EL JUEGO DE LOS ABALORIOS: del Último Teorema de Fermat a los Solitones Ópticos

Siguiendo la idea del Juego de los Abalorios (de Hermann Hesse), en este trabajo investigamos qué relación existe entre el último Teorema de Fermat (UTF) y los solitones ópticos. Para encontrar esta relación examinamos los pasos principales que condujeron a la demostración del UTF, empezando por la conjetura de Taniyama-Shimura, y pasando por las contribuciones de Hellegouarch, Frey y Ribet, hasta llegar al trabajo de Wiles. Posteriormente examinamos algunas de las ecuaciones que describen a los solitones ópticos. De este análisis se desprende que las curvas elípticas constituyen el puente que relaciona ambos temas. Veremos, además, que las ecuaciones que describen solitones ópticos también podrían tener alguna relación con la criptografía. Finalmente veremos que los resultados encontrados en este trabajo nos permiten proponer 2 conjeturas que constituyen temas de investigación para el futuro. Following the idea of the Glass Bead Game (by Hermann Hesse), in this work we investigate what relation exists between Fermat´s Last Theorem (FLT) and the optical solitons. To find such a relationship we examine the principal steps which lead to the demonstration of FLT, starting from Taniyama-Shimura´s conjecture, then paying attention to the contributions of Hellegouarch, Frey and Ribet, and finally the work of Wiles. Then we examine some of the equations which describe optical solitons. From this analysis it follows that the elliptic curves constitute the bridge that connects both topics. Moreover, we will observe that the equations which describe optical solitons might also be related to cryptography. Finally, we will see that the results found in this communication permit us to propose 2 conjectures that constitute research topics for future works.

El juego de los abalorios: del Último Teorema de Fermat a los Solitones Ópticos

Siguiendo la idea del Juego de los Abalorios (de Hermann Hesse), en este trabajo investigamos qué relación existe entre el último Teorema de Fermat (UTF) y los solitones ópticos. Para encontrar esta relación examinamos los pasos principales que condujeron a la demostración del UTF, empezando por la conjetura de Taniyama-Shimura, y pasando por las contribuciones de Hellegouarch, Frey y Ribet, hasta llegar al trabajo de Wiles. Posteriormente examinamos algunas de las ecuaciones que describen a los solitones ópticos. De este análisis se desprende que las curvas elípticas constituyen el puente que relaciona ambos temas. Veremos, además, que las ecuaciones que describen solitones ópticos también podrían tener alguna relación con la criptografía. Finalmente veremos que los resultados encontrados en este trabajo nos permiten proponer 2 conjeturas que constituyen temas de investigación para el futuro. Following the idea of the Glass Bead Game (by Hermann Hesse), in this work we investigate what relation exists between Fermat´s Last Theorem (FLT) and the optical solitons. To find such a relationship we examine the principal steps which lead to the demonstration of FLT, starting from Taniyama-Shimura´s conjecture, then paying attention to the contributions of Hellegouarch, Frey and Ribet, and finally the work of Wiles. Then we examine some of the equations which describe optical solitons. From this analysis it follows that the elliptic curves constitute the bridge that connects both topics. Moreover, we will observe that the equations which describe optical solitons might also be related to cryptography. Finally, we will see that the results found in this communication permit us to propose 2 conjectures that constitute research topics for future works.

The Opposites and Unity: A Study of Chinese Taoist Thought Found in Hermann Hesse’s The Glass Bead Game

Hermann Hesse was keenly aware of the spiritual and social crises of war-torn Europe. He explored possible solutions to these problems in his writing and was interested in drawing on the resources of oriental philosophies. Of particular importance was the thought of Chinese Taoism. Hesse frequently mentioned his understanding of the Taoist philosophies of Laozi (老子) and Zhuangzi (庄子) in letters to his friends, and Taoist ideas such as ‘Tao’ (道) or ‘One’ and ‘polar opposites and unity’ recur across his work. This article will trace Hesse’s understanding of the Taoist thought of Laozi and Zhuangzi, and analyse the influence of Chinese Taoism on Hesse’s masterpiece, The Glass Bead Game (1943).

A New Glass Bead Game: Redesigning the Academy

The academy has gained a reputation as a place of authoritative statements, truth, and insight as a result of its long history. Yet during that history its authority to make definitive statements has been built on different foundations—now overlapped and layered. Each source of authority has buried, overlaid, or sometimes supplanted the previous one while the institution has carried on. Is this historical value still solid or is it threatened by the conditions we find ourselves in today? As members of the academy, perhaps we need to ask ourselves about the foundations on which we build and the functions that the Academy may yet serve in society. Using thoughts inspired by Herman Hess’s Magister Ludi, this paper explores those questions.