I was inspired to write this article a couple years ago at a brain storming session held by the European Commission. Participants were supposed to be bold and propose radical visions about where the most promising avenues for research lay in the near future (this was in the context of information and computing technology). One Belgian researcher gave a fascinating talk on the application of quantum mathematics to human decision making, claiming that quantum logic fits actual human behaviour more closely than does classical logic. There are many famous "anomalies" -- such as the Ellsberg Paradox -- where people systematically violate the laws of classical logic and probability when making decisions of economic importance. The Belgian researcher explained that the quantum formalism is able to accommodate such behaviour, and was therefore surprisingly useful in understanding how people organize and use concepts.
What struck me then was the derision with which several other scientists (physicists) greeted this suggestion, while completely mis-understanding what the man had said. One physicist came close to screaming that this was "embarrassing mumbo jumbo" somehow linked to the idea that quantum physics underlies brain function (the idea proposed over a decade ago by Roger Penrose in his profound book Shadows of the Mind). He had dismissed the idea so quickly that he hadn't listened. The Belgian physicist had actually pointed out that he wasn't at all suggesting that quantum physics plays a role in the brain, only that the mathematics of quantum physics is useful in describing human behaviour.
This is a very important point -- the mathematics of quantum theory (the mathematics of Hilbert spaces) isn't identical with the theory and somehow owned by it, but stands quite independent of that theory and existed for at least a century before quantum theory was invented. The Belgian was saying -- this mathematics which turned out to be so useful for quantum physics is now turning out to be profoundly useful in quite another setting.
The New Scientist article is just a very brief introduction to some of the work. A few other things I found utterly fascinating while researching the article are:
1. This research paper called A Quantum Logic of Down Below which falls somewhere in between philosophy, psychology and computer science. The second author Dominic Widdows is a computer scientist at Google working on information retrieval. The paper essentially argues that philosophers historically devised classical logic and then took it as a model for what human logic must be or at least should be. They suggest this was the wrong way around. Pure logic isn't our best example of reasoning. The best example of reasoning systems is people, and so a logic of what reasoning is and can be ought to start with people rather than mathematics. This is a powerful idea. As the authors put it:
... what reasoning is (or should be) can only be read off from what reasoners are (and can be). Such a view one finds, for example in [Gabbay and Woods, 2001] and [Gabbay and Woods, 2003b], among logicians, and, also in the social scientific literature [Simon, 1957, Stanovich, 1999, Gigerenzer and Selten, 2001b]. Here the leading idea of the “new logic” is twofold. First, that logic’s original mission as a theory of human reasoning should be re-affirmed. Second, that a theory of human reasoning must take empirical account of what human reasoners are like – what they are interested in and what they are capable of.They then go on to argue that whatever the accurate logic of human reasoning is, it is more similar to quantum logic than to classical.
2. A second fascinating paper is more technical and describes some applications of this in computer science and information retrieval. Here the idea is that if people create concepts and texts and organize them using a quantum-style logic, then search methods based on classical logic aren't likely to search such conceptual spaces very effectively. This paper describes applications in which literature search can be improved by using quantum logic operations. Most interesting (and I did mention this in the New Scientist piece) is the use of quantum operations to generate what might be closely akin to "hunches" or "guesses" about where in a mass of textual data interesting ideas might be found -- guesses not based on logical deduction, but on something less tightly constrained and ultimately more powerful.
