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PHILOSOPHY & FUN OF ALGEBRA, Chapter 7, How to Choose Our Hypotheses, part 3

Chapter 7, How to Choose Our Hypotheses, part 3

The ancient Hebrews used their imaginations very freely, and sometimes really very logically. And sometimes the free use of the imagination produced sensations in the eyes and ears as if of seeing and hearing. They considered this quite natural, as it really was. Many great mathematicians in modern Europe have had these sensations. The Hebrews called these sensations by a Hebrew word which is translated by the English word “angel,” from the Greek “angelos,” a messenger. The Hebrews were quite right. The sensations are messengers from the Great Unknown. They bring no information about outside facts. No angel tells you how many petals there are in a buttercup; if you want to know that, you are supposed to ask the buttercup itself. No angel tells you the price of sugar; you ought to ask your grocer. No angel tells you how to invest your money; you ought to ask your banker or your lawyer. There are people foolish enough to ask angels about investments, or about which horse will win a race; which is just as foolish as asking your banker in town how many blossoms there are on the rose tree in your country garden. It is not his business, and if he made a guess it would most likely turn out a wrong one. All that sort of thing is quackery and superstition.

But the angels do bring us very reliable information from a vast region of valuable truth about which most of us know very little as yet. They guide us how to frame our next provisional working hypothesis, how to choose the particular hypothesis which at our present stage of knowledge and development will be most illuminating for us. Some of the angels come during sleep; we call them dreams. Dreams sometimes suggest the best working hypothesis to experiment on next. More often they warn us against thinking upon some hypothetical basis which for the present will not suit us.


Chapter 7, How to Choose Our Hypotheses, part 3 Chapter 7, How to Choose Our Hypotheses, part 3 Capítulo 7, Cómo elegir nuestras hipótesis, parte 3 Capítulo 7, Como escolher nossas hipóteses, parte 3

The ancient Hebrews used their imaginations very freely, and sometimes really very logically. Os antigos hebreus usavam sua imaginação com muita liberdade e, às vezes, com muita lógica. And sometimes the free use of the imagination produced sensations in the eyes and ears as if of seeing and hearing. E às vezes o livre uso da imaginação produzia sensações nos olhos e ouvidos como se estivessem vendo e ouvindo. They considered this quite natural, as it really was. Eles consideraram isso bastante natural, como realmente era. Many great mathematicians in modern Europe have had these sensations. Muitos grandes matemáticos da Europa moderna tiveram essas sensações. The Hebrews called these sensations by a Hebrew word which is translated by the English word “angel,” from the Greek “angelos,” a messenger. Os hebreus chamavam essas sensações por uma palavra hebraica que é traduzida pela palavra portuguesa “anjo”, do grego “angelos”, um mensageiro. The Hebrews were quite right. Os hebreus estavam certos. The sensations are messengers from the Great Unknown. As sensações são mensageiras do Grande Desconhecido. They bring no information about outside facts. Eles não trazem nenhuma informação sobre fatos externos. No angel tells you how many petals there are in a buttercup; if you want to know that, you are supposed to ask the buttercup itself. Nenhum anjo lhe diz quantas pétalas há em um botão de ouro; se você quiser saber isso, deve perguntar ao próprio botão de ouro. No angel tells you the price of sugar; you ought to ask your grocer. Nenhum anjo lhe diz o preço do açúcar; você deve perguntar ao seu merceeiro. No angel tells you how to invest your money; you ought to ask your banker or your lawyer. Nenhum anjo lhe diz como investir seu dinheiro; você deve perguntar ao seu banqueiro ou ao seu advogado. There are people foolish enough to ask angels about investments, or about which horse will win a race; which is just as foolish as asking your banker in town how many blossoms there are on the rose tree in your country garden. Existem pessoas tolas o suficiente para perguntar aos anjos sobre investimentos, ou sobre qual cavalo vai ganhar uma corrida; o que é tão tolo quanto perguntar ao banqueiro da cidade quantas flores há na roseira do jardim do campo. It is not his business, and if he made a guess it would most likely turn out a wrong one. Não é da conta dele, e se ele desse um palpite, provavelmente acabaria errado. All that sort of thing is quackery and superstition. Todo esse tipo de coisa é charlatanismo e superstição.

But the angels do bring us very reliable information from a vast region of valuable truth about which most of us know very little as yet. Mas os anjos nos trazem informações muito confiáveis de uma vasta região de verdade valiosa sobre a qual a maioria de nós sabe muito pouco ainda. They guide us how to frame our next provisional working hypothesis, how to choose the particular hypothesis which at our present stage of knowledge and development will be most illuminating for us. Eles nos orientam sobre como enquadrar nossa próxima hipótese de trabalho provisória, como escolher a hipótese particular que, em nosso atual estágio de conhecimento e desenvolvimento, será mais esclarecedora para nós. Some of the angels come during sleep; we call them dreams. Alguns dos anjos vêm durante o sono; nós os chamamos de sonhos. Dreams sometimes suggest the best working hypothesis to experiment on next. Às vezes, os sonhos sugerem a melhor hipótese de trabalho para experimentar a seguir. More often they warn us against thinking upon some hypothetical basis which for the present will not suit us. Mais frequentemente, eles nos advertem contra pensar em alguma base hipotética que no momento não nos convém.