Gangsters and Sigma Fields

Several months ago, during one of our crazy lunch discussions, one of my colleagues came up with the following line: “The Godfather is a sigma field, machaan.”

Now, most people would be bewildered by this statement. However, the geeks that we all were at that table, it struck us as a brilliant analogy and has stayed with us ever since.

Aside: The guy who made this comment was Rajendran, the only human being I know who thinks that explaining the geometry of least squares regression makes girls go weak in the knees. That might serve to explain why he came up with this one.

For the uninitiated (which is, I assume, most people reading this blog), a sigma field is a collection S of subsets of a set X such that:

  1. If the set E is a subset of X and a member of S, then so is X-E
  2. The union of countably many sets in S is also in S
  3. The null set as well as X belong to S

In other words, the set S is a self-contained universe of sorts. Which, when you think about it, describes The Godfather perfectly. The moral universe that the movie inhabits is entirely within the premises of the Mafia. We consider Carlo Rizzi to be a bad guy because he betrayed Santino. Never mind that Santino himself was a gangster and had enough bad karma waiting to bite him in the ass. We cheer when Michael orchestrates the killing of the heads of all the other New York crime families. Rooting for the bad guy is not particularly new, but what makes The Godfather so interesting is that it created a universe that was almost entirely independent of the society we know.

In earlier movies where we rooted for the bad guy, the law still had a part to play. Either it was portrayed as corrupt, or bumbling, or benignly admonishing, or something on those lines. In the ones with a moral, the bad guy you rooted for got killed in the end. But in The Godfather, the law enforcement is hardly seen on screen. The only one you remember is the corrupt cop who is in cahoots with a drug dealer and punched Michael in the face. Self-contained universe, like I said. Almost like Star Wars, except there are no people with snouts and three eyes on their head.

The long opening sequence has much to do with how this is accomplished: the first time you see Don Corleone, he is dispensing favours to a bunch of people on his daughter’s wedding day. A few days after that, he meets with a drug dealer who wants his assistance and refuses on “ethical” grounds. The fact that his empire itself is built on the other side of the law is not dealt with at all at this point. You only see the power he wields, and how he uses it to do good, not how he got it in the first place. So, by the time he is shot by the drug dealer, he’s gotten you to root for him and his son.

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3 thoughts on “Gangsters and Sigma Fields

  1. S says:

    I haven’t seen The Godfather yet but read the Puzo book and watched Nayagan, about which br’s said the same thing (“it’s a self-contained universe”). I’m no math whiz but safe to say two independently arrived at conclusions proves the hypothesis on this S field stuff?? 🙂

    Also, genuinely curious to know if there’s a mathematical analogy of sorts for Life Imitating Art. Like yesterday, I distractedly dropped the oil canister while cooking and it splattered the fridge, the hardwood floor and dish washer with olive oil… spent the next hour scrrubbing it clean. Then I saw the Rani Theni song video where a similar scenario plays in somewhat slow motion…

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