Recursively enumerable sets of positive integers and their decision problems
Emil L. Post
Introduction. Recent developments of symbolic logic have considerable importance for mathematics both with respect to its philosophy and practice. That mathematicians generally are oblivious to the importance of this work of Gödel, Church, Turing, Kleene, Rosser and others as it affects the subject of their own interest is in part due to the forbidding, diverse and alien formalisms in which this work is embodied. Yet, without such formalism, this pioneering work would lose most of its cogency. But apart from the question of importance, these formalisms bring to mathematics a new and precise mathematical concept, that of the general recursive function of Hërbrand-GödelKleene, or its proved equivalents in the developments of Church and Turing. It is the purpose of this lecture to demonstrate by example that this concept admits of development into a mathematical theory much as the group concept has been developed into a theory of groups. Moreover, that stripped of its formalism, such a theory admits of an intuitive development which can be followed, if not indeed pursued, by a mathematician, layman though he be in this formal field. It is this intuitive development of a very limited portion of a sub-theory of the hoped for general theory that we present in this lecture. We must emphasize that, with a few exceptions explicitly so noted, we have obtained formal proofs of all the consequently mathematical theorems here developed informally. Yet the real mathematics involved must lie in the informal development. For in every instance the informal "proof" was first obtained; and once gotten, transforming it into the formal proof turned out to be a routine chore. We shall not here reproduce the formal definition of recursive function of positive integers. A simple example of such a function is an
738 sitasi
en
Mathematics
Mathematical methods and human thought in the age of AI
Tanya Klowden, Terence Tao
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become exponentially sophisticated and pervasive, the justifications for their rapid development and integration into society are frequently called into question, particularly as they consume finite resources and pose existential risks to the livelihoods of those skilled individuals they appear to replace. In this paper, we consider the rapidly evolving impact of AI to the traditional questions of philosophy with an emphasis on its application in mathematics and on the broader real-world outcomes of its more general use. We assert that artificial intelligence is a natural evolution of human tools developed throughout history to facilitate the creation, organization, and dissemination of ideas, and argue that it is paramount that the development and application of AI remain fundamentally human-centered. With an eye toward innovating solutions to meet human needs, enhancing the human quality of life and expanding the capacity for human thought and understanding, we propose a pathway to integrating AI into our most challenging and intellectually rigorous fields to the benefit of all humankind.
Editorial
Julián Ramiro Numpaque García
N/A
Philosophy. Psychology. Religion, Philosophy (General)
Embedding Reliability Verification Constraints into Generation Expansion Planning
Peng Liu, Lian Cheng, Benjamin P. Omell
et al.
Generation planning approaches face challenges in managing the incompatible mathematical structures between stochastic production simulations for reliability assessment and optimization models for generation planning, which hinders the integration of reliability constraints. This study proposes an approach to embedding reliability verification constraints into generation expansion planning by leveraging a weighted oblique decision tree (WODT) technique. For each planning year, a generation mix dataset, labeled with reliability assessment simulations, is generated. An WODT model is trained using this dataset. Reliability-feasible regions are extracted via depth-first search technique and formulated as disjunctive constraints. These constraints are then transformed into mixed-integer linear form using a convex hull modeling technique and embedded into a unit commitment-integrated generation expansion planning model. The proposed approach is validated through a long-term generation planning case study for the Electric Reliability Council of Texas (ERCOT) region, demonstrating its effectiveness in achieving reliable and optimal planning solutions.
Large Language Models for History, Philosophy, and Sociology of Science: Interpretive Uses, Methodological Challenges, and Critical Perspectives
Arno Simons, Michael Zichert, Adrian Wüthrich
This paper explores the use of large language models (LLMs) as research tools in the history, philosophy, and sociology of science (HPSS). LLMs are remarkably effective at processing unstructured text and inferring meaning from context, offering new affordances that challenge long-standing divides between computational and interpretive methods. This raises both opportunities and challenges for HPSS, which emphasizes interpretive methodologies and understands meaning as context-dependent, ambiguous, and historically situated. We argue that HPSS is uniquely positioned not only to benefit from LLMs' capabilities but also to interrogate their epistemic assumptions and infrastructural implications. To this end, we first offer a concise primer on LLM architectures and training paradigms tailored to non-technical readers. We frame LLMs not as neutral tools but as epistemic infrastructures that encode assumptions about meaning, context, and similarity, conditioned by their training data, architecture, and patterns of use. We then examine how computational techniques enhanced by LLMs, such as structuring data, detecting patterns, and modeling dynamic processes, can be applied to support interpretive research in HPSS. Our analysis compares full-context and generative models, outlines strategies for domain and task adaptation (e.g., continued pretraining, fine-tuning, and retrieval-augmented generation), and evaluates their respective strengths and limitations for interpretive inquiry in HPSS. We conclude with four lessons for integrating LLMs into HPSS: (1) model selection involves interpretive trade-offs; (2) LLM literacy is foundational; (3) HPSS must define its own benchmarks and corpora; and (4) LLMs should enhance, not replace, interpretive methods.
Generating temporal networks with the Ascona model
Samuel Koovely
We introduce a queueing-based sampling framework for continuous-time temporal networks. We focus on a Markovian parametrization in which link start times follow a homogeneous Poisson process and link durations are exponentially distributed. We derive stochastic properties of the resulting link streams and exploit them to generate synthetic temporal networks with controllable smoothness and prescribed event patterns, relevant for the validation and interpretation of methods for community, scale, change-point, and periodicity detection. By coupling this temporal mechanism with block-structured endpoint distributions, we obtain a continuous-time analogue of stochastic block models. We also discuss extensions of the framework, including discrete-time and instantaneous-contact limits.
en
physics.soc-ph, math.PR
An Investigation of Computer Coaching for Informal Learning Activities.
R. Burton, J. Brown
602 sitasi
en
Computer Science, Political Science
Progressive-Era Racism and Another 'Blaming the Victim' Narrative
Luca Fiorito
This note reproduces a brief article by Thomas Nixon Carver, a leading Progressive Era American economist on what was then called the ‘Negro Question’. This virtually unknown piece represents a striking instance of blaming the victim for her/his condition which is to be found in the economic literature of the period.
Economic theory. Demography, Philosophy (General)
Applications of Tao General Difference in Discrete Domain
Linmi Tao, Ruiyang Liu, Donglai Tao
et al.
Numerical difference computation is one of the cores and indispensable in the modern digital era. Tao general difference (TGD) is a novel theory and approach to difference computation for discrete sequences and arrays in multidimensional space. Built on the solid theoretical foundation of the general difference in a finite interval, the TGD operators demonstrate exceptional signal processing capabilities in real-world applications. A novel smoothness property of a sequence is defined on the first- and second TGD. This property is used to denoise one-dimensional signals, where the noise is the non-smooth points in the sequence. Meanwhile, the center of the gradient in a finite interval can be accurately location via TGD calculation. This solves a traditional challenge in computer vision, which is the precise localization of image edges with noise robustness. Furthermore, the power of TGD operators extends to spatio-temporal edge detection in three-dimensional arrays, enabling the identification of kinetic edges in video data. These diverse applications highlight the properties of TGD in discrete domain and the significant promise of TGD for the computation across signal processing, image analysis, and video analytic.
In Which Sense Can We Say That First-Class Constraints Generate Gauge Transformations?
Álvaro Mozota Frauca
In this paper, I consider a recent controversy about whether first-class constraints generate gauge transformations in the case of electromagnetism. I argue that there is a notion of gauge transformation, the extended notion, which is different from the original gauge transformation of electromagnetism, but at the same time not trivial, which allows the making of that claim. I further argue that one can expect that this claim can be extended to more general theories, and that Dirac's conjecture may be true for some physically reasonable theories and only in this sense of gauge transformation. Finally, I argue that the extended notion of gauge transformation seems unnatural from the point of view of classical theories, but that it nicely fits with the way quantum versions of gauge theories are constructed.
en
physics.hist-ph, gr-qc
Potential and limitations of digital ethnographic research: A case study on a web community
Giuseppe Masullo, Marianna Coppola
IntroductionThis work aims at transposing ethnographic research into digital contexts to probe its potential and limitations in a specific field of study: that of sexuality, particularly suited to ethnographic exploration. We chose as our case study a web community of Italian asexual people. As we shall see, this allowed us to simultaneously explore both the various techniques called into play in digital ethnography and the digital as a specific sphere within which sexuality takes on a very peculiar meaning. Digital sociality is paramount for the definition of imaginaries, meanings, and practices that could not be explored elsewhere. This is due to the implicit characteristics of the population studied, which does not find corresponding physical spaces of aggregation.MethodsThe paper will present the research design using this specific case study to address some of the typical dilemmas that researchers face when following the digital ethnographic approach and will explore the research results as an example of the kind of analysis available with the information and data collected through this method.Results and discussionThe conclusions will attempt to briefly outline the shortfalls and advantages of this method, considering its application to this specific field of study.
Underdetermination in Classic and Modern Tests of General Relativity
William J. Wolf, Marco Sanchioni, James Read
Canonically, `classic' tests of general relativity (GR) include perihelion precession, the bending of light around stars, and gravitational redshift; `modern' tests have to do with, inter alia, relativistic time delay, equivalence principle tests, gravitational lensing, strong field gravity, and gravitational waves. The orthodoxy is that both classic and modern tests of GR afford experimental confirmation of that theory in particular. In this article, we question this orthodoxy, by showing there are classes of both relativistic theories (with spatiotemporal geometrical properties different from those of GR) and non-relativistic theories (in which the lightcones of a relativistic spacetime are `widened') which would also pass such tests. Thus, (a) issues of underdetermination in the context of GR loom much larger than one might have thought, and (b) given this, one has to think more carefully about what exactly such tests in fact are testing.
en
physics.hist-ph, gr-qc
<null> me <null>: Algorithmic Governmentality and the Notion of Subjectivity in Project Itoh's Harmony
Fatemeh Savaedi, Maryam Alavi Nia
Algorithmic governmentality is a new form of political governance interconnected with technology and computation. By coining the term “algorithmic governmentality,” Antoinette Rouvroy argues that this mode of governance reduces everything to data, and people are no longer individuals but dividuals (able to be divided) or readable data profiles. Implementing the concept of algorithmic governmentality, the current study analyses Project Itoh’s award-winning novel Harmony in terms of such relevant concepts as “subjectivity,” “infra-individuality” and “control,” as suggested by Rouvroy and colleagues. The analysis further draws on Foucault’s ideas of “governmentality” and “neoliberalism” and Deleuze’s concepts of “dividuality” and “society of control.” In Itoh’s fictional world, the entire society is subject to the new medical government, which replaced the chaotic world with a perfect but harrowing benevolent society, eradicating disease, suicide and crime. As elucidated in this paper, despite the dominant controlling government, there is a hope for humans to regain and reestablish their subjectivity and give meaning to their own personality by defying the nihilistic computational system.
Philosophy (General), Literature (General)
Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)
Nikos Mantzakouras
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the final field of the roots of the equation will be the union of these subfields. We have a wide range of applications by solving hyperbolic in all sciences, especially in physics and chemistry. In this paper, we solve the generalized trinomial and some important applications in physics and astronomy like the generalized solution of the Kepler equation.
Investigating Emotions as Functional States Distinct From Feelings
R. Adolphs, D. Andler
We defend a functionalist approach to emotion that begins by focusing on emotions as central states with causal connections to behavior and to other cognitive states. The approach brackets the conscious experience of emotion, lists plausible features that emotions exhibit, and argues that alternative schemes (e.g., focusing on feelings or on neurobiology as the starting point) are unpromising candidates. We conclude with the benefits of our approach: one can study emotions in animals; one can look in the brain for the implementation of specific features; and one ends up with an architecture of the mind in which emotions are fully accommodated through their relations to the rest of cognition. Our article focuses on arguing for this general approach; as such, it is an essay in the philosophy of emotion rather than in the psychology or neuroscience of emotion.
93 sitasi
en
Psychology, Medicine
Military Diaries: Content, Features, and Potential (Based on the Great Patriotic War Sources)
A. S. Kuznetsov
The present research featured the content, specific features, and potential of military diaries as a historical source in the anthropology of the Great Patriotic War. The study was based on the views of the leading Soviet and modern specialists in the field of source studies and historical methodology. The author defined three approaches to the place of diaries in the classification of historical sources: 1) diaries as ego-documents, 2) military diaries as memoirs, 3) diaries as a separate group of personal documents. The research objective was to determine the potential of military diaries as a source for anthropological studies of the Great Patriotic War. The method of content analysis revealed the most important aspects for the dairy writers in extreme military environment. The biographical method based on the diary analysis made it possible to describe the image of homo militaris during the Great Patriotic War. Military diaries demonstrated a great potential for studies of war routine, healthcare, psychology, and enemy perception through the eyes of an ordinary military participant, the psychology of warring man, the perception of an enemy during World War I.
History of Russia. Soviet Union. Former Soviet Republics, Psychology
PROBLEMATIKA PEMBELAJARAN AL-QUR’AN DI ERA INDUSTRI DALAM KONTEKS INDONESIA
Dewi Ratnawati, Ahmad Zainal Abidin, Eko Zulfikar
There are at least two factors that trigger problems in the Qur`an learning in the industrial era 4.0: the rejection of changes that occur in educators and acceptance of changes, but the available technological infrastructure cannot support learning of the Qur`an into the realm of education in the era industry 4.0. This resulted in failure in learning the Qur`an. The manifestations of this failure are in the form of unsuccessful character building for students to have Qur`anic characters, fading love of students for the Qur`an, loss of students' polite behavior, and limited material received only limited to cognitive knowledge without performance abilities. By using the descriptive-explorative method, this paper produces findings that the problems of learning the Qur`an in the industrial era, namely: the use of the Qur`an learning method which is monotonous, the learning strategy of the Qur`an is not yet right, the lack of facilities. infrastructure that supports learning Qur`an, there has not been any transformation and innovation of the Qur`an learning that takes advantage of technological sophistication, the lack of professional educators, and lack of support from the environment for the realization of a triple education center.
Education, Education (General)
“Uma perigosa travessia”. Equilibrista e bufão em Assim falava Zaratustra
Katharina Grätz
Resumo Livro para todos e para ninguém, Assim falava Zaratustra ocupa, com efeito, um lugar especial no conjunto da obra de Nietzsche. Já no Prólogo do livro, o filósofo alemão faz intervir concepções únicas e personagens sui generis, tais como, por exemplo, a noção de além-do-homem e as figuras do equilibrista e do bufão. Explorando a rica mediação narrativa e as finas referências textuais que constituem essas duas simbólicas personagens, bem como os possíveis sentidos conferidos à ideia de superação do tipo “homem”, o presente artigo conta lançar uma nova luz sobre um dos núcleos temáticos mais discutidos do legado nietzschiano.
Estrategias metodológicas utilizadas en Ingeniería: una revisión sistemática
Victor Manuel Tepe Atoche, Juan Pedro Soplapuco Montalvo
La formación de los ingenieros es un tema que involucra a docentes y estudiantes, los avances tecnologico obliga a los centros de formación superior buscar alternativas para mejorar o proponer nuevas estrategias de enseñanza en ingeniería. El objetivo de la Investigacion realizada fue hacer una revisión bibliográfica de manera cualitativa, que nos permita conocer las estrategias metodologias de enseñanza utilizadas por los docentes en las carreras de ingeniería en universidades de Latinoamérica y el mundo, teniendo en consideración el impacto que estas generan en la formación de los futuros ingenieros, se consideró cuarenta(40) artículos publicados entre los años 2010 al 2020 que tengan relación a procesos de formación, se utilizó el buscador Google Académico y las ecuaciones de búsqueda, con la finalidad de encontrar en bases de datos la información, que nos permitirán hacer un análisis del desarrollo de las estrategias metodológicas, que los docentes utilizan en la formación de los futuros ingenieros, esto no lleva a concluir que todavía es un área que requiere ser atendida por los investigadores.
Philosophy (General), Education (General)
Weighted surface algebras: general version. Corrigendum
Karin Erdmann, Andrzej Skowroński
In [arXiv:1902.04063] we generalize the original definition of weighted surface algebras in [arXiv:1703.02346] by allowing the possibility that arrows might not be part of the Gabriel quiver, which gives a much larger class of algebras. This means that the zero relations need modification, to make sure that the algebras are symmetric, and of the appropriate dimension. We found recently that we had missed one necessary modification for the zero relations. Here we give the correct definition, and revise the parts of [arXiv:1902.04063] which are affected by this modification.