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PHILOSOPHY & FUN OF ALGEBRA, Chapter 4, Partial Solutions and the Provisional Elimination of Elements of Complexity, part 2

Chapter 4, Partial Solutions and the Provisional Elimination of Elements of Complexity, part 2

If she forgot again, the teacher might say,—I think I should be inclined to say:—“If you cannot remember not to distract the class by talking about what is irrelevant to the business on hand, I shall have to request you to keep outside my class-room till you can.” In an orderly school the teachers have time to be polite, and it is their business to set the example of being so. In history, especially such history as that of half-civilised countries 3000 years ago, teachers were under too much strain to cultivate either a polite manner of saying things, or, what is of far more consequence, that genuine intellectual courtesy which is the absolutely necessary condition for the development of any really perfect mathematical system. The great Hebrew Algebra, therefore, never became quite perfect. It was only rough hewn, so to speak; and its manners and customs were rough too. The teachers had ways of saying, “Hold your tongue, or else go out of my class-room,” which perhaps we should now call bigoted and brutal. But what I want you to notice is that “Hold your tongue, or get out of my class-room,” is not the same thing as “My hypothesis is right, and yours ought not to be tried anywhere.”

This latter is contrary to the essential basis of Algebra, viz., a recognition of one's own ignorance. The other, a rough way of saying “Get out of my class-room,” is only contrary to that fine intellectual courtesy which is essential to the perfection of mathematical method.


Chapter 4, Partial Solutions and the Provisional Elimination of Elements of Complexity, part 2 Capítulo 4, Soluções Parciais e a Eliminação Provisória de Elementos de Complexidade, parte 2

If she forgot again, the teacher might say,—I think I should be inclined to say:—“If you cannot remember not to distract the class by talking about what is irrelevant to the business on hand, I shall have to request you to keep outside my class-room till you can.” In an orderly school the teachers have time to be polite, and it is their business to set the example of being so. Si se olvidó de nuevo, la maestra podría decir, creo que debería inclinarme a decir: “Si no puede recordar no distraer a la clase hablando de lo que es irrelevante para el asunto en cuestión, tendré que pedirle que Manténgase fuera de mi salón de clases hasta que pueda. En una escuela ordenada los maestros tienen tiempo para ser corteses, y es asunto suyo dar el ejemplo de serlo. Se ela esquecesse de novo, o professor poderia dizer, - acho que deveria estar inclinado a dizer: - "Se você não consegue se lembrar de não distrair a classe falando sobre o que é irrelevante para o assunto em questão, terei que pedir que você fique fora da minha sala de aula até que você possa. Numa escola ordeira, os professores têm tempo para serem educados, e cabe a eles dar o exemplo disso. In history, especially such history as that of half-civilised countries 3000 years ago, teachers were under too much strain to cultivate either a polite manner of saying things, or, what is of far more consequence, that genuine intellectual courtesy which is the absolutely necessary condition for the development of any really perfect mathematical system. En la historia, especialmente en una historia como la de los países semicivilizados hace 3000 años, los maestros estaban sometidos a demasiada presión para cultivar una manera cortés de decir las cosas o, lo que es mucho más importante, esa genuina cortesía intelectual que es la razón absoluta. condición necesaria para el desarrollo de cualquier sistema matemático realmente perfecto. Na história, especialmente na história dos países semi-civilizados há 3.000 anos, os professores estavam sob muita pressão para cultivar uma maneira educada de dizer as coisas ou, o que é muito mais importante, aquela cortesia intelectual genuína que é a forma absolutamente condição necessária para o desenvolvimento de qualquer sistema matemático realmente perfeito. 在历史上,尤其是在3000年前半文明国家的历史上,教师承受着很大的压力,无法培养礼貌的说话方式,或者更重要的是,真正的知识分子礼节是绝对的。开发任何真正完善的数学系统的必要条件。 The great Hebrew Algebra, therefore, never became quite perfect. La gran álgebra hebrea, por lo tanto, nunca llegó a ser del todo perfecta. A grande álgebra hebraica, portanto, nunca se tornou perfeita. It was only rough hewn, so to speak; and its manners and customs were rough too. Solo estaba tallado toscamente, por así decirlo; y sus modales y costumbres también eran toscos. Era apenas tosco, por assim dizer; e suas maneiras e costumes também eram rudes. The teachers had ways of saying, “Hold your tongue, or else go out of my class-room,” which perhaps we should now call bigoted and brutal. Los maestros tenían formas de decir: “Cállate la lengua o sal de mi salón de clases”, lo que tal vez ahora deberíamos llamar intolerante y brutal. Os professores tinham maneiras de dizer: “Segure sua língua, ou então saia da minha sala de aula”, que talvez devêssemos agora chamar de fanático e brutal. But what I want you to notice is that “Hold your tongue, or get out of my class-room,” is not the same thing as “My hypothesis is right, and yours ought not to be tried anywhere.” Pero lo que quiero que noten es que "Cierre su lengua o salga de mi salón de clases" no es lo mismo que "Mi hipótesis es correcta, y la suya no debe probarse en ninguna parte". Mas o que eu quero que você perceba é que “Segure sua língua ou saia da minha sala de aula” não é a mesma coisa que “Minha hipótese está certa e a sua não deve ser testada em lugar nenhum”.

This latter is contrary to the essential basis of Algebra, viz., a recognition of one's own ignorance. Esto último es contrario a la base esencial del Álgebra, a saber, un reconocimiento de la propia ignorancia. Este último é contrário à base essencial da álgebra, isto é, um reconhecimento da própria ignorância. The other, a rough way of saying “Get out of my class-room,” is only contrary to that fine intellectual courtesy which is essential to the perfection of mathematical method. La otra, una forma tosca de decir "Fuera de mi salón de clases", es sólo contraria a esa fina cortesía intelectual que es esencial para la perfección del método matemático. A outra, uma maneira grosseira de dizer “Saia da minha sala de aula”, é apenas contrária àquela refinada cortesia intelectual que é essencial para a perfeição do método matemático.