Digital Commons Network^™

A Mathematician Expresses Grief, Richard Delaware

Journal of Humanistic Mathematics

A famous Scottish mathematician of the eighteenth century shares a tragic sorrow.

Making Mathematical Art Via The Harmonic And Perturbed Harmonic Functions, Mehmet Pakdemirli

Journal of Humanistic Mathematics

Starting from the definition of a harmonic function series, we define a new series which we call the perturbed harmonic function series. We explore the relationship of the new series with the Weierstrass and Riemann fractal functions as well as its convergence and differentiability properties. We then illustrate the potential of the harmonic functions in generating complex figures that sometimes resemble natural objects, with explicit numerical examples.

A Note On Modeling Prejudice, Alan Lockard, Edwin Harcourt

Journal of Humanistic Mathematics

We model prejudice in the context of an iterated prisoner’s dilemma tournament. Prejudice here is defined as the inability to distinguish amongst members of an identifiable group. We run a computer simulation where agents of one of two groups with defined strategies are randomly matched against each other. The agents either cooperate with or defect against the agent they are matched with. Our focus is on agents who play an unprejudiced version of the Tit-for-Tat strategy (cooperate with any player in the first encounter, and then apply the same strategy [defect or cooperate] that the opposing player played against them …

How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez

Journal of Humanistic Mathematics

In his article “Mémoire sur les Intégrales Définies, prises entre des limites imaginaires” of 1825, Cauchy proves that the integral of a complex function f defined on complex numbers is independent of the path of integration if the function f remains finite and continuous along the chosen path. In contemporary literature that analyzes the mathematics of Cauchy, the specific mathematical process that allowed Cauchy to prove this result is not explicitly presented. The purpose of this manuscript is to communicate a symbolic-algebraic derivation that justifies the narrative argument used by Cauchy to support his proof, thus hopefully filling this gap. …

Gold And Silver In Balance: Khayyam’S Mathematical Analysis Of Binary Alloys, Yousef Yassi, Reza Yassi

Journal of Humanistic Mathematics

The history of titration dates back to Archimedes who established that an object submerged in a liquid displaces an amount of liquid whose weight is equal to the buoyant force acting on the object. Since then, many scientists and engineers have tried to optimize his approach or devise new instruments for titration purposes. Omar Khayyam (1048–1123), in addition to designing a hydro-static balance, developed mathematical approaches for titration of binary alloys, that is, alloys made up of only two elements. Here we explore the different versions of Khayyam’s work on titration given by various sources. We also compare the accuracy …

A Just Balance And The Teaching And Learning Of Mathematics, Marshall Gordon

Journal of Humanistic Mathematics

Society’s response to the question of what is worth sharing and how it best can be provided as conceived by the educational establishment shapes the education of every individual in school. As the classroom experience is a commitment to the future of society, it is good and just for society to support the educational development of each person in order that all can participate productively. In this way a “just balance” is established. In the particular case of educating students in mathematics, however, there is apparently an unjust balance, for despite the considerable time and effort students and teachers in …

Polygonal Number Similarity, Gunhan Caglayan

Journal of Humanistic Mathematics

This note takes an exploratory approach to define and then visualize the notion of polygonal number similarity between pairs of k-gonal numbers P_k(αn) and P_k(n) , where α is an integer scale factor of 2 or greater.

Translating Trattato Dell'alcibra Amuchabile, Olympia Nicodemi

Journal of Humanistic Mathematics

We present a detailed look at one small section of a premodern algebra manuscript from circa 1365 C.E. The manuscript, Tratatto dell’Alcibra Amuchabile (Anonimo), is written in the Tuscan vernacular, with no symbols, no punctuation, and wildly inconsistent (pre-printing press) spellings. We present some of the hurdles to translating this “rhetorical algebra” followed by an annotated translation of one of its algebra rules, Rule 5, through which we learn the methods and mindset of algebra that preceded and seeded the breakthroughs in algebra of the 16^th century. We also point to some of the significant differences between algebra then …

Mathematics And Ethics: Narratives And Conversations, David Pritchard

Journal of Humanistic Mathematics

We provide an eclectic overview of various narratives that mathematicians use to describe mathematics. We discuss some of the ethical issues and approaches that each narrative tends to emphasise, and how these can lead to productive conversation in the absence of a universally agreed philosophical or ethical framework. We also discuss the dangers of a deficit model of ethical engagement, and other threats to conversation.

A Schur-Fire Way To Make Matrix Products Coincide, Keith Copenhaver, Josh Hiller, Christopher Sciortino

Journal of Humanistic Mathematics

When are the Schur product and the matrix product of two matrices the same? With the help of Morpheus (from The Matrix) and more, we explore this question and find both mathematical answers and math-memes.

Exploring The Dynamics Of Romantic Relationships Through The Lens Of Prem Rog, Umang Jain, Dheeraj Sharma, Pranay Goswami, Kuldeep Malik

Journal of Humanistic Mathematics

Romantic relationships are dynamic events that begin, grow, and frequently remain for a long time in a stagnant or fluctuating state until possibly dissipating. Although they are unquestionably the most significant dynamic events in our lives, dynamic systems theory has only recently included them in its formal framework. Without a mathematical model, it would be impossible to analyze and comprehend the dynamics because, in general, love stories are too brief to allow things to stabilize and are affected by the ups and downs of the surrounding community. In this paper, we set up models made up of four ordinary differential …

The More Things Change..., Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Critical Design And The Robotic Imaginary: Design Criticism And Critical Robots, Jörgen Behrendtz

The Journal of Sociotechnical Critique

This paper brings critical design and design criticism to critical robot studies. Critical design can be described as an umbrella term for approaches making use of speculative designs to highlight and challenge narrow assumptions, preconceptions or even taken-for-granted truths about the role products play (in a wide sense) in everyday life. Design criticism refers to a reasoned procedure that investigates emancipatory and/or limiting potentials of designs, theorizes the roles of affordances, materials and embodied perception as epistemological resources in media interaction, and clarifies connections between specific design choices and their associated experiential qualities, seductive powers, ideological underpinnings, material operations, and …

Imaginary Fathers, Jonathan Holden

Creative Nonfiction Magazine

No abstract provided.

Land Use And Sovereignty Along The Catawba River, Thomas C. Brugh, Lucile C. Rencher

Student Scholarship

This document-based case study explains how land-use change along the Catawba River Corridor (Lancaster and York Counties, South Carolina) has been produced through the interaction of property rights (dominium) and rule-setting authority (imperium), showing why sovereignty continues to shape development even after land disputes appear “settled.” Through analyzing legal records (Treaty of Nation Ford, the 1959 Catawba Division of Assets Act, the 1986 Supreme Court timing decision, and the 1993 Settlement Act), planning documents, parcel records, and field observations, we trace how shifting jurisdiction and title certainty structured what kinds of land uses were possible and when. We argue that …

Ultrafast Terahertz Spectroscopy And The Suppression Of Superconductivity In Strained Iron Selenide Below 1 Kelvin, Tracy Glen Hastings

ETDs from 2020-2029

We report on terahertz time-domain spectroscopy measurements of iron selenide thin films of various thicknesses grown on a magnesium oxide substrate, focusing on the frequency-dependent complex conductivity in the range of 0.25 - 7 THz. By an- alyzing films with and without an approximately 100 nm thick Se capping layer, we examined the role of oxidation in the suppression of superconductivity. X-ray photo- electron spectroscopy data confirmed that oxidation was effectively mitigated, yet the films exhibited insulating behavior down to 200 mK, a temperature range that has not been extensively studied in this system. Our results indicate that the suppression …

A Constructive-Engaging Analysis Of Descarrtes (European) And Oyeshile (African) On Personhood, Olanrewaju Shitta-Bey

Comparative Philosophy

An examination of the nature of the human person provides a crucial foundation for understanding human life and identity. Conceptions of personhood have far-reaching implications beyond philosophy, influencing politics, ethics, religion, and epistemology. Beliefs about what constitutes a person shapes theories of rights, responsibility, and justice; moral views on duty and accountability; religious understandings of the soul and the afterlife; and epistemological reflections on the sources and limits of knowledge. Inquiry into human nature is therefore not merely abstract, but central to understanding social organization and individual conduct. This paper examines two influential accounts of human nature drawn from distinct …

A Cross-System Analysis Of Structural Commensurability Between Axiomatic Foundations Of Set Theory (Zfc) And The Principles Of Transcendent Wisdom, Mohammadjavad Maarefvand

Comparative Philosophy

Building on observed similarities in uniqueness proofs for the empty set and the Necessary Existent (Wājib al-Wujūd), this study engages the meta-methodological issue of cross-system commensurability. It identifies four instances of structural commensurability between Zermelo-Fraenkel set theory with Choice (ZFC) and Mulla Sadra's Transcendent Wisdom (Ḥikmat al-Muta'āliyah). First, identity principles: the Axiom of Extensionality provides a formal operational criterion analogous to the philosophical principle of identity through absence of distinguishing features. Second, multiplicity mechanisms: ZFC's constructor axioms (bottom-up construction) and emanation principles (top-down explanation) address analogous problems with inverse orientations. Third, transcending limitation: the Axiom of Infinity ensuring quantitative extensional …

Challenging The Double-Negation Principle: An Analysis Of Strategic Theories Of Sun Zi, Carnot, And Clausewitz Through Intuitionist Logic, Antonino Drago

Comparative Philosophy

To study a subject similarly represented in Eastern and Western cultures, I examine some classical theories of war strategy according to a new analytical method. This method is based on the recognition that the most important strategic theories are organized as theories essentially not deduced from axioms according to classical logic. Such theories reason through doubly negated propositions (DNPs), whose meanings differ from those of their affirmative counterparts. This corresponds to the use of intuitionist logic instead of classical logic. An inspection of the works of the texts of Sun Zi, Lazare Carnot, and Clausewitz reveals many such propositions, and …

Relating To Ai, Nick Breems

Faculty Work Comprehensive List

"As users of technology, we do have a choice."

Posting about ­­­­­­­­exercising discernment in using technological tools from In All Things, an online hub that offers insight into maintaining and faithful and orthodox Reformed Christian worldview while fearlessly engaging in every aspect of contemporary life – until all is made new.

Relating to AI

Equipping Beyond Campus: A Look At Dordt Faculty As Public Scholars, Sarah Moss

The Voice

No abstract provided.

Restorative Justice, Human Dignity, And The Capabilities Approach, Reed Mcfeely

Acta Cogitata: An Undergraduate Journal in Philosophy

As a value-driven and transformative approach to criminal justice, restorative justice is inherently philosophical. Despite this, however, its philosophical underpinnings remain underdeveloped. This manuscript argues for the necessity of grounding restorative justice in moral philosophy, specifically through the framework offered by Martha Nussbaum’s capabilities approach. The paper first addresses the fragmented nature of restorative justice values, suggesting a new uniform framework centered on respect, equality, agency, and active striving. It then explores what victims are materially owed in the restorative justice process, advancing Nussbaum’s list of basic capabilities as a foundation. However, the central aim of this manuscript transcends these …

Western Mansions In The Gardens Of Perfect Brightness, Another History Of High Qing Sino-European Exchanges, Nicolas Woreth

Swarthmore Undergraduate History Journal

The Gardens of Perfect Brightness, the favorite residence of Chinese Emperors in the High Qing era (1683-1799), held mysteries that will remain forever concealed from the public eye after French and British imperialist forces looted it and burned it beyond repair during the Second Opium War (1856-1860). Behind the doors of the secret garden, scarcely open to anyone but the emperor, his wives, and servants, worked European artists and scientists. Most of them were Jesuit missionaries who served the emperor in the hope of gaining his favor and support for the spread of Christianity in China.

This paper aims to …

Gold, Manuscripts, And Misunderstanding: The Forgotten Intellectual Wealth Of Timbuktu, Caroline A. Valdovinos

Swarthmore Undergraduate History Journal

This article re-examines Timbuktu’s legacy, challenging European myths that imagined the city as a hidden African “El Dorado” while overlooking its intellectual wealth. From the fourteenth to sixteenth centuries, Timbuktu thrived as a hub of trade, religion, and scholarship, home to mosques, libraries, and networks of learning that drew scholars from across the Islamic world. Manuscripts on theology, law, medicine, and science circulated widely, placing the city at the heart of West Africa’s intellectual life. Yet European explorers and mapmakers, influenced by accounts like those of Leo Africanus, recast Timbuktu as a treasure-laden city of gold. This obsession, reinforced by …

What Kind Of Relationality Does Quantum Mechanics Exhibit?, Emily Adlam

Philosophy Faculty Articles and Research

In this article I elaborate on the approach to relational quantum mechanics suggested by Adlam and Rovelli (2023). I suggest that this approach fills an important gap in the spectrum of relational approaches, because it posits that the relational aspects of quantum mechanics are both inherent and dynamical. I compare this approach to Orthodox RQM, arguing that it has a number of advantages, and I show how some possible objections can be resolved.

From Desire To Decision (A Syllabic Synopsis Of A Short Story), Ken Stange

Ontario Review

KEN STANGE, a psychology lab instructor in North Bay, Ontario, edits Nebula Magazine and has poems published or forthcoming in The Canadian Forum, The Dalhousie Review, Event, Waves, and elsewhere.

The Man Who Changed Overnight, Fielding Dawson

Ontario Review

FIELDING DAWSON, a resident of New York City, is the author of The Dream/Thunder Road (stories), The Greatest Story Ever Told (novella), and The Sun Rises into the Sky (stories), and other books. "The Man Who Changed Over-night" will be the title story of a new collection of fiction to be published by The Black Sparrow Press this year.

C. S. Lewis And Artificial Intelligence: An Ai Ethics Problem, Justin E. Edgerly

Sehnsucht: The C. S. Lewis Journal

This paper demonstrates that the quest for safe and ethical AI is undermined by much of the philosophy, implicit and explicit, in AI literature and undergirding AI research and development. C. S. Lewis’s writings provide a prescient and penetrating critique of this philosophy and point toward a “regenerate science” that addresses the present need for wisdom in AI development. This paper contributes to the field of AI ethics by presenting several Lewisian concerns about the nature, application, and undergirding philosophy of current and future AI technologies, as well as a Lewisian perspective on the requirements for safe and ethical AI.

Beyond Black And White: Embracing Every Hue Through Words, Stories, And Unapologetic Truths, Darius M. Phelps

New Jersey English Journal

Literacy shapes how students interpret and engage with the world, yet traditional education often compartmentalizes it. This article explores racial literacy and poetry as transformative, interdisciplinary tools for critical inquiry and identity formation. Grounded in scholarship and practical strategies, it calls for reimagining literacy instruction as empowerment across disciplines and lived experiences.