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# The Shape of Stories¶

### 13/01/2020¶

There’s a great clip of Kurt Vonnegart giving a lecture on “the shape of stories”. He makes the case that stories can be distilled down to a two-dimensional plot. The y-axis is the valence of the story (what he calls the "G-B axis" for good to bad), and the x-axis is time (which he calls the "B-E" axis, for - you guessed it - beginnging to entropy). Not only does Vonnegart say that stories can be distilled to these shapes, but also that:

There's no reason why the simple shapes of stories can't be fed into computers.

That is, we should be able to extract the shape of a story using algorithms! And so, in this post I will attempt to do just that; I will use sentiment analysis to try and empirically recreate the curves which Vonnegart attributes to several stories.

Let's start by importing the libraries we'll need and looking into some sentiment analysis.

## Sentiment Analysis¶

There are many approaches to sentiment analysis. The easiest is a simple bag-of-words model, in which we count up the number of positive words (“happy”, “good”, “amazeballs”) in the text, then count the number of negative words (“hangry”, “bleh”, “stanky”), and the valence of the text is the number of positive words minus the number of negative words. This approach will probably do for our purposes.

After a little Googling, I came across this page of sentiment analysis resources. I decided to go with SentiWordNet because it's built on WordNet which I'm already familiar with. SentiWordNet gives a positive sentiment and negative sentiment score to every synset (group of synonymous words) in WordNet's lexicon. Because a given word could have several associated synsets, each corresponding to a different meaning of the word, there are several possible sentiment values associated with each word. I decided to simply use the sentiment associated with the first synset of each word.

Let's make sure that this sentiment function returns sensible results:

Looks ok. Ideally terrible would be worse than bad, and misery would be worse than poverty.

## Text Extraction¶

We'll use Beautiful Soup to extract the text of the story from the web.

Let's see if we can extract the text for Cinderella.

Hmmm... this is looking a bit Grimm, and doesn't really match the narrative arc that Vonnegart described. Here's another version I found that looks better suited to this project:

# Data Inspection¶

We'll split this text up into 100 chunks of words, and calculate the mean sentiment for each chunk.

Let's look at the points where the highest and lowest sentiments occur:

Some of these make sense, others not so much. On the whole, I think this will be acceptable, but it will certainly be worth trying other sentiment analysis tools in the future.

# The Sentiment Plot¶

We now need to decide how to plot the sentiment over the course of the story. For Cinderella, the plot Vonnegart drew looked something like this:

The progress goes something like this:

• 0-20\%: Cinderella's mother has died and is forced to do nasty chores.
• 20-40\%: The fairy godmother gives Ciderella lots of nice clothes, makeup, and dresses so she can go to the ball.
• 40-60\%: Cinderella dances with the Prince and has a wonderful time.
• 60-80\%: After the midnight bell rings, she goes back down to a low valence. But not as low as she was originally because now she's got a wonderful memory.
• 80-100\%: Cinderella marries hte prince and lives happilly ever after.

Let's now compare this to the empirical sentiment over time.

# Smoothing the Sentiment Plot¶

The empirical sentiment plot is so jagged it's hard to discern any overall pattern. Let's smooth out the curve so that we can get a better sense of some high-level trends.

### Sliding Window¶

First, let's try running a sliding window across the sentiments. The width of the window is a hyperparameter we need to tune, so I plotted a few reasonable sounding values to see which looks best.

Window sizes of 5\%, 10\%, and 25\% all look reasonable. I decided to go with the middle one of these: 10\%.

### EWMA¶

Another approach to smoothing out the graph would be to use an exponentially weighted moving average (EWMA). This has the nice property that the contribution of words to the current sentiment value decays exponentially as you move through time. If the sentiment in the current window is given by $s_i$, then the EWMA sentiment value is given by

$$S_i = \alpha \cdot S_{i-1} + (1-\alpha)\cdot s_i.$$

Again, we have a hyperparameter: $\alpha$, the decay constant. And again, I plotted a few reasonable sounding values to see what looks best.

I think $\alpha=0.75$ is probably the best of these. But not as good as the sliding window with window size = 10\%, so I've used that one from now on. Let's now put that on the same axes as Vonnegart's plot, and see how well it matches up. Note that the range of the sliding window sentiments is very small, so we have to normalise it.

Not too bad. The main problem I see with this is that the empirical sentiment starts at a high point, whereas the Vonnegart curve starts at a low point. Looking back at the first paragraph, the opening is a little ambiguous:

A rich man's wife became sick, and when she felt that her end was drawing near, she called her only daughter to her bedside and said, "Dear child, remain pious and good, and then our dear God will always protect you, and I will look down on you from heaven and be near you." With this she closed her eyes and died.

# All The Stories!¶

Now that we've got our sentiment plotting procedure down, we can plot all the kinds of stories mentioned in Vonnegart's talk. In addition to Cinderella, we've got

• Man in hole: the protagonist starts in a comfortable environment, gets into trouble, then gets out again richer for the experience. I used The Hobbit as a typical example of this type of story, and approximated Vonnegart's curve as a cosine with linearly increasing amplitude.
• Boy meets girl: a boy meets a girl, is over the moon, everything goes to custard, but then he gets her back again and everything is wonderful. I had a hard time thinking of an example of this genre. I eventually settled on Jane Eyre, which doesn't quite fit the mould but seems to be close enough. I modelled Vonnegart's curve as a sine with linearly increasing amplitude.
• Kafka: not very pleasant man turns into a bug and everything is terrible forever. Easy enough to model as negative parabola with y-intercept of -0.5.
• Hamlet: a bunch of stuff happens, but it's never clear if it's good or bad. So we stay at -0.5 throughout the whole story.

Let's see how the Vonnegart plots compare to the empirical sentiment for each of these stories.