The math behind Gravity’s Rainbow (Part 6): Power Series

Gravity’ Rainbow can be a lot of fun. But there are also these episodes being absolutely bleak and repulsive. There is this famous scene where a character eats shit. But I think all the stuff about sexual violence is much harder to stomach:

power_series1
power_series2

I think it’s worth to think about a minute why this mathematical imagery is here in the first place. Even if you tend to think a lot about math: Are power series really the first thing coming to mind in such a situation? So maybe this tells us more about the narrator of the scene than the personality of Katje. It’s a very paranoid theory, but I like to imagine the scene being narrated by Franz Pökler, a character working as an engineer for the V2 Rocket. “Captain Blicero” (aka Weissmann) is his boss, who Pökler hates for various reasons, so he may imagine him being this outlandish evil person torturing people, which are (naturally) using math as a coping mechanism.

But anyway: A power series is an infinite series of the form:

A simple example of this is the geometric series:

Setting x=2 this could be used to model the exponential growth of bacteria, doubling every n-th time-step:

source

2^n is the general term. If you have this formula, you can calculate every element of the series.

But what if you have only some elements of the series? Is it possible to reconstruct the general term? What could it be for the following example?

2 + 6 + 18 + 54 + …

Spoiler: No, it’s not possible. Sure, it could be:

But it could also be this:

That’s the problem with being held captive by Blicero or reading Pynchon’s books: You never know what surprises they’ve got in store for you..

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