It all started with a flip of a coin, 11 months ago…

I recently watched The Butterfly Effect. I must say, I think the director is very gifted (apart from, of course, the actors available to him… this movie top-lined Ashton Kutcher of That 70s' Show fame). The manner in which he tells the story is quite interesting, to say the least. I also saw Pi, another very good movie directed by Darren Aronofsky. He is more famous for a later movie, Requiem for a Dream, a movie I'll never see (I don't believe I can take depression of such a manic kind). His next movie, The Fountain, however, is a movie I watched, and found very interesting (expect a blog on that movie pretty soon, methinks).

Anyway, what connects Pi and The Butterfly Effect? Both touch, directly or indirectly, variants of a celebrated mathematical idea called the chaos theory (Pi talks more about chaos). And they both present very interesting ideas, which are worth exploring, at the very least (Fear not, for I shall do only that).

Chaos theory is a very catchy name for what is really a theory about the significant impact of initial conditions. No prizes for choosing the more glamorous one correctly (aap paanchvi paas se tez nahi hain). The theory says that changing the initial inputs to a process by very negligible amounts can sometimes have non-negligible effects on final conditions. What this means is that what seems to be a disorderly situation is actually a deterministic effect of some invisible changes in the manner in which things started. Therefore, and I think this is very interesting, chaos theory actually says that there is order in everything. One very good example of how initial conditions can affect what happens in the end is a Honda advertisement made a few years ago. The advertisement starts with a very harmless gear rolling into a slightly bigger one. The ad goes on for about 2 min, with every new auto component moving another, till, ultimately, an SUV moves a bit. Any slight change in the momentum of the first gear or its direction would probably have derailed the experiment long before culmination. And as expected, the ad-makers required 606 takes to get everything right. I don't know whether I can post YouTube videos here, so I'll just paste the link. Do go have a look.

http://in.youtube.com/watch?v=g2VCfOC69jc

See what I mean? Anyway, The Butterfly Effect is named after the famous chaos theory quote: The flapping of a butterfly's wings can cause a typhoon halfway across the world. Cool, huh? Well, not exactly true, but you get the drift. The protagonist is a guy who realizes that he can alter his memories, and in so doing, can actually modify the past. Now, the few of us who saw Back to the Future III know that this is not really true; all he does is create a parallel universe. But hey, guys, this is just a movie! Allow the guy some directorial license! Jokes apart, the movie is about how this guy keeps going back in time, changing every little thing, but coming back to the present to find out that something else has gotten messed up. There's another discrepancy too, which we shall ignore (after I mention it, of course). None of the changes he makes (like killing a guy) are negligible in any manner of speaking. But the movie ends very well, and all in all, was a good investment of my time (not a very busy boy, am I?). The line of the movie, for me, was when this kid goes to meet his father in a psychiatric hospital. His father was put in there, for he suffered from the safe gift/curse (Spider-Man fan alert!) as his son, the protagonist. So he tells his father, 'I'll send you a post-card once I make everything right.' The father says, 'You'll never be able to do it, son, for your actions will always have unintended effects.' And then proceeds to try and kill him.

Pi is slightly different, in that it talks of chaos, not chaos theory. It's about a crazed mathematician who believes that numbers alone can explain all natural phenomena. The apparent chaos will clear away once one is able to see the numerical patterns. And his goal in life is to find such a pattern in the stock markets (something malicious-looking stock-pickers constantly hound him about). Somewhere along the way, a Jewish mathematician (also crazed, I am sure) starts trying to attract him towards the search for a 216-digit number that will unlock future prosperity. When our hero's computer spews a 216-digit error code (actually 218 digits – a directorial error), he begins to smell a connection, and the plot thickens considerably (and how, for one sees brains lying around in railway stations, and drills are no longer used just for making holes in walls). The underlying theme of this movie is the search for this elusive (and incredibly long) number that will help the protagonist see the whole world clearly (and give him Matrix-type powers too, I bet). Whether he gets it or not, is for you to see and find out.

Looking at things one way, we can see that the chaos theory does make a lot of sense. An example from the book Black Swan can be paraphrased as follows. A path of a billiard ball as it hits the sides of a billiards table can be calculated reasonably accurately for a few bounces by taking into account the coefficients of friction of the table and the sides, the coefficients of cohesion, etc. But new factors keep being introduced as the number of bounces off the sides increases, as their effects become important. For instance, after the 7^th bounce, the masses of the people standing next to the table become important. After the 50^th bounce, the movement of an electron at the edge of the universe will also make a tangible difference to the path. This is bad news for those among us who suffer from over-analysis (they have problems anyway). But let me also say that if lightning strikes you as you make your way to work tomorrow, rest assured, it's not because you left your residence at 9:00:23 a.m. as opposed to your usual 9:00:10 a.m. And of course, you're already dead, so it's a moot point.

Don’t Look Now, But There’s Money in the Trunk

Conspiracy theories make people rich. Not you and me, of course (unless you are paranoid or have an extensive imagination, in which case there's hope for you). The conspiracy theory industry makes millions of bucks a year, at the very least. This includes books, movies, lecture series, and even serialized newspaper reports.

Organizations like the Ku Klux Klan, which have been near-defunct for many years now, still make huge amounts in membership fees, presumably because at any point of time, there will always be some people seeing Birth of a Nation (a highly controversial movie, banned in many countries) for the first time. And I'm sure almost all of you remember the furor that rose in journalistic circles when Princess Diana died. The then-Premier of the UK, Tony Blair, had to publicly denounce the 'Diana Death Industry', as he put it, and even then, the gold rush was scarcely derailed.

There are numerous books, periodicals, etc that focus on such sensationalist theories. Don't take my word for it, search for the word conspiracy on Amazon.com. In fact, I read in an excellent article on the subject that a new edition of the afore-mentioned Protocols of the Elders of Zion is available on Amazon, and has sold at least 64000 copies, which is a pretty handsome number (for a book whose origins have been proven to be fake).

When we talk of movies, many conspiracy movies have done well. The Fugitive, Men in Black, and to a lesser extent, The Matrix (although people like the series for different reasons) are all examples of movies where someone suspects that life isn't all that ordinary at all. And surprises of surprises, they are right. The biggest fish of all, of course, is the X-Files franchise. This series made tons of money for its producers, and was even made into a movie.

This is, more or less, all that I have to say on the subject (and Thank God for that!). I hope I have managed to convince at least some readers that conspiracy theories need to be consumed with a ton of salt. Of course, maybe this is all a conspiracy too, hatched by some evil sociologist who's cashing on our gullibility by forming an international syndicate of conspiracy theorists …

The Truth is Out There! (haunting music in the background)

The above line, made hugely famous by the X-Files TV show, conjures up the equally famous background score to mind almost immediately. The innumerable number of subplots of the main one – that there is information about extra-terrestrials that the government is hiding – have helped the producers mint quite a bit of money. But more on that later (surprise surprise). For now, we'll move to something at least as interesting.

Let us look at a few conspiracy theories, and I'll try to show where they come up short. The Pearl Harbor conspiracy is fairly popular. The proponents say that US officials were aware of the imminent Japanese attack, but purposefully chose to do nothing. Such an allegation is based on two assumptions: that the US officials had all the necessary information, and that they consequently acted rationally. Graham Allison (of Rationality Theorem fame) found that while the government did have all the necessary information, this information was scattered across departments. The entire picture wasn't formed in time. Bureaucracy was thus the main reason for the government not acting in time. Also, some of the information was actually misunderstood – the harbor was on alert, but for Japanese sabotage, not an aerial attack.

The Bible Code, a book by Michael Drosnin, was fairly popular a few years ago. In this book, he shows that many things that happen today in the world have actually been coded into the Old Testament, i.e. the Torah, which is written in Hebrew. He uses a computer to find certain terms in the Torah, by searching rows, columns and diagonals. He also went on to show how the Bible predicts the assassination of Yitzhak Rabin, the then Premier of Israel. Now, this is not a true blue conspiracy theory, but it does have elements of one (if you receive a lot of forwards, you might be able to draw parallels with how one can fold a $1 bill in a certain manner to predict the 9/11 mishap). The problems with such a theory are equally obvious and startling. Such a finding is quite random, in the sense that if one looks in any voluminous book in an old language (which the Torah certainly is) one is bound to find a column or diagonal that matches a certain word. This is just plain old and simple probability. A similar error occurs in Zeitgeist, where the filmmaker says that the advent of Jesus was simply an announcement of the beginning of the age of Pisces (see the movie to understand what this means). He goes on to prove this by presenting approximately ten paragraphs from the New Testament that mention the words 'two' and 'fish', and mind you, they don't always occur together in these chosen lines. Consider an exercise, where one uses a computer to generate a million paragraphs randomly, using nouns and filler sentences that are present in the Bible. Any math professor (or student) will guarantee that in a million such randomly-generated paragraphs, one will be quite likely to find at least 10 with these two words in them. This is akin to the famous analogy coined by Nashim Nicholas Taleb in Fooled By Randomness, where he says that if one has a billion monkeys typing on typewriters, one of these monkeys will definitely end up writing the Hamlet (Although it is widely believed today that Shakespeare was a plagiarist, I in no way want to add to speculation that he kept a private army of lesser primates).

One last theory must be debunked, at least partially, before I call it a day. Let me move on to the Pentagon conspiracy. Proponents say that a Boeing never hit the Pentagon, as the only released photos show no sign of the debris that one would expect from a Boeing collision (of course, the reasons are more numerous, but this is the basic one). The fact that the FBI refused to release any security camera footage has added to the speculation. The simple reason (Occam's Razor) for the fact that the photographs show a shadow approaching the Pentagon, and then show the damage, is that the number of frames captured per second is less than that required to capture such a collision. And the simple reason for the lack of any debris is that probably the debris fell on spots that the camera didn't capture (recall the no evidence of disease = evidence of no disease fallacy).

So you see, conspiracy theories are, more often than not, simply an indication that somebody out there is making some elementary logical errors. As a consumer of such theories, one must curb one's appetite for sensationalism, if one wants to maintain a realistic perspective. But of course, there's one more angle to this long-winding story – the economic one. When we look at that, we'll probably understand the most emphatic reason yet for the existence of these amazing inventions of idle minds.

Rabbits are DUMB!

And why is that? Is it because of their overzealous imagination, their propensity for disbelief, or their extreme paranoia? All three, actually. Especially since they mean the same thing (ok, don’t snigger at my cheap trick). Let me continue what I was saying earlier, about conspiracy theories. In particular, let’s look at what the common mistakes made are.

The first mistake that many conspiracy theorists make is that they do not account for the famous rule-of-thumb known as Occam’s Razor: Complicated stories are less probable than simple ones. Many such theories unnecessarily complicate what happened, usually to account for one tiny flaw in the ‘official’ story. There’s nothing wrong with such an approach, except that from the universe of possible corrections, the theorist chooses the potentially controversial one. Further, such theories very often employ logical fallacies. One example of a widely noticed fallacy is analogous to a doctor assuming that a person definitely doesn’t have cancer when evidence of cancer is absent. Such an assumption is valid only when evidence of no cancer is present. Putting this slightly differently, one could say that inconsistencies in a narrative are not necessarily indications of the opposite. Another important thing to think about is the number of conspirators. A simple rule is, ‘The more the number of conspirators required in a theory, the less likely it is to be the actual turn of events’. Conspiracy theories also need to be falsifiable. This means that the specific claims of the theory have to be such that they can be disproved. If this is not the case, it might mean that the theory is nothing but a convenient explanation of the facts.

Very often, conspiracy theories are like old-age economics. Just like the latter, they believe that all individuals act rationally, and always maximize the utility of consequences to them. However, most of us would realize that this is not the case at most times. This is the reason people doing MBAs have subjects like Behavioral Finance along with Economics. This argument was developed by Graham Allison in his book Essence of Decision, and he called it the Rationality Theorem. When people believe in rationality, they automatically exclude factors like bureaucracy and misunderstandings from their explanations of events, and consider only available data and results. In the rational world, all events are explained on the basis of rationality of participants. But a stubborn teenager’s fight with his dad should be more than enough to convince us that the opposite is often the case.

There are more problems with conspiracy theories, which I am sure you aren’t surprised to hear. Many such theories use ‘never-before seen government documents’ or ‘restricted files’ to arrive at conclusions. There is no way one can prove or disprove such claims of convenience. All one can say of such theories is that their veracity is questionable, at the very least. Finally, coming back to an allusion I made earlier, people tend to believe that significant events have significant causes. A study has been reported, in which four versions of an event were presented to the subjects where a foreign president was

1. Successfully assassinated
2. Wounded but survived
3. Survived with wounds but died of natural causes at a later date
4. Was unharmed

The subjects were significantly more likely to suspect conspiracy in the case of major events, i.e. where the president died, than in the other versions.

I don’t know about you, but I certainly was startled when I read of this study. But somewhere in my head, I think it all fits in with our subliminal need for excitement. Like our Indian batsmen, who play badly to make the game more exciting for the audience (unrelated, actually, but what the hell! … all bloggers voice their opinions on matters of public interest). Next time, I’ll try to be a little more interesting, considering that I myself fell asleep writing this portion. I’ll try to trash some popular theories. Won’t do too much, but hopefully, you’ll get the idea…