【文摘1】Birds and Frogs《鸟与青蛙》（节选）-量子电动力学奠基人戴森的演讲
Some mathematicians are birds, others are frogs.Birds fly high in the air and survey broad vistas of mathematics out to the farhorizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds.
有些数学家是鸟，其他的则是青蛙。鸟翱翔在高高的天空，俯瞰延伸至遥远地平线的广袤的数学远景。他们喜欢那些统一我们思想、并将不同领域的诸多问题整合起来的概念。青蛙生活在天空下的泥地里，只看到周围生长的花儿。他们乐于探索特定问题的细节，一次只解决一个问题。我碰巧是一只青蛙，但我的许多最好朋友都是鸟。
Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.
数学既需要鸟也需要青蛙。数学丰富又美丽，因为鸟赋予它辽阔壮观的远景，青蛙则澄清了它错综复杂的细节。数学既是伟大的艺术，也是重要的科学，因为它将普遍的概念与深邃的结构融合在一起。如果声称鸟比青蛙更好，因为它们看得更遥远，或者青蛙比鸟更好，因为它们更加深刻，那么这些都是愚蠢的见解。数学的世界既辽阔又深刻，我们需要鸟们和青蛙们协同努力来探索。
Einstein was not a mathematician, but a physicist who had mixed feelings about mathematics.On the one hand, he had enormous respect for the power of mathematics to describe the workings of nature, and he had an instinct for mathematical beauty which led him onto the right track to find nature’s laws. On the other hand, he had no interest in pure mathematics, and he had no technical skill as a mathematician. In his later years he hired younger colleagues with the title of assistants to do mathematical calculations for him. His way of thinking was physical rather than mathematical. He was supreme among physicists as a bird who saw further than others.
爱因斯坦不是一位数学家，而是一位融合了数学感觉的物理学家。一方面，他对数学描述自然界运作的力量极为尊重，他对数学之美有一种直觉，引导他进入发现自然规律的正确轨道；另一方面，他对纯数学没有兴趣，他缺乏数学家的技能。晚年时，他聘请一位年轻同事以助手身份帮助他做数学计算。他的思考方式是物理而非数学。他是物理学界的至高者，是一只比其他鸟瞭望得更远的鸟。
Francis Bacon and René Descartes
At the beginning of the seventeenth century, two great philosophers, Francis Bacon in England and René Descartes in France, proclaimed the birth of modern science.Descartes was a bird, and Bacon was a frog. Each of them described his vision of the future. Their visions were very different. Bacon said, “All depends on keeping the eye steadily fixed on the facts of nature.” Descartes said, “I think, therefore I am.” According to Bacon, scientists should travel over the earth collecting facts, until the accumulated facts reveal how Nature works.The scientists will then induce from the facts the laws that Nature obeys.According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought. In order to deduce the laws correctly, the scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes led the way, science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature’s secrets by itself, but both together have been amazingly successful.
弗兰西斯•培根和勒奈•笛卡尔17世纪初，两位伟大的哲学家，英国的弗兰西斯•培根（Francis Bacon）和法国的勒奈•笛卡尔（Rene Descartes），正式宣告了现代科学的诞生。笛卡尔是一只鸟，培根是一只青蛙。两人分别描述了对未来的远景，但观点大相径庭。培根说：“一切均基于眼睛所见自然之确凿事实。”笛卡尔说：“我思，故我在。”按照培根的观点，科学家需要周游地球收集事实，直到所积累的事实能揭示出自然的运动方式。科学家们从这些事实中推导出自然运作所遵循的法则。根据笛卡尔的观点，科学家只需要呆在家里，通过纯粹的思考推导出自然规律。为了推导出正确的自然规律，科学家们只需要逻辑规则和上帝存在的知识。在开路先锋培根和迪卡尔的领导之下，400多年来，科学同时沿着这两条途径全速前进。然而，解开自然奥秘的力量既不是培根的经验主义，也不是笛卡尔的教条主义，而是二者成功合作的神奇之作。
……
（注：量子电动力学的奠基人之一，数学物理学家弗里曼·约翰·戴森（Freeman John Dyson 1923年12月15日出生），2020年2月28日去世，享年96岁。他在20世纪60年代提出的“戴森球”（Dyson Sphere）——一些高级外星文明为了尽可能利用能量，可能会将主星用太阳能收集器包裹起来。）
Some mathematicians are birds, others are frogs.Birds fly high in the air and survey broad vistas of mathematics out to the farhorizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds.
有些数学家是鸟，其他的则是青蛙。鸟翱翔在高高的天空，俯瞰延伸至遥远地平线的广袤的数学远景。他们喜欢那些统一我们思想、并将不同领域的诸多问题整合起来的概念。青蛙生活在天空下的泥地里，只看到周围生长的花儿。他们乐于探索特定问题的细节，一次只解决一个问题。我碰巧是一只青蛙，但我的许多最好朋友都是鸟。
Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.
数学既需要鸟也需要青蛙。数学丰富又美丽，因为鸟赋予它辽阔壮观的远景，青蛙则澄清了它错综复杂的细节。数学既是伟大的艺术，也是重要的科学，因为它将普遍的概念与深邃的结构融合在一起。如果声称鸟比青蛙更好，因为它们看得更遥远，或者青蛙比鸟更好，因为它们更加深刻，那么这些都是愚蠢的见解。数学的世界既辽阔又深刻，我们需要鸟们和青蛙们协同努力来探索。
Einstein was not a mathematician, but a physicist who had mixed feelings about mathematics.On the one hand, he had enormous respect for the power of mathematics to describe the workings of nature, and he had an instinct for mathematical beauty which led him onto the right track to find nature’s laws. On the other hand, he had no interest in pure mathematics, and he had no technical skill as a mathematician. In his later years he hired younger colleagues with the title of assistants to do mathematical calculations for him. His way of thinking was physical rather than mathematical. He was supreme among physicists as a bird who saw further than others.
爱因斯坦不是一位数学家，而是一位融合了数学感觉的物理学家。一方面，他对数学描述自然界运作的力量极为尊重，他对数学之美有一种直觉，引导他进入发现自然规律的正确轨道；另一方面，他对纯数学没有兴趣，他缺乏数学家的技能。晚年时，他聘请一位年轻同事以助手身份帮助他做数学计算。他的思考方式是物理而非数学。他是物理学界的至高者，是一只比其他鸟瞭望得更远的鸟。
Francis Bacon and René Descartes
At the beginning of the seventeenth century, two great philosophers, Francis Bacon in England and René Descartes in France, proclaimed the birth of modern science.Descartes was a bird, and Bacon was a frog. Each of them described his vision of the future. Their visions were very different. Bacon said, “All depends on keeping the eye steadily fixed on the facts of nature.” Descartes said, “I think, therefore I am.” According to Bacon, scientists should travel over the earth collecting facts, until the accumulated facts reveal how Nature works.The scientists will then induce from the facts the laws that Nature obeys.According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought. In order to deduce the laws correctly, the scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes led the way, science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature’s secrets by itself, but both together have been amazingly successful.
弗兰西斯•培根和勒奈•笛卡尔17世纪初，两位伟大的哲学家，英国的弗兰西斯•培根（Francis Bacon）和法国的勒奈•笛卡尔（Rene Descartes），正式宣告了现代科学的诞生。笛卡尔是一只鸟，培根是一只青蛙。两人分别描述了对未来的远景，但观点大相径庭。培根说：“一切均基于眼睛所见自然之确凿事实。”笛卡尔说：“我思，故我在。”按照培根的观点，科学家需要周游地球收集事实，直到所积累的事实能揭示出自然的运动方式。科学家们从这些事实中推导出自然运作所遵循的法则。根据笛卡尔的观点，科学家只需要呆在家里，通过纯粹的思考推导出自然规律。为了推导出正确的自然规律，科学家们只需要逻辑规则和上帝存在的知识。在开路先锋培根和迪卡尔的领导之下，400多年来，科学同时沿着这两条途径全速前进。然而，解开自然奥秘的力量既不是培根的经验主义，也不是笛卡尔的教条主义，而是二者成功合作的神奇之作。
……
（注：量子电动力学的奠基人之一，数学物理学家弗里曼·约翰·戴森（Freeman John Dyson 1923年12月15日出生），2020年2月28日去世，享年96岁。他在20世纪60年代提出的“戴森球”（Dyson Sphere）——一些高级外星文明为了尽可能利用能量，可能会将主星用太阳能收集器包裹起来。）
