On Method: Computational Compressibility in Complex Natural and Cultural Phenomena

New working paper. Title above, abstract, contents, and introduction below:

Academia.edu: https://www.academia.edu/166054951/On_Method_Computational_Compressibility_in_Complex_Natural_and_Cultural_Phenomena
SSRN: https://papers.ssrn.com/abstract=6666638
ResearchGate: https://www.researchgate.net/publication/404263330_On_Method_Computational_Compressibility_in_Complex_Natural_and_Cultural_Phenomena

Abstract: Various machine learning techniques have been used to develop models of complex systems from empirical data. Through discussions with Claude, this paper examines several examples, including: weather, protein folding, chess, language, asset pricing, ticket sales for movies, the 19th century English-language novel. These models differ from one another in various ways, but all are fundamentally descriptive in character. Explanations must necessarily reside with their respective disciplines. In some cases we already have fundamental accounts of the phenomena, while in other cases we do not. With respect to economics in particular, it is clear that such models reveal phenomena for which no explanations are currently available, presenting a challenge to economic theory.

Contents 

Part I: Computational Compressibility, Implications for Economics, Description and Explanation 5
Part II: Weather, Protein Folding, Chess, and Language 16
Part III: Interim Summary: Compressibility Without Reducibility 26
Part IV: Pricing Theory, Movies, 19th Century Novels, and Cultural Evolution 28
Part V: To Infinity and Beyond! – Hollywood Redux, Blockbusters, the Spreadsheet, Economics Going Forward 38

Introduction: Describing Computationally Compressible Systems 

This a transcription of a dialog I had with Claude 4.6 and 4.7 on April 21 - 23, 2026. While I started it with a specific case from Chapter 4 of Tyler Cowen’s recent monograph on marginalism, now that the dialog has concluded with Chomsky’s distinction between descriptive and explanatory adequacy (Aspects of the Theory of Syntax), I realize that I’ve been thinking about the underlying issues for some time. While I read Aspects in about 1970, give or take a year, I didn’t think much about description as such until the 2000s, and then I was thinking about describing individual texts; but that’s not directly relevant to these cases in this paper. Then in the second decade of this century I began thinking about computational criticism, aka digital humanities, which typically involve some kind of statistical or machine learning investigation of a corpus of texts. In particular, I gave a great deal of attention to Macroanalysis (2013), where Matthew Jockers studied a corpus of roughly 3000 English-language novels published in the 19th century. That investigation culminated in a directed graph showing depicting relationships of close-similarity among the novels in the corpus. I decided that that graph, in effect, was fundamentally descriptive in character, depicting, in effect, the 19th century Anglophone Geist, or Spirit.

But Jockers’s graph wasn’t on my mind when I started my dialog with Claude. Rather, I was thinking about the distinction between computationally reducible and irreducible phenomena that Stephen Wolfram had introduced in his New Kind of Science (2001). As Claude notes in its summary of the dialog, “a reducible system admits shortcuts through its dynamics; an irreducible one must be simulated step by step.” My target was a paper about asset pricing that Cowen discussed in his monograph, which produced a model having 360,000 parameters but which defied intuitive understanding.

The weather is a canonical example of phenomenon that is computationally irreducible. Thus forecasting the weather generally involves running a simulation of the weather and stepping through it interval after interval. This requires enormous computing resources and takes time. But DeepMind has created a machine learning system, GraphCast, that abstracts over historical data in a way that allows more accurate forecasts with less compute. Thus the weather system is computationally irreducible, but it is also compressible.

I take that as my paradigm case of computational compressibility (pp. 16 ff.) and then move on to other examples: protein folding (another physical phenomenon, pp. 18 ff.), chess (human activity, pp. 22 ff.), and natural language (a different human activity, pp. 23 ff.), each of which is compressible using machine learning techniques. Each example sharpens and extends the idea of computational compressibility. At that point I asked Claude to summarize the discussion (pp. 26 ff)..

Then, and only then do I ask Claude to consider Cowen’s problematic example, AI Pricing Theory (pp. 28 ff.). In its analysis of the paper, Claude notice that it introduces something fundamentally new to the discussion, reflexivity. Asset pricing is done by a large group of actors over time who thus influence one another’s decisions. And that, in turn, brings up Arthur De Vany’s work on Hollywood Economics (pp. 30 ff.). De Vany discovered that box-office success cannot be predicted by such analytic variables as producer, screen writer, director, movie stars, or opening weekend box office. Rather the success of a film depends on a word-of-mouth cascade which cannot be predicted. That leads me, in turn, to suggest a thought experiment involve a hypothetical system capable to abstracting over entire films and developing a high-dimensional model which could be used to predict the success of individual films.

And that, in turn, led me to the work that Matthew Jockers had done on 19th century English-language novels (pp. 33 ff.), something that had not been on my mind when I began this dialog on April 21. Jockers used machine learning, albeit nothing so elaborate and computationally expensive as using a transformer to create an LLM – it only had roughly 600 parameters. What his model revealed, and what made it so fascinating to me, is that there is an inherent directionality to the production of novels over the course of a century. It’s not simply that later novels are systematically different from earlier ones, but that that difference has a direction in the 600-dimensional measurement space. What we’d really like to know, now, is a say to characterize that diction. The model shows us that there is a direction, but it doesn’t tell us what that direction is. Though the model is much simpler than that asset pricing model – it has three orders of magnitude fewer parameters – its significance is no more legible.

After that I have two discussions that are not based on existing models, but that do have implications for economists who want to study them. First, I consider the phenomenon of the blockbuster, arguing that it reveals audience preferences that had previously been unrecognized (pp. 41 ff.). Then I consider the spreadsheet (e.g. VisiCalc), which transformed the personal computer market from a small niche market into a large mainstream market (pp. 43 ff.). How do you create a model that allows you to predict markets that don’t even exist at the time you make your model? What kind of a problem is that? After that I took a brief look at Cowen’s argument in The Great Stagnation (pp. 45 ff.), where Claude remarked:

If the VisiCalc model is right, then what matters about ChatGPT and its successors is not primarily that they do existing things faster or cheaper—though they do—but whether they are constitutive technologies in the VisiCalc sense. Do they reorganize the space of possible wants, making new activities imaginable and practical that previously had no well-formed representation in anyone's preference space? With that I brought the exploration to a halt.

I then asked Claude to summarize the entire dialog, which I’ve placed immediately following these remarks (pp. XX ff), with a special emphasis on implications for economics (pp. 7 ff.). Then I introduce Chomsky’s distinction from the 1960s, description vs. explanation (pp. 9 ff.). Each of these cases involves a complex phenomenon that is irreducible, but can be compressed into a model that is descriptive in character. They have that in common. As for explanations, those must necessarily be specific to each phenomenon. Note that in some cases we have explanatory theories grounded in a fundamental understanding of the underlying system (weather, protein folding) while in others we do not (chess, asset pricing, cultural evolution).

Finally, I’ve added a coda from a different conversation with Claude (pp. 13 ff.), one I had with the AI that accompanied Cowen’s book. That conversation is about Hollywood Economics and Rational Ritual and argues that the factoring of intellectual space that we’ve inherited from the 19th century German university has outgrown its usefulness.