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科学路上,数学不是绊脚石

原文作者:佚名

 似乎很多人小时候都有一个“长大要当科学家”的理想。如今“长大”已经实现了,说好的“科学家”呢?也许你早就发现了,要想成为科学家并不是那么容易,要为科学奉献一生需要多么浓厚的兴趣和刻苦钻研的精神啊!什么?你是因为数学不好才断了当科学家的念想?那还来得及,赶快重新投入科学的怀抱吧,谁告诉你数学不好就当不了科学家的?[论文网] 
   for many young people who aspire to be scientists, the great bugbear1) is mathematics. without advanced math, how can you do serious work in the sciences? well, i have a professional secret to share: many of the most successful scientists in the world today are mathematically no more than semiliterate.
   during my decades of teaching biology at harvard, i watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. this mistaken assumption has deprived science of an immeasurable amount of sorely needed talent.
   i speak as an authority on this subject because i myself am an extreme case. having spent my precollege years in relatively poor southern schools, i didn’t take algebra until my freshman year at the university of alabama. i finally got around to2) calculus as a 32-year-old tenured3) professor at harvard, where i sat uncomfortably in classes with undergraduate students only a bit more than half my age. a couple of them were students in a course on evolutionary biology i was teaching. i swallowed my pride and learned calculus.
   i was never more than a c student while catching up, but i was reassured by the discovery that superior mathematical ability is similar to fluency in foreign languages. i might have become fluent with more effort and sessions talking with the natives, but being swept up with field and laboratory research, i advanced only by a small amount.
   fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures4) images and processes by intuition.
   everyone sometimes daydreams like a scientist. ramped up5) and disciplined, fantasies are the fountainhead of all creative thinking. newton dreamed, darwin dreamed, you dream. the images evoked are at first vague. they may shift in form and fade in and out. they grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.
   pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. most of the stereotypical photographs of scientists studying rows of equations on a blackboard are instructors explaining discoveries already made. real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. eureka moments6) require hard work. and focus.

 ideas in science

emerge most readily when some part of the world is studied for its own sake. they follow from thorough, well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence. when something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. if that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator.
   in the late 1970s, i sat down with the mathematical theorist george oster to work out the principles of caste7) and the division of labor in the social insects. i supplied the details of what had been discovered in nature and the lab, and he used theorems8) and hypotheses from his tool kit to capture these phenomena. without such information, mr. oster might have developed a general theory, but he would not have had any way to deduce which of the possible permutations9) actually exist on earth.
   over the years, i have co-written many papers with mathematicians and statisticians, so i can offer the following principle with confidence. call it wilson’s principle no. 1: it is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.
   this imbalance is especially the case in biology, where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. the annals10) of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. possibly no more than 10% have any lasting value. only those linked solidly to knowledge of real living systems have much chance of being used.
   if your level of mathematical competence is low, plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have. think twice, though, about specializing in fields that require a close alternation of experiment and quantitative analysis. these include most of physics and chemistry, as well as a few specialties in molecular biology.
   newton invented calculus in order to give substance to his imagination. darwin had little or no mathematical ability, but with the masses of information he had accumulated, he was able to conceive a process to which mathematics was later applied.

 for aspiring scientists, a key first step is to find a subject that interests them deeply and focus on it. in doing so, they should keep in mind wilson’s principle no. 2: for every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.
   对于很多有志于成为科学家的年轻人来说,数学是个大难题。wWW.11665.CoM离开了高等数学,你怎么能在科学领域开展需要认真思考的工作呢?不过,我有一个职业秘密要分享:当今世界上很多非常成功的科学家在数学方面不过是半文盲罢了。
   我在哈佛教授生物学的几十年间,曾遗憾地看到一些聪明的本科生放弃了从事科学工作的可能性,他们担心自己会因没有出色的数学技

能而失败。这种错误的臆断使科学界痛失了无数亟需的人才。
   在这方面我可是个权威,因为我自己就是一个极端的例子。大学之前,我在条件相对较差的南部学校上学,在我去亚拉巴马大学上大学一年级之前,我可没学过代数。我到32岁才终于开始学习微积分,那时我已是哈佛大学的终身教授,不自在地与本科生坐在一起上课。那些本科生的年龄仅仅是我的一半多一点儿,其中有几个还是我当时正在教授的进化生物学课上的学生。但我抛开了自尊,学会了微积分。
   尽管我紧追猛赶,但我顶多也就是个c等生。不过令我安心的是,我发现出色的数学能力类似于流利的外语水平。如果我付出更多努力,花更多时间与母语人士交谈,我的外语可能会变得很流利,但是因为忙于实地研究和实验室研究,我只进步了一点点。
   幸运的是,对数学能力有极高要求的仅仅是少数几个学科,如粒子物理学、天体物理学和信息论等。在科学的其他领域,更重要的是形成概念的能力,在此过程中,研究者利用直觉来想象出图像和过程。
   人人都有像科学家那样做白日梦的时候。经过升华与约束的幻想是所有创造性思维的源头。牛顿做过梦,达尔文做过梦,你也做梦。脑海中被唤起的那些图像最初是模糊的,它们可能会变换形状,渐渐显形又渐渐消失。当你把它们画在纸上,形成图形时,它们就变得更明确一些;当你探寻并找到了真实的例证时,它们就开始有了生气。
   科学先驱们的发现极少是通过从纯数学中提炼观点而得来的。那些展现科学家研究黑板上一行一行方程式的老套照片其实大都是老师在解释已有的发现。真正的科学进步源自实地考察所做的笔记中,源自到处堆着涂鸦纸张的办公室里,源自在走廊里努力向朋友解释某事时,源自独自吃午饭时。“灵感突发时刻”的到来需要你努力工作并且专注其中。
   科学领域的观点最容易出现在为了世上某物本身而进行研究时。当人们对现存事物中的真正实体和过程的所有已知情况或可想象情况有了详尽和条理清晰的了解后,科学观点才会诞生。当某种新发现出现时,后续的步骤往往需要用数学和统计学方法来推进分析。如果做出发现的人觉得这一步骤的技术难度太大,那可以增加一位数学家或统计学家作为其合作者。
   在20世纪70年代末,我与数学理论家乔治·奥斯特一起研究社会性昆虫中的等级原则和劳动分工。我提供了自然界中和实验室内已经发现的细节,他则使用其“工具包”内的定理和假设来描述这些现象。如果没有我提供的那些信息,奥斯特先生或许可以提出一个笼统的理论,但他将无法推断出哪些可能的排列是地球上真正存在的。
   多年来,我与数学家和统计学家合写过很多论文,所以我可以自信地给出以下定律,姑且称之为“威尔逊第一定律”:比起让数学家和统计学家找到能运用其方程式的科学家,让科学家从数学家和统计学家处得到其所需的合作要容易得多。
   这种不平衡在生物学领域尤为显著,因为在这个领域,真实生活中某个现象的某些因素往往被误解,或者一开始就根本没被注意到。理论生物学的历史记载中充斥着要么可以完全忽略、要么经过验证是错误的数学模型,有长久价值的模型可能顶多只占10%。只有那些与真实生命系统的知识紧密相连的模型才有较大可能得到运用。
   如果你的数学能力较低,那就做个计划提升一下。但同时你也要知道,运用现有的数学能力你同样可以完成杰出的科学工作。但是,如果你想专攻需要不断交替进行实验和定量分析的领域时,那就要三思了。这些领域包括物理学和化学的大多数专业,还有分子生物学方面的几个专业。
   牛顿发明了微积分,以便为他的想象赋予实质内容。达尔文几乎或者说根本没有数学能力,但他却能凭借自己积累的大量信息构想出一个过程,数学被应用于此过程是后来的事了。
   对于有抱负的科学家来说,关键的第一步是找到一个非常感兴趣的学科,并专攻该学科。在这样做时,他们应当牢记“威尔逊第二定律”:对于每一位科学家来说,都有一个学科是其数学能力足以使之取得杰出成就的。
   1. bugbear [?b?ɡ?be?(r)] n. 棘手的问题,难题;恐惧(或烦恼)的原因
  2. get around to:抽出时间做(或考虑)某事
  3. tenured [?tenj?(r)d] adj. 〈主美〉享有终身职位的
  4. conjure [?k?nd??(r)] vt. 想象;提出
  5. ramp up:增加,提高
  6. eureka moment:“尤里卡”(eureka)原是古希腊语,意思是“好啊!有办法啦!”古希腊学者阿基米德有一次在浴盆里洗澡,突然来了灵感,发现了他久未解决的计算浮力问题的办法,于是惊喜地叫了一声“尤里卡”。“尤里卡时刻”因此用来形容灵感突现、豁然开朗的时刻。
   7. caste [kɑ?st] n. [昆]级(社会性昆虫中成熟个体如兵、工等的不同型)
  8. theorem [?θ??r?m] n. [数]定理
  9. permutation [?p??(r)mj??te??(?)n] n. [数]排列,置换
  10. annals [??n(?)lz] n. [复]历史记载
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  •  更新时间:2013-11-05 09:30:05  作者:佚名 [标签: 数学 进身之阶 ]
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