1、Angels on a pin by Alexander CalandraSome time ago, I received a call from a colleague who asked if I would be the referee(裁判) on the grading（定等级） of an examination question. He was about to give a student a zero for his answer to a physical question, while the student claimed he should receive a pe
2、rfect score and would if the system were not set up against the student. The instructor and the student agreed to submit this to an impartial arbiter（公平仲裁人） and I was selected. I went to my colleagues office and read the examination question. “Show how it is possible to determine the height of a tal
3、l building with the aid of a barometer.（气压表）援助晴雨表“ The student had answered: “Take the barometer to the top of the building, attach a long rope to it, lower（跌落） the barometer to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building.“
4、 一段时间以前，我接到一个教师同行打来的电话。他问我是否愿意当一回裁判，给一名参加考试的学生所答的的题评分。他说那是一道物理题，就那个学生的答案他准备判零分，但那个学生声称自己应该得满分，而且如果现存的制度不是与应该得满分，而且如果现存的制度不是与学生作对的话，他会得满分的。因此教师和学生争执不下，最后同意找一个公正的人来裁决一下，于是选中了我。我来到那个同行的办公室，看了考试题：“借助气压计，表示一下如何能确定一座大楼的高度。 ”那个学生是这样答的：“把气压计拿到楼顶，系上一根绳子，垂到街面，然后提起绳子，量一量绳子的长度。绳长即是楼高。 ”I pointed out that the st
5、udent really had a strong case for full credit, since he had answered the question completely and correctly. On the other hand, if full credit（学分） were given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify competence in physics, bu
6、t the answer did not confirm this. I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed, but I was surprised that the student did. 我指出那学生确实有足够的理由得满分，因为总是回答得既完整又无误。但话又说回来，如果给他满分，就等于他的物理成绩得了高分，而高分就证明他在物理上能力强，但他的答案无法确定这一点，我建议再给这学生一次机会解答那道
7、题。对此，我的教师同行没有异议，我不觉得奇怪。但那个学生爽快答应，倒使我颇感惊奇。I gave the student six minutes to answer the question, with the warning that his answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said no. He had many answers to thi
8、s problem; he was just thinking of the best one. I excused myself for interrupting him, and asked him to please go on. In the next minute, he dashed off his answer which read: “Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with
9、a stopwatch（码表）. Then, using the formula（公式） S = ?at2, calculate the height of the building.“ 把气压计放在大楼的顶端,靠在楼顶的边缘。让气压计向下坠落,用秒表记下它降落的时间。然后用公式 S = ?at2 计算出大楼的高度。At this point, I asked my colleague if he would give up. He conceded（承认）, and I gave the student almost full credit.我给他 6 分钟解题，并提醒说答案应显示出某些物理
10、学知识。5 分钟过去了，他只字未写。我问他是否想放弃，他说不。他说答案有很多。他正在考虑哪个是最好的。我对打断他表示歉意，请他继续思考。最后一分钟里，他迅速写下了答案：“把气压计拿到楼顶，倚身楼边，让气压计落下，用秒表计时，然后由公式 S=1/2AT2 导出楼高。 ”此时，我问同行是否让步，他同意了。我给了那学生接近满分的成绩。In leaving my colleagues office, I recalled that the student had said he had other answers to the problem, so I asked him what they wer
11、e. “Oh yes,“ said the student. “There are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and
12、by the use of a simple proportion（比例）, determine the height of the building.“ 在离开同事办公室时 ,我记得这个学生说他还有其它答案，然后我问他答案是什么。学生说，哦，是的。有许多的方法计算出一座楼的高度如果有晴雨表的援助。利用它的影子的长度，以及大楼影子的长度，然后利用简单的比例关系就可以计算大楼的高度。“Fine,“ I said. “And the others?“ “很好， ”我说，还有其他的办法吗？“Yes,“ said the student. “There is a very measurement me
13、thod that you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct m
14、ethod. 还有“，学生说。有一个你会很喜欢的测量方法。你把测量器带着然后爬楼，当你爬楼梯的时候，你用测量器标记下墙的高度。然后你来数数标记的数量。这将让你得到以气压计为单位的建筑的高度。这是个非常直接的办法。“Of course, if you want a more sophisticated（复杂的，精致的） method, you can tie the barometer to the end of a string, swing（摇摆） it as a pendulum（钟摆） and determine the value of g at the street level an
15、d at the top of the building. From the difference between the two values of g, the height of the building can, in principle, be calculated.“ 当然了，如果你想要更复杂的方法,你可以把气压计绑在一条绳子的末端，让它作为种摆旋转，然后分别确定水平状态以及在大楼顶部 g 的价值。从两者 g 价值的区别来看，从原则上看，大楼的高度就可以算出来了。Finally he concluded 做结论 , there are many other ways of solv
16、ing the problem. “Probably the best,“ he said, “is to take the barometer to the basement（地下室） and knock on the superintendents door. When the superintendent answers, you speak to him as follows: Mr. Superintendent 负责人, here I have a fine barometer. If you will tell me the height of this building, I
17、will give you this barometer. “最后他总结说，还有很多其他的方法来解决这个问题，也许还是最好的，他说，比如把气压计带到地下室然后敲管理者的门，管理员先生，我有个很好的气压计，如果你能告诉我大楼的高度，我就把他送个你。At this point, I asked the student if he really did not know the conventional 常见的 answer to this question. He admitted that he did, but said that he was fed up（感到厌倦） with high s
18、chool and college instructor trying to teach him how to think, to use the “scientific method,“ and to explore the deep inner logic of the subject in a pedantic（迂腐的）way, as is often done in the new mathematics, rather than teaching him the structure of the subject. With this in mind, he decided to revive 苏醒 scholasticism（墨守成规） as an academic lark to challenge the Sputnik 人照卫星 panicked 惊恐 classrooms of America 在这时 ,我问学生他是否是真的不知道这个问题的传统回答，他承认他知道，但他说他厌倦了高中和大学的老师试图想要教他如何用科学的方法进行思考和用专业的方式探讨深层的内在逻辑学。就像在新数学上那样做的一样,而不是教他的学科的结构。考虑到这一点, 他便决定重新搬出中世纪经院哲学作为一个学术的新武器,挑战的美国课堂让人惊慌失措的人造地球卫星的问题。
