Monday, September 5, 2011

Quantum thinking

I just had a feature article for New Scientist magazine covering research showing some rather peculiar connections between the mathematics of quantum theory and patterns of human decision making. I don't want to say too much more here, but would like to clarify one very important point and give some links.

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.


3 comments:

  1. This is quite a fascinating angle on the issue of reasoning and logic. It is clear to anyone who thinks about it that the evolutionary process has produced heuristic logic, rather than deductive logic, as the fundamental ability of people. We have also developed this deductive formalism that we call deductive logic and which we revere as the primary way to find truth, but we use it very little in daily life.

    The idea that the heuristic process resulting from evolutionary development is able to be described mathematically (a) strengthens my belief that evolution does move organisms towards some type of optimised ability which conforms to mathematical rules, and (b) strengthens my suspicion that binary logic, on which most modern science (especially computer science) is based, is relatively primitive.

    Bi-valent logic (true/false logic) is very deeply embedded in our languages. We find it very difficult to think outside of this linguistic box.

    Some years ago I came across a book which explores the tri-valent logic of the Aymara people of South America. (Ivan Guzman de Rojas, "Logical and Linguistic Problems of Social Communication with the Aymara People", International Development and Research Centre, Canada, IDRC-MR66e, January 1985.) Virtually all other cultures and languages on Earth are based on bi-valent logic, and have a plethora of techniques to address the excluded middle. In English, these techniques include the use of words like should, could, would, might, unlikely, probably, maybe, possibly and more. In the Aymaran language, formal logic has 27 statements in place of the 8 we must use. (e.g. if then...else; and; or; nor; etc.)

    That is to say, by allowing a truth value of 'maybe' in addition to the standard 'true' and 'false', they more that triple the number of formal logical tools in their toolkit.

    de Rojas explains some of these additional tools as plausibility, possibility, liklihood, contingency, total ignorance, and doublt. Each of these are distinct formal statements, as different as 'and' and 'or' in bi-valent logic.

    So, here is the second insight that your blog entry gives me. If evolution is moving the human race towards some mathematically optimal heuristic approach to decision making (describable by Hamiltonian mathematics), and if along the path of that evolutionary movement, via some historical contingencies, logic becomes encoded in languages that fail to express the varied nature of those heuristics, are we trapped in a primitive mode of making arguments due to language. If we developed a new kind of formal logic in which, say, bi-valent and tri-valent logic are subsets, which approaches natural logic, which is describable by Hamiltonian mathematics, could we reformulate our social problems (and economic problems) in this new formal logic in such a way that the apparent conundrums of modern society become understandable?

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  2. The Physics of Finance RSS feed request to Before It's News

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  3. It is certainly understanable why a market maker would up the bid ask spread during volatile times if hundreds of trades could pass by before their quotes were taken by someone. How apple pay works with passbook?

    In the book "The Black Swan", there are terms coined for events in the world as coming from "mediocristan" and "extremistan". He noted in general the world is moving towards extrimistan, I suppose it is not surprising the markets are following suit.

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