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PHILOSOPHY & FUN OF ALGEBRA, Chapter 15

Chapter 15

When you come to quadratic equations you will√ confronted with an entitybe (or non-entity) whose name is written this way— −1, and pronounced ”square root of minus one.” Many people let this nonentity persuade them to foolish courses. A story is told of a man at Cambridge who was expected to be Senior Wrangler; but he got thinking about the square root of minus one as if it were a reality, till he lost his sleep and dreamed that he was the square root of minus one and could not extract himself; and he became so ill that he could not go to his examination at all. Angels, and square roots of negative quantities, and the other things that have no existence in three dimensions, do not come to us to gossip about themselves; or the place they came from; or where they are going to; or where we are going to in the far future. They are messengers from the As-Yet-Unknown; and come to tell us where we are to go next; and the shortest road to get there; and where we ought not to go just at present. When square root of minus one comes to you, behave reasonably about him. Treat him logically, exactly as if he were six or nine; only always remember to keep well in front of you the fact of your own ignorance. You may never find out any more about him than you know now; but if you treat him sensibly he will tell you plenty of truths about your x's and y's, and other unknown things. Please don't suppose that I have always behaved sensibly to angels. I have often made serious mistakes in dealing with them. I have acted in haste and have had plenty of reason to repent at leisure. But one thing they have taught me is that we need never be afraid of angels, whether white or black, as long as we keep the laws of logic. Another thing they have shown me is that angels ever really gossip. They have often pretended to gossip to me; but I have found out afterwards that they have been talking clever nonsense in order to test me and prove me; so that I might see in what an illogical state of mind I have met them. Angels leave real gossip to old women who have done their life's work and have time to sit in the chimney corner and tell tales about their past experiences to their child friends.


Chapter 15 Capítulo 15 Capítulo 15 Bölüm 15

When you come to quadratic equations you will√ confronted with an entitybe (or non-entity) whose name is written this way— −1, and pronounced ”square root of minus one.” Many people let this nonentity persuade them to foolish courses. Quando se chega a equações quadráticas, o utilizador will√ é confrontado com uma entidade, seja (ou não entidade) cujo nome é escrito desta forma - -1, e pronuncia-se "raiz quadrada de menos um". Muitas pessoas deixam que esta não-entidade os persuada a seguir cursos tolas. A story is told of a man at Cambridge who was expected to be Senior Wrangler; but he got thinking about the square root of minus one as if it were a reality, till he lost his sleep and dreamed that he was the square root of minus one and could not extract himself; and he became so ill that he could not go to his examination at all. Conta-se uma história de um homem em Cambridge que se esperava que fosse o Wrangler Sénior; mas ele começou a pensar na raiz quadrada de menos um como se fosse uma realidade, até que perdeu o sono e sonhou que era a raiz quadrada de menos um e não se conseguia extrair; e ficou tão doente que não pôde ir ao seu exame. Angels, and square roots of negative quantities, and the other things that have no existence in three dimensions, do not come to us to gossip about themselves; or the place they came from; or where they are going to; or where we are going to in the far future. Anjos, e raízes quadradas de quantidades negativas, e as outras coisas que não têm existência em três dimensões, não vêm até nós para nos fofocar sobre si mesmos; ou o lugar de onde vieram; ou para onde vão; ou para onde vamos no futuro distante. They are messengers from the As-Yet-Unknown; and come to tell us where we are to go next; and the shortest road to get there; and where we ought not to go just at present. São mensageiros do As-Yet-Unknown; e vêm dizer-nos onde devemos ir a seguir; e o caminho mais curto para lá chegar; e para onde não devemos ir só de momento. When square root of minus one comes to you, behave reasonably about him. Quando a raiz quadrada de menos um chegar até si, comporte-se razoavelmente em relação a ele. Treat him logically, exactly as if he were six or nine; only always remember to keep well in front of you the fact of your own ignorance. Trate-o logicamente, exactamente como se tivesse seis ou nove anos; apenas lembre-se sempre de manter bem à sua frente o facto da sua própria ignorância. You may never find out any more about him than you know now; but if you treat him sensibly he will tell you plenty of truths about your x's and y's, and other unknown things. Nunca mais poderá find sobre ele do que sabe agora; mas se o tratar com sensatez, ele dir-lhe-á muitas verdades sobre os seus x e y's, e outras coisas desconhecidas. Please don't suppose that I have always behaved sensibly to angels. Por favor, não suponhamos que sempre me tenha comportado de forma sensata para com os anjos. I have often made serious mistakes in dealing with them. Tenho cometido frequentemente erros graves ao lidar com eles. I have acted in haste and have had plenty of reason to repent at leisure. Agi com pressa e tive razões de sobra para me arrepender à vontade. But one thing they have taught me is that we need never be afraid of angels, whether white or black, as long as we keep the laws of logic. Mas uma coisa que me ensinaram é que nunca precisamos de ter medo dos anjos, brancos ou negros, desde que mantenhamos as leis da lógica. Another thing they have shown me is that angels ever really gossip. Outra coisa que eles me mostraram é que os anjos alguma vez fizeram realmente mexericos. They have often pretended to gossip to me; but I have found out afterwards that they have been talking clever nonsense in order to test me and prove me; so that I might see in what an illogical state of mind I have met them. Têm muitas vezes fingido fazer fofocas para mim; mas descobri depois que têm dito disparates inteligentes para me testarem e me provarem; para que eu possa ver em que estado de espírito ilógico os conheci. Angels leave real gossip to old women who have done their life's work and have time to sit in the chimney corner and tell tales about their past experiences to their child friends. Os anjos deixam verdadeiros mexericos a velhas mulheres que fizeram o trabalho da sua vida e têm tempo para se sentarem no canto da chaminé e contarem histórias sobre as suas experiências passadas aos seus amigos filhos.