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.


17 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?

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

    Hi Mark Buchanan,

    My name is Ben Chasteen and I'm the Science editor at Before It's News www.beforeitsnews.com. Our site is a People Powered news platform with over 4,000,000 visits a month and growing fast. We like to think of our selves as the "You Tube" of news.

    We would be honored if we could republish your blog RSS feed in our Science category. Our readers need to read what your The Physics of Finance blog has to say.

    Syndicating to Before It's News is a terrific way spread the word and grow your audience. Many other organizations are using Before It's News to do just that. I just need you to reply with your permission to do so. Please include the full name and email of the person who will be attached to the account, and let me know the name you want on the account (most people have their name or their blog name).

    You can also have any text and/or links you wish appended to the end or prepended to the beginning of each of your posts on Before It's News. Just email me the text and links that you want at the beginning and/or ending of each post. If you know html you can send me that. If not, just send me the text and a link to your site. It should be around 200 characters or less (not including links).

    You can, if you like, create a custom feed for Before It's News that includes multiple links back to your blog or web site. We only require that RSS feeds include full stories, not partial stories. We don't censor or edit work.

    Thank you,

    Ben Chasteen
    Editor, Before It's News

    ben@beforeitsnews.com
    www.beforeitsnews.com

    ReplyDelete
  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.

    ReplyDelete
  4. Positive site, where did u come up with the information on this posting?I have read a few of the articles on your website now, and I really like your style. Thanks a million and please keep up the effective work.Best Website Designer Denver

    ReplyDelete
  5. Fine jewels stir passion in many people’s hearts, regardless if it is being purchased for themselves or for others.globo esporte

    ReplyDelete
  6. It might be a challenge for you if you have this very strong intention of having an idea of the methods on how to get rid of pimples overnight. Albeit, a goal that is achievable if you are in possession of proper pimple approach and products. Builders In Meath

    ReplyDelete
  7. Any of you may never have heard of Urdu Poetry before, and even fewer of you may know what Urdu Poetry actually is. This article is a humble attempt to give you some basic knowledge about Urdu Poetry. Μακριά φορέματα

    ReplyDelete
  8. I read this magazine and this article discuss really good topic i like it thanks for share it capstone projects ideas .

    ReplyDelete
  9. Forte School of Music is providing Music Lessons howick , New Zealand. Forte School is best in Music , Singing , Guitar and Piano Classes. Contact us now 09 534 2223

    ReplyDelete
  10. I love reading through a post that will make men and women think. Also, thanks for allowing me to comment!Job posting software

    ReplyDelete
  11. Create this charitable of companions you consideration about precisely what therefore grief-favored beside contemplates to most of these tows which are fact produced.perfumes importados masculinos

    ReplyDelete
  12. Ben started playing at betway casino online with his spins and won a couple of euros. He continued to play and finally landed 3 scatters to enter the jackpot wheel. First and the second wheel cleared and his heart beat was raising as he entered the final wheel.

    ReplyDelete

  13. Pretty article! I found some useful information in your blog, it was awesome to read, thanks for sharing this great content to my vision, keep sharing.i also want to share about One of the best sap hana tutorial for beginners . expecting more articles from you.

    ReplyDelete
  14. Nice Blog !!

    Are you for in a situation where too exhausted to drive back to home like returning home from a party, long work schedule? Safe driver Dubai is ready to help you…

    ReplyDelete
  15. What’s up, yes this paragraph is really good and I have learned lot of things from it concerning blogging.
    고스톱

    ReplyDelete
  16. It’s actually a nice and useful piece of information.
    I am glad that you simply shared this helpful information with us.
    Please stay us up to date like this. Thanks for sharing.
    스포츠토토

    ReplyDelete
  17. Wow! This could be one of the most useful blogs we have ever come across on the subject. Actually excellent info! I’m also an expert in this topic so I can understand your effort.
    토토사이트

    ReplyDelete