The math behind Gravity’s Rainbow (Part 4): The Poisson Distribution

Pynchon’s work is often accused of being quite ‘random’. But while Gravity’s Rainbow contains a lot of text about bananas, it could certainly not have been written by a monkey with a typewriter. There is an order to the madness. And I will show this by employing the same technique as one of the book’s characters!

Roger Mexico is a statistician working for the ‘White Visitation’ (a fictional top-secret psychological warfare agency) and concerned with the distribution of rocket impacts over London:

The rockets are distributing about London just as Poisson’s equation in the textbooks predicts. As the data keep coming in, Roger looks more and more like a prophet. Psi Section people stare after him in the hallways. It’s not precognition, he wants to make an announcement in the cafeteria or something . . . have I ever pretended to be anything I’m not? all I’m doing is plugging numbers into a well-known equation, you can look it up in the book and do it yourself. . . .

His little bureau is dominated now by a glimmering map, a window into another landscape than winter Sussex, written names and spidering streets, an ink ghost of London, ruled off into 576 squares, a quarter square kilometer each. Rocket strikes are represented by red circles. The Poisson equation will tell, for a number of total hits arbitrarily chosen, how many squares will get none, how many one, two, three, and so on.

Pynchon, Thomas. Gravity’s Rainbow (Classic, 20th-Century, Penguin) (S.54-55). Penguin Publishing Group. Kindle-Version.

Later in the book, we even get the formula he is using to calculate all this:

So the equation describes how events distribute over N different intervals. In this case, the intervals are different sections of London. The formula describes how many intervals there are where no more than n events happen, where the probability of an event happening in a certain interval is m.

e is Euler’s number and the “!” denotes the factorial.

We will now use this formula to see if the word “rocket” follows a Poisson distribution in  Gravity’s Rainbow. There are 346 mentions of this word in the 760 pages of the book. So the probability of the word occurring is 346/760 = ~45.53%. If the word appeared completely independently from previous mentions, it would follow this Poisson Distribution:

n=0 =>  428 pages should have no mention of the word rocket

n=1 =>  702 pages should have no more than 1 mention

n=2 => 751 pages should have no more than 2 mentions

n=3 => 759 pages should have no more than 3 mentions

n=4 => There should be no page with more than 4 mentions

Now let’s compare this with the actual mentions of rockets per page:

n=0 => 565 pages have no mention of the word rocket

n=1 => 678 pages have no more than 1 mention

n=2 => 722 pages have no more than 2 mentions

n=3 => 741 pages have no more than 3 mentions

n=4 => 751 pages have no more than 4 mentions

n=5 => 757 pages have no more than 5 mentions

n=6 => 758 pages have no more than 6 mentions

n=7 => 759 pages have no more than 7 mentions

n = 8 => 759 pages have no more than 8 mentions

n = 9  => No page has more than 9 mentions (only page 727 has)

Here is a little visualisation of how many pages there are where “rocket” is mentioned a certain number of times (P means as predicted by Poisson Distribution, B as in the real book)

So there are many pages where no rockets are mentioned at all, only a few where they are mentioned exactly once, but a lot more pages where they are mentioned much more often as would happen if the word was spread randomly.

To quantify this difference we can use a measure like Kullback-Leibler divergence, but it’s already pretty clear that the distribution is not Poisson. This means that we can go ahead and assert that Pynchon put a lot of thought into his writing and is not just a random number generator!

P.S.: Of course, the Poisson distribution is, in fact, a very crappy way to determine thoughtfulness. Just think about the book that would maximise the Kullback-Leiber distance to the Poisson distribution:

Page1: This This This This

Page2: is is is is

Page3: a a a a

Page4: great great great great

Page5: book book book book!