Translation of the NKS [PAUSED]

marveloustau

Page 6 http://www.wolframscience.com/nksonline/page-6-text

One can always in principle find out how a particularsystem will behave just by running an experiment and watching whathappens. But the great historical successes of theoretical science havetypically revolved around finding mathematical formulas that insteaddirectly allow one to predict the outcome. Yet in effect this relies onbeing able to shortcut the computational work that the system itselfperforms.
理论上，人们总能够通过进行试验，或者观察现象来计算出一个特定的系统将如何运行。但是历史上理论科学的巨大成功，却总是围绕着数学公式的发现，而不是人们对运行结果的直接预测。然而事实上它可以大大简化对系统运行的计算工作。


And the Principle of ComputationalEquivalence now implies that this will normally be possible only forrather special systems with simple behavior. For other systems willtend to perform computations that are just as sophisticated as those wecan do, even with all our mathematics and computers. And this meansthat such systems are computationally irreducible--so thatin effect the only way to find their behavior is to trace each of theirsteps, spending about as much computational effort as the systemsthemselves.
同时，计算等价性原理现在暗示了上述情况只会发生在拥有简单行为的相当特殊系统中。[某些系统能够进行和我们所能够做的同样复杂的计算]，甚至包括我们所有的数学和计算机。这意味着这样的系统是[计算不可约]的以至于事实上唯一去发现其行为的方法就是跟踪它的每一步运行，而这将产生在计算上的代价，和系统本身进行计算的代价是一样的。


So this implies that there is in a sensea fundamental limitation to theoretical science. But it also shows thatthere is something irreducible that can be achieved by the passage oftime. And it leads to an explanation of how we as humans--even though we may follow definite underlying rules--can still in a meaningful way show free will.
Onefeature of many of the most important advances in science throughouthistory is that they show new ways in which we as humans are notspecial. And at some level the Principle of Computational Equivalencedoes this as well. For it implies that when it comes to computation--or intelligence--we are in the end no more sophisticated than all sorts of simple programs, and all sorts of systems in nature.
所以它说明，在某种程度上理论科学存在一个基本的极限。但是它同样显示出某些东西由于时间的流逝而无法规约。并且这导致了这样一个解释，即我们作为人类能够以一种有意义的方式显示出我们的自由意志，尽管我们可能受制于确定的法则。
纵观历史，在众多重要的科学进展中有这样一个特性，[就是它们所展示的新方法面向的是我们，而我们作为人类不是特殊的]。并且在某种程度上计算等价性原理也表现了这一点。它体现了对于计算——或者是智慧——我们最终并不比各种简单程序以及自然界的各种系统复杂到哪去。


Butfrom the Principle of Computational Equivalence there also emerges anew kind of unity: for across a vast range of systems, from simple programs to brains to our whole universe, the principle impliesthat there is a basic equivalence that makes the same fundamentalphenomena occur, and allows the same basic scientific ideas and methodsto be used. And it is this that is ultimately responsible for the greatpower of the new kind of science that I describe in this book.
但是从计算等价性原理又能得到一种新的一致性：对于广泛的系统，从大脑中简单的程序到整个宇宙，这个原理暗示着存在一个基础的等价性，使得同样的基本现象发生，并且允许基础的科学思想和方法被应用。同时，它指出新科学的伟大力量是绝对可靠的。


[ 本帖最后由 marveloustau 于 2008-8-20 13:13 编辑 ]

bainhome

原帖由 smarten 于 2008-8-19 10:47 发表
Word 可能越来越强了，不过一般说来如果在Word里面插了一些图表，当文件大小有10Mb的时候，比较容易死 （某页出现错误）。 另外大概就是打数学公式不太强。 Word是WYSIWYG, (what you get is what you see, you bett ...

同意。
可以肯定地说：word干这个事情不好，前期估计还可以，因为没图片、没公式也没长度。到后期几百页时，打开一次都是问题；公式和图表的索引word是通过“域”来完成的，这种方式也比较麻烦，而latex用table环境则根本无需担心索引的问题；另外Mathematica可以把出现的公式用TexForm转为latex形式，也应该可以生成eps或者pdf式的图形文件，到时候直接用includegraphic引入即可。

waynebuaa

即便是没有插多少图表，如果页数很多，有几百页的，ms word也很卡

marveloustau

要不然干脆输出成网页得了。这样每个文件都不会太大。

bainhome

网页也好办，可以通过tex2html直接制作，这一页就是这样做的：
http://www.math.zju.edu.cn/ligan ... c.htm#The%20TeXbook
这好像是王垠老大的网页中的，他的主页latex内容写得非常好，可以说是娓娓道来不急不徐，一点儿不像他退学时的风骚强悍:victory:

waynebuaa

对，Latex确实有这功能。
有了Latex，其实我们根本不用担心拍板问题

marveloustau

行，那不然关于排版的内容到此为止，现在重点放在翻译和校对上。有一众TeX高手在此排版的事情就等定了稿再说吧！

marveloustau

Page 7  http://www.wolframscience.com/nksonline/page-7-text

Relations to Other Areas
与其他领域的关系

Mathematics.
It is usually assumed that mathematics concerns itself with the studyof arbitrarily general abstract systems. But this book shows that thereare actually a vast range of abstract systems based on simple programsthat traditional mathematics has never considered. And because thesesystems are in many ways simpler in construction than most traditionalsystems in mathematics it is possible with appropriate methods ineffect to go further in investigating them.
Someof what one finds are then just unprecedentedly clear examples ofphenomena already known in modern mathematics. But one also finds somedramatic new phenomena. Most immediately obvious is a very high levelof complexity in the behavior of many systems whose underlying rulesare much simpler than those of most systems in standard mathematicstextbooks.
数学。通常认为数学是研究一切抽象系统的学科。但是这本书将显示出事实上还有更为广泛的基于简单程序的抽象系统是传统数学从未考虑过的。并且因为这些系统在很多方面相比于传统的数学上的系统都更容易构建，所以应用合适的方法可以进行更深刻的研究。其中一些范例是最为明确的现象，它们已经通过现代数学所了解了。但是此外还有一些引人关注的新现象。最为明显的是，有很多显示出极高复杂行为的系统，它们所基于的规则要比大多数标准数学教科书中描述的系统简单很多。


And one of the consequences of thiscomplexity is that it leads to fundamental limitations on the idea ofproof that has been central to traditional mathematics. Already in the1930s Gödel's Theorem gave some indications of such limitations. But inthe past they have always seemed irrelevant to most of mathematics asit is actually practiced.

同时这种复杂性的一个结果就是导致了传统数学在证明方面的一个基本的限制。在1930年代哥德尔不完备性定理就已经对这样的限制进行了描述，但是在过去他们看起来和大多数正在应用的数学并不相关。


Yet what the discoveriesin this book show is that this is largely just a reflection of howsmall the scope is of what is now considered mathematics. And indeedthe core of this book can be viewed as introducing a majorgeneralization of mathematics--with new ideas and methods, and vast new areas to be explored.

然而在这本书中所揭示的是，当前被认为叫做数学的东西，其实很大程度上只是思考了极小的视野。并且这本书的核心其实可以看做引入了一个数学上的重要的一般化过程，包括新的想法和方法，以及大量有待研究的新领域。


Theframework I develop in this book also shows that by viewing the processof doing mathematics in fundamentally computational terms it becomespossible to address important issues about the foundations even ofexisting mathematics.
我在这本书中建立的框架同时也显示，[以基本的计算规则来看待数学，使得描述数学基础的重要事实成为可能。]

[ 本帖最后由 marveloustau 于 2008-8-20 20:53 编辑 ]

marveloustau

Page 8 http://www.wolframscience.com/nksonline/page-8-text



Physics. The traditional mathematical approach to science has historically had its great success in physics--andby now it has become almost universally assumed that any seriousphysical theory must be based on mathematical equations. Yet with thisapproach there are still many common physical phenomena about whichphysics has had remarkably little to say. But with the approach ofthinking in terms of simple programs that I develop in this book itfinally seems possible to make some dramatic progress. And indeed inthe course of the book we will see that some extremely simple programsseem able to capture the essential mechanisms for a great many physicalphenomena that have previously seemed completely mysterious.
物理学。传统的数学方法在物理学上获得了巨大的成功，同时到现在为止，任何物理学理论必须基于数学方程是一个基本的假定。然而应用了数学方法，仍然有很多很常见的物理现象却是物理学只字未提的。然而应用了我所发现的以简单程序思考的方法在这一方面却会取得一些极大的进展。并且事实上本书中我们将会看到一些极端简单的程序却抓住了很多物理现象的本质，而这些现象之前看起来完全是神秘的。


Existing methods in theoretical physics tend to revolve around ideas of continuous numbers and calculus--orsometimes probability. Yet most of the systems in this book involvejust simple discrete elements with definite rules. And in many ways itis the greater simplicity of this underlying structure that ultimatelymakes it possible to identify so many fundamentally new phenomena.
现有的理论物理模型趋向于以连续的数字和微积分的形式思考——偶尔包含概率。然而本书中大多数系统只涉及简单的离散元素和有限的规则。并且很多情况下这种基础结构具有更高的简单性使得我们能够发现很多基本的新的现象。


Ordinarymodels for physical systems are idealizations that capture somefeatures and ignore others. And in the past what was most common was tocapture certain simple numerical relationships--that couldfor example be represented by smooth curves. But with the new kinds ofmodels based on simple programs that I explore in this book it becomespossible to capture all sorts of much more complex features that canonly really be seen in explicit images of behavior.
通常对于物理系统的建模就是一种理想化，去抓住某些特性并且忽略掉另外一些。并且在以前最普遍的就是去获取某些简单的数字上的关系——比如说能以光滑曲线表示出来。但是基于简单程序的模型，使得获取各种更为复杂的特性成为可能，而它们能够以清晰的图景呈现在眼前。


Inthe future of physics the greatest triumph would undoubtedly be to finda truly fundamental theory for our whole universe. Yet despiteoccasional optimism, traditional approaches do not make this seem closeat hand. But with the methods and intuition that I develop in this bookthere is I believe finally a serious possibility that such a theory canactually be found.
物理学的未来，最伟大的胜利毋庸置疑是寻找一种对于我们整个宇宙都适用的真正基础的理论。然而除了偶然性的乐观，传统方法解决这个问题似乎显得遥遥无期。但是用了俺的新方法，俺确定一定肯定我们最终肯定会找到这个理论。

[实在抱歉，SW同学每段话里都强调一遍"the new kind of science that I develop in this book"，翻得我实在心烦]


Biology.Vast amounts are now known about the details of biological organisms,but very little in the way of general theory has ever emerged.Classical areas of biology tend to treat evolution by natural selectionas a foundation--leading to the notion that generalobservations about living systems should normally be analyzed on thebasis of evolutionary history rather than abstract theories. And partof the reason for this is that traditional mathematical models havenever seemed to come even close to capturing the kind of complexity wesee in biology. But the discoveries in this book show that simpleprograms can produce a high level of complexity. And in fact it turnsout that such programs can reproduce many features of biologicalorganisms--and for example seem to capture some of theessential mechanisms through which genetic programs manage to generatethe actual biological forms we see. So this means that it becomespossible to make a wide range of new models for biological systems--andpotentially to see how to emulate the essence of their operation, sayfor medical purposes. And insofar as there are general principles forsimple programs, these principles should also apply to biologicalorganisms--making it possible to imagine constructing new kinds of general abstract theories in biology.
生物学。到现在已经有很多关于生命体的细节已经为我们所知，但是在统一的理论上却鲜有进展。经典的生物学理论趋向于将自然选择的进化论作为基础。这里应当说明，普遍的对于生命系统的观察通常应该基于进化的历史而非抽象的理论进行分析。并且导致此情况发生的部分原因是由于传统的数学模型里我们在生物学中所看到的复杂性相距甚远。但是在这本书中的发现将会展示简单程序可以创造出很高程度的复杂事物。并且事实上证明这样的一种程序能够重现很多生物有机体的特性——[比如通过控制遗传来创造实际的生命形式的程序，来获取遗传的真正机制]。所以这意味着它能够创造广泛的生命系统的新模型——并且，处于医疗目的，还具有模拟其操作本质的潜在能力。并且到现在，这些简单的程序也有了一般理论，这些理论同样应该应用在生物学方面。使得在生物学方面建立一般的抽象理论是可以预见的。



[我有话要说：

到现在为止翻了8页, 当然这一页包含了第9页的一半，因为最后那段话太长。平均一页大概300词，那么现在也有差不多3 000词了。我的想法是，到现在为止说的全都是废话。几乎每段话都在阐释这样一个观点：传统科学在某些方面不行，而我的新科学("我在这本书中所发展的以简单程序为基础的新科学")在这些方面很行。他不告诉局限出在哪里，也不告诉为什么他的新科学就行。无论他肚子里是否有真货，我是指新科学真就这么神，这种描述的方法非常缺乏说服力，让人很容易厌烦，并且觉得这人忒自大了。我的阅读和翻译的进度一致，而到现在为止，我还没有关于新科学的任何收获。

我大二的时候帮老师做活的时候看过很多文档，然后又因为GRE以及美国数模竞赛的缘故参考了很多关于英文写作的书。其中最著名的一本是the Elements of Style作者是E.B.White(《夏洛的网》和《精灵鼠小弟》的作者)，书中提倡简明清晰的写作风格，尤其强调了段落结构和例证的必要性。这应该是每个科研工作者必读的书目，SW同学也是在加州理工念过书的，但是看起来他不知道怎么用有说服力和吸引力的表达方式阐述自己的观点。顺便一提，此书极力推荐大家阅读，美国人写得科技论文都是参考着这本书写的，看懂了以后看他们写的论文会很轻松，同时我们自己写的论文也会很专业。我指的是中英文均适用。


所以我建议，真正有兴趣翻译的人，请从后面的章节开始。我遇见本书不会有太强的逻辑性，从哪里翻都一样。

从明天开始我会先去看一下后面的几节，如果内容仍然和现在一样，我就在这里写一个总述，这张内容就不再翻译了。SW同学可能没听说过“浪费别人的时间就是谋财害命”一说。

]

FreddyMusic

Is that possible to restart from charpter 2, usually there is some talking in a written book.
Therefore I said notebook is essential and tell the fact.
Different style for different people, it's just a new kind of style.

marveloustau

我当然尽可能适应，但是我觉得我也可以表达一下我的不喜欢。好的论述应该以最小的时间代价让读者明白他说的什么，尽管如SW同学所说也许花的时间不会短，但是每一个试图让读者理解其思想的人自己不应该制造理解上的麻烦，时间上的浪费以及反感的情绪。

并且我到现在也不清楚notebook到底哪点好？