Embodied Lives: Figuring Ancient Maya and Egyptian Experience

Posted on by Simon Fokt

Publisher’s note: Examining a wide range of archaeological data, and using it to explore issues such as the sexual body, mind/body dualism, body modification, and magical practices, Lynn Meskell and Rosemary Joyce offer a new approach to the Ancient Egyptian and Mayan understanding of embodiment. Drawing on insights from feminist theory, art history, phenomenology, anthropology and psychoanalysis, the book takes bodily materiality as a crucial starting point to the understanding and formation of self in any society, and sheds new light on Ancient Egyptian and Maya cultures.

The book shows how a comparative project can open up new lines of inquiry by raising questions about accepted assumptions as the authors draw attention to the long-term histories and specificities of embodiment, and make the case for the importance of ancient materials for contemporary theorization of the body. For students new to the subject, and scholars already familiar with it, this will offer fresh and exciting insights into these ancient cultures.

An Animating Principle in Confrontation with Christianity? De(re)constructing the Nahua ‘Soul’

Posted on by Simon Fokt

-Yolia is one of the principal indigenous terms present in Christian Nahua terminology in the first decades of European contact. It is employed for “soul” or “spirit” and often forms a doublet with ánima in Nahuatl texts of an ecclesiastical, devotional, or secular nature. the term -Yolia/teyolia has also lived a rich and fascinating life in scholarly literature. Its etymology (“the means for one’s living”) is strikingly similar to that of the Spanish word “ánima”, or “soul.” Taking into account the possibility that attestations of the seemingly pre-Hispanic -Yolia can be identified in some of the written sources, we have reviewed historical, linguistic, and anthropological evidence concerning this term in order to revisit the Nahua concept of the “soul.” we also scrutinize the very origin of -Yolia in academic discourse. this analysis, based on broader historical and linguistic evidence referring to both pre-Conquest beliefs and Christianization in sixteenth-century central Mexico, is the point of departure for proposing and substantiating an alternative hypothesis about the origin of -yolia. Our precise focus has been to trace and pinpoint a pervasive Christian influence, manifest both in indigenous Colonial texts and conceptual frameworks of modern scholars interpreting them. we conclude that -Yolia is a neologism created in the early Colonial period.

Cantares Mexicanos: Songs of the Aztecs.

Posted on by Simon Fokt

Adapted from prologue. “Since its rediscovery in the mid-nineteenth century the codex Cantares Mexicanos has come to be recognized as the chief source of Aztec poetry and one of the monuments of American Indian literature (…) Over the years a tradition has gradually been established that views the Cantares as a poet’s miscellany, studded with lyrics composed by famous kings (…) [Bierhorst’s edition] breaks with this tradition (…) The findings [of the present study] in brief are these: The ninety-one songs in the Cantares, without exception, belong to a single genre, which flourishes during the third quarter of the sixteenth century. Netotiliztli (or dance associated with worldly entertainment) is the native name that appears to have been applied to the genre in its entirety. But for lack of certainty on this point, and for the sake of convenience, I have chosen to designate it by the term “ghost songs.” (…) the Aztec ghost song may be described as a musical performance in which warrior-singers summon the ghosts of ancestors in order to swell their ranks and overwhelm their enemies. (…) The Cantares itself (…) is limited to songs belonging to the city-state of Mexico, or to Mexico and its close ally, Azcapotzalco (…) Although it is possible that a few of the songs in the Cantares manuscripts were composed before the Conquest, by far the greater number belong to the post-Conquest period.”

Philosophy of the Ancient Maya: Lords of Time

Posted on by Simon Fokt

This book investigates some of the central topics of metaphysics in the philosophical thought of the Maya people of Mesoamerica, particularly from the Preclassic through Postclassic periods. This book covers the topics of time, change, identity, and truth, through comparative investigation integrating Maya texts and practices — such as Classic Period stelae, Postclassic Codices, and Colonial-era texts such as the î and the books of Chilam Balam — and early Chinese philosophy.

A Group Theory of Group Theory: Collaborative Mathematics and the ‘Uninvention’ of a 1000-page Proof

Posted on by Simon Fokt

Over a period of more than 30 years, more than 100 mathematicians worked on a project to classify mathematical objects known as finite simple groups. The Classification, when officially declared completed in 1981, ranged between 300 and 500 articles and ran somewhere between 5,000 and 10,000 journal pages. Mathematicians have hailed the project as one of the greatest mathematical achievements of the 20th century, and it surpasses, both in scale and scope, any other mathematical proof of the 20th century. The history of the Classification points to the importance of face-to-face interaction and close teaching relationships in the production and transformation of theoretical knowledge. The techniques and methods that governed much of the work in finite simple group theory circulated via personal, often informal, communication, rather than in published proofs. Consequently, the printed proofs that would constitute the Classification Theorem functioned as a sort of shorthand for and formalization of proofs that had already been established during personal interactions among mathematicians. The proof of the Classification was at once both a material artifact and a crystallization of one community’s shared practices, values, histories, and expertise. However, beginning in the 1980s, the original proof of the Classification faced the threat of ‘uninvention’. The papers that constituted it could still be found scattered throughout the mathematical literature, but no one other than the dwindling community of group theorists would know how to find them or how to piece them together. Faced with this problem, finite group theorists resolved to produce a ‘second-generation proof’ to streamline and centralize the Classification. This project highlights that the proof and the community of finite simple groups theorists who produced it were co-constitutive–one formed and reformed by the other.

Diagrams and Proofs in Analysis

Posted on by Simon Fokt

This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that ‘visualization’ is used in two different ways. In the first sense ‘visualization’ denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense ‘visualization’ denotes a diagram or representation of something.

An Inquiry into the Practice of Proving in Low-Dimensional Topology

Posted on by Simon Fokt

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology.

Proofs Versus Experiments: Wittgensteinian Themes Surrounding the Four-Color Theorem

Posted on by Simon Fokt

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970’s, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem.

Authorship in top-ranked mathematical and physical journals: Role of gender on self-perceptions and bibliographic evidence

Posted on by Simon Fokt

Despite increasing rates of women researching in math-intensive fields, publications by female authors remain underrepresented. By analyzing millions of records from the dedicated bibliographic databases zbMATH, arXiv, and ADS, we unveil the chronological evolution of authorships by women in mathematics, physics, and astronomy. We observe a pronounced shortage of female authors in top-ranked journals, with quasistagnant figures in various distinguished periodicals in the first two disciplines and a significantly more equitable situation in the latter. Additionally, we provide an interactive open-access web interface to further examine the data. To address whether female scholars submit fewer articles for publication to relevant journals or whether they are consciously or unconsciously disadvantaged by the peer review system, we also study authors’ perceptions of their submission practices and analyze around 10,000 responses, collected as part of a recent global survey of scientists. Our analysis indicates that men and women perceive their submission practices to be similar, with no evidence that a significantly lower number of submissions by women is responsible for their underrepresentation in top-ranked journals. According to the self-reported responses, a larger number of articles submitted to prestigious venues correlates rather with aspects associated with pronounced research activity, a well-established network, and academic seniority.

Groundwork for a Fallibilist Account of Mathematics

Posted on by Simon Fokt

According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices.