A quantum logic

Peter and Rupert pass in the hallway of an Australian ICT research organisation. Peter, a research scientist utters to Rupert, the business development manager, “How is it going with John?” This utterance is the tip of an ice-berg rich in implicit associations. Due to their shared context, Peter and Rupert both know that “John” refers to “John Smith” of “ACME Corp”, who is negotiating a commercial license for “Guidebeam”, a next generation web-based search technology.

In the not so distant future our information environment will feature all sorts of devices and displays. Imagine the existence of a technology looming in the background which processes the above utterance, draws appropriate context sensitive associations in order to flesh it out, and thereafter uses the result to query for emails, license documents, podcasts of relevant conversations and so on, and tacitly retrieves these to prime Rupert and Peter's immediate information environment.

For example, the licence document and associated emails could be brought up on the wall display should they be needed for further reference in Peter and Rupert's spontaneous hallway discussion.

The above scenario illustrates that human beings are adept at drawing context-sensitive associations and inferences across a broad range of situations ranging from the mundane to the creative inferences that lead to scientific discovery.

Such reasoning has a strong pragmatic character and is transacted with comparatively scarce cognitive assets. The question is how to get technology to reliably replicate this? The need for such technology is pressing. Paradoxically, the information explosion is leading to diminished awareness. Expertise is becoming ever more specialised: individuals, groups, communities, enterprises are consequently becoming increasingly insular.

We need computational systems which have the capability to enhance our awareness, for example, by suggesting associations in context that we could make, but increasingly don't, as we generally lack the cognitive resources to do so. We believe that information processing technology has to manipulate context sensitive meanings which accord with those we harbour.

In other words, the “meanings” manipulated by the technology should be cognitively motivated. This point of departure readily gives rise to the question of how to get access to the meanings we carry in our heads and have technology manipulate them to good effect.

The field of cognitive science has recently produced an ensemble of models which have an encouraging, and at times impressive track record of replicating human information processing, such as human word associations norms. For example, primed with the word “Beatles” a common associate produced by human subjects may be “band”, or “John Lennon”. These models are generally referred to as “semantic space models”. The term “semantic” derives from the intuition that the meaning of a word is derived from the “company it keeps'', a famous quote originally from the linguist J.R. Firth (1890-1960).

For example, the words “mobile” and “cellular” would exhibit a strong association in semantic space as the distribution of words they co-occur tends to be similar, even though the two words almost never co-occur themselves.

Although the details of the individual semantic space models differ, they all process a corpus of text and “learn” representations of words in high dimensional space. That is, the meanings of words are given a geometric representation. Semantic space models are interesting in light of the scenario presented above as they open the door to gaining some operational command of the meanings we carry around in our heads together with mechanisms to replicate our ability to draw relevant context-sensitive associations.

One of the big questions is how to effectively model the interplay between meaning, context and such human pragmatic inference mechanisms. Surprisingly, quantum mechanics may provide some innovative and ground breaking inspiration in relation to this challenging question.

Recently a highly speculative but potentially far reaching discovery was made by the theoretical physicist Diederik Aerts and his collaborators. In a letter to the editors of a journal dealing with mathematical physics, they showed the formalisation of quantum mechanics (QM) shows very strong connections with the mathematical basis of semantic space models.

What are the implications of this intriguing connection given that semantics space models have an established track record of cognitive compatibility with human across a variety of information processing tasks?

In order to provide some intuition about how QM relates to human semantic space, consider the word “suit”. In isolation it is ambiguous - it may refer to an item of clothing, a legal procedure, or even a deck of cards. However, when seen in the context of words such as "wore" or “grey”, the ambiguity resolves into the sense of the word dealing with clothing.

The connection with QM is the following. Consider an electron moving towards a TV screen. Before it impinges on the screen it is a set of potentialities, that is, a collection of all the possibilities of hitting each and every place on the screen. In other words, before impingement, all these possibilities are “superimposed”. The quantum state includes all of them, and then, in the atemporal process of quantum collapse, one of the possibilities is singled out and becomes actual - the electron impinges at a specific location on the screen.

Now going back to our example word “suit”. In human memory the meaning of this word is like the electron in the following way. In the past, this word has been seen and heard in many circumstances, for example, “John wore a grey suit”, Thjese become superimposed in human memory as different potential meanings, or senses, of the word “suit”. When we see the word “suit” in the context of other words, i.e., its “company”, the superimposed potential meanings of this word “collapse” onto a specific one. At that point the meaning is resolved which is akin to the electron becoming actual at a specific location.

Human beings do this effortlessly, which may suggest the process is happening below the symbolic level of cognition. This raises the speculation that something like a quantum logic operating on semantic space may provide the sought after model capturing the interplay between meaning, context and human sub-symbolic reasoning mechanisms. (The author was recently awarded a three-year grant from the Australian Research Council to pursue this line of research.)

Some may view this is as drawing a very long bow, and QM can only ever being used as an analogy. It would be misunderstanding to assume QM has anything to do with something physical. Strident philosophical debate aside, QM is an abstract framework. It is the responsibility of a specific theory at hand to plug into it, and then the handle of the abstract framework is cranked.

As it is an abstract framework, this opens the door for its application outside of physics, and in recent years QM has increasingly permeated other areas. In March, 2007, the first Quantum Interaction symposium will be held drawing together for the first time researchers from all over world who are using QM outside of physics.

Presentations will be given detailing how QM interacts with logic, artificial intelligence, meaning, cognition, search, and even finance (“Quantum Econophysics”). It is very significant the highly reputed and distinguished philosopher of science, Emeritus Professor Patrick Suppes (Stanford University) agreed to present an invited talk on QM and the brain. This shows that speculation about quantum effects in the brain has some serious traction way beyond the circle of new age literature.

Some, perhaps many, physicists may frown on such developments and deem it an abuse of QM.

Time will tell whether a “deep result” using QM outside of physics is possible. The author has an open mind and believes it just may be possible. It could be such a result may manifest in relation to human memory.

Professor Douglas Nelson will present a paper at the Quantum Interaction symposium titled “Entangled associative structures and context”. After extensively studying human word association norms for over 30 years, he puts forward the intriguing hypothesis that word associates in human memory behave like particles exhibiting quantum entanglement. Quantum entanglement is when a measurement on a particle, e.g., measuring its position, causes the instantaneous quantum collapse of another particle even though they may be separated by an astronomical distance.

When a human subject is cued by a word in a memory experiment, the probability they will recall a target word depends on the number of links between its associates. By way of illustration, say the cue word is “planet”. There is a probability that the word “earth” will be recalled. In memory, “earth” has a link with “moon”, but there is no link back from “moon” to the cue word “planet” as this word is not typically recalled when subjects are cued with the word “moon”. (After all, the moon isn’t a planet) The “earth - moon” link nevertheless contributes to remembering the word “planet”.

Nelson refers to this as “spooky action at a distance”, the intuition here being that “moon” and “planet” are distant as, in memory, there is not a directed link from “moon” back to “planet”. Nelson argues that such findings are inconsistent with widely held views in psychological science and support the incorporation of quantum mechanics in our attempts to understand how prior knowledge interacts with recent experience and context.