PHILOSOPHY & FUN OF ALGEBRA, Chapter 2, The Making of Algebras, part 2

Chapter 2, The Making of Algebras, part 2

Now you will observe that both these babies have learnt by experience. Some people say that experience is the mother of Wisdom; but you see that both babies cannot be right; and, as a matter of fact, both are wrong. If they could talk, they might argue and quarrel for years; and vote; and write in the newspapers; and waste their own time and other people's money; each trying to prove he was right. But there is no wisdom to be got in that way. What a wise baby knows is that he cannot tell, by the mere look of a tea-pot, whether it is hot or cold. The fact that is most prominent in his mind when he sees a tea-pot is the fact that he does not know whether it is hot or cold. He puts that fact along with the other fact:—that he would very much like to play with the picture in the tea-pot supposing it would not burn his ﬁngers; and he deals logically with both these facts; and comes to the wise conclusion that it would be best to go very cautiously and ﬁnd out whether the tea-pot is hot, by putting his ﬁngers near, but not too near. That baby has begun his mathematical studies; and begun them at the right end. He has made an Algebra for himself. And the best wish one can make for his future is that he will go on doing the same for the rest of his life. Perhaps the best way of teaching a baby Algebra would be to get him thoroughly accustomed to playing with a bright vessel of some kind when cold; then put it and another just like it on the table in front of him, one being ﬁlled with hot water. Let him play with the cold one; and show him that you do not wish him to play with the other. When he persists, as he probably will, let him ﬁnd out for himself that the two things which look so alike have not exactly the same properties. Of course, you must take care that he does not hurt himself seriously.

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Chapter 2, The Making of Algebras, part 2 الفصل الثاني، صنع الجبر، الجزء الثاني Capítulo 2, La formación de las álgebras, parte 2 第2章, 代数の作り方その2 2 skyrius, Algebrų kūrimas, 2 dalis Capítulo 2, Fazendo Álgebras, parte 2 Глава 2. Создание алгебр, часть 2 Bölüm 2, Cebirlerin Oluşumu, kısım 2 第 2 章，代数的形成，第 2 部分

Now you will observe that both these babies have learnt by experience. ||||||these||||| ستلاحظ الآن أن هذين الطفلين قد تعلما بالتجربة. Ahora observará que estos dos bebés han aprendido por experiencia. Agora você observará que esses dois bebês aprenderam por experiência. Some people say that experience is the mother of Wisdom; but you see that both babies cannot be right; and, as a matter of fact, both are wrong. يقول بعض الناس أن التجربة هي أم الحكمة؛ لكنك ترى أن كلا الطفلين لا يمكن أن يكونا على حق؛ وفي واقع الأمر، كلاهما مخطئ. Algunas personas dicen que la experiencia es la madre de la Sabiduría; pero ves que los dos bebés no pueden tener razón; y, de hecho, ambos están equivocados. Algumas pessoas dizem que a experiência é a mãe da Sabedoria; mas você vê que ambos os bebês não podem estar certos; e, de fato, ambos estão errados. If they could talk, they might argue and quarrel for years; and vote; and write in the newspapers; and waste their own time and other people's money; each trying to prove he was right. ||||||||se disputer||||||||||||||||||||||||| ||||||||dispute|||||||||||||||||||each|||||| لو استطاعوا التحدث، قد يتجادلون ويتشاجرون لسنوات؛ والتصويت؛ والكتابة في الصحف؛ ويضيعون وقتهم وأموال الآخرين؛ كل يحاول أن يثبت أنه كان على حق. Si pudieran hablar, podrían discutir y pelearse durante años; y votar; y escribir en los periódicos; y malgastar su propio tiempo y el dinero de otras personas; cada uno tratando de demostrar que tenía razón. Se pudessem falar, poderiam discutir e brigar por anos; e votar; e escrever nos jornais; e desperdiçam seu próprio tempo e o dinheiro dos outros; cada um tentando provar que estava certo. But there is no wisdom to be got in that way. ولكن ليس هناك حكمة يمكن الحصول عليها بهذه الطريقة. Pero no se puede obtener sabiduría de esa manera. Mas não há sabedoria a ser obtida dessa maneira. What a wise baby knows is that he cannot tell, by the mere look of a tea-pot, whether it is hot or cold. ما يعرفه الطفل الحكيم هو أنه لا يستطيع أن يعرف، بمجرد نظرة إبريق الشاي، ما إذا كان ساخنًا أم باردًا. Lo que sabe un bebé sabio es que no puede decir, con solo mirar una tetera, si está caliente o fría. O que um bebê sábio sabe é que não pode dizer, pelo mero olhar de um bule de chá, se está quente ou frio. The fact that is most prominent in his mind when he sees a tea-pot is the fact that he does not know whether it is hot or cold. |truth||||most noticeable||||||||||||||||||||||| والحقيقة التي تبرز في ذهنه عندما يرى الإبريق هو أنه لا يدري أهو حار أم بارد. El hecho que más destaca en su mente cuando ve una tetera es el hecho de que no sabe si está caliente o fría. O fato que mais se destaca em sua mente quando ele vê um bule de chá é o fato de que ele não sabe se está quente ou frio. He puts that fact along with the other fact:—that he would very much like to play with the picture in the tea-pot supposing it would not burn his ﬁngers; and he deals logically with both these facts; and comes to the wise conclusion that it would be best to go very cautiously and ﬁnd out whether the tea-pot is hot, by putting his ﬁngers near, but not too near. |||||||||||||||||||||||||||||||||||||||||||||||||||||||找出|||||||||||||||| |||fact|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||||||||tal|||||||||||||||| وهو يضع هذه الحقيقة جنبًا إلى جنب مع الحقيقة الأخرى: - أنه يود بشدة أن يلعب بالصورة الموجودة في إبريق الشاي على افتراض أنه لن يحرق أصابعه؛ وهو يتعامل بشكل منطقي مع هاتين الحقيقتين؛ ويتوصل إلى استنتاج حكيم مفاده أنه من الأفضل أن يذهب بحذر شديد ويكتشف ما إذا كان إبريق الشاي ساخنًا، وذلك عن طريق وضع أصابعه بالقرب منه، ولكن ليس بالقرب منه كثيرًا. Pone ese hecho junto con el otro hecho: que le gustaría mucho jugar con el dibujo en la tetera suponiendo que no le quemara los dedos; y trata lógicamente con estos dos hechos; y llega a la sabia conclusión de que lo mejor sería ir con mucha cautela y averiguar si la tetera está caliente, acercando los dedos, pero no demasiado. Ele coloca esse fato junto com o outro fato: - que ele gostaria muito de brincar com a imagem no bule de chá, supondo que não queimasse seus dedos; e ele lida logicamente com esses dois fatos; e chega à sábia conclusão de que seria melhor ir com muito cuidado e descobrir se o bule está quente, colocando os dedos perto, mas não muito perto. That baby has begun his mathematical studies; and begun them at the right end. لقد بدأ هذا الطفل دراساته الرياضية؛ وبدأهم في النهاية اليمنى. Ese bebé ha comenzado sus estudios matemáticos; y las comencé por el extremo derecho. Esse bebê começou seus estudos matemáticos; e começou-os na extremidade direita. He has made an Algebra for himself. لقد صنع الجبر لنفسه. Ha hecho un Álgebra para sí mismo. Ele fez uma álgebra para si mesmo. And the best wish one can make for his future is that he will go on doing the same for the rest of his life. وأفضل أمنية يمكن للمرء أن يتمناها لمستقبله هي أن يستمر في فعل الشيء نفسه لبقية حياته. Y el mejor deseo que uno puede hacer para su futuro es que siga haciendo lo mismo por el resto de su vida. E o melhor desejo que alguém pode fazer para o futuro é que continue fazendo o mesmo pelo resto da vida. Perhaps the best way of teaching a baby Algebra would be to get him thoroughly accustomed to playing with a bright vessel of some kind when cold; then put it and another just like it on the table in front of him, one being ﬁlled with hot water. ||||||||||||||||||||||||||||||||||||||||||||装满了||| Maybe||||||||||||||||||||||||||||||||||||||||||||filled up||| ||||||||||||||||||||||||||||||||||||||||||||töltve||| ربما تكون أفضل طريقة لتعليم الطفل الجبر هي تعويده تمامًا على اللعب بوعاء لامع من نوع ما عندما يكون باردًا؛ ثم يضعه وآخر مثله على الطاولة أمامه، أحدهما مملوء بالماء الساخن. Quizá la mejor manera de enseñar álgebra a un bebé sería acostumbrarlo por completo a jugar con algún tipo de recipiente brillante cuando hace frío; luego colóquelo y otro igual sobre la mesa frente a él, uno de ellos lleno de agua caliente. Talvez a melhor maneira de ensinar álgebra a um bebê seja acostumá-lo completamente a brincar com algum tipo de vaso brilhante quando está frio; em seguida, coloque-o e outro igual na mesa à sua frente, um deles cheio de água quente. Let him play with the cold one; and show him that you do not wish him to play with the other. ||||||||||||||||||the other|| دعه يلعب مع البرد. وبيني له أنك لا ترغبين أن يلعب مع الآخر. Que juegue con el frío; y demuéstrale que no quieres que juegue con el otro. Deixe-o brincar com o frio; e mostre a ele que você não deseja que ele brinque com o outro. When he persists, as he probably will, let him ﬁnd out for himself that the two things which look so alike have not exactly the same properties. وعندما يصر، كما سيفعل على الأرجح، دعه يكتشف بنفسه أن الشيئين المتشابهين ليس لهما نفس الخصائص تمامًا. Cuando insista, como probablemente lo hará, descubra por sí mismo que las dos cosas que se parecen tanto no tienen exactamente las mismas propiedades. Quando ele persistir, como provavelmente irá, deixe-o descobrir por si mesmo que as duas coisas que parecem tão semelhantes não têm exatamente as mesmas propriedades. Of course, you must take care that he does not hurt himself seriously. ||||||||||||gravely بالطبع يجب أن تحرصي على ألا يؤذي نفسه بشكل خطير. Eso sí, debes cuidar de que no se haga daño de gravedad. Claro, você deve tomar cuidado para que ele não se machuque gravemente.