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量子思维:为什么我们像夸克一样思考

2012-02-26  芝诺
 

量子思维:为什么我们像夸克一样思考

天朝不仁于2011-09-07 22:48:54翻译

 

为什么人类的经常会有一些模糊的想法,类似于冷还是热。通过量子物理的数学理论能够很好的解释这一切。

粒子的模糊性和行为的奇异性出奇的和人类怎么思考不谋而合。
THE quantum world defies the rules of ordinary logic. Particles routinely occupy two or more places at the same time and don't even have well-defined properties until they are measured. It's all strange, yet true - quantum theory is the most accurate scientific theory ever tested and its mathematics is perfectly suited to the weirdness of the atomic world.

量子的世界无法用通常的逻辑规则来解释。粒子在一个时间占据着两个或者多个地方。直到测量到它们以后,他们才有定义明确的性质。尽管这些很奇怪,但绝对是正确的。量子理论是经过测试最精确的科学理论。而他的数学理论很完美的适用于量子世界的奇异性。

Yet that mathematics actually stands on its own, quite independent of the theory. Indeed, much of it was invented well before quantum theory even existed, notably by German mathematician David Hilbert. Now, it's beginning to look as if it might apply to a lot more than just quantum physics, and quite possibly even to the way people think.
而这套数学理论实际上是独立于量子理论之外的。甚至可以说,大部分的数学理论在量子理论建立之前就存在了,尤其是德国数学家大卫·希尔伯特(David Hilbert)所建立的数学理论。现在,这些数学理论可以用在不只量子理论的领域,很可能用于研究人类思考的方式。
Human thinking, as many of us know, often fails to respect the principles of classical logic. We make systematic errors when reasoning with probabilities, for example. Physicist Diederik Aerts of the Free University of Brussels, Belgium, has shown that these errors actually make sense within a wider logic based on quantum mathematics. The same logic also seems to fit naturally with how people link concepts together, often on the basis of loose associations and blurred boundaries. That means search algorithms based on quantum logic could uncover meanings in masses of text more efficiently than classical algorithms.

我们所知道的人类思考方式通常不遵守经典的逻辑理论中的原则。例如,当有多种可能性的时候我们会犯很多系统的错误。例如,比利时布鲁塞尔自由大学的物理学家Diederik Aerts实际上已经用基于量子数学理论的更广泛逻辑来解释这些错误。同样的逻辑似乎也很自然的符合人类如何联系不同的概念,而这些概念都只有松散的联系和模糊的边界。这意味着基于量子逻辑的搜索算法能从大量的文字中比传统算法更高效的发现其中的含义。

It may sound preposterous to imagine that the mathematics of quantum theory has something to say about the nature of human thinking. This is not to say there is anything quantum going on in the brain, only that "quantum" mathematics really isn't owned by physics at all, and turns out to be better than classical mathematics in capturing the fuzzy and flexible ways that humans use ideas. "People often follow a different way of thinking than the one dictated by classical logic," says Aerts. "The mathematics of quantum theory turns out to describe this quite well."

从量子理论的数学说到人类思考的本质似乎有些荒唐。并不是说有量子在大脑里面,只是实际上不属于物理的“量子”数学能比传统的数学方法更好的抓到人类在使用想法时的模糊性和灵活性。“人类常常用不同的方法来思考,不只使用经典逻辑来进行决定。”Aerts说。“量子理论的数学方法证实能准确的描述这些逻辑。”

It's a finding that has kicked off a burgeoning field known as "quantum interaction", which explores how quantum theory can be useful in areas having nothing to do with physics, ranging from human language and cognition to biology and economics. And it's already drawing researchers to major conferences.

这个发现开始了一个称为“量子互动(quantum interaction)”的急速发展领域,来探索将如何量子理论用于和物理无关的方向,例如从人类的语言到感知再到生物学乃至经济学。现在已经有很多研究者开过大型的研讨会。

One thing that distinguishes quantum from classical physics is how probabilities work. Suppose, for example, that you spray some particles towards a screen with two slits in it, and study the results on the wall behind (see diagram). Close slit B, and particles going through A will make a pattern behind it. Close A instead, and a similar pattern will form behind slit B. Keep both A and B open and the pattern you should get - ordinary physics and logic would suggest - should be the sum of these two component patterns.

区分量子物理和经典物理的一种方法是可能性实现的不同。假设我可以向屏幕发射粒子,而这个屏幕前有一个带两条平行裂缝的挡板,而后研究屏幕上所出现的结果。关闭裂缝B,粒子会从A通过并且会成一个对应的形状。关闭A,粒子就会通过裂缝B并且形成类似的形状。而如果同时打开,应该会得到经典物理和逻辑所认为的两条对应的投影。

But the quantum world doesn't obey. When electrons or photons in a beam pass through the two slits, they act as waves and produce an interference pattern on the wall. The pattern with A and B open just isn't the sum of the two patterns with either A or B open alone, but something entirely different - one that varies as light and dark stripes。

但是量子世界并不遵守这些。当一束电子或者光子通过这两条裂缝,他们就像波纹一样并产生互相干涉的图案。A和B同时打开产生的图案并不是简单的单独开A或者B图案的和,而是完全不同的东西,类似于明亮条纹。


Such interference effects lie at the heart of many quantum phenomena, and find a natural description in Hilbert's mathematics. But the phenomenon may go well beyond physics, and one example of this is the violation of what logicians call the "sure thing" principle. This is the idea that if you prefer one action over another in one situation - coffee over tea in situation A, say, when it's before noon - and you prefer the same thing in the opposite situation - coffee over tea in situation B, when it's after noon - then you should have the same preference when you don't know the situation: that is, coffee over tea when you don't know what time it is.

干涉效果是很多量子现象的重点,并在希尔伯特的数学理论中找到了本质的描述。但是,这个现象可能超越了经典物理理论的范围,上面的例子就是违背了“确定性”原则。这种观点类似于你在某种特定的情况下比起一个行为更可能更喜欢另外一个。类似在情况A下比起茶更喜欢咖啡,假如说在正午以前。而你可能在相反的情况下偏向于相同的东西,就是说在中午以后,也就是情况B下比起茶同样更喜欢咖啡。所以在不确定的情况下你应该有同样的偏好,不知道确定时间的情况下,比起茶,更喜欢咖啡。

Remarkably, people don't respect this rule. In the early 1990s, for example, psychologists Amos Tversky and Eldar Shafir of Princeton University tested the idea in a simple gambling experiment. Players were told they had an even chance of winning $200 or losing $100, and were then asked to choose whether or not to play the same gamble a second time. When told they had won the first gamble (situation A), 69 per cent of the participants chose to play again. If told they had lost (situation B), only 59 per cent wanted to play again. That's not surprising. But when they were not told the outcome of the first gamble (situation A or B), only 36 per cent wanted to play again.

显然,人是不会遵守这条规则的。例如在1990年代初,普林斯顿大学心理学家Amos Tversky和Eldar Shafir用一个简单的赌博游戏来测试这种想法。参与者会有相同的概率赢得200美元或者输掉100美元,随后在第二轮的时候会被问是否继续参与游戏。当他们被告知赢了第一局的时候(情况A),69%的人选择继续参与。当他们得知输了的时候(情况B),只有59%的人想再玩一局。而不告诉第一局结果的人(情况A或B),只有36%的人会继续玩下去。

Classical logic would demand that the third probability equal the average of the first two, yet it doesn't. As in the double slit experiment, the simultaneous presence of two parts, A and B, seems to lead to some kind of weird interference that spoils classical probabilities.

经典逻辑认为第三种可能性应该是等于前面两种可能性的平均,而事实上不是。就像在双缝实验中,同时出现的两部分A和B,看起来导致了一些奇异的不符合经典可能性的干涉。

Flexible logic

灵活的逻辑

Other experiments show similar oddities. Suppose you ask people to put various objects, such as an ashtray, a painting and a sink, into one of two categories: "home furnishings" and "furniture". Next, you ask if these objects belong to the combined category "home furnishings or furniture". Obviously, if "ashtray" or "painting" belongs in home furnishings, then it certainly belongs in the bigger, more inclusive combined category too. But many experiments over the past two decades document what psychologists call the disjunction effect - that people often place things in the first category, but not in the broader one. Again, two possibilities listed simultaneously lead to strange results.


另外一个实验显示了同样的古怪的情况。假设你让其他人对物品进行分类,例如烟灰缸,油画和水槽分到两类中:“家居用品”和“家具”中。然后你问他们这些物品是否属于一个结合分类“家居用品和家俱”中。显然,如果“烟灰缸”或“油画”属于家居用品,那么它们当然属于一个大的包含更多的分类中。但是在过去20年的实验者通常会把物品放在第一个分类中,而不是更大的那个分类中。心理学家称之为“隔离效应”。再次的,两种同时出现的可能性导致了陌生的结果。

These experiments demonstrate that people aren't logical, at least by classical standards. But quantum theory, Aerts argues, offers richer logical possibilities. For example, two quantum events, A and B, are described by so-called probability amplitudes, alpha and beta. To calculate the probability of A happening, you must square this amplitude alpha and likewise to work out the probability of B happening. For A or B to happen, the probability amplitude is alpha plus beta. When you square this to work out the probability, you get the probability of A (alpha squared) plus that of B (beta squared) plus an additional amount - an "interference term" which might be positive or negative.

这些实验证明人类不是逻辑性的,至少按照经典逻辑的标准。但是Aerts认为,量子理论提供更丰富的逻辑可能性。例如,两个量子事件A和B,描述为所谓的概率幅,分别为alpha和beta。为了计算A发生的可能性,你必须对概率幅alpha进行平方运算。同样的也要对B进行类似计算。如果让A或者B发生时,那么概率幅是alpha加上beta。当你进行平方运算来得到可能性的时候,你得到结果是A的概率(alpha的平方)加上B(beta的平方)加上一个额外的总计--一个可能为正或者负的“干扰(物理学)”。

This interference term makes quantum logic more flexible. In fact, Aerts has shown that many results demonstrating the disjunction effect fit naturally within a model in which quantum interference can play a role. The way we violate the sure thing principle can be similarly explained with quantum interference, according to economist Jerome Busemeyer of Indiana University in Bloomington and psychologist Emmanuel Pothos of the University of Wales in Swansea. "Quantum probabilities have the potential to provide a better framework for modelling human decision making," says Busemeyer.

'干扰’让量子逻辑有着更好的灵活性。实际上,Aerts已经展示了很多经过证明的隔离效应的结果可以很自然的与一个在量子干涉中起作用的模型相匹配。根据布卢明顿的印第安纳大学的经济学家Jerome Busemeyer和在Swansea的威尔士大学的心理学家Emmanuel Pothos的理论,我们违反确定性原则的情况可以简单的用量子干涉进行解释。Busemeyer说,“量子概率可以提供更好的架构来为人类决定如何形成进行建模”。

The strange links go beyond probability, Aerts argues, to the realm of quantum uncertainty. One aspect of this is that the properties of particles such as electrons do not exist until they are measured. The experiment doing the measuring determines what properties an electron might have.

这些奇怪的联系超出了量子不确定性领域的可能性,Aerts表示。其中的一个方面是粒子的属性就像电子在测量到以前是不存在的。这个进行测量的实验决定了电子可能有什么属性。

Hilbert's mathematics includes this effect by representing the quantum state of an electron by a so-called "state vector" - a kind of arrow existing in an abstract, high-dimensional space known as Hilbert space. An experiment can change the state vector arrow, projecting it in just one direction in the space. This is known as contextuality and it represents how the context of a specific experiment changes the possible properties of the electron being measured.

希尔伯特的数学理论包含一种方法,这个方法可以表示电子的量子状态,即所谓的“量子态”。“量子态”就是一种在抽象的,通常成为希尔伯特空间的高维空间中的指示向量。一个实验能改变量子态方向,让它只在空间的一个方向上。这个被认为是语境性(contextuality)并且用来表示一个特定的实验内容如何改变的已测量电子可能的属性。

The meaning of words, too, changes according to their context, giving language a "quantum" feel. For instance, you would think that if a thing, X, is also a Y, then a "tall X" would also be a "tall Y" - a tall oak is a tall tree, for example. But that's not always the case. A chihuahua is a dog, but a tall chihuahua is not a tall dog; "tall" changes meaning by virtue of the word next to it. Likewise, the way "red" is defined depends on whether you are talking about "red wine", "red hair", "red eyes" or "red soil". "The structure of human conceptual knowledge is quantum-like because context plays a fundamental role," says Aerts.

同样,单词的含义随着内容的改变也有不同,语言就有了“量子”的感觉。例如,你可能认为一件物品是X,同样也是Y.那么“高的X”也是“高的Y”--高的橡树是高的树。但是这个并不总是正确的。一条吉娃娃是一条狗,但是一条高的吉娃娃不是高的狗。“高”在不同的词前面会有不懂的意思。同样的,“红”这个字在所谈论的“红酒”“红头发”“红眼睛”或者“红土”中有不同的定义。“人类概念知识的结构很像量子因为内容起着基本的作用”,Aerts说。

These peculiar similarities also apply to how search engines retrieve information. Around a decade ago, computer scientists Dominic Widdows, now at Google Research in Pittsburgh, Pennsylvania, and Keith van Rijsbergen of the University of Glasgow, UK, realised that the mathematics they had been building into search engines was essentially the same as that of quantum theory.

这些特殊的相似性也用于搜索引擎如何获得信息。大概在10年以前,在宾夕法尼亚匹兹堡google研究中心的计算机学家Dominic Widdows和英国格拉斯哥大学的Keith van Rijsbergen实现一种集成在搜索引擎内使用了量子理论的数学方法。

Quantum leaps

量子跃迁

It didn't take long for them to find they were on to something. An urgent challenge is to get computers to find meaning in data in much the same way people do, says Widdows. If you want to research a topic such as the "story of rock" with geophysics and rock formation in mind, you don't want a search engine to give you millions of pages on rock music. One approach would be to include "-songs" in your search terms in order to remove any pages that mention "songs". This is called negation and is based on classical logic. While it would be an improvement, you would still find lots of pages about rock music that just don't happen to mention the word songs.

意识到一些关于量子概念并没有花太多的时间。一个迫切的挑战是让电脑有能力和人类一样获得数据的含义,Widdows说。如果你想一个类似关于地理和岩石形成的“岩石故事(tory of rock)”的主题,你肯定不想让搜索引擎给出上百万页关于摇滚音乐的结果。一种方法可以是在搜索关键字中包括“-song”就可以移除结果中出现“song”的页面。这个称为基于经典逻辑的否定。就算这个功能可能会被开发,你也依旧会发现很多关于摇滚音乐的页面,尽管这些页面中没有出现“song”这个单词。

Widdows has found that a negation based on quantum logic works much better. Interpreting "not" in the quantum sense means taking "songs" as an arrow in a multidimensional Hilbert space called semantic space, where words with the same meaning are grouped together. Negation means removing from the search pages that shares any component in common with this vector, which would include pages with words like music, guitar, Hendrix and so on. As a result, the search becomes much more specific to what the user wants.

Widdows发现使用基于量子逻辑的否定可以更好的工作。在量子语境中的解释“不”意为把“song”作为在称为语义环境的多维希尔伯特空间中的标志,所有有相同意思的单词都集中在这个标志附近。否定意味着移除基于这个向量的所有同样含义组件,就像含有音乐,吉他或者亨德里克斯的页面。作为结果,搜索会更好地给用户提供想要的结果。

"It seems to work because it corresponds more closely to the vague reasoning people often use when searching for information," says Widdows. "We often rely on hunches, and traditionally, computers are very bad at hunches. This is just where the quantum-inspired models give fresh insights."

“这开起来是可行的,因为更符合人平常搜索信息的的模糊想法。”Widdows说。“我们通常基于直觉,而通常电脑很不擅长于这种感觉。这就是量子激发模型所给的新鲜的洞察能力。”

That work is now being used to create entirely new ways of retrieving information. Widdows, working with Trevor Cohen at the University of Texas in Houston, and others, has shown that quantum operations in semantic Hilbert spaces are a powerful means of finding previously unrecognised associations between concepts. This may even offer a route towards computers being truly able to discover things for themselves.

这个方法正在被用于编写一个全新检索信息的方法。Widdows和休斯敦德州大学的Trevor Cohen以及其他合作者已经说明了在希尔伯特语义空间中的量子运算能够更好的发现以前未发被现的概念之间的联系。这个可能提供一个能让电脑真正靠自己发现事物的途径。

To demonstrate how it might work, the researchers started with 20 million sets of terms called "object-relation-object triplets", which Thomas Rindflesch of the National Institutes of Health in Bethesda, Maryland, had earlier extracted from a database of biomedical journal citations. These triplets are formed from pairs of medical terms that frequently appear in scientific papers, such as "amyloid beta-protein" and "Alzheimer's disease", linked by any verb that means "associated with".

为了证明是怎么工作的,研究者从称为“对象联系三联体(object-relation-object triplets)”含有20,000,000的术语对集合开始。马里兰州的贝塞斯达的国立卫生研究院的Thomas Rindflesch从生物医学期刊数据库中提取到上述集合。这些三联体由一些常见于科学论文的医学术语如“amyloid beta-protein”或者“阿尔茨海默氏症”组成。这些医学术语可以联系到任何“与...有关”的动词。

The researchers then create a multi-dimensional Hilbert space with state vectors representing the triplets and applied quantum mathematics to find other state vectors that, loosely speaking, point in the same direction. These new state vectors represent potentially meaningful triplets not actually present in the original list. Their approach makes "logical leaps" or informed hypotheses about pairs of terms, which are outside the realms of classic logic but seem likely promising avenues for further study. "We're aiming to augment scientists' own mental associations with associations that have been learned automatically from the biomedical literature," says Cohen.

研究者然后创造了一个含有表示三联体的状态向量多维的希尔伯特空间,使用量子数学方法来寻找其他的状态向量,宽松的说,这些状态向量指向相同方向的。这些新的状态向量表现出一些传统列表中没有的具有潜在意义的三联体。他们所做到造成了“量子跃迁”或着是关于词对的假说,这些假说已经超出了经典逻辑的领域,但是看起来预示着以后研究的新方向。“我们的目的是通过自动学习到的生物论文之间的联系来增加科学家的心理联想,”Cohen说。

He and his colleagues then asked medical researchers to use the approach to generate hypotheses and associations beyond what they could come up with on their own. One of them, molecular biologist Graham Kerr Whitfield of the University of Arizona in Phoenix, used it to explore the biology of the vitamin D receptor and its role in the pathogenesis of cancer. It suggested a possible link between a gene called ncor-1 and the vitamin D receptor, something totally unexpected to Kerr Whitfield, but now the focus of experiments in his lab.

然后他和他的同事请求医学研究者使用这个方法来产生超出了他们能够自我提出的假说和关联。他们中一人,凤凰城亚利桑那大学的分子生物学家Graham Kerr Whitefield使用这个方法来探索关于维他命D的受体以及它在癌症发病机理中的作用。它表明一种可能在ncor-1和维他命D受体之间的关联。一些结论完全出乎了Kerr Whitfield的意料,但是现在成了他实验室实验的核心。

Yet one big question remains: why should quantum logic fit human behaviour? Peter Bruza at Queensland University of Technology in Brisbane, Australia, suggests the reason is to do with our finite brain being overwhelmed by the complexity of the environment yet having to take action long before it can calculate its way to the certainty demanded by classical logic. Quantum logic may be more suitable to making decisions that work well enough, even if they're not logically faultless. "The constraints we face are often the natural enemy of getting completely accurate and justified answers," says Bruza.

但是还有另一个问题:为什么量子逻辑符合人类行为?澳大利亚布里斯班昆士兰理工大学Peter Bruza提出一种原因,认为我们有限的大脑被复杂的环境压制着,因为如果按照正常逻辑计算所获得结果会花更多的时间。量子逻辑可能更加适合起作用的决定,尽管这些决定不是逻辑完美无缺的。“我们通常面对的约束是完全精确的获得自然中的敌人并判断结果,”Bruza说。

This idea fits with the views of some psychologists, who argue that strict classical logic only plays a small part in the human mind. Cognitive psychologist Peter Gardenfors of Lund University in Sweden, for example, argues that much of our thinking operates on a largely unconscious level, where thought follows a less restrictive logic and forms loose associations between concepts.

这个概念符合一些心理学家的观点,这些心理学家认为严谨的经典逻辑在人类想法中只占很小的部分。例如,瑞典隆德大学的Peter Gardenfors认为我们大多数的思维过程是在很大的无意识的层面完成的,在这个层面想法通常按照不严谨的逻辑并在概念之间形成了松的关联。

Aerts agrees. "It seems that we're really on to something deep we don't yet fully understand." This is not to say that the human brain or consciousness have anything to do with quantum physics, only that the mathematical language of quantum theory happens to match the description of human decision-making.

Aerts同意这个观点“看起来我们的想法工作在一些我们不是完全理解的深层事物上。”这个并不是说人类的大脑或者意识有按照量子物理工作的事物,而是描述量子物理理论的数学语言恰好符合人类做决定的描述。

Perhaps only humans, with our seemingly illogical minds, are uniquely capable of discovering and understanding quantum theory. To be human is to be quantum.

或许只有人类有着看上去不合逻辑的大脑,具有发现和理解量子物理的独一无二的能力。作为人类也同时成为量子。

 
 
 

周易、太极代数与直觉思维

(一) 周易与太极代数
本人在《周易研究》1992年第一期(总第十一期)上发表了"太极代数"一文。
太极代数源于周易是显而易见的。读者可以看出,一元三级太极模型源于"伏羲八卦次序图",一元六级太极模型源于"伏羲六十四卦次序图"。而二元、三元太极模型只是将一维的"伏羲次序图"推广到二维和三维。并由此推出三维以上的多维太极模型。
太极代数的二分法源于《周易 系辞》的"太极生两仪,两仪生四象,四象生八卦"。太极数的二进制表示法也依照易卦阴阳两爻的二值逻辑,因此也同易卦一样具有简明、直观的特点。
太极代数中"隶属程度"的概念,可以使我们更深刻地理解汉易中,"亲比"、"得比"、"相应"等不仅反映出儒家的"中庸"思想,同时也符合现代科学的系统思想。
易中"太极"这一概念,非常接近我们今天从最广义的意义上理解的"系统"概念。
我们今天应用系统思想和系统方法,针对提出的目标和问题作出系统模型,求得解决的方案,以指导我们的行动,这和古人应用《周易》以解决疑难问题是类似的。
正因为《周易》极大地影响了东方人的思维方式,所以,源于《周易》的太极代数必然反映了东方思维方式中的某些本质的特点,使得太极代数不同于
(二) 定性与定量 
《周易》中蕴含着精辟的哲学思想,这一点今天已是人们不争的共识。
然而,当初《周易》除了担负着哲学的任务,还担负着科学的使命。哲学只要求定性的判断,科学还要求有定量的分析。
太极代数采用一分为二的方式层层推进,逐步达到令人满意的精度要求。
一分为二的方法,在人们进行思维判断时屡屡采用。但是人们仅仅用它作为"定性"的方法,以判断是非、曲直、真假、善恶、美丑……然而,从科学的立场出发,仅有"定性"的判断是远远不够的,还需要"定量"的分析。太极代数采用层层"定性"的方法,逐步逼近"定量"的要求。
例如,当班主任说某学习成?quot;不好"时,这只是一个定性的判断,这是在一元一级(两仪)层次上,如果说该生学习成绩"较差"。意思是说他在学习成绩不好的学生中还不算是"很差"的,这就不仅是一个定性的判断,而是其中已经包含有一点"定量"的成分了。即在"很好、较差、很差"这四个等级中他属于第三等级。这是在一元二级太极(四象)层次上,如果班主任将该学生六门学科的每一门都进行一次"好"与"不好"的定性的判断,根据太极代数可以将他的成绩列出,例如为100111,它是在S16的64个等级中列第40位。如果将该生每一门学科成绩进行二次定性,经太极代数的"合运算"例如为100111,000011,即在S26的2,816个等级中列第2,500位,其定量的程度已相当高了。
因此,可以说,太极代数通过层层定性的方法达到适当的定量化,能够使许多不严谨、不科学、缺少量化的领域(如社会科学、思维科学等)有可能加强定量化,从而更为科学化。 
(三)精确与模糊
太极代数逐步逼近的终点并不是绝对的精确,而只是达到适当(令人满意)的精度为止。因此,太极代数从本质上说是一种模糊数学。或者说,模糊性是太极代数的基本特性。
模糊!不精确!这并不是太极代数的缺陷,而恰恰是太极代数的优点所在。
在很多情况下,绝对精确是完全必要的。这时,我们可以采用西方的、机械分解的、微观的思维方式以及已掌握的数学方法。太极代数绝对没有取而代之的意图。 
但是,也在很多情况下,绝对精确不仅是完全不可能的,而且常常是没有必要的,有时甚至是有害的。这时,"模糊"常常不仅是可行的,甚至是更好的选择。
在现实生活中,很多系统十分庞大,不仅包含诸多的因素,而且每一个因素又包含诸多的变量。这时,如果要求每一个因素的每一个变量都十分精确,计算工作量是相当大的。尽管电子计算机的产生和发展大大提高了运算速度,使得许多人们不可能完成的运算成为可能,但是仍然有很多计算是现代电子计算机也无法承受的。 
例如,下棋是一种数学性很强的游戏。棋手每下一步棋,都要经过认真的计算。一个好的棋手往往能够计算出以后的十几步甚至几十步棋。最近,名为"更深的蓝"的大型电子计算机战胜了国际象棋世界冠军卡斯帕罗夫。据一些与电子计算机较量过的国际大师们介绍,与计算机对弈必须有很大的耐心,因为"计算机下得太慢了"。
中国象棋比国际象棋要复杂一些。吴韧是研究中国象棋计算机的权威,他研制的名为"NKW"的计算机是目前该领域中最好的。记者采访吴先生时观看了一盘人机对局。NKW的对手是曾获全国高校中国象棋赛冠军的石刚。经过32分5秒的战斗,NKW败下阵来。
吴先生说:"人总是比计算机聪明。"并且指出计算机与人的根本不同在于"人有直觉","能够整体的把握棋势"。这说明人更为深谋远虑,能够预想更多步以后的棋势。这难道不需要更多的计算时间吗?难道人脑的运算速度比计算机更快吗?显然不是。
人虽然在某一个具体的、局部的计算上不如计算机,但在棋势整体的"把握"上优于计算机。这种对整体把握并不是局部精确计算的简单累加。否则,在局部精确计算方面不如计算机的人脑,怎么可能在累加后反而超过计算机呢?这种对于整体的把握显然采用了另外的方法。
这"直觉"就是另外的方法。
直觉是什么?是说不清、道不明,不可捉摸的吗?不是。 
一个没有经验的棋手,不可能凭"直觉"把握整个棋势。
人的所谓"直觉",是知识和经验的积累,是在瞬间对诸多复杂因素的诸多复杂变化的综合判断。这种判断的依据是"模糊"的。正因为它模糊,所以简单明了,使人可以在较短的时间里得出结论。
同时,也正因为它模糊,所以容易出现差错。绝大多数人是不能战胜NKW的,他们的直觉并不一定引导他们走向胜利,这是因为"直觉"往往缺乏充足的依据,这种定性判断的先天不足就是缺乏定量分析。
直觉常常令人感到作捉摸不定,虽然没有充足的理由来肯定它,可没有充足的理由来否定它。所以人们一说到"这是一种直觉"时,就意味着到此为止,不需要再做更多的解释了。
太极代数就是要对人们的这种所谓"直觉"思维做进一步的分析研究。看看"直觉"到底是怎样对诸多复杂因素的诸多复杂变化进行综合从而在整体上"把握"事物的,同时给以科学的数学描述。
仅有模糊是不够的,仅有精确也是不够的。只有在模糊和精确之间找到一个合适的点,即"令人满意的精度"。这正是太极代数中一个重要的概念。

 

(四)太极代数与直觉思维
人们在生活中总是面对不断变化的实际问题,思考、计算、判断,寻找对策,然后作出抉择,这正如下棋一样。这时我们可以依赖"直觉",也可以应用太极代数。
当面对一个复杂的问题时,我们可以把它作为一个多元系统来考察。
首先,我们要明确系统的"元"数,从我们的考察目的出发,找出影响系统的各个因素。保证一切与之相关的因素包括在系统之内,不要有所遗漏;同时将不相关的因素排除于系统之外。
其次,我们要明确系统的边界,确定各相关因素变量的最大值与最小值。将不相关的变量值排除于系统边界之外。
接着要确定在这些因素中,哪些是最主要的,哪些是次要的,将这些因素按照主次排出一个顺序。有些因素的主次顺序是一目了然的,可是常常一些因素的主次没有明显的顺序关系。这时我们可以从某种特定的角度来看,也许顺序关系就比较明显了。依此可以制订出一个排序的准则。因为太极模型要求元素必须是有序的。此时必须牢记我们自己制订的排序准则,只是在这一前提下模型才是成立的。如果排序准则变化了,模型也必须随之而变,才能保证它的正确性。当我们不能确定某一排序是绝对正确时,我们可以从不同的角度出发,分别制订不同的排序,建立起相应不同的太极模型,最终将得到不同的对策,供我们选择。仍以下棋为例,不同的排序准则能够体现不同棋手的风格特点。
接下来我们要开始具体分析了。当然是从一级子太极入手。将每个因素作为一元,M个因素就有M元,对它们分别作一分为二的"定性"判断,就会得到2m 个方案可供选择。这时,也许我们已经可以淘汰一批方案,留下一个或几个方案。但是这只是粗略的方案,其精确还不能令我们满意。于是可以将这几个子太极作进一步的考察。已经淘汰的子太极可以放弃不再考虑,这就大大减少了计算量。正如围棋中棋手在下一个棋子时,并不需要将棋盘上所有空着的点都考虑计算一番,"直觉"能够告诉他只有哪些部分才是棋局的关键所在,除此以外的部分是想也不想的。
当我们层层筛选,最后只剩下几个乃至一个方案,而且这个方案的精确度已经令人满意时,先不要忙于作出决定。再回过头来考虑一下,我们原来制订的排序准则有没有问题,是否换一个角度出发,产生另外的排序,从而产生另外的方案。好像棋手在下围棋时,已经找到了最佳攻击点,这时仍不急于落子,而是再从防守的角度来考虑,自己的棋是否还有弱点,是否给对手留下了对自己更为严厉的攻击点。 
随着排序准则的改变,太极模型将提供不同的方案。将几套方案进行比较,也许还需要找出新的元素,建立新的太极模型,然后再来分析、判断、定性、定量……最终确定自己的决策。
如此作出决策,也许比单?quot;直觉"要慢一些,却更可靠、更科学
将来根据"太极代数"的思想编制出"太极思维"程序软件,不仅能面对庞大、复杂的问题迅速作出正确、科学的抉择,而且开发出真正意义上的"人工智能"机器人也不是不可能的。

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