---
title: "Fluid Dynamics-Inspired Emotional Analysis in Shakespearean"
description: "A modified Navier-Stokes equation describes the sentiment flow, and each physical term gets a textual… 18 references, cited by 1 paper here."
authors: ["Davide Picca"]
year: 2024
venue: "Proceedings of the 2nd Workshop on Mathematical Natural Language Processing @ LREC-COLING 2024"
source: "https://aclanthology.org/2024.mathnlp-1.2/"
licence: "CC BY-NC 4.0 (ELRA, LREC proceedings)"
licence_url: "https://creativecommons.org/licenses/by-nc/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/picca-2024-fluid-dynamics-inspired-emotional-analysis/"
---
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# Fluid Dynamics-Inspired Emotional Analysis in Shakespearean Tragedies: A Novel Computational Linguistics Methodology

**Authors:** [Davide Picca](https://md.research.elamur.ai/free/en/authors/davide-picca/) · **Year:** 2024 · **Venue:** Proceedings of the 2nd Workshop on Mathematical Natural Language Processing @ LREC-COLING 2024 · **Publisher:** [European Language Resources Association (ELRA)](https://md.research.elamur.ai/free/en/publishers/european-language-resources-association-elra/) · **Licence:** [CC BY-NC 4.0 (ELRA, LREC proceedings)](https://creativecommons.org/licenses/by-nc/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2024.mathnlp-1.2/) · [PDF](https://aclanthology.org/2024.mathnlp-1.2.pdf) · [OpenAlex](https://openalex.org/W7131777343)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · 1 in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper argues that standard sentiment analysis, which assigns discrete labels or polarity scores, misses how emotion moves through a narrative. As an alternative, it borrows the vocabulary of fluid mechanics. A modified Navier-Stokes equation describes the sentiment flow, and each physical term gets a textual counterpart computed from the SenticNet 7 lexicon (Cambria et al., 2022):

- **Time** is the position in the text.
- **Density** is the summed absolute sentiment.
- **Pressure** comes from the scores of a user-chosen list of strong keywords.
- **Viscosity** is the spread (standard deviation) of scores.
- **External force** is overall polarity.

The framework is applied to "Hamlet" and "Romeo and Juliet". Emotional curves are interpreted against SparkNotes plot commentary rather than measured with metrics. The author reports that the resulting trajectories are more nuanced than conventional sentiment scoring. The author also presents the approach as a metaphor whose variables could later absorb cultural or reader-dependent context, and possibly feed into machine learning. Its main value is conceptual: it turns a single sentiment number into several complementary per-segment signals over narrative time.

## Key points
- The texts are two Shakespeare tragedies, "Hamlet" and "Romeo and Juliet". The paper refers to "three" tragedies but names only these two.
- All quantities come from the SenticNet 7 lexicon:
  - density is the sum of absolute scores;
  - viscosity is the standard deviation of scores;
  - external force is the polarity value;
  - pressure is the sum of scores for words found in a predefined high-impact keyword list (e.g. love, hate).
- Velocity is interpreted as how quickly sentiment changes, for example a sharp swing from positive to negative.
- The evaluation is explicitly qualitative. Curves are compared with SparkNotes interpretations, and no quantitative benchmark or baseline score is reported.
- The paper was published at MathNLP 2024 (LREC-COLING), and the author claims there is no prior work applying Navier-Stokes ideas to emotion in text.

## Interesting ideas
- Instead of one sentiment score per segment, compute separate signals for magnitude regardless of sign (density), mixedness (standard deviation), and net direction (polarity); they can disagree in revealing ways.
- High dispersion of sentiment inside a segment is read as emotional complexity or ambiguity, a cheap marker of passages where simple polarity is misleading.
- Rate of change of sentiment over textual position is treated as its own quantity, so turning points become first-class objects rather than side effects of a curve.
- A curated short list of high-impact words is scored separately from the general lexicon, giving strong emotional anchors extra weight.
- Model curves are checked against human-written plot commentary, which is cheap external validation but purely qualitative.

## For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

- **I1** (world): the text world could track a character's affective state along event order as several fields (intensity, ambivalence, direction), derived from frames rather than raw word lists.
- **I2** (frames): prag could use strong positive-and-negative co-occurrence within one utterance as a candidate cue that triggers the irony and implicature checks.
- **I3** (answer): fable and tale QA could locate the narrative turn (for example, "when did things go wrong?") by finding the largest jump in frame-level affect between consecutive events.
- **I4** (tokens): the crate en lexicon could mark lemmas with an "intensity anchor" flag, which later stages use to weight affect without falling back on bag-of-words scoring.
- **I5** (learn): plot summaries could serve as reference for affect arcs, adding a shuffled-sentence negative control that the paper lacks to show the arcs reflect narrative order.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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🧭 Topics (1): [😊 Sentiment & emotion](https://md.research.elamur.ai/free/en/topics/sentiment-emotion/) · 972 works

## Cite

Cite as: Davide Picca. 2024. Fluid Dynamics-Inspired Emotional Analysis in Shakespearean Tragedies: A Novel Computational Linguistics Methodology. Proceedings of the 2nd Workshop on Mathematical Natural Language Processing @ LREC-COLING 2024.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{picca2024fluid,
  title = {{Fluid Dynamics-Inspired Emotional Analysis in Shakespearean Tragedies: A Novel Computational Linguistics Methodology}},
  author = {Davide Picca},
  booktitle = {Proceedings of the 2nd Workshop on Mathematical Natural Language Processing @ LREC-COLING 2024},
  year = {2024},
  doi = {10.63317/557ywmokikze},
  url = {https://doi.org/10.63317/557ywmokikze}
}
```

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## References

18 references, 3 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. D. J. Acheson. 1990. Elementary Fluid Dynamics. Oxford University Press. [↗](https://doi.org/10.1093/oso/9780198596608.001.0001)
2. David Bamman, Ted Underwood, and Noah A. Smith. 2014. [A Bayesian mixed effects model of literary character](https://md.research.elamur.ai/free/en/papers/bamman-2014-bayesian-mixed-effects-model-literary/). In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 370–379, Baltimore, Maryland. Association for Computational Linguistics. [↗](https://doi.org/10.3115/v1/p14-1035)
3. G. Bohner and M. Wanke. 2002. Attitudes and Attitude Change, 1st edition. Psychology Press. [find](https://scholar.google.com/scholar?q=G%2E+Bohner+and+M%2E+Wanke%2E+2002%2E+Attitudes+and+Attitude+Change%2C+1st+edition%2E+Psychology+Press%2E)
4. Erik Cambria, Qian Liu, Sergio Decherchi, Frank Xing, and Kenneth Kwok. 2022. SenticNet 7: A commonsense-based neurosymbolic AI framework for explainable sentiment analysis. In Proceedings of the Thirteenth Language Resources and Evaluation Conference, pages 3829–3839, Marseille, France. European Language Resources Association. [find](https://scholar.google.com/scholar?q=Erik+Cambria%2C+Qian+Liu%2C+Sergio+Decherchi%2C+Frank+Xing%2C+and+Kenneth+Kwok%2E+2022%2E+SenticNet+7%3A+A+commonsense%2Dbased+neurosymbolic+AI+framework+for+explainable+sentiment+analysis%2E+In+Proceedings+of+the+Thir)
5. Zulfadzli Drus and Haliyana Khalid. 2019. Sentiment analysis in social media and its application: Systematic literature review. Procedia Computer Science, 161:707–714. The Fifth Information Systems International Conference, 23-24 July 2019, Surabaya, Indonesia. [↗](https://doi.org/10.1016/j.procs.2019.11.174)
6. Bing Liu. 2012. Sentiment analysis and opinion mining. Synthesis Lectures on Human Language Technologies, 5:1–167. [↗](https://doi.org/10.2200/s00416ed1v01y201204hlt016)
7. Qiang Lu, Xia Sun, Yunfei Long, Zhizezhang Gao, Jun Feng, and Tao Sun. 2023. Sentiment analysis: Comprehensive reviews, recent advances, and open challenges. IEEE Transactions on Neural Networks and Learning Systems. [↗](https://doi.org/10.1109/tnnls.2023.3294810)
8. Franco Moretti. 2013. Books. Verso Distant reading. [find](https://scholar.google.com/scholar?q=Franco+Moretti%2E+2013%2E+Books%2E+Verso+Distant+reading%2E)
9. Gunjan Pahlani, Thomas Schwartzentruber, and Richard D. James. 2023. A constitutive relation generalizing the navier–stokes theory to high-rate regimes. Journal of Fluid Mechanics, 974:A30. [↗](https://doi.org/10.1017/jfm.2023.727)
10. Bo Pang, Lillian Lee, and Shivakumar Vaithyanathan. 2002. [Thumbs up? sentiment classification using machine learning techniques](https://md.research.elamur.ai/free/en/papers/pang-2002-thumbs-up-sentiment-classification-machine/). In Proceedings of the 2002 Conference on Empirical Methods in Natural Language Processing (EMNLP 2002), pages 79–86. Association for Computational Linguistics. [↗](https://doi.org/10.48550/arxiv.cs/0205070)
11. John Pavlopoulos, Alexandros Xenos, and Davide Picca. 2022. Sentiment analysis of homeric text: The 1st book of iliad. In Proceedings of the Thirteenth Language Resources and Evaluation Conference, Marseille, France. European Language Resources Association. [find](https://scholar.google.com/scholar?q=John+Pavlopoulos%2C+Alexandros+Xenos%2C+and+Davide+Picca%2E+2022%2E+Sentiment+analysis+of+homeric+text%3A+The+1st+book+of+iliad%2E+In+Proceedings+of+the+Thirteenth+Language+Resources+and+Evaluation+Conference%2C+Ma)
12. Patrícia Pereira, Helena Moniz, and Joao Paulo Carvalho. 2022. Deep emotion recognition in textual conversations: A survey. arXiv preprint arXiv:2211.09172v1. [↗](https://arxiv.org/abs/2211.09172)
13. Davide Picca and John Pavlopoulos. 2024. Deciphering emotional landscapes in the iliad: A novel french-annotated dataset for emotion recognition. In Proceedings of the 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation, Turin, Italy. European Language Resources Association. [find](https://scholar.google.com/scholar?q=Davide+Picca+and+John+Pavlopoulos%2E+2024%2E+Deciphering+emotional+landscapes+in+the+iliad%3A+A+novel+french%2Dannotated+dataset+for+emotion+recognition%2E+In+Proceedings+of+the+2024+Joint+International+Confere)
14. Davide Picca and Caroline Richard. 2023. Unveiling emotional landscapes in plautus and terentius comedies: A computational approach for qualitative analysis. In Proceedings of the Ancient Language Processing Workshop, Varna, Bulgaria. INCOMA Ltd. [find](https://scholar.google.com/scholar?q=Davide+Picca+and+Caroline+Richard%2E+2023%2E+Unveiling+emotional+landscapes+in+plautus+and+terentius+comedies%3A+A+computational+approach+for+qualitative+analysis%2E+In+Proceedings+of+the+Ancient+Language+Pro)
15. Margarita Rodríguez-Ibánez, Antonio Casánez-Ventura, Félix Castejón-Mateos, and Pedro-Manuel Cuenca-Jiménez. 2023. A review on sentiment analysis from social media platforms. Expert Systems with Applications, 223:119862. [↗](https://doi.org/10.1016/j.eswa.2023.119862)
16. Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D. Manning, Andrew Ng, and Christopher Potts. 2013. [Recursive deep models for semantic compositionality over a sentiment treebank](https://md.research.elamur.ai/free/en/papers/socher-2013-recursive-deep-models-semantic-compositionality/). In Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing, pages 1631–1642, Seattle, Washington, USA. Association for Computational Linguistics. [↗](https://doi.org/10.18653/v1/d13-1170)
17. Yosephine Susanto, Andrew G. Livingstone, Bee Chin Ng, and Erik Cambria. 2020. The Hourglass Model Revisited. IEEE Intelligent Systems, 35(5):96–102. 105 citations (Crossref) [2023-10-18]. [↗](https://doi.org/10.1109/mis.2020.2992799)
18. Henk Tennekes and John L. Lumley. 1972. A First Course in Turbulence. MIT Press. [↗](https://doi.org/10.7551/mitpress/3014.001.0001)

*Updated 1 November 2026*