Go into any bookstore and you can find books on ‘quantum computation’, ‘quantum healing’, and even ‘quantum golf’. But quantum mechanics describes stuff in the microworld of subatomic particles, right? What good is it to apply it to macroscopic stuff like computers and golf, let alone psychological stuff like thoughts, feelings, and ideas?
Perhaps it’s being applied as an analogy, to help make something complicated easier to understand. But quantum mechanics itself is complicated; it’s one of the most enigmatically complex theories humans have ever come up with. So how could we better understand something by drawing an analogy to quantum mechanics?
Observer Effect in Physics
I don’t know about ‘quantum healing’ or ‘quantum golf’, but I started to think about a possible connection between quantum theory and how people use concepts in 1998 when I was talking to a graduate student in physics at an interdisciplinary research center in Belgium. The student, Franky, was telling me about some of the paradoxes that inspired quantum mechanics. One paradox is the observer effect: we can’t know anything about a quantum particle without performing a measurement of it, but quantum particles are so sensitive that any measurement we might make unavoidably changes the state of the particle, indeed generally destroys it entirely!
Entanglement Effect in Physics
Another paradox is that quantum particles can interact in such a profound way that they lose their individual identity and behave as one. Moreover, the interaction results in a new entity with properties different from either of its constituents. When this happens it is not possible to perform a measurement of one without affecting the other, and vice versa. A whole new kind of mathematics had to be developed to deal with this kind of merging together or entanglement, as it is called. This second paradox -- entanglement -- may be deeply related to the first paradox -- the observer effect -- in the sense that when the observer makes a measurement, the observer and the observed may become an entangled system.
I noted to Franky that similar paradoxes arise with respect to the description of concepts. Concepts are generally thought to be what enable us to interpret situations in terms of previous situations that we judge as similar to the present. They can be concrete, like CHAIR, or abstract, like BEAUTY. Traditionally they have been viewed as internal structures that represent a class of entities in the world. However, increasingly they are thought to have no fixed representational structure, their structure being dynamically influenced by the contexts in which they arise.
For example, the concept BABY can be applied to a real human baby, a doll made of plastic, or a small stick figure painted with icing on a cake. A songwriter might think of BABY in the context of needing a word that rhymes with maybe. And so forth. While in the past the primary function of concepts has been thought to be the identification of items as instances of a particular class, increasingly they are seen not just to identify but to actively participate in the generation of meaning. For example, if one refers to a small wrench as a BABY WRENCH, one is not trying to identify the wrench as an instance of BABY, nor identify a baby as an instance of WRENCH. Thus concepts are doing something more subtle and complex than internally representing things in the external world.
What this ‘something more’ is and how it functions may well be the most important task facing psychology today; it is vital to understanding the adaptability and compositionality of human thought. It is vital, for instance, to understanding how paintings, or movies, or passages of text, come together to have a meaning for us that is not just the sum of their words or other compositional elements.
To get a handle on this ‘something more’ requires a mathematical theory of concepts. Psychologists tried to develop a mathematical theory of concepts for decades. Although they did pretty well at coming up with theories that could describe and predict how people deal with single, isolated concepts, they were not able to come up with a theory that could describe and predict how people deal with combinations or interactions amongst concepts, or even a theory that could describe how their meanings flexibly shift when they appear in different contexts. And the phenomena that made it difficult to come up with a mathematical theory of concepts are very reminiscent of the phenomena that made it difficult to come up with a theory that could describe the behavior of quantum particles!
Observer Effect for Concepts
At the heart of the paradoxes of both quantum mechanics and concepts is the effect of context. In quantum mechanics there is the notion of a ground state, the state a particle is in when it is not interacting with any other particle, i.e., when it is not affected by any context. This is a state of maximum potentiality because it has the possibility of manifesting a multitude of different ways given the different contexts it could interact with. The instant a particle starts to leave the ground state and fall under the influence of a measurement, it trades in some of this potentiality for actuality; a measurement of it has been made and some aspect of it is better understood. Similarly, when you are not thinking of a concept, such as the concept TABLE a minute ago, it may have existed in your mind in a state of full potentiality. At that moment, the concept TABLE could apply to a KITHCEN TABLE, or a POOL TABLE, or even a MULTIPLICATION TABLE. But a few seconds ago the instant you read the word TABLE, it came under the influence of the context of reading this article. When you read the concept combination POOL TABLE, some aspects of the potentiality of TABLE became more remote (such as its potential to hold food), while others became more concrete (such as its potential to hold rolling balls). Any particular context brings to life some aspects of what is potential, while burying other aspects.
Thus, much as the properties of a quantum entity do not have definite values except in the context of a measurement, features or properties of a concept do not have definite applicabilities except in the context of a particular situation. In quantum mechanics, the states and properties of a quantum entity are affected in a systematic and mathematically well-modeled way by the measurement. Similarly, the context in which a concept is experienced inevitably colors how one experiences that concept. One could refer to this as an observer effect for concepts.
Entanglement of Concepts
Not only is there an ‘observer effect’ for concepts, there is also an ‘entanglement effect’. To explain this, consider the concept ISLAND. If ever there was an identifying or defining feature of a concept it would be that the feature ‘surrounded by water’ for the concept ISLAND. Surely ‘surrounded by water’ is central to what it means to be an island, right? But one day I happened to notice that we say ‘kitchen island’ all the time without any expectation that the thing we are referring to is surrounded by water (indeed it would be disturbing if it were surrounded by water!) When KITHCEN and ISLAND come together they exhibit properties that cannot be predicted on the basis of either the properties of kitchens or the properties of islands. They combine to become a single unit of meaning that is greater than that of the constituent concepts. This combining of concepts in new and unexpected ways is central to human intelligence and it is the heart of the creative process, and it can be thought of as an entanglement problem for concepts.
It may seem kooky to apply quantum mechanics to something like concepts, been seen in a historical context this is not such a strange move. Many theories that were historically part of physics have now been classified as part of mathematics, such as geometry, probability theory, and statistics. At the times when they were considered physics they focused on modeling parts of the world pertaining to physics. In the case of geometry this was shapes in space, and in the case of probability theory and statistics this was the systematic estimate of uncertain events in physical reality. These originally physical theories have now taken their most abstract forms and are readily applied in other domains of science, including the human sciences, since they are considered mathematics, not physics. (An even simpler example of how a theory of mathematics is applicable in all domains of knowledge is number theory. We all agree that counting, as well as adding, subtracting, and so forth, can be done independent of the nature of the object counted.)
It is in this sense that I started thinking using mathematical structures coming from quantum mechanics to build a contextual theory of concepts, without attaching the physical meaning attributed to them when applied to the microworld. I excitedly told my doctoral advisor, Diederik Aerts, about this idea. He had already used generalizations of quantum mechanics to describe the liar paradox (e.g., how when you read a sentence such as ‘This sentence is false’, your mind switches back and forth between ‘true’ and ‘not true’). If there was anyone who could appreciate the idea of applying quantum structures to concepts, surely it would be him. When I told him, however, he said that for technical reasons what I was trying to do would not work.
I couldn’t give on the idea, however. Intuitively it felt right. And it turned out, neither could my advisor. We both kept thinking about it. And in the ensuing months it started to look as if we had both been right. That is, the mathematical approach I’d suggested was wrong, but the underlying idea was right, or at least, there was a way to go about it.
Now, over a decade later, there is a community of people working on this and other related applications of quantum mechanics to how the mind handles words, concepts, and decision making, a special issue of the ‘Journal of Mathematical Psychology’ devoted to the topic, and an annual ‘Quantum Interaction’ conference that’s been held at places like Oxford and Stanford. There was even a symposium on it at the 2011 Annual Meeting of the Cognitive Science Society. It isn't a mainstream branch of psychology, but it isn't as 'fringe' as it once was.
In another post I will discuss the strange new ‘nonclassical’ mathematics that was developed to describe the behavior of quantum particles, and how it has been applied to the description of concepts and how they interact in our minds. To be continued…..