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PHILOSOPHY & FUN OF ALGEBRA, Chapter 16, Infinity, part 2

Chapter 16, Infinity, part 2

Well, that depends on two things: the size of the cake, and the share which each child eats. If the cake weighs two pounds, and each child eats two ounces, it will be all eaten up when sixteen children have gone through the room. If the cake weighs only one pound, it will be eaten up when eight children have gone through the room. But if each child eats only one ounce, then again sixteen children will have to go through the room before the cake is eaten up, and so on. Many questions could be asked, all depending on the size of the cake and the size of each child's share. All this time you are tied to an hypothesis that the children eat cake (more or less). But now suppose we are freed from that hypothesis. Suppose no cake is given to the children. How many can pass through the room before it is all eaten up? The answer to that is: “An infinite number.” Infinity does not mean any particular number, or a very large number. It means a loosened chain, a discarded hypothesis, escape from the rule we were working under. Something else, not the size of the cake, determines the number of children. Infinity does not mean that there are enough children in the world now to go on passing through the room for ever, but that the number of children who pass through the room, now that the share of each child is 0 (zero), will have to be determined by the number of children that there are in the school, or the parish, or wherever it is that the children are supposed to come from; and not by the size of the cake. The size of the cake has no longer anything to do with answering the question: “How many children can pass through the room before the cake is all eaten?”


Chapter 16, Infinity, part 2 Capítulo 16, Infinidad, parte 2 第16章 インフィニティ その2 Capítulo 16, Infinity, parte 2

Well, that depends on two things: the size of the cake, and the share which each child eats. Bem, isso depende de duas coisas: o tamanho do bolo, e a parte que cada criança come. If the cake weighs two pounds, and each child eats two ounces, it will be all eaten up when sixteen children have gone through the room. Se o bolo pesar dois quilos, e cada criança comer duas onças, será todo comido quando dezasseis crianças tiverem passado pela sala. If the cake weighs only one pound, it will be eaten up when eight children have gone through the room. Se o bolo pesar apenas um quilo, será comido quando oito crianças tiverem atravessado a sala. But if each child eats only one ounce, then again sixteen children will have to go through the room before the cake is eaten up, and so on. Mas se cada criança comer apenas uma onça, então novamente dezasseis crianças terão de passar pela sala antes de o bolo ser comido, e assim por diante. Many questions could be asked, all depending on the size of the cake and the size of each child's share. Muitas perguntas poderiam ser feitas, todas dependendo do tamanho do bolo e do tamanho da parte de cada criança. All this time you are tied to an hypothesis that the children eat cake (more or less). Todo este tempo está ligado a uma hipótese de que as crianças comem bolo (mais ou menos). But now suppose we are freed from that hypothesis. Mas agora suponha que nos libertamos dessa hipótese. Suppose no cake is given to the children. Suponhamos que não é dado bolo às crianças. How many can pass through the room before it is all eaten up? Quantos podem passar pela sala antes de tudo ser consumido? The answer to that is: “An infinite number.” Infinity does not mean any particular number, or a very large number. A resposta a isso é: "Um número infinite". Infinity não significa qualquer número em particular, ou um número muito grande. It means a loosened chain, a discarded hypothesis, escape from the rule we were working under. Significa uma cadeia solta, uma hipótese descartada, uma fuga à regra a que estávamos a trabalhar. Something else, not the size of the cake, determines the number of children. Algo mais, não o tamanho do bolo, determina o número de crianças. Infinity does not mean that there are enough children in the world now to go on passing through the room for ever, but that the number of children who pass through the room, now that the share of each child is 0 (zero), will have to be determined by the number of children that there are in the school, or the parish, or wherever it is that the children are supposed to come from; and not by the size of the cake. Infinity não significa que existem agora suficientes crianças no mundo para continuar a passar pela sala para sempre, mas que o número de crianças que passam pela sala, agora que a parte de cada criança é 0 (zero), terá de ser determinado pelo número de crianças que existem na escola, ou na paróquia, ou de onde quer que seja que as crianças devam vir; e não pelo tamanho do bolo. The size of the cake has no longer anything to do with answering the question: “How many children can pass through the room before the cake is all eaten?” O tamanho do bolo já não tem nada a ver com a resposta à pergunta: "Quantas crianças podem passar pela sala antes de o bolo ser todo comido?"