不确定性的困惑与NP理论分享 http://blog.sciencenet.cn/u/liuyu2205 平常心是道

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整体性和隐秩序 - 引言(玻姆)

已有 767 次阅读 2024-10-27 17:41 |个人分类:解读哥德尔不完全性定理|系统分类:科研笔记

本书是一本论文集(见致谢),代表了我过去二十年来的思想发展。简短的介绍也许有助于说明将要讨论的主要问题是什么,以及它们之间的联系。

我想说,在我的科学和哲学工作中,我主要关注的是理解现实的本质,特别是意识的本质,作为一个连贯的整体,它从来都不是静止的或完整的,而是处于一个永无止境的运动和展开过程中。

因此,当我回首往事时,我发现,即使是在孩提时代,我也对运动本质的谜题,甚至是奥秘着迷。每当人们思考任何事情时,它似乎要么被理解为静态的,要么被理解为一系列静态图像。然而,在实际的运动体验中,人们感觉到一个不间断、不分割的流动过程,思维中的一系列静态图像与这一过程相关,就像一系列静止照片与一辆飞驰的汽车的现实相关一样。当然,这个问题早在 2000 多年前芝诺的悖论中就已经在哲学上被提出;但到目前为止,还不能说它有一个令人满意的解决办法。

然后还有一个问题,即思想与现实的关系是什么。仔细观察就会发现,思想本身就处于一个实际的运动过程中。也就是说,人们可以在意识流中感受到一种流动的感觉,这种感觉与一般物质运动中的流动感觉并无二致。因此,思想本身难道不是整个现实的一部分吗?但是,现实的一部分了解另一部分意味着什么?在多大程度上这是可能的?思想的内容是否仅仅为我们提供了抽象而简化的现实快照,或者它能否更进一步,以某种方式把握我们在实际体验中感受到的生命运动的本质?

显然,在思考和沉思思想和思想对象的运动的本质时,人们不可避免地会遇到整体性或总体性的问题。思考者(自我)至少在原则上完全独立于他所思考的现实,这一观念当然牢牢植根于我们的整个传统中。(显然,这一观念在西方几乎被普遍接受,但在东方,人们普遍倾向于在口头和哲学上否认这一观念,同时,这种方法在大多数生活和日常实践中也像在西方一样普遍存在。)上述一般经验,以及有关大脑作为思想中心的性质和功能的大量现代科学知识,强烈表明这种划分不能始终如一地维持。但这给我们带来了一个十分艰巨的挑战:我们如何才能连贯地思考一个单一的、不间断的、流动的存在现实作为一个整体,既包含思想(意识),也包含我们所体验到的外部现实?

显然,这让我们开始思考我们的整体世界观,其中包括我们关于现实本质的一般概念,以及关于宇宙整体秩序的概念,即宇宙学。为了应对我们面临的挑战,我们的宇宙学概念和现实的一般性质必须有空间来允许对意识进行一致的解释。反之,我们的意识概念必须有空间来理解其内容是现实作为整体的含义。这两组概念结合起来应该能够让我们理解现实和意识之间的关系。

当然,这些问题非常庞大,而且无论如何都不可能得到彻底的解决。尽管如此,我始终认为,继续研究旨在应对本文指出的挑战的提案非常重要。当然,现代科学的主流趋势是反对这种事业,而是主要致力于相对详细和具体的理论预测,这些预测至少显示出最终实用应用的希望。因此,似乎需要解释一下我为什么如此强烈地反对主流潮流。

除了我认为这些基本而深刻的问题本身所具有的意义之外,在这方面,我想提请大家注意第一章中讨论的人类意识分裂的普遍问题。第一章提出,人与人之间广泛而普遍的差异(种族、民族、家庭、职业等)阻碍了人类为了共同利益甚至生存而共同努力,而这种差异产生的关键因素之一在于一种将事物视为天生分裂、不连贯和分解成更小组成部分的思想。每个部分都被认为本质上是独立和自存的。

当人以这种方式思考自己时,他不可避免地会倾向于捍卫自己的自我需求,而反对他人的需求;或者,如果他认同同一类人的一个群体,他会以类似的方式捍卫这个群体。他无法认真地将人类视为基本现实,人类的诉求是第一位的。即使他确实试图考虑人类的需求,他也倾向于将人类与自然分开,等等。我在这里提出的是,人类对整体的一般思维方式,即他的一般世界观,对于人类心灵本身的整体秩序至关重要。如果他认为整体是由独立的碎片构成的,那么他的心灵就会倾向于这样运作,但如果他能将所有事物连贯和谐地纳入一个整体,这个整体是不可分割的、完整的、没有边界的(因为每个边界都是一个分裂或断裂),那么他的心灵就会倾向于以类似的方式移动,由此产生整体内的有序行动。

当然,正如我已经指出的,我们的总体世界观并不是在这种情况下唯一重要的因素。确实,必须关注许多其他因素,例如情绪、身体活动、人际关系、社会组织等,但也许是因为我们目前没有连贯的世界观,所以普遍倾向于几乎完全忽视这些问题的心理和社会重要性。我的建议是,适合时代的正确世界观通常是个人和整个社会和谐所必需的基本因素之一。

1 章表明,科学本身需要一种新的、非碎片化的世界观,因为目前将世界分析为独立存在的部分的方法在现代物理学中效果不佳。文章表明,无论是在相对论还是量子理论中,暗示宇宙不可分割整体的概念将提供一种更有序的方式来考虑现实的普遍性质。

在第 2 章中,我们探讨了语言在思想分裂中所起的作用。文中指出,现代语言的主谓宾结构意味着所有动作都发生在一个单独的主语中,并且要么作用于一个单独的对象,要么反身作用于自身。这种普遍的结构导致整个生命产生一种功能,将整个存在划分为单独的实体,这些实体被认为本质上是固定的和静态的。然后,我们探讨是否有可能尝试新的语言形式,在这些语言形式中,动词而不是名词将发挥基本作用。这些形式的内容将是一系列相互流动和融合的动作,没有明显的分离或中断。因此,无论是在形式上还是在内容上,语言都将与整个存在的不间断流动运动相协调。

这里提出的并不是新的语言,而是一种使用现有语言的新模式——流变模式。我们开发这种模式是为了进行语言实验,其主要目的是深入了解普通语言的零散功能,而不是提供一种可用于实际交流的新说话方式。

3 章在不同的背景下考虑了同样的问题。它首先讨论了如何将现实视为潜在的普遍运动或过程中的一组形式,然后询问如何以同样的方式考虑我们的知识。这样,就可以开辟一种世界观,在这种世界观中,意识和现实不会相互分裂。对这个问题进行了深入讨论,我们得出了这样的观点:我们的一般世界观本身就是一种整体的思想运动,它必须是可行的,因为从中流出的所有活动总体上都是和谐的,无论是在本身还是在整个存在方面。只有当世界观本身参与到发展、进化和展开的永无止境的过程中时,这种和谐才有可能实现,而这个过程是作为所有存在的基础的普遍过程的一部分。

接下来的三章则更加偏向技术和数学。然而,其中的大部分内容对于非技术读者来说应该是可以理解的,因为技术部分对于理解来说并不是完全必要的,尽管它们为那些能够理解的人来说增加了重要的内容。

4 章讨论量子理论中的隐变量。量子理论是目前物理学中理解物质及其运动的基本和普遍规律的最基本方法。因此,在试图形成整体世界观时,显然必须认真考虑它。

如果我们对这样的尝试感兴趣的话,那么现在所形成的量子理论将给我们带来巨大的挑战,因为在这个理论中,根本没有一致的概念来说明物质的普遍构成和结构背后的现实是什么。因此,如果我们试图使用基于粒子概念的现行世界观,我们会发现粒子(如电子)也可以表现为波,它们可以不连续地运动,根本没有任何适用于单个粒子实际运动的详细定律,只能对这些粒子的大集合做出统计预测。另一方面,如果我们应用将宇宙视为连续场的世界观,我们会发现这个场也必须是不连续的,也是粒子状的,而且它的实际行为与整个粒子关系观所要求的一样被削弱了。

那么,如果我们试图思考我们的物理定律所处理的现实是什么,那么显然我们面临的是深刻而根本的分裂和彻底的混乱。目前,物理学家倾向于回避这个问题,他们采取的态度是,我们对现实本质的整体看法并不重要。物理理论中最重要的应该是开发数学方程,这些方程使我们能够预测和控制大量粒子统计集合的行为。这一目标不仅仅被视为具有实用性和技术性,相反,它已成为大多数现代物理学工作的预设,即这种预测和控制就是人类知识的全部。

这种预设确实符合我们这个时代的普遍精神,但我在本书中的主要建议是,我们不能就这样简单地放弃一个整体的世界观。如果我们试图这样做,我们会发现,我们只能依靠手头现有的(通常不充分的)世界观。事实上,我们发现物理学家实际上不能只进行旨在预测和控制的计算:他们确实发现有必要使用基于某种关于现实性质的一般概念的图像,例如构成宇宙的粒子;但这些图像现在非常混乱(例如,这些粒子不连续地运动,也是波)。简而言之,我们在这里面对的一个例子表明,我们的思维中对某种现实概念的需求是多么深刻和强烈,即使它是零碎和混乱的。

我认为,在每一个阶段,正确的思维运作顺序要求全面掌握一般已知的事物,不仅包括形式、逻辑和数学术语,还包括直观的、形象的、感觉的、诗意的语言用法等。(也许我们可以说,这就是左脑右脑和谐相处的意义所在。)这种全面的思维方式不仅是新理论思想的丰富源泉,而且是人类思维以普遍和谐的方式运作所必需的,这反过来又有助于建立一个有序、稳定的社会。然而,正如前面几章所指出的,这需要我们对现实的一般观念不断流动和发展。

4 章则着重于开始发展一种连贯的观点,即什么样的现实可能是量子理论中正确的数学预测的基础。物理学家界对这种尝试的反应通常有些混乱,因为人们普遍认为,如果要有任何普遍的世界观,就应该把它当作关于现实本质的公认最终的概念。但我的态度从一开始就是,我们关于宇宙学和现实的一般性质的概念处于一个不断发展的过程,人们可能必须从一些仅仅是对迄今为止已有概念的某种改进的想法开始,然后再从那里继续发展更好的想法。第 4 章介绍了任何试图提供量子力学现实一致概念所面临的实际和严重的问题,并指出了从隐藏变量的角度解决这些问题的某种初步方法。

5 章探讨了解决同一问题的不同方法。这是对我们基本秩序概念的探究。秩序从整体上看显然是无法定义的,因为它渗透到我们的一切事物和行为中(语言、思想、感觉、知觉、身体活动、艺术、实践活动等)。然而,在物理学中,几个世纪以来的基本秩序一直是笛卡尔直线网格(在相对论中略微扩展到曲线网格)。在此期间,物理学取得了巨大的发展,出现了许多全新的特征,但基本秩序基本保持不变。

笛卡尔秩序适用于将世界分析为独立存在的部分(例如粒子或场元素)。然而,在本章中,我们将更全面、更深入地探讨秩序的本质,并发现无论是在相对论中还是在量子理论中,笛卡尔秩序都会导致严重的矛盾和混乱。这是因为这两种理论都意味着实际状态是宇宙的完整整体,而不是分析为独立的部分。然而,这两种理论在秩序的具体概念上存在根本差异。因此,在相对论中,运动是连续的、因果确定的和定义明确的,而在量子力学中,运动是不连续的、非因果确定的和定义不明确的。每种理论都致力于其本质上静态和零碎的存在模式的概念(相对论是独立事件的概念,可通过信号连接,量子力学是定义明确的量子态)。因此,人们认为需要一种新的理论,这种理论可以抛弃这些基本承诺,最多恢复旧理论的一些基本特征,作为源自更深层次现实的抽象形式,其中占主导地位的是完整的整体。

在第 6 章中,我们进一步开始更具体地发展一种新的秩序概念,这种概念可能适用于一个完整的宇宙。这就是隐秩序或折叠序。在折叠序中,空间和时间不再是决定不同元素之间依赖或独立关系的主导因素。相反,一种完全不同的元素基本联系是可能的,从中我们通常的空间和时间概念,以及独立存在的物质粒子概念,被抽象为源自更深层秩序的形式。这些通常的概念实际上出现在所谓的显秩序或展开秩序中,它是包含在所有隐秩序的一般总体中的一种特殊而独特的形式。

6 章以一般方式介绍了隐秩序,并在附录中从数学角度进行了讨论。然而,第七章也是最后一章是对隐秩序及其与意识的关系的更深入(尽管不是技术性的)介绍。这指明了一些思路,沿着这些思路,我们可能能够应对紧迫的挑战,即发展一套适合我们时代的宇宙学和一套关于现实本质的一般概念。

最后,希望这些文章中材料的呈现能够帮助向读者传达这个主题本身实际上是如何展开的,这样这本书的形式就可以成为其内容的一个例子。

原文:

https://en.wikipedia.org/wiki/Wholeness_and_the_Implicate_Order

http://www.gci.org.uk/Documents/DavidBohm-WholenessAndTheImplicateOrder.pdf

Wholeness and the Implicate Order

INTRODUCTION

This book is a collection of essays (see Acknowledgments) representing the development of my thinking over the past twenty years. A brief introduction will perhaps be useful in order to indicate what are the principal questions that are to be discussed, and how they are connected.

I would say that in my scientific and philosophical work, my main concern has been with understanding the nature of reality in general and of consciousness in particular as a coherent whole, which is never static or complete, but which is in an unending process of movement and unfoldment. 

Thus, when I look back, I see that even as a child I was fascinated by the puzzle, indeed the mystery, of what is the nature of movement. When- ever one thinks of anything, it seems to be apprehended either as static, or as a series of static images. Yet, in the actual experience of movement, one senses an unbroken, undivided process of flow, to which the series of static images in thought is related as a series of ‘still’ photographs might be related to the actuality of a speeding car. This question was, of course, already raised in essence philosophically more than 2,000 years ago in Zeno’s paradoxes; but as yet, it cannot be said to have a satisfactory resolution.

Then there is the further question of what is the relationship of thinking to reality. As careful attention shows, thought itself is in an actual process of movement. That is to say, one can feel a sense of flow in the ‘stream of consciousness’ not dissimilar to the sense of flow in the movement of matter in general. May not thought itself thus be a part of reality as a whole? But then, what could it mean for one part of reality to ‘know’ another, and to what extent would this be possible? Does the content of thought merely give us abstract and simplified ‘snapshots’ of reality, or can it go further, somehow to grasp the very essence of the living movement that we sense in actual experience?

It is clear that in reflecting on and pondering the nature of movement, both in thought and in the object of thought, one comes inevitably to the question of wholeness or totality. The notion that the one who thinks (the Ego) is at least in principle completely separate from and independent of the reality that he thinks about is of course firmly embedded in our entire tradi- tion. (This notion is clearly almost universally accepted in the West, but in the East there is a general tendency to deny it ver- bally and philosophically while at the same time such an approach pervades most of life and daily practice as much as it does in the West.) General experience of the sort described above, along with a great deal of modern scientific knowledge concerning the nature and function of the brain as the seat of thought, suggest very strongly that such a division cannot be maintained consistently. But this confronts us with a very dif- ficult challenge: How are we to think coherently of a single, unbroken, flowing actuality of existence as a whole, containing both thought (consciousness) and external reality as we experience it?

Clearly, this brings us to consider our overall world view, which includes our general notions concerning the nature of reality, along with those concerning the total order of the universe, i.e., cosmology. To meet the challenge before us our notions of cos- mology and of the general nature of reality must have room in them to permit a consistent account of consciousness. Vice versa, our notions of consciousness must have room in them to under- stand what it means for its content to be ‘reality as a whole’. The two sets of notions together should then be such as to allow for an understanding of how reality and consciousness are related.

These questions are, of course, enormous and could in any case probably never be resolved ultimately and completely. Nevertheless, it has always seemed important to me that there be a continuing investigation of proposals aimed at meeting the challenge that has been pointed out here. Of course, the prevail- ing tendency in modern science has been against such an enter- prise, being directed instead mainly toward relatively detailed and concrete theoretical predictions, which show at least some promise of eventual pragmatic application. Some explanation of why I want to go so strongly against the prevailing general current seems therefore to be called for.

Aside from what I feel to be the intrinsic interest of questions that are so fundamental and deep, I would, in this connection, call attention to the general problem of fragmentation of human consciousness, which is discussed in chapter 1. It is proposed there that the widespread and pervasive distinctions between people (race, nation, family, profession, etc., etc.), which are now preventing mankind from working together for the com- mon good, and indeed, even for survival, have one of the key factors of their origin in a kind of thought that treats things as inherently divided, disconnected, and ‘broken up’ into yet smaller constituent parts. Each part is considered to be essentially independent and self-existent.

When man thinks of himself in this way, he will inevitably tend to defend the needs of his own ‘Ego’ against those of the others; or, if he identifies with a group of people of the same kind, he will defend this group in a similar way. He cannot seriously think of mankind as the basic reality, whose claims come first. Even if he does try to consider the needs of mankind he tends to regard humanity as separate from nature, and so on. What I am proposing here is that man’s general way of thinking of the totality, i.e. his general world view, is crucial for overall order of the human mind itself. If he thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border (for every border is a division or break) then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole.

Of course, as I have already indicated, our general world view is not the only factor that is important in this context. Attention must, indeed, be given to many other factors, such as emotions, physical activities, human relationships, social organizations, etc., but perhaps because we have at present no coherent world view, there is a widespread tendency to ignore the psychological and social importance of such questions almost altogether. My suggestion is that a proper world view, appropriate for its time, is generally one of the basic factors that is essential for harmony in the individual and in society as a whole.

In chapter 1 it is shown that science itself is demanding a new, non-fragmentary world view, in the sense that the present approach of analysis of the world into independently existent parts does not work very well in modern physics. It is shown that both in relativity theory and quantum theory, notions implying the undivided wholeness of the universe would provide a much more orderly way of considering the general nature of reality.

In chapter 2 we go into the role of language in bringing about fragmentation of thought. It is pointed out that the subject-verb- object structure of modern languages implies that all action arises in a separate subject, and acts either on a separate object, or else reflexively on itself. This pervasive structure leads in the whole of life to a function that divides the totality of existence into separate entities, which are considered to be essentially fixed and static in their nature. We then inquire whether it is possible to experiment with new language forms in which the basic role will be given to the verb rather than to the noun. Such forms will have as their content a series of actions that flow and merge into each other, without sharp separations or breaks. Thus, both in form and in content, the language will be in harmony with the unbroken flowing movement of existence as a whole.

What is proposed here is not a new language as such but, rather, a new mode of using the existing language – the rheomode (flowing mode). We develop such a mode as a form of experimentation with language, which is intended mainly to give insight into the fragmentary function of the common lan- guage rather than to provide a new way of speaking that can be used for practical communications.

In chapter 3 the same questions are considered within a dif- ferent context. It begins with a discussion of how reality can be considered as in essence a set of forms in an underlying uni- versal movement or process, and then asks how our knowledge can be considered in the same manner. Thus, the way could be opened for a world view in which consciousness and reality would not be fragmented from each other. This question is dis- cussed at length and we arrive at the notion that our general world view is itself an overall movement of thought, which has to be viable in the sense that the totality of activities that flow out of it are generally in harmony, both in themselves and with regard to the whole of existence. Such harmony is seen to be possible only if the world view itself takes part in an unending process of development, evolution, and unfoldment, which fits as part of the universal process that is the ground of all existence.

The next three chapters are rather more technical and math- ematical. However, large parts of them should be comprehen- sible to the non-technical reader, as the technical parts are not entirely necessary for comprehension, although they add significant content for those who can follow them.

Chapter 4 deals with hidden variables in the quantum theory. The quantum theory is, at present, the most basic way available in physics for understanding the fundamental and universal laws relating to matter and its movement. As such, it must clearly be given serious consideration in any attempt to develop an overall world viewing.

The quantum theory, as it is now constituted, presents us with a very great challenge, if we are at all interested in such a ven- ture, for in this theory there is no consistent notion at all of what the reality may be that underlies the universal constitution and structure of matter. Thus, if we try to use the prevailing world view based on the notion of particles, we discover that the ‘par- ticles’ (such as electrons) can also manifest as waves, that they can move discontinuously, that there are no laws at all that apply in detail to the actual movements of individual particles and that only statistical predictions can be made about large aggregates of such particles. If on the other hand we apply the world view in which the universe is regarded as a continuous field, we find that this field must also be discontinuous, as well as particle-like, and that it is as undermined in its actual behaviour as is required in the particle view of relation as a whole.

It seems clear, then, that we are faced with deep and radical fragmentation, as well as thoroughgoing confusion, if we try to think of what could be the reality that is treated by our physical laws. At present physicists tend to avoid this issue by adopting the attitude that our overall views concerning the nature of re- ality are of little or no importance. All that counts in physical theory is supposed to be the development of mathematical equa- tions that permit us to predict and control the behaviour of large statistical aggregates of particles. Such a goal is not regarded as merely for its pragmatic and technical utility: rather, it has become a presupposition of most work in modern physics that prediction and control of this kind is all that human knowledge is about.

This sort of presupposition is indeed in accord with the gen- eral spirit of our age, but it is my main proposal in this book that we cannot thus simply dispense with an overall world view. If we try to do so, we will find that we are left with whatever (gener- ally inadequate) world views may happen to be at hand. Indeed, one finds that physicists are not actually able just to engage in calculations aimed at prediction and control: they do find it necessary to use images based on some kind of general notions concerning the nature of reality, such as ‘the particles that are the building blocks of the universe’; but these images are now highly confused (e.g. these particles move discontinuously and are also waves). In short, we are here confronted with an example of how deep and strong is the need for some kind of notion of reality in our thinking, even if it be fragmentary and muddled.

My suggestion is that at each stage the proper order of oper- ation of the mind requires an overall grasp of what is generally known not only in formal, logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the ‘left brain’ and the ‘right brain’.) This kind of over- all way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society. As indicated in the earlier chapters, however, this requires a continual flow and development of our general notions of reality.

Chapter 4 is then concerned with making a beginning in the pro- cess of developing a coherent view of what kind of reality might be the basis of the correct mathematical predictions achieved in the quantum theory. Such attempts have generally been received among the community of physicists in a somewhat confused way, for it is widely felt that if there is to be any general world view it should be taken as the ‘received’ and ‘final’ notion con- cerning the nature of reality. But my attitude has, from the beginning, been that our notions concerning cosmology and the general nature of reality are in a continuous process of develop- ment, and that one may have to start with ideas that are merely some sort of improvement over what has thus far been available, and to go on from there to ideas that are better. Chapter 4 pres- ents the real and severe problems that confront any attempt to provide a consistent notion of ‘quantum-mechanical reality’, and indicates a certain preliminary approach to a solution of these problems in terms of hidden variables.

In chapter 5 a different approach to the same problems is explored. This is an inquiry into our basic notions of order. Order in its totality is evidently ultimately undefinable, in the sense that it pervades everything that we are and do (language, thought, feeling, sensation, physical action, the arts, practical activity, etc.). However, in physics the basic order has for centur- ies been that of the Cartesian rectilinear grid (extended slightly in the theory of relativity to the curvilinear grid). Physics has had an enormous development during this time, with the appearance of many radically new features, but the basic order has remained essentially unchanged.

The Cartesian order is suitable for analysis of the world into separately existent parts (e.g. particles or field elements). In this chapter, however, we look into the nature of order with greater generality and depth, and discover that both in relativity and in quantum theory the Cartesian order is leading to serious contra- dictions and confusion. This is because both theories imply that the actual state of affairs is unbroken wholeness of the universe, rather than analysis into independent parts. Nevertheless, the two theories differ radically in their detailed notions of order. Thus, in relativity, movement is continuous, causally determin- ate and well defined, while in quantum mechanics it is dis- continuous, not causally determinate and not well defined. Each theory is committed to its own notions of essentially static and fragmentary modes of existence (relativity to that of separate events, connectable by signals, and quantum mechanics to a well-defined quantum state). One thus sees that a new kind of theory is needed which drops these basic commitments and at most recovers some essential features of the older theories as abstract forms derived from a deeper reality in which what prevails is unbroken wholeness.

In chapter 6 we go further to begin a more concrete develop- ment of a new notion of order, that may be appropriate to a universe of unbroken wholeness. This is the implicate or enfolded order. In the enfolded order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely differ- ent sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the explicate or unfolded order, which is a special and distinguished form contained within the general totality of all the implicate orders.

In chapter 6 the implicate order is introduced in a general way, and discussed mathematically in an appendix. The seventh and last chapter, however, is a more developed (though non- technical) presentation of the implicate order, along with its relationship to consciousness. This leads to an indication of some lines along which it may be possible to meet the urgent challenge to develop a cosmology and set of general notions concerning the nature of reality that are proper to our time.

Finally, it is hoped that the presentation of the material in these essays may help to convey to the reader how the subject itself has actually unfolded, so that the form of the book is, as it were, an example of what may be meant by the content.



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