off, free, while the other will be given an extremely heavy punishment. However, if both decide to squeal, both will be heavily sentenced. If neither lets out any information, the police still have enough evidence to convict both of you but the sentence will be much lighter compared to the earlier scenarios. The ultimate decision will, however, be left to the prisoners themselves. Finally both of you are told that the other prisoner is being offered exactly the same deal at the same time.
The 'dilemma' comes from the fact that you, being cut off from you partner, have no opportunity to communicate with him and come to a joint decision. Therefore, your sentence depends not just on your decision but also on how your partner behaves. The best option, rationally speaking, would be to keep your mouth shut, hoping that your partner would do the same. If your ruse succeeds, the police will not be able to get a confession and therefore will have comparatively lesser evidence in court, thereby forcing the court to award a light sentence. But what if you don't trust your partner that much? What if you expect him to squeal? In such a case, the apposite move would be to confess as well since you will have no wish to languish in prison while your partner roams around free. Your partner, not trusting you either, will come to the same rational conclusion. As a result, both of you end up confessing – which means that both of you end up in jail for a long long time! In real life, the outcome of this dilemma depends very much on how your partner behaves as well as how you expect him to behave.
All this is very well but how does it relate to birds suffering from the itch or Hollywood movies? I got the bird example from a book by biologist Richard Dawkins called the Selfish Gene (Chapter 12 - "Nice Guys Finish First"). This book, by the way, happens to be one of my favourites. Do read it if you can. Coming back to the bird example, Dawkins explains that these birds end up helping themselves by picking the ticks from each others' heads (should be a funny sight, I must say). Through this symbiotic agreement, all birds put in little bits of individual effort to get rid of a common anathema. But problems arise when some birds become 'cheats' that is, they get ticks picked off their own heads while not performing the same tasks for others. In such cases, the birds face a Prisoner's Dilemma – will the other bird co-operate or cheat? What should be my decision? Whether birds get rid of their itch or not may seem to be a prosaic subject to the layperson but such examples often form the basis of evolutionary theory as Dawkins illustrates in his book.
The Dark Knight example must now seem fairly easy. The Joker planted explosives on both boats and placed the trigger for each boat's explosives on the other boat. He then told the people on both boats that unless one of them pressed their trigger first (and in the process, exploding the other boat), he would destroy all of them. The people on both boats faced a Prisoner's Dilemma (incidentally, with real prisoners). How would the people on the other boat act? Can they trust the others to not blow them up?
What about the oil crisis? The oil crisis of the 1970s was brought about largely due to the actions of OPEC (Organization of Petroleum Exporting Countries) which is often cited as the quintessence of cartelization. Cartels, by their economic definition, are collaborative groups of players in a market who come together for mutual benefit. A standard strategy that most producer cartels follow is to collectively raise prices of the product that they are selling (in OPEC's case, the product was oil). This allows all the players to get better revenues since they are now charging higher prices for their products – something that would have been impossible in perfect markets since competition drives prices down. However, cartels, in normal circumstances, are fundamentally unstable because they always face a Prisoner's Dilemma, especially when demand for the product is less. When demand is low, the producer always has an incentive to cut prices to attract more customers. Therefore, in a cartel, the partners are constantly watching each other. Will the other dude cut prices and attract more customers? More importantly, should I cut mine first and gain a larger market share? Cartels usually fall apart because of questions such as these. It's only in special cases (oil, diamonds, uranium) that cartels usually have a good chance of surviving (OPEC, De Beers and the Nuclear Suppliers Group).
Prisoner's Dilemma and similar game theory concepts are not the only things which connect several varied subjects. There are more connections being found every day between what were often considered fundamentally disparate subjects. Recent years have seen the development of interdisciplinary sciences such as Econophysics, an offbeat area where formulae and concepts used in physics are incorporated into economic theories (though I have no clue how effective this has been). School students who take up biology hoping to escape the influence of mathematics may be horrified to know how calculus has become an important part of higher biology. Again, in economics, more and more researchers are realizing the need to understand human psychology in order to formulate theories better (something which, in my opinion, ought to have been done a long time ago). I hope this trend continues. For a geek like me, the more knowledge one acquires, the more satisfied one feels.
