Slope One as Cultural Engine

Working Paper No. 2024-VII/3

Abstract

The Slope One algorithm (Lemire & Maclachlan, 2005) computes the average difference in ratings between pairs of items and uses these deltas to predict unknown preferences. It was designed for recommender systems. We have been using it to write operas. This paper reports on four years of work at the Institute for Applied Recommendation in which Slope One has served as the primary compositional, literary, and architectural engine for a programme of cultural production that has, by any measure, exceeded the algorithm’s original specification. We describe our methodology, present selected outputs, and address the question—raised with increasing frequency by our review board—of whether what we are doing constitutes a valid use of collaborative filtering or, as one reviewer put it, “something else entirely.”

1. Introduction

The appeal of Slope One has always been its simplicity. Where other collaborative filtering approaches require matrix factorisation, gradient descent, or a doctoral student, Slope One asks only: what is the average difference? If users who rated Don Giovanni a 4 and La Bohème a 5 have established a delta of +1, and a new user rates Don Giovanni a 3, then surely they would rate La Bohème a 4. The arithmetic is primary-school. The implications, as we have discovered, are unbounded.

Our initial application was orthodox. In 2020, the Institute was commissioned by the city of Turku to build a recommendation engine for the municipal library system. The system worked well. Too well, some argued—the library reported a 340% increase in holds on Finnish-language crime fiction, which the algorithm recommended to everyone because everyone had already read Finnish-language crime fiction, creating a feedback loop of such intensity that the acquisitions department briefly considered abandoning all other genres. But the system functioned. It predicted preferences. It was correct.

The question that preoccupied our team was different. If the delta between Don Giovanni and La Bohème is +1, what is that +1? What does the +1 contain? Is it merely an arithmetic residue, or does it encode, in some compressed form, the cultural distance between two works—the difference in emotional register, structural ambition, historical context? And if it encodes that distance, could one not, in principle, traverse it?

Reader, we traversed it.

2. Methodology: The Delta as Creative Unit

Our methodology rests on a proposition that we acknowledge is not standard in the information retrieval literature: that the Slope One delta between two cultural artifacts is itself a cultural artifact. We call this the Generative Delta Hypothesis (GDH). If the average rating difference between Tolstoy’s Anna Karenina and a moderately successful IKEA shelving unit (the Kallax) is −1.3, then that −1.3 is not merely a number. It is the aesthetic object that, when added to Anna Karenina, produces the Kallax. It is, in a sense, the anti-novel: the precise quantity of creative energy one must subtract from a masterwork of Russian realism to arrive at flat-pack furniture.

The practical implications are immediate. If the delta between A and B is known, and the delta between B and C is known, one can compute the delta between A and C without ever having compared them directly. Cultural production becomes a matter of addition. This is not a metaphor. We have produced artifacts by literal arithmetic on deltas, and we present the results below.

2.1 The Rating Corpus

To compute deltas across domains, we required a corpus in which the same individuals had rated items of radically different kinds. We constructed this corpus by surveying 2,340 residents of Turku, asking each to rate, on a scale of 1 to 5, a list of 400 items including operas, municipal infrastructure projects, sandwich fillings, weather events, and selected passages of Finnish civil code. The survey instrument was 74 pages long. Completion rates were low (11%), but those who finished demonstrated the kind of thoroughness the algorithm rewards.

2.2 Delta Extraction and Composition

With the completed ratings, we computed pairwise Slope One deltas for all 79,800 item pairs. The resulting delta matrix is, we believe, the first comprehensive mapping of the aesthetic distance between every object in a heterogeneous cultural field. Some representative deltas:

Several features of this matrix are noteworthy. The near-zero delta between August and a well-organized sock drawer suggests a deep structural affinity that, while surprising, is difficult to refute on aesthetic grounds. The strong negative delta between parking regulations and Puccini confirms what many have suspected: that opera is the precise inverse of municipal governance, and that moving between them requires significant creative energy in a defined direction.

3. Selected Outputs

3.1 Opera: “The Parking Variations” (2022)

Our first major production was generated by applying the delta between Turku parking regulation §17.4 and Puccini’s Tosca (Δ = −1.9) to the full text of Turku parking regulation §17.4–19.2. The resulting libretto preserves the regulatory structure—time-limited zones, penalty schedules, exemptions for diplomatic vehicles—while imbuing each provision with the emotional intensity the delta demands. The aria in which the protagonist discovers her vehicle has been towed (“Non mi lasciare, Volvo mio”) was described by Helsingin Sanomat as “unexpected.”

The opera was performed once, at a municipal parking structure, to an audience of forty-three. The acoustics were adequate. The soprano reported that singing in a concrete stairwell between levels B2 and B3 was “not the worst venue she had performed in, but close.” The algorithm rated the production 3.7.

3.2 Architecture: The Turku Deltahaus (2023)

Encouraged by the opera’s reception—or at least not deterred by it—we applied the method to architecture. By composing the deltas between several highly-rated buildings (the Alvar Aalto Library, the Helsinki Central Station) and several lowly-rated ones (a specific bus shelter on Ratapihankatu that received a mean rating of 1.2), we computed what we termed the “ideal building”: the structure that would, by Slope One prediction, receive a rating of 5.0 from all users.

The resulting design was submitted to the city planning office. It was described in the planner’s report as “a three-storey structure that appears to be simultaneously a library, a sauna, and a bus shelter, with a façade that transitions from Finnish National Romantic to brutalist at a rate determined by a mathematical function we do not understand.” Planning permission was denied, though the planner noted that the sauna component was “quite good, actually.”

3.3 Literature: “The Collected Deltas” (2024)

Our most ambitious project applies the method to literature itself. The Collected Deltas is a novel-length work generated entirely from the composition of Slope One deltas. The plot—if that is the word—follows a protagonist who exists at a rating of 2.8, slightly below the mean, as she navigates a world in which every object, person, and event has a known and published Slope One rating relative to every other. She falls in love with a man rated 4.1, but the delta between them (−1.3) is identical to the delta between Dostoevsky and the Kallax, and she cannot determine whether her feelings are genuine or a collaborative filtering artefact.

The novel has not found a publisher, though two editors described it as “interesting,” which in Finnish publishing is technically a positive outcome.

4. Discussion: On the Accusation of Slop

We must address a criticism that has followed the project since its inception. Several colleagues, and one funding body, have suggested that our outputs constitute what the contemporary discourse terms “slop”—that is, content produced by algorithmic processes that is superficially coherent but culturally vacuous, a kind of aesthetic landfill. The accusation is made more pointed by the phonetic similarity between “Slope” and “slop,” which we maintain is a coincidence of English orthography and not, as one reviewer suggested, “a warning the universe is trying to give you.”

We reject this characterisation on both theoretical and empirical grounds. Slop, properly understood, is content generated without methodology—the exhaust of optimisation, the residue of scale. Our outputs are generated with extremely specific methodology. Each delta is computed from real human ratings. Each composition follows strict arithmetic. If the result is that a parking regulation becomes an opera, this is not because the process lacks rigour but because it has too much. The algorithm does not hallucinate. It averages. That the average of human cultural preferences, expressed as arithmetic deltas and composed across domains, produces results that are—we concede—unusual is not a failure of the method. It is an empirical finding about the nature of culture.

Moreover, we note that “slope” and “slop” are not, in fact, etymologically related. “Slope” derives from the Middle English aslope, meaning at an angle, while “slop” enters the language from the Old English sloppe, referring to a loose outer garment and only later to liquid refuse. The cultural products of Slope One may be at an angle to conventional aesthetics. They are not refuse. They are, at worst, a loose outer garment draped over the body of culture, which is, if one thinks about it, not an unflattering description of art in general.

5. Future Work

The Institute has submitted a grant proposal to the Academy of Finland for a five-year programme titled “Slope One as National Cultural Policy.” The proposal argues that Finland’s cultural output could be optimised by computing deltas between all existing Finnish cultural artifacts and those of competing nations, then generating new works calibrated to maximise the national rating. Early simulations suggest that the optimal Finnish novel is one that combines the structural rigour of Sibelius, the emotional restraint of a well-organized sock drawer, and a plot in which very little happens but with great specificity. Several members of the review panel noted that this describes most Finnish novels already, which we take as validation.

We are also exploring the possibility that the delta matrix itself—the 79,800-entry table of pairwise cultural distances—may be the most significant cultural artifact the Institute has produced. A proposal to exhibit it at the Turku Art Museum is under consideration. The museum has asked whether it can be displayed as a physical object. We have suggested a very large spreadsheet, printed on linen.

6. Conclusion

Slope One was never intended for this. We are aware of that. Daniel Lemire, in his original 2005 paper, proposed the algorithm as a computationally efficient alternative to more complex collaborative filtering methods, suitable for e-commerce applications. He did not propose it as a theory of aesthetics, a compositional method, or a framework for understanding why August and a sock drawer feel the same. These extensions are ours, and we accept responsibility for them.

What we will not accept is the suggestion that the method is meaningless. The deltas are real. They emerge from real preferences expressed by real people. If the composition of those deltas produces an opera about parking, a building that is also a sauna, and a novel about a woman who cannot distinguish love from collaborative filtering, then these are facts about human culture, arrived at by arithmetic. One may find the facts surprising. One may find them unwelcome. But one does not get to blame the algorithm for what the data contains.

Response

Prof. Matti Koskinen, Department of Actual Music, Sibelius Academy

I attended the premiere of The Parking Variations on level B2 of the Kupittaa parking structure. I have been asked to provide a scholarly response. I will try.

The fundamental difficulty with Dr. Lassfolk’s programme is not that it is wrong. It is that it is correct in a way that helps no one. The delta between a parking regulation and Puccini is indeed −1.9. I have checked the arithmetic. The arithmetic is fine. The arithmetic has always been fine. The question is whether correctness of this kind constitutes knowledge, or whether it is something more like a parlour trick performed by a very earnest person who does not realise it is a parlour trick, which is—and I say this with professional respect—the most Finnish possible form of comedy.

The opera itself was not without merit. The soprano was excellent. The parking structure contributed a reverb that would cost thousands to simulate in a proper hall. The libretto, being derived from municipal regulations, was unusually precise about time limits and penalty schedules, which is more than can be said for most contemporary libretti. I laughed twice, though I could not determine whether the algorithm intended this.

My substantive objection is to the Generative Delta Hypothesis. A delta is a number. It is not a cultural artifact any more than the distance between Helsinki and Turku is itself a city. Dr. Lassfolk’s team has confused the map for the territory, then built a house on the map, and then submitted the house for planning permission, and is now writing a paper about why the planning office was wrong to refuse. At some point the metaphor collapses, which is fitting, because at some point the methodology does too.

Nevertheless, I note that the novel—the one about the woman who cannot tell love from collaborative filtering—is not terrible. This bothers me more than I would like to admit. The possibility that averaging the aesthetic preferences of 2,340 residents of Turku and performing arithmetic on the result can produce something that resembles literature is either a profound insight about the nature of art or a profound insult to it, and I have not yet determined which. I suspect it is both, which is, as Dr. Lassfolk would no doubt observe, a delta of approximately zero.

The 4th Nordic Workshop on Algorithmic Culture (NorAlgKul) was held in Turku, Finland, September 12–14, 2024. Proceedings are available from the Institute for Applied Recommendation, though the Institute notes that availability should not be confused with endorsement, as several papers were accepted by a recommendation algorithm that the programme committee is still evaluating.