Given a word $w(x_{1},\ldots,x_{r})$, i.e. an element in the free group on r elements, and an integer $d\geq1$, we study the characteristic polynomial of the random matrix $w(X_{1},\ldots,X_{r})$, where $X_{i}$ are Haar-random independent $d\times d$ unitary matrices. If $c_{m}(X)$ denotes the mth coefficient of the characteristic polynomial of X, our main theorem implies that there is a positive constant $\epsilon(w)$, depending only on w, such that

\[|\mathbb{E}(c_{m}(w(X_{1},\ldots,X_{r})))|\leq\binom{d}{m}^{\!\!1-\epsilon(w)},\]

$1\leq m\leq d$

$\mathbb{E}(c_{m}(w))$

A number of authors have observed that epistemic externalists seem to face a dilemma: Either deny that Conditionalization is the rational update rule, thereby rejecting traditional Bayesian epistemology, or deny that the rational update rule maximizes expected accuracy, thereby rejecting accuracy-first epistemology. Call this the Bayesian Dilemma. I’m not convinced by this argument. Once we make the premises explicit, we see that it relies on assumptions the externalist rejects. In this paper, I argue that the Bayesian Dilemma is nevertheless a genuine dilemma. My argument does not make any assumptions that the externalist rejects.

Scholars have long maintained that Irenaeus rejected the use of Hellenic resources in Christian theology. While recent decades have seen better recognition of Irenaeus’ philosophical and rhetorical knowledge, Irenaeus’ use of poetic literature, especially Homer, has received little attention. The present article rectifies this deficiency. First, it defines the role of Homeric material in Irenaeus’ broader theological project. Then, studying Irenaeus’ use of a unique Homeric word, proprocylindomene (Haer. 1.11.4), it demonstrates that Irenaeus appropriates Homer to his theological project with the facility that Quintilian associates with a practiced and skillful rhetorician. In light of this, the article concludes by contending that Irenaeus likely composed the Homeric cento in Haer. 1.9.4 himself. If this is the case, Haer. 1.9.4 constitutes perhaps Irenaeus’ most skillful appropriation of Homer to his theological project. It best illustrates how for Irenaeus the poet could be used in a Christian theological project.

The past decade saw the proliferation of projects that use 3D and related technologies to engage with Indigenous heritage through museum collections and cultural heritage site digitization projects involving the documentation and sometimes physical replication of objects and landscapes; some of these projects involved Indigenous origin communities. Although 3D technologies have become more widespread and accessible, ethical considerations in practice lag behind. The “Ethical Considerations in Three-Dimensional Digitization of Indigenous Heritage” project unites researchers, members of Indigenous communities, and 3D heritage specialists to develop a set of best practices for the responsible conduct of research (RCR). These practices promote ethical cultures in science, technology, engineering, and math (STEM) fields, recognizing Indigenous heritage 3D modeling as a critical part of the broader conversation around decolonization and core methodologies. This article proposes incorporating best practices developed from the RCR findings for 3D digitization projects of Indigenous cultural heritage. We suggest utilizing Collective benefit, Authority to control, Responsibility, and Ethics (CARE) principles, Indigenous Data Sovereignty, and a co-production of knowledge (CPK) framework.

One profound yet relatively understudied contribution to tafsīr (Qur’an commentary) is that of Ibn ʿArafah al-Warġammī (d. 803/1401), a leading Mālikī scholar of eighth/fourteenth-century Ḥafṣid Tunisia. Although no separate commentary by Ibn ʿArafah has come down to us, his commentary on the Qur’an is accessible through the lecture notes that were compiled by his students. This article will examine one significant aspect of Ibn ʿArafah’s Qur’anic discourse that is barely acknowledged—his understanding of the relationship between the Qur’an and logic, and his use of logic in Qur’anic interpretation. It suggests that Ibn ʿArafah conceived of logic as embedded in the fabric of the Qur’an and felt a sense of urgency in using logic as an instrument for tafsīr. It also shows that the application of logic to Qur’anic interpretation is dominant in Ibn ʿArafah’s commentary to an extent that is not found in earlier works of tafsīr. Through identifying the different ways in which he intertwined the science of logic with tafsīr, this article will highlight Ibn ʿArafah’s role in the logical hermeneutics of the Qur’an and expand our understanding of how logic was used as an instrument for other sciences—in particular, for the interpretation of the Qur’an.

The concept of projectile point series was first developed in California and the Great Basin in the 1950s and 1960s. In 1981, applying the Monitor Valley projectile point key, Thomas (1981) assigned chronological ranges to five projectile point series for the Great Basin, the Gatecliff Series, the Humboldt Series, the Elko Series, the Rosegate Series, and the Desert Series, which were based on the Berkeley projectile point naming conventions. Each of these series, which are still in use today, include different morphological point forms that—although sharing the same primary designator—do not share the same temporal spans or geographic distributions. Morphologically different projectile points do not share a priori temporal, geographic, or cultural associations simply by virtue of sharing a series label. The use of the series concept and chronology in projectile point analyses in the West should be discontinued and replaced with analyses of morphological forms, geographic distributions, and temporal spans of individual point types.

Paleoindians buried Spirit Cave Man in a Nevada cave, and archaeologists excavated these remains in 1940. Radiocarbon testing in 1996 dated the burial and associated grave goods as older than 10,700 years. Living just 10 miles from Spirit Cave, the Fallon Paiute-Shoshone Tribe filed a NAGPRA claim in 1997 requesting the repatriation of the Spirit Cave ancestor they call “The Storyteller.” This claim ignited a 20-year legal dispute that led the Fallon Paiute-Shoshone Tribe to make the gut-wrenching decision to permit DNA testing. This article documents a 10,000-year genetic continuity firmly linking Paleoindians at Spirit Cave to the Lovelock culture and that strongly suggests continuities to modern Paiutes living there today with no population replacement. We explore the associated radiocarbon record of these dynamics to understand the syncopated population movements that responded to shifting resource distributions. Resilience theory provides an operational way to understand this extraordinary continuity through key concepts, including tipping points, early warning signals, sunk-cost effects, and loss-of-resilience hypotheses. The Spirit Cave case also underscores the moribund concepts and assumptions underlying a century of Great Basin anthropological study that misread this long-term episode of Indigenous resilience and survivance.

Genesis 9:20–27 raises difficult exegetical questions, such as why Noah curses Canaan rather than Ham in 9:25–27. Additionally, the text has an infamous history of providing a popular defense of slavery in Africa and the United States. Some African American interpreters have argued that Noah’s curse should not be understood as divinely sanctioned words because Noah is still under the influence of alcohol when he speaks. Linking Noah’s actions in Gen 9:20–24 with his words in 9:25–27, these interpreters attend to the literary context of Noah’s speech while also combatting one of the most noxious uses of the Bible in recent centuries. This article adds exegetical support to this approach, demonstrating how this interpretation avoids the pitfalls of other treatments while working exceptionally well on a literary level with the passage itself. All of Noah’s behaviors in 9:21–27 align with clinical descriptions of alcohol intoxication.

Scholars have long noted the prevalence of exile as a theme in John Calvin’s theology, which responded to times unsettled by religious persecution and migration. However, research has only begun to describe with precision how Calvin portrayed exile. This article examines the theme in Calvin’s biblical exegesis, demonstrating how his commentaries and sermons problematize exile by establishing two requirements for faithfulness from the exilic experiences of Abraham and David: 1) open confrontation with idolatry; and 2) the pursuit of sacramental nurture. In both cases, the reformer’s exegesis is notable for reflexively invoking Nicodemism, persistently deploying Abraham and David as counterexamples against this contemporary problem. This intersection of crypto-religion and exile, considered spiritually and politically, displays how context drove Calvin’s exegesis toward readings distinctive in the history of interpretation. It also sharpens exile’s polemical potential as a differentiated category Calvin used to encourage the community of believers while disciplining its behavior.