最早接触柯林斯(Collins)词典还是通过金山词霸的爱词霸在线词典,也是我用得最多的查词网站,我喜欢这部词典的两点:一是释义的顺序,我隐隐觉得它是按照常用度来排序的,不常用的意义根本不列出,我觉得这比列一大堆义项更好;二是他的整句翻译,比如查 dart,第一个解释是 If a person or animal darts somewhere, they move there suddenly and quickly,我认为这样的整句解释明显比传统词典更实用。
COBUILD, an acronym for Collins Birmingham University International Language Database, is a British research facility set up at the University of Birmingham in 1980 and funded by Collins publishers. https://en.wikipedia.org/wiki/COBUILD
It will take you some time to understand what should happen in different circumstances. You will have to solve the equations. Each time you solve the equations, you will learn something about the character of the solutions. To keep these solutions in mind, it will be useful also to study their meaning in terms of field lines and of other concepts. This is the way you will really “understand” the equations. That is the difference between mathematics and physics. Mathematicians, or people who have very mathematical minds, are often led astray when “studying” physics because they lose sight of the physics. They say: “Look, these differential equations—the Maxwell equations—are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out.” Only it doesn’t work that way. Mathematicians who study physics with that point of view—and there have been many of them—usually make little contribution to physics and, in fact, little to mathematics. They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.
What it means really to understand an equation—that is, in more than a strictly mathematical sense—was described by Dirac. He said: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” So if we have a way of knowing what should happen in given circumstances without actually solving the equations, then we “understand” the equations, as applied to these circumstances. A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist.