Simon DeDeo

Robin W. Na, Simon DeDeo

What kinds of arguments do people make, and what effect do they have on others? Normative constraints on argument-making are as old as philosophy itself, but little is known about the diversity of arguments made in practice. We use NLP tools to extract patterns of argument-making from the Reddit site "Change My View" (r/CMV). This reveals six distinct argument patterns: not just the familiar deductive and inductive forms, but also arguments about definitions, relevance, possibility and cause, and personal experience. Data from r/CMV also reveal differences in efficacy: personal experience and, to a lesser extent, arguments about causation and examples, are most likely to shift a person's view, while arguments about relevance are the least. Finally, our methods reveal a gradient of argument-making preferences among users: a two-axis model, of "personal--impersonal" and "concrete--abstract", can account for nearly 80% of the strategy variance between individuals.

Zhengqin Fan, Simon DeDeo

We present the results from Meno, a simple autoformalizer that proves theorems in Lean by systematically exploring the space of both formal and informal proofs, and tactic ablation, a new method for exploring mathematical creativity under constraint. We show these tools in action on simple theorems found in Terrence Tao's Analysis I, selectively ablating solution paths associated with non-constructive proofs, and analyze the properties of the resulting population using Goedel Prover embeddings. Among other things, our analysis of this novel population reveals that they lie on low (one or two) dimensional submanifolds of the much higher-dimensional representation space, and far away from their corresponding human constructions.

Claire Augusta Bergey, Simon DeDeo

Conversation demands attention. Speakers must call words to mind, listeners must make sense of them, and both together must negotiate this flow of information, all in fractions of a second. We used large language models to study how this works in a large-scale dataset of English-language conversation, the CANDOR corpus. We provide a new estimate of the information density of unstructured conversation, of approximately 13 bits/second, and find significant effects associated with the cognitive load of both retrieving, and presenting, that information. We also reveal a role for backchannels -- the brief yeahs, uh-huhs, and mhmms that listeners provide -- in regulating the production of novelty: the lead-up to a backchannel is associated with declining information rate, while speech downstream rebounds to previous rates. Our results provide new insights into long-standing theories of how we respond to fluctuating demands on cognitive resources, and how we negotiate those demands in partnership with others.

Gülce Kardeş, Simon DeDeo

Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a matter of logical necessity. We present a framework, based in computational complexity, where explanations for deductive truths co-emerge with discoveries of simplifying steps during the search process. When such structures are missing, we revert, in turn, to error-based reasons, where a (corrected) mistake can serve as fictitious, but explanatory, contingency-cause: not making the mistake serves as a reason why the truth takes the form it does. We simulate human subjects, using GPT-4o, presented with SAT puzzles of varying complexity and reasonableness, validating our theory and showing how its predictions can be tested in future human studies.

Zachary Wojtowicz, Simon DeDeo

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The resulting taxonomy provides a set of predictors for which explanations people prefer and shows how core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework. In addition to operationalizing the explanatory virtues associated with, for example, scientific argument-making, this framework also enables us to reinterpret the explanatory vices that drive conspiracy theories, delusions, and extremist ideologies.

Scott Viteri, Simon DeDeo

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows exponentially as the argument expands. When a mathematician encounters a proof, how does she come to believe it? Here we show that, under a cognitively-plausible belief formation mechanism combining deductive and abductive reasoning, belief in mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with five hand-constructed cases including Euclid, Apollonius, Hernstein's Topics in Algebra, and Andrew Wiles's proof of Fermat's Last Theorem. Our results bear both on recent work in the history and philosophy of mathematics on how we understand proofs, and on a question, basic to cognitive science, of how we justify complex beliefs.

Dong Nguyen, Maria Liakata, Simon DeDeo et al.

In this article we describe our experiences with computational text analysis. We hope to achieve three primary goals. First, we aim to shed light on thorny issues not always at the forefront of discussions about computational text analysis methods. Second, we hope to provide a set of best practices for working with thick social and cultural concepts. Our guidance is based on our own experiences and is therefore inherently imperfect. Still, given our diversity of disciplinary backgrounds and research practices, we hope to capture a range of ideas and identify commonalities that will resonate for many. And this leads to our final goal: to help promote interdisciplinary collaborations. Interdisciplinary insights and partnerships are essential for realizing the full potential of any computational text analysis that involves social and cultural concepts, and the more we are able to bridge these divides, the more fruitful we believe our work will be.

Elise Jing, Simon DeDeo, Devin Robert Wright et al.

Cultural evolution is driven by how we choose what to consume and share with others. A common belief is that the cultural artifacts that succeed are ones that balance novelty and conventionality. This balance theory suggests that people prefer works that are familiar, but not so familiar as to be boring; novel, but not so novel as to violate the expectations of their genre. We test this idea using a large dataset of fanfiction. We apply a multiple regression model and a generalized additive model to examine how the recognition a work receives varies with its novelty, estimated through a Latent Dirichlet Allocation topic model, in the context of existing works. We find the opposite pattern of what the balance theory predicts$\unicode{x2014}$overall success decline almost monotonically with novelty and exhibits a U-shaped, instead of an inverse U-shaped, curve. This puzzle is resolved by teasing out two competing forces: sameness attracts the mass whereas novelty provides enjoyment. Taken together, even though the balance theory holds in terms of expressed enjoyment, the overall success can show the opposite pattern due to the dominant role of sameness to attract the audience. Under these two forces, cultural evolution may have to work against inertia$\unicode{x2014}$the appetite for consuming the familiar$\unicode{x2014}$and may resemble a punctuated equilibrium, marked by occasional leaps.

William H. W. Thompson, Zachary Wojtowicz, Simon DeDeo

We present a structured random-walk model that captures key aspects of how people communicate in groups. Our model takes the form of a correlated Lévy flight that quantifies the balance between focused discussion of an idea and long-distance leaps in semantic space. We apply our model to three cases of increasing structural complexity: philosophical texts by Aristotle, Hume, and Kant; four days of parliamentary debate during the French Revolution; and branching comment trees on the discussion website Reddit. In the philosophical and parliamentary cases, the model parameters that describe this balance converge under coarse-graining to limit regions that demonstrate the emergence of large-scale structure, a result which is robust to translation between languages. Meanwhile, we find that the political forum we consider on Reddit exhibits a debate-like pattern, while communities dedicated to the discussion of science and news show much less temporal order, and may make use of the emergent, tree-like topology of comment replies to structure their epistemic explorations. Our model allows us to quantify the ways in which social technologies such as parliamentary procedures and online commenting systems shape the joint exploration of ideas.

Christina Boyce-Jacino, Simon DeDeo

Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy, establishes two orthogonal dimensions of question difficulty: obscurity (the rarity of the answer) and opacity (the indirectness of question cues, operationalized with word2vec). The importance of opacity, and the role of synergistic information in resolving it, suggests that accounts of difficulty in terms of prior expectations captures only a part of the question-asking process. A further regression analysis shows the presence of additional dimensions to question-asking: question complexity, the answer's local network density, cue intersection, and the presence of signal words. Our work shows how question-askers can help their interlocutors by using contextual cues, or, conversely, how a particular kind of unfamiliarity with the domain in question can make it harder for individuals to learn from others. Taken together, these results suggest how Bayesian models of question difficulty can be supplemented by process models and accounts of the heuristics individuals use to navigate conceptual spaces.

Jaimie Murdock, Colin Allen, Simon DeDeo

From 1837, when he returned to England aboard the $\textit{HMS Beagle}$, to 1860, just after publication of $\textit{The Origin of Species}$, Charles Darwin kept detailed notes of each book he read or wanted to read. His notes and manuscripts provide information about decades of individual scientific practice. Previously, we trained topic models on the full texts of each reading, and applied information-theoretic measures to detect that changes in his reading patterns coincided with the boundaries of his three major intellectual projects in the period 1837-1860. In this new work we apply the reading model to five additional documents, four of them by Darwin: the first edition of $\textit{The Origin of Species}$, two private essays stating intermediate forms of his theory in 1842 and 1844, a third essay of disputed dating, and Alfred Russel Wallace's essay, which Darwin received in 1858. We address three historical inquiries, previously treated qualitatively: 1) the mythology of "Darwin's Delay," that despite completing an extensive draft in 1844, Darwin waited until 1859 to publish $\textit{The Origin of Species}$ due to external pressures; 2) the relationship between Darwin and Wallace's contemporaneous theories, especially in light of their joint presentation; and 3) dating of the "Outline and Draft" which was rediscovered in 1975 and postulated first as an 1839 draft preceding the Sketch of 1842, then as an interstitial draft between the 1842 and 1844 essays.

Jaimie Murdock, Colin Allen, Simon DeDeo

Search in an environment with an uncertain distribution of resources involves a trade-off between exploitation of past discoveries and further exploration. This extends to information foraging, where a knowledge-seeker shifts between reading in depth and studying new domains. To study this decision-making process, we examine the reading choices made by one of the most celebrated scientists of the modern era: Charles Darwin. From the full-text of books listed in his chronologically-organized reading journals, we generate topic models to quantify his local (text-to-text) and global (text-to-past) reading decisions using Kullback-Liebler Divergence, a cognitively-validated, information-theoretic measure of relative surprise. Rather than a pattern of surprise-minimization, corresponding to a pure exploitation strategy, Darwin's behavior shifts from early exploitation to later exploration, seeking unusually high levels of cognitive surprise relative to previous eras. These shifts, detected by an unsupervised Bayesian model, correlate with major intellectual epochs of his career as identified both by qualitative scholarship and Darwin's own self-commentary. Our methods allow us to compare his consumption of texts with their publication order. We find Darwin's consumption more exploratory than the culture's production, suggesting that underneath gradual societal changes are the explorations of individual synthesis and discovery. Our quantitative methods advance the study of cognitive search through a framework for testing interactions between individual and collective behavior and between short- and long-term consumption choices. This novel application of topic modeling to characterize individual reading complements widespread studies of collective scientific behavior.

David H. Wolpert, Joshua A. Grochow, Eric Libby et al.

To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the thermodynamic properties of a large collection of point particles undergoing reversible dynamics, the variables in a macroeconomic model describing the individuals that participate in an economy, and the summary state of a cell composed of a large set of biochemical networks. Often these high-level descriptions are constructed without considering the ultimate reason for needing them in the first place. Here, we formalize and quantify one such purpose: the need to predict observables of interest concerning the high-dimensional system with as high accuracy as possible, while minimizing the computational cost of doing so. The resulting State Space Compression (SSC) framework provides a guide for how to solve for the {optimal} high-level description of a given dynamical system, rather than constructing it based on human intuition alone. In this preliminary report, we introduce SSC, and illustrate it with several information-theoretic quantifications of "accuracy", all with different implications for the optimal compression. We also discuss some other possible applications of SSC beyond the goal of accurate prediction. These include SSC as a measure of the complexity of a dynamical system, and as a way to quantify information flow between the scales of a system.

Will Landecker, Rick Chartrand, Simon DeDeo

In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$, of elements from an overcomplete dictionary. While many algorithms are competitive at both problems when $x$ is very sparse, it can be challenging to recover $x$ when it is less sparse. We present the Difference Map, which excels at sparse recovery when sparseness is lower and noise is higher. The Difference Map out-performs the state of the art with reconstruction from random measurements and natural image reconstruction via sparse coding.

Greg Ver Steeg, Aram Galstyan, Fei Sha et al.

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate that this intuition suffers from a fundamental conceptual flaw that causes clustering performance to deteriorate as the amount of data increases. Instead, we return to the axiomatic foundations of information theory to define a meaningful clustering measure based on the notion of consistency under coarse-graining for finite data.