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PHILOSOPHY & FUN OF ALGEBRA, Chapter 17, From Bondage to Freedom, part 2

Chapter 17, From Bondage to Freedom, part 2

They might quarrel till the end of the world, and know no more about it at the end than at the beginning. They are all tied by the same hypothesis:—that everybody lives under water. It is a very good working hypothesis for them; for if one of them got out of the water it would die. If they knew algebra properly, they would understand that water is only their present working hypothesis, and that it is quite possible there may be people who live out of it. But it is not sure that they do know enough algebra to be aware of their own ignorance. If you watch them carefully, you will some day see a wiggler come out of the water. He has got wings. The water-hypothesis no longer concerns him. Some link in the chain that bound him down to water has opened; he is set free; Infinity has come to him. That is what happened to Isaiah when he got out of the kind of Mosaism by which such people as Joshua and Samuel were tied down. That is what will happen to you (if you learn your algebra properly) when you are no longer tied √ down to a, b, c, and −1, as the values of x; and learn to see that the answer to a problem may sometimes be

X = Infinity.

Please notice that if a winged gnat fell back into the water he would die. You will find this a good working rule:—Whenever anything comes near your imagination which calls itself either “Infinity” or “The Liberation from Bondage,” go slack for a few minutes; say over the Ten Commandments; and make a mind-picture of the gnat-grub in the water. Tell yourself that his best chance of growing strong wings and being able to fly, when Infinity comes and calls him to go up higher, is to stay in the water till the wings have grown strong and work out the water-hypothesis to its logical conclusion. Then make another mind-picture: The gnat who has got wings, and therefore must not try to amuse himself in the water.

Please observe:—There is nothing in this rule contrary to any commandment. Moreover, there is nothing slavish or degrading in it; nothing in the least like giving up your own liberty, or hampering your own initiative, or being a slave to past ages; nothing which prevents your being up to date and fit for the generation to which you belong. You are not asked to have any opinions about it; or to think that it is a duty in itself; or to think that you are better than other people because you do it, or that every one is wrong who does not do it. If you do it, it will be for no reason that you know of, except that an old woman who has been trying to amuse you asks you to do it as a token of friendly feeling towards her.

Chapter 17, From Bondage to Freedom, part 2 Capítulo 17, De la esclavitud a la libertad, parte 2 Capítulo 17, De Bondage à Liberdade, parte 2

They might quarrel till the end of the world, and know no more about it at the end than at the beginning. Eles podem discutir até ao fim do mundo, e não sabem mais sobre isso no fim do que no início. They are all tied by the same hypothesis:—that everybody lives under water. Estão todos ligados pela mesma hipótese:- que todos vivem debaixo de água. It is a very good working hypothesis for them; for if one of them got out of the water it would die. É uma hipótese de trabalho muito boa para eles; pois se um deles saísse da água, morreria. If they knew algebra properly, they would understand that water is only their present working hypothesis, and that it is quite possible there may be people who live out of it. Se conhecessem bem a álgebra, compreenderiam que a água é apenas a sua actual hipótese de trabalho, e que é bem possível que haja pessoas que vivam fora dela. But it is not sure that they do know enough algebra to be aware of their own ignorance. Mas não é certo que eles conheçam álgebra suficiente para estarem cientes da sua própria ignorância. If you watch them carefully, you will some day see a wiggler come out of the water. Se os observar com cuidado, verá um dia um peruca a sair da água. He has got wings. Ele tem asas. The water-hypothesis no longer concerns him. A hipótese da água já não lhe diz respeito. Some link in the chain that bound him down to water has opened; he is set free; Infinity has come to him. Abriu-se algum elo na cadeia que o ligava à água; ele foi libertado; Infinity veio ter com ele. That is what happened to Isaiah when he got out of the kind of Mosaism by which such people as Joshua and Samuel were tied down. Foi o que aconteceu a Isaías quando saiu do tipo de Mosaísmo pelo qual pessoas como Josué e Samuel foram amarrados. That is what will happen to you (if you learn your algebra properly) when you are no longer tied                      √ down to a, b, c, and −1, as the values of x; and learn to see that the answer to a problem may sometimes be É o que lhe acontecerá (se aprender correctamente a sua álgebra) quando já não estiver amarrado √ a a, b, c, e -1, como os valores de x; e aprenda a ver que a resposta a um problema pode por vezes ser

X = Infinity. X = Infinidade.

Please notice that if a winged gnat fell back into the water he would die. Note-se que se um mosquito alado voltasse a cair na água, morreria. You will find this a good working rule:—Whenever anything comes near your imagination which calls itself either “Infinity” or “The Liberation from Bondage,” go slack for a few minutes; say over the Ten Commandments; and make a mind-picture of the gnat-grub in the water. Vai find esta é uma boa regra de trabalho:- Sempre que algo se aproxima da sua imaginação que se intitula "Infinity" ou "The Liberation from Bondage", descuide-se por alguns minutos; diga sobre os Dez Mandamentos; e faça uma imagem mental do mosquito na água. Tell yourself that his best chance of growing strong wings and being able to fly, when Infinity comes and calls him to go up higher, is to stay in the water till the wings have grown strong and work out the water-hypothesis to its logical conclusion. Diga-lhe que a sua melhor hipótese de crescer asas fortes e poder fly, quando Infinity chega e o chama para subir mais alto, é ficar na água até que as asas tenham crescido fortes e resolver a hipotese da água até à sua conclusão lógica. Then make another mind-picture: The gnat who has got wings, and therefore must not try to amuse himself in the water. Depois fazer outra imagem mental: O mosquito que tem asas, e por isso não deve tentar divertir-se na água.

Please observe:—There is nothing in this rule contrary to any commandment. Por favor, observe:- Não há nada nesta regra que seja contrário a qualquer mandamento. Moreover, there is nothing slavish or degrading in it; nothing in the least like giving up your own liberty, or hampering your own initiative, or being a slave to past ages; nothing which prevents your being up to date and fit for the generation to which you belong. Além disso, não há nada de escravo ou degradante nele; nada no mínimo como abdicar da sua própria liberdade, ou dificultar a sua própria iniciativa, ou ser um escravo de idades passadas; nada que impeça o seu estar actualizado e fit para a geração a que pertence. You are not asked to have any opinions about it; or to think that it is a duty in itself; or to think that you are better than other people because you do it, or that every one is wrong who does not do it. Não lhe é pedido que tenha quaisquer opiniões sobre o assunto; ou que pense que é um dever em si mesmo; ou que é melhor do que as outras pessoas porque o faz, ou que todos os que não o fazem estão errados. If you do it, it will be for no reason that you know of, except that an old woman who has been trying to amuse you asks you to do it as a token of friendly feeling towards her. Se o fizer, não será por nenhuma razão que saiba, excepto que uma velha mulher que tem tentado divertir-se lhe pede que o faça como sinal de sentimento de amizade para com ela.