Chapter 22: Geometric Film & Television — Narrative Trajectories and Editing Rhythm

RUNNING EXAMPLE — Sam’s Cutting Room

Sam is a film editor who has been working on the same sequence for three weeks. The director wants it to feel right; the producer wants a runtime; the studio wants a trailer moment. Sam has a Premiere timeline with thirty-two candidate cuts of the same scene, ranging from a four-minute long take to a ninety-second montage, and she knows — in the way editors know — that each cut is a different film. What she does not have is a language for the difference, beyond the workshop vernacular of rhythm, breath, energy, propulsion. Her producer wants something more precise; her director wants something more honest; her own intuition wants something more describable than itself. Sam is the protagonist of this chapter because her problem is the chapter’s unrunnable experiment: film has a trajectory geometry, and that geometry has a sign we have not yet measured.

We state at the top what we have not done. The Gutenberg–Goodreads experiment of Chapter 20 is real data. The FMA–MERT experiment of Chapter 21 is real data. The film experiment in this chapter has not been run. Everything we say below is speculative-but-principled: we describe what the pipeline would look like, what predictions the framework makes, what empirical outcomes would support or falsify those predictions, and we state the predictions before anyone runs the experiment so that the prediction is honestly adjudicable rather than retroactively rationalized.

22.1 Why Film is Harder

Film is a harder modality than either text or audio for three structural reasons that bear directly on the geometric framework.

First, the token boundary is constructed. A book has paragraphs that the author set. A track has discrete timesteps from the encoder. A film has a shot, bounded by cuts, and the cut is an editorial decision that shaped the film; the shot boundary is itself part of what the film is. This is not a bug in the framework; it is a feature of the modality that the framework will need to respect. The shot-sequence is a paragraph-analog, but unlike paragraphs, it was chosen by the editor as an aesthetic act.

Second, the encoder is less mature. LaBSE is a fifteen-language-family-portable sentence encoder with sharp cross-lingual alignment properties we leaned on in Chapter 20. MERT-v1-330M is a 160,000-hour music-pretrained encoder that beat Spotify’s features in Chapter 21 head-to-head. The shot encoder does not have a comparably canonical option. CLIP (Radford et al., 2021) encodes single frames against natural-language captions; VideoMAE (Tong et al., 2022) and related video-masked-autoencoder models encode short clips. Neither is as widely validated on aesthetic downstream tasks as LaBSE or MERT. Whichever we pick imports an encoder-specific bias the books and music experiments did not have to reckon with.

Third, film has a layered temporal structure the other modalities do not. A shot has internal motion (camera, subject, light); a sequence of shots has editing rhythm (shot-duration distribution, cut-boundary intensity); a scene is a shot-sequence with narrative coherence; an act is a scene-sequence with structural function. The geometric pipeline can work at any of these four levels, and each level gives different features. Books and music have roughly two such levels (sentence/paragraph, timestep/section); film has four. A principled application of the framework will need to decide, for each of the four channels, at which level of aggregation the channel is measured.

These difficulties are not reasons to avoid the framework. They are reasons to be explicit about what we are computing and why. We now sketch the pipeline.

22.2 The Pipeline — Four Channels, Three Levels

We propose a film-adapted pipeline at three hierarchical levels. For each level, the four structural channels from Chapters 20 and 21 are computed and reported separately.

Level 1 — Shot tokens. Each shot is encoded by pooling a shot-length window of CLIP frame embeddings, or alternatively by running a VideoMAE encoder over the shot clip, yielding a per-shot embedding vector $\mathbf{x}_s \in \mathbb{R}^d$. A film with $S$ shots becomes a trajectory $(\mathbf{x}_1, \ldots, \mathbf{x}_S)$. The four channels — spectral divergence vs. corpus, pair-sim mean and std, trajectory step/curvature/recurrence/path-efficiency, Lasso on PCA of shot distribution — are computed exactly as in Chapters 20 and 21.

Level 2 — Editing-rhythm channel. Unlike books or music, film admits a rhythmic feature that lives at the cut boundary rather than in the embedding space. Let $\tau_s$ be the duration of shot $s$ in seconds. The sequence $(\tau_1, \ldots, \tau_S)$ is the film’s shot-duration time series. We compute its mean, standard deviation, skewness, autocorrelation, and its power-spectral signature. We call these the editing-rhythm features and treat them as a fifth channel specific to this modality. This is not a deviation from the framework; it is the framework’s acknowledgement that film’s cut is an aesthetic primitive that text and audio do not possess.

Level 3 — Scene aggregates. Scenes — connected sequences of shots with narrative unity — are detected by an existing scene-boundary detector (PySceneDetect or a learned scene-boundary classifier). Each scene is represented by the aggregated shot-embedding trajectory within it. The four structural channels are computed at the scene level as well as the shot level, giving a nested hierarchy: within-scene trajectory features, between-scene trajectory features.

The target variable is more fraught than in books or music. track_listens is too poor a proxy; IMDb rating and critical score are both noisy and both confounded by celebrity and studio effects. A realistic target basket would include Letterboxd averaged user rating, Metacritic critic aggregated score, a measure of enduring viewership (rewatch rate on streaming platforms), and possibly a cinephile-community rating (Mubi, Criterion). Any single target is compromised; a principled study would run the analysis against several and report the headline as the intersection of signals surviving all residualizations.

22.3 The Prediction — Which Way Does the Sign Flip Go?

The central result of Chapter 21 is a cross-modality sign flip on $\texttt{pair\_sim\_mean}$ and $\texttt{step\_mean}$: books reward continuity ($+$ coherence, $-$ step size), music rewards contrast ($-$ coherence, $+$ step size). The unrun film experiment has a natural prediction question: on which side of the sign flip does film sit?

We state our prediction here, in advance of running the experiment, so it is adjudicable. The prediction has three versions, corresponding to three aesthetic traditions within film that pull in different directions.

Prediction A — Film is book-like. If film narrative is organized primarily by dramatic continuity — shots that belong to each other, a scene that stays close to itself, editing that preserves spatial and temporal coherence — then the books sign applies: $\texttt{pair\_sim\_mean}$ rewards rating positively, $\texttt{step\_mean}$ rewards it negatively. Classical Hollywood continuity editing (Bordwell and Thompson’s “classical style”) would predict this. So would the long-take tradition André Bazin championed: Ford’s The Searchers, Ozu’s domestic interiors, Tarkovsky’s Stalker, Cuarón’s Roma. On this prediction, $\texttt{pair\_sim\_mean}$ coefficient is positive, $\texttt{step\_mean}$ coefficient is negative, and the framework says film is aesthetically continuous with the book tradition.

Prediction B — Film is music-like. If film rewards attentional engagement over narrative coherence — shots that surprise, cuts that accelerate, a visual rhythm that pulls the viewer forward by contrast rather than continuity — then the music sign applies: $\texttt{pair\_sim\_mean}$ coefficient is negative, $\texttt{step\_mean}$ coefficient is positive. Eisenstein’s dialectical montage theory (Film Form, The Film Sense) would predict this: each cut is an intellectual collision, meaning arises from juxtaposition rather than continuity, the audience is built up by shock. Post-1990s blockbuster action editing — Michael Bay, Tony Scott, the Bourne films, much of the Marvel Cinematic Universe — would predict this. On this prediction, film sits on the music side of the sign flip.

Prediction C — Film is mixed, and the sign depends on the sub-corpus. If the framework is honest, the sign will not be modality-uniform across all of film. We conjecture that the sign will flip within film between sub-corpora: art-house and drama films will sit on the book side of $\texttt{pair\_sim\_mean}$, action and thriller films will sit on the music side. This is not hedging; it is a substantive prediction that the corpus will split by genre in the same way that books split by fiction-vs-nonfiction and music splits by pop-vs-classical. Prediction C would say: the framework’s single-modality claims (“books reward continuity, music rewards contrast”) were always statements about aggregate sub-corpora, and a film corpus with both Tarkovsky and Bay will not support a uniform sign.

We prefer Prediction C as the prior. Predictions A and B are too clean for a modality as internally variegated as film. We state C in advance and will adjudicate against A, B, and C when the data run.

22.4 Eisenstein, Bazin, and the Theory Prior

The prediction basket above is not ours originally. The twentieth century’s two dominant film-theoretic traditions — dialectical montage and realist long-take — give exactly the two poles of Prediction C.

Sergei Eisenstein’s montage theory (articulated across Film Form, 1949, and The Film Sense, 1942) argued that film’s essential aesthetic operation is the collision of shots. A cut is not a transition; it is a dialectical synthesis in which the juxtaposition of two images produces a meaning neither contained. The baby carriage in Potemkin’s Odessa Steps sequence works not because it is continuous with the preceding shots but because it is discontinuous with them. Eisenstein’s prediction, in our framework’s terms, is: $\texttt{step\_mean}$ coefficient is strongly positive (shots that jump in embedding space carry more aesthetic weight), $\texttt{pair\_sim\_mean}$ is negative (internal coherence of a sequence is aesthetically inert or negative). Eisenstein’s film is music-like.

André Bazin’s realist theory (across What Is Cinema?, 1958–1962) argued the opposite: film’s essential aesthetic operation is the preservation of spatial and temporal continuity. The cut fragments reality; the long take preserves it. Renoir, Welles’s deep-focus compositions, Italian neorealism, the early Rossellini — these directors’ aesthetic achievement lies in letting the camera hold the real world open rather than cutting it into dialectical fragments. Bazin’s prediction: $\texttt{step\_mean}$ coefficient is strongly negative (small step-to-step motion rewards the viewer), $\texttt{pair\_sim\_mean}$ is positive (internal coherence is what makes a scene work). Bazin’s film is book-like.

Prediction C, which we prefer, says that Eisenstein and Bazin were both empirically correct about the sub-corpora they analysed, and that a mixed film corpus will show both signs depending on genre-residualization. The empirical test is which of the two has larger weight in the global regression across all films, and where the sign flips within genre breakdowns.

We flag the reference: Bordwell, Thompson, and Smith’s Film Art: An Introduction provides the standard twentieth-century framework for these distinctions; David Bordwell’s Narration in the Fiction Film (1985) develops the narratological side in detail. We cite them as the theory prior the empirical result will be adjudicated against.

22.5 Editing-Rhythm Predictions

The editing-rhythm channel (Level 2 above) generates its own set of predictions the books and music experiments did not constrain.

Shot-duration variance. A film with high variance in shot durations — long takes punctuated by rapid cuts — makes rhythmic choices a film with uniform shot durations does not. We predict that shot-duration variance has a non-monotone relationship with rating. At low variance, rhythmic monotony depresses engagement. At moderate variance, rhythm becomes expressive. At very high variance, the film risks becoming incoherent. A principled experiment would report both linear and quadratic regression coefficients; we predict the quadratic is negative and significant.

Shot-duration power-law slope. Cutler and colleagues (Psychological Science, 2010, “Attention and the Evolution of Hollywood Film”) documented that the distribution of shot durations in Hollywood films has followed approximately 1/f statistics, and that the slope has steepened (shorter average shots) over the twentieth century. If 1/f shot-duration statistics are aesthetically privileged — the same way 1/f statistics are argued to be privileged in music and visual art — the framework predicts a positive coefficient on “closeness to 1/f” across the film corpus. This is a testable prediction distinct from the book/music sign flip.

Cut-boundary intensity and the pair-sim measure. A cut at which the embedding jumps sharply — high step-to-step distance at the cut — is a hard cut. A cut with small jump is a soft cut, or a match cut. Films with mostly soft cuts should read as internally coherent in the $\texttt{pair\_sim\_mean}$ metric; films with mostly hard cuts will read as internally incoherent. The modality-specific sign we are predicting will apply here with particular force: if film is mixed (Prediction C), the sign of the pair-sim coefficient will depend on the distribution of cut intensities within the sub-corpus, not just on the sub-corpus’s genre label.

22.6 Television as a Limit Case

Television — or rather, serialized long-form television as it has developed since roughly 1999 — is a limit case that the film framework can absorb with care.

A long-form television series differs from a film in two structural ways relevant to the framework. First, the temporal scale is larger by a factor of roughly ten to fifty: a ten-episode season is five to ten hours of content, compared to a ninety-to-one-hundred-fifty-minute feature. Second, the rhythmic unit is bimodal: within-episode editing rhythm is film-like, but between-episode pacing operates at a different temporal scale and with different engagement dynamics (the cliffhanger, the slow-building character arc, the season finale). The shot-token, scene-aggregate, and editing-rhythm channels all transfer; what changes is that a fourth level — the episode — is added, and a fifth level — the season — above that.

We predict that long-form television will sit closer to the book side of the sign flip than feature film does. The argument: long-form television’s aesthetic achievement is character continuity and world-coherence over many hours of runtime. The shows canonized by the “Third Golden Age of Television” critical vocabulary — The Wire, Mad Men, Breaking Bad, The Americans, Better Call Saul — are celebrated precisely for the slow accumulation of internal coherence. The viewer rewards these shows for their book-like structural properties. Action-oriented series (24, The Boys) will pull in the music-like direction, as in the film case.

This is a prediction, not a finding. We have not run the television version of the experiment. We state the prediction in advance.

22.7 Honest Limits and Falsifying Outcomes

The chapter would be dishonest without a statement of what an empirical result would have to look like to falsify the framework’s predictions for film.

Falsifier 1 — Predictions A, B, and C all fail. If the shot-token $\texttt{pair\_sim\_mean}$ and $\texttt{step\_mean}$ regression coefficients come out null on a sufficiently large film corpus ($n \geq 10{,}000$ films, residualized by genre and director, under held-out evaluation), that is a failure. The framework’s cross-modality claim would need to be narrowed: text and audio have directional aesthetic geometry; film does not. We would accept this as a real negative result.

Falsifier 2 — Prediction C fails by sub-corpus homogeneity. If the sign does not flip between art-house and action sub-corpora — if both sit on the same side of $\texttt{pair\_sim\_mean}$ — that falsifies Prediction C specifically. We would be forced to one of the cleaner alternatives (A or B), which would be a genuine surprise given the theoretical divergence of Eisenstein and Bazin.

Falsifier 3 — The editing-rhythm channel dominates. If the shot-embedding channels come out null but the editing-rhythm channel shows a large residualized effect, the framework’s generalization is: film’s aesthetic geometry lives in the cut, not in the shot. The modality-shared structure with books and music would be partial. We would flag this honestly rather than trying to reinterpret shot-token features post hoc.

Falsifier 4 — The shot encoder matters more than the pipeline. If CLIP-based shot embeddings give one result and VideoMAE-based shot embeddings give another, the finding is encoder-specific and the framework cannot make modality-level claims without an encoder-agnostic validation. We would need to re-run with multiple encoders and report intersection before claiming a modality result.

These are real falsifiers. We state them in advance so that a future experimentalist — perhaps Sam of the opening example, perhaps a reader of this chapter — can adjudicate our predictions without the temptation to retrofit.

22.8 What a Practicing Editor Would Do With This

Return to Sam. She has thirty-two cuts. Suppose, for the sake of argument, Prediction C survives empirical test, and the framework is validated to the point where a publicly available shot-embedding-and-editing-rhythm analysis can be run on a Premiere timeline in an evening. What does Sam do with it?

She does not use it to pick the cut. The cut is hers; the director’s; the producer’s; the audience’s. The framework does not replace those judgments. What the framework does is describe each of her thirty-two cuts along a named set of axes — continuity, step-size, editing-rhythm variance, distance-from-1/f, curvature, coherence against corpus-wide reference distributions — so that she can say, in concrete geometric terms, what she would be doing if she chose this cut over that one. The four-minute long take sits at one end of the $\texttt{pair\_sim\_mean}$ axis. The ninety-second montage sits at the other. Each of them is a different aesthetic act, with a different reception implication, and Sam can now name the act she is performing.

This is the offering to film studies. Close readers of film — the tradition of Bordwell, Thompson, the Warren Buckland-school cognitive film theorists, the neuro-cinematics program of Hasson — have always articulated these axes qualitatively. The geometric framework, if validated empirically, allows those articulations to be computed at scale, surfaced for individual films, and connected to reception data. Whether this validation happens depends on the experiment being run. We have described what that experiment would look like. We have predicted its result. We have stated what would disconfirm the prediction. The next move is empirical, and it is not one we have made yet.

22.9 Bridge to Visual Art

The next chapter turns to visual art. The move from film to a single still image is, in one sense, the opposite of the move from books to film: visual art collapses the temporal trajectory down to zero time. A painting or sculpture is a single embedding vector, not a walk through a high-dimensional space. This appears to strip the framework of its defining structure — the four channels are all computed over trajectories, and a single vector has no trajectory — but the framework survives by moving to within-image structure (the painting’s regions, the sculpture’s views) and to between-work structure (the oeuvre, the school, the period). We will argue that visual art’s aesthetic manifold is not degenerate but re-parameterized: the trajectory becomes a structure, and the four channels reappear as properties of that structure. Like this chapter, Chapter 23 will be speculative-but-principled, and will state its predictions before running.