芝诺 / 我的图书馆 / 量子思维:为什么我们像夸克一样思考




2012-02-26  芝诺


天朝不仁于2011-09-07 22:48:54翻译



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.


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."


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.


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。


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.


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.


Flexible logic


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.


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.


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.


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.


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.


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


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.


"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."


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.


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.


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




(一) 周易与太极代数
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。
(二) 定性与定量 


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。




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