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general relativity and quantum mechanics, cannot be stated in the same mathematical language, and thus are inconsistent with one another, as the Ptolemaic and Copernican theories were in the sixteenth century, although both contemporary theories continue to be used, but for different calculations. Oxford mathematician Roger Penrose, in The Emperors New Mind (1989), contends that this inconsistency requires a change in quantum theory to provide a new theory he calls \Furthermore, the observations astronomers make with new technologies disclose a total mass in the universe that is less than about 10 percent of the total mass that mathematical calculations require the universe to contain on the basis of its observed rate of expansion. If the universe contains no more mass than we have been able to observe directly, then according to all current theories it should have expanded in the past, and be expanding now, much more rapidly than the rate actually observed. It is therefore believed that 90 percent or more of the mass in the universe is some sort of \matter\that has not yet been observed and the nature of which is unknown. Current theories favor either WIMPs (weakly interacting massive particles) or MACHOs (massive compact halo objects). Other similar mysteries abound and increase in number as our ability to observe improves.
The progress of biological and life sciences has been similar to that of the physical sciences, except that it has occurred several centuries later. The theory of biological evolution first came to the attention of scientists with the publication of Darwin's Origin of Species in 1859. But Darwin lacked any explanation of the causes of variation and inheritance of characteristics. These were provided by Gregor Mendel, who laid the mathematical foundation of genetics with the publication of papers in 1865 and 1866.
Medicine, according to Lewis Thomas, is the youngest science, having become truly scientific only in the 1930s. Recent and ongoing research has created uncertainty about even such basic concepts as when and how life begins and when death occurs, and we are spending billions in an attempt to learn how much it may be possible to know about human genetics. Modern medicine has demonstrably improved both our life expectancies and our health, and further improvements continue to be made as research progresses. But new questions arise even more rapidly than our research resources grow, as the host of problems related to the Human Genome Project illustrates.
From even such an abbreviated and incomplete survey of science as this, it appears that increasing knowledge does not result in a commensurate decrease in ignorance, but, on the contrary, exposes new lacunae in our comprehension and confronts us with unforeseen questions disclosing areas of ignorance of which we
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were not previously aware.
Thus the concept of science as an expanding body of knowledge that will eventually encompass or dispel all significant areas of ignorance is an illusion. Scientists and philosophers are now observing that it is naive to regard science as a process that begins with observations that are organized into theories and are then subsequently tested by experiments. The late Karl Popper, a leading philosopher of science, wrote in The Growth of Scientific Knowledge (1960) chat science starts from problems, not from observations, and chat every worthwhile new theory raises new problems. Thus there is no danger that science will come to an end because it has completed its task, clanks to the \
At least since Thomas Kuhn published The Structure of Scientific Revolutions (1962), it has been generally recognized that observations are the result of theories (called paradigms by Kuhn and other philosophers), for without theories of relevance and irrelevance there would be no basis for determining what observations to make. Since no one can know everything, to be fully informed on any subject (a claim sometimes made by those in authority) is simply to reach a judgment that additional data are not important enough to be worth the trouble of securing or considering. To carry the analysis another step, it must be recognized that theories are the result of questions and questions are the product of perceived ignorance. Thus it is chat ignorance gives rise to inquiry chat produces knowledge, which, in turn, discloses new areas of ignorance. This is the paradox of knowledge: As knowledge increases so does ignorance, and ignorance may increase more than its related knowledge.
My own metaphor to illustrate the relationship of knowledge and ignorance is based on a line from Matthew Arnold: \dark chat surrounds us, chat, indeed, envelops our world, is ignorance. Knowledge is the illumination shed by whatever candles (or more technologically advanced light sources) we can provide. As we light more and more figurative candles, the area of illumination enlarges; but the area beyond illumination increases geometrically. We know chat there is much we don't know; but we cannot know how much there is chat we don't know. Thus knowledge is finite, but ignorance is infinite, and the finite cannot ever encompass the infinite.
This is a revised version of an article originally published in COSMOS 1994. Copyright 1995 by Lee Loevinger.
Lee Loevinger is a Washington lawyer and former assistant attorney general of the United States who writes frequently for scientific c publications. He has
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participated for many years as a member, co-chair, or liaison with the National Conference of Lawyers and Scientists, and he is a founder and former chair of the Science and Technology Section of the American Bar Association. Office address: Hogan and Hartson, 555 Thirteenth St. NW, Washington, DC 20004.
人类从古类人猿进化到当前的状态这个长久的进化过程中的最大成就是有关于人类自身、世界以及宇宙众多知识的获得和积聚。这些知识的产物就是那些我们总称为―文化‖的所有的东西,包括语言、科学、文学、艺术、所有的物质机器、仪器、我们所用的结构以及社会所依赖的物质基础设施。我们之中大多数人认为现代社会中各种知识在不断增长,与此同时社会或群体对新知识的积累也在稳步减少我们对人类自身、世界及宇宙的未知。然而,现有的无垠的未知领域在不断提示着我们需要批判性地分析这个设想。
普遍的观点认为,智力的演变与身体的发育相似,虽然要快上许多。生物的进化经常被描述为―个体的进化重演物种的进化‖,意思就是个体的胚胎在其从受精卵发展到人类胎儿的过程中经历了几个阶段,在这些阶段中个体胚胎类似人类物种的祖先形式。普遍的观点认为人类从天真无邪的状态进步的,这个状态可以比作婴儿,然后逐渐的获得越来越多的知识,就像一个小孩通过学习通过了教育体系的几个年级一样。这种观点中暗含着一种臆断,那就是种系发育类似个体发育,知识的积累最终能达到一个基本完整的阶段,至少在特定的领域中是如此,就好像社会已获得了所有的高等学位,这些学位表明它已经掌握了各个重要学科的知识。
实际上,一些杰出的科学家已经表达了这样的观点。1894年伟大的物理学家Albert Michelson在芝加哥大学的一个演讲中讲到:虽然不能断言未来的物理学不会再取得比过去更惊人的成就,但很可能大多数的重要的基本原理都已经牢固的确立了,那么,进一步的发展将可能主要是如何将这些基本原理精确地应用到我们注意的现象上去。人们很难在物理学领域再作突破。
在迈克尔逊讲述上一段话之后的一个世纪,科学家们在物理学上的发现远远超出了对小数点第六位测量的改进,而今天没有人会再进行与Michelson相似的阐述。但是仍有许多人坚持认为知识有迟早达到穷尽的可能性。英国伟大的科学家斯蒂芬·霍金在他的非常流行的<<时间简史>>一书中, 推测得出以下结论, 我们可以―发现一种终极理论,那将是人类理性的最终胜利, 那时候我们将知道上帝在想什么‖。澳大利亚物理学家保罗·戴维斯附和斯蒂芬·霍金的观点,在他的书名为《上帝的智慧》一书中提出人类才智能使人类掌握一些上帝的思想的一些秘密。其他一些同时代的科学家有提及―万物之理‖,也就是解释所有可以观察到的物理现象的理论。物理理论的现代标准模型的构建者之一诺贝尔奖获得者斯蒂芬·温伯格则提到他的著作《终极理论之梦》。
尽管这些科学家和现代的其他科学家做出了卓越贡献并且对知识孜孜以求,但是在科学史上没有任何事情表明任何对于科学知识体系增加的数据和理论曾经给任何领域的所有问题提供答案。相反,科学史表明,增加的知识使人们认识
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到新的无知的领域并带来新的问题。
天文学是最古老的科学,它的发展是其他领域知识发展的模型。自从有史记载以来,人们一直在观察星星和天体。早在公元前3000年,巴比伦人认识了一定数量的星座。在第一个五千年或者更早一些的时间,天文学观察仅限于狭窄的可见光波长范围内。在过去的这半个世纪,天文学观察已经可以在电磁辐射波长(包括广播电波、红外、紫外、X射线、伽玛射线)范围内进行,还可以通过大气层外的卫星来观察。可以毫不夸张地说,自从第二次世界大战以来收集的天文学数据,比在人类持续的几千年历史中收集的数据还要多。
然而,虽然仪器的应用有了长足的改进,由于计算机以及大量数据和知识的积累,分析和计算的复杂程度有了大幅度的提高,但是我们仍然难以预测出行星未来的运动以及另一些原理甚至是太阳系中被高度确定的原理。一个训练有素的科普作家以及科学新闻的编辑Ivars Peterson,在他的书―牛顿的时钟‖里提到一种奇妙的细微的混乱弥漫着太阳系中。他写到:
两百多年以来,太阳系的稳定性问题以一种或是另一种方式吸引着并且困扰着天文学家和数学家。而这仍然是天体力学中最为困扰并且未能解决的问题,当代的科学家们对此也感到很尴尬。每一步对于此问题以及与此相关的问题的解决都会产生而外的不确定的问题甚至是更深的奥秘。
相似的问题在天文学中中也很流行。关于宇宙的最主要的两个理论,广义相对论以及量子力学不能够用形同的数学语言来表达,因此两者是不一致的,就像16世纪时托勒密和哥白尼的理论一样,虽然当代的理论仍在被应用,但是所用的计算公式不同。牛津大学的数学家Roger Penrose在他的书―新思想的帝国‖中提到由于量子论中存在不可调和的争论,因此他提出了一种名为―修正的量子重力―理论‖。
生物和生命科学的发展过程与物理学的发展过程相似,只是它的发生晚了几个世纪。生物进化论第一次引起科学家的注意是在1859年达尔文的―物种起源―的出版。但是达尔文没有解释造成性状遗传和变异的原因。孟德尔在1865年和1866年发表的论文中运用了基于基因的数学理论解释了这些原因。
按照Lewis Thomas的观点,医学是最年轻的科学,二十世纪三十年代才成为真正的科学。正在进行的和将要进行的研究产生了很多不确定东西。有些是关于一些基本的概念,比如:生命是何时诞生的,是怎样诞生的,死亡会在什么时候发生;并且我们现在花费数十亿美元来设法了解我们对于人类的基因能够知道多少。现代医学显著的提高了我们的寿命和健康状况,而且随着研究过程的深入将来还会继续改善。但是新的问题的出现速度要比我们得到的研究成果的增长速度快得多,比如说在有关人类基因工程项目中所出现的大量的问题。
仅仅通过对科学如此粗略而浅显的认识来看,认识的增加并没有造成无知相称的减少,相反揭露了我们理解中的新的空缺,还使我们面临着意料之外的问题,这些问题揭开我们不可预料的未知领域。
因此,把科学作为能够包围和消除一切重要无知领域的不断扩充的知识的这
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