Does a detective story have a shape?

Kurt Vonnegut had a theory that stories have shapes you could draw on a blackboard — man-in-hole, boy-meets-girl, Cinderella. The premise of this whole project is to test that literally: embed each sentence, add the vectors up one at a time, and watch the path the story traces through the space. If Vonnegut was right, stories of the same kind should trace similar paths.

I had a clean test. Take Sherlock Holmes — twelve formulaic detective stories, the closest public-domain thing to a Perry Mason box set — and ask: do the twelve resemble each other more than they resemble Grimm fairy tales or Moby-Dick chapters? If detective stories have a shared shape, the answer is yes.

I ran it with several embeddings. The number to watch is a separation ratio: how much more a series' stories resemble each other than they resemble other genres. Above 1 means a shared shape exists.

• Content shape (ordinary SBERT): Sherlock scored 0.87 — below one. Detective stories are no more alike each other, by content-shape, than they are like fairy tales. Vonnegut's blackboard, drawn in meaning-space, is empty.
• Structure shape (our form + entity embedding): Sherlock scored 2.70. Detective stories cluster hard, away from the other genres.

A 2.70! The content-free structure trajectory sees exactly what content-shape is blind to: detective stories move the same way. I was thrilled for about an hour.

The graph was secretly a clock

Then I did the thing this repo exists to do, which is to try to kill my own result. One of the features feeding the structure embedding was cum_cast — the number of distinct characters introduced so far. That number only ever goes up. It is, quietly, a monotonic function of "how far into the story you are." A sentence counter wearing a trench coat.

And a sentence counter will make every story look like the same rising ramp, which will make them all resemble each other, which inflates the separation for reasons that have nothing to do with narrative. This is the original sin the whole storyshape project was built to avoid — the naive version of "story shape" is dominated by PC1 ≈ sentence index — and I'd let it back in.

So I removed the one strictly-monotonic feature and re-ran. Separation fell from 2.70 to 1.37. Roughly half the beautiful result was a clock.

But — and this is why the stage was worth it — it didn't fall to one. Counting removed, Sherlock stories are still 1.37× more alike each other than other genres, and still more alike than shuffled versions of themselves. There is a real, if smaller, shared detective-form-shape underneath the artifact.

The bigger lesson: the picture is the wrong instrument

The other thing this stage taught me is that the 2-D shape plot — the pretty Vonnegut curve you'd actually draw — is a bad way to see any of this. I measured how much the dominant axis of the 2-D trajectory correlates with the plain sentence index, across every embedding I had. The answer was ~0.74, and for the skeleton embedding it was 0.90. The "shape" you plot is mostly just a clock, no matter what you embed. The real signal lives in dimensions the projection throws away.

That reframed the entire project. If the shape-as-a-picture is uninformative, the interesting question isn't "what does the curve look like" — it's "is the sequence of structural states predictable?" Can you, given the story so far, guess the shape of the next sentence?

That's a language-modelling question. And to ask it, I first had to turn stories into a language.