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PHILOSOPHY & FUN OF ALGEBRA, Chapter 11, Macbeth’s Mistake, part 1

Chapter 11, Macbeth's Mistake, part 1

The whole question of choosing one's next working hypothesis has been fogged, owing to people's neglect of a very simple principle. Suppose you are out bicycling in a strange place. You come to a bit of smooth, good road, which is either flat or goes very gently down hill; and presently curves in a nice, big, easy sweep round a bit of wood or a cliff, so that you cannot see far along it. What you know at once is that you can, if you choose, get up great speed without overmuch exertion. That is obvious, and needs no discussion. The question you have to settle is: Shall you choose to do it? If you have heard the whole road spoken of, in general terms, as a nice safe one to go on, you probably do choose to make use of the specially easy bit of the road to get up a lively spin.

But supposing that, at the beginning of the gentle slope down, you come upon a notice board with an inscription “Go slowly,” or “Dangerous to cyclists,” I hope you would have sense enough not to think—“What do those old fogies know about the needs of the young generation? I have a right to go fast if I choose, and I shall have my jolly spin in spite of them.” Nor would you say: “I can take care of myself, and if I run into somebody else that is his look out.” If you are an experienced cyclist you would keep on your seat, and go cautiously; if you are still a very inexperienced one, it would be wise to get off your cycle, and not mount again till you had come to the curve, and gone round it, and seen what is beyond.

The notice board is not an actual prohibition to go along the “King's highway” if you choose. The people who put up the board have no authority over you. But your own instincts of self-preservation, and I hope also your instinct of loyalty and good comradeship with the possible other cyclist who may be at the bottom of the hill, would suggest to you not to throw away the guardianship of a caution from those who know more than you do about the road.

Having given you this general indication of the principle which I am trying to explain, we will go back to the question of an imaginary working hypothesis.

Chapter 11, Macbeth’s Mistake, part 1 Capítulo 11, El error de Macbeth, parte 1 Capítulo 11, O erro de Macbeth, parte 1 第 11 章，麦克白的错误，第 1 部分

The whole question of choosing one's next working hypothesis has been fogged, owing to people's neglect of a very simple principle. Toda a questão de escolher a próxima hipótese de trabalho foi obscurecida, devido à negligência das pessoas de um princípio muito simples. Suppose you are out bicycling in a strange place. Suponha que você esteja andando de bicicleta em um lugar estranho. You come to a bit of smooth, good road, which is either flat or goes very gently down hill; and presently curves in a nice, big, easy sweep round a bit of wood or a cliff, so that you cannot see far along it. Você chega a um pedaço de estrada boa e lisa, que é plana ou desce uma colina muito suavemente; e atualmente se curva em uma curva agradável, grande e fácil ao redor de um pedaço de madeira ou de um penhasco, de modo que você não pode ver muito ao longo dele. What you know at once is that you can, if you choose, get up great speed without overmuch exertion. O que você sabe imediatamente é que pode, se quiser, aumentar a velocidade sem muito esforço. That is obvious, and needs no discussion. Isso é óbvio e não precisa de discussão. The question you have to settle is: Shall you choose to do it? A questão que você deve resolver é: você deve escolher fazer isso? If you have heard the whole road spoken of, in general terms, as a nice safe one to go on, you probably do choose to make use of the specially easy bit of the road to get up a lively spin. Se você já ouviu falar de toda a estrada, em termos gerais, como um bom caminho seguro para seguir, provavelmente optou por usar a parte especialmente fácil da estrada para dar uma volta animada.

But supposing that, at the beginning of the gentle slope down, you come upon a notice board with an inscription “Go slowly,” or “Dangerous to cyclists,” I hope you would have sense enough not to think—“What do those old fogies know about the needs of the young generation? Mas supondo que, no início da descida suave, você encontre um quadro de avisos com a inscrição “Vá devagar” ou “Perigoso para os ciclistas”, espero que você tenha bom senso o suficiente para não pensar: “O que aqueles velhos os fogies sabem sobre as necessidades da geração jovem? I have a right to go fast if I choose, and I shall have my jolly spin in spite of them.” Nor would you say: “I can take care of myself, and if I run into somebody else that is his look out.” If you are an experienced cyclist you would keep on your seat, and go cautiously; if you are still a very inexperienced one, it would be wise to get off your cycle, and not mount again till you had come to the curve, and gone round it, and seen what is beyond. Tenho o direito de ir rápido se assim o desejar, e terei meu giro alegre apesar deles. Você também não diria: “Eu posso cuidar de mim mesmo, e se eu encontrar outra pessoa, esse cuidado é dele”. Se você é um ciclista experiente, mantenha-se sentado e ande com cautela; se você ainda é muito inexperiente, seria sensato descer de sua bicicleta e não montar novamente até chegar à curva, contorná-la e ver o que está além.

The notice board is not an actual prohibition to go along the “King's highway” if you choose. O quadro de avisos não é uma proibição real de seguir pela “rodovia do rei”, se você escolher. The people who put up the board have no authority over you. As pessoas que montam o quadro não têm autoridade sobre você. But your own instincts of self-preservation, and I hope also your instinct of loyalty and good comradeship with the possible other cyclist who may be at the bottom of the hill, would suggest to you not to throw away the guardianship of a caution from those who know more than you do about the road. Mas seus próprios instintos de autopreservação, e espero também seu instinto de lealdade e boa camaradagem com o possível outro ciclista que possa estar no sopé da colina, sugerem a você que não jogue fora a guarda de um aviso daqueles que sabem mais do que você sobre a estrada.

Having given you this general indication of the principle which I am trying to explain, we will go back to the question of an imaginary working hypothesis. Tendo dado esta indicação geral do princípio que estou tentando explicar, voltaremos à questão de uma hipótese de trabalho imaginária.