The idea that quantum physics is not only relevant to consciousness or the “mind” is pretty widely known. After all, in addition to a plethora of popular books by authors with questionable expertise and/or knowledge, eminent physicists such as Sir Roger Penrose and Henry Stapp have supported this idea. This post isn’t about quantum theories of mind (which I don’t find persuasive). It’s about a large number of papers that begin by making this distinction, e.g., “We note that this article is not about the application of quantum physics to brain physiology.”; “In our approach “quantumness of mind” has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles”; etc.

Simply put, the idea is that cognitive psychologists, neuroscientists, etc., should use the mathematical framework, notation, and terminology found in quantum physics (in particular, quantum mechanics) to model thinks like decisions, opinions, attitudes, and other cognitive processes or mental states. The reason? Well, it doesn’t take much thought to realize that e.g., the mood “happy” isn’t binary. That is, a person isn’t simply either “happy” or “not happy” but rather there are degrees of happiness and sadness. The same is true of things like political orientation, value judgments, and in general all the kinds of things that psychologists and neuroscientists studying the mind are interested in measuring. Also, not only are most of these mental states and cognitive processes not binary or discrete, they also don’t really lie along a continuum. For example, a person can be happy-excited, or happy-euphoric, or happy-content. So a person’s mental “state” with respect to some attribute, mood, etc., is really more like a composite of indistinguishable states (none of which can be simply encapsulated by a true/false or yes/no binary method).

Many people who have never opened a physics texts have nonetheless heard of quantum superposition. The sensationalist, simplistic version of this phenomena is that a quantum system can exist in multiple distinct states at the same time (for example, it can be described as being in more than one place at once, as moving in incompatible ways, etc.). As in classical physics (and biology, chemistry, and so forth) systems are modelled using mathematics, which means that in quantum mechanics the mathematics must be able to represent systems in superposition states and must “work” according to the logic of quantum mechanics (which, unlike classical logic, can allow a statement to be true and false at once, and other fundamental paradoxes).

Thus dozens and dozens of papers in many journals written by many different authors have argued that the mathematical formalisms of quantum mechanics should be used to represent things like attitudes in cognitive neuroimaging studies, behavioral studies, and other research on cognition. For example:

“Superposition, entanglement, incompatibility, and interference are all related aspects of QP theory, which endow it with a unique character. Consider a cognitive system, which concerns the cognitive representation of some information about the world… Questions posed to such systems (“Is Linda feminist?”) can have different outcomes (e.g., “Yes, Linda is feminist”). Superposition has to do with the nature of uncertainty about question outcomes. The classical notion of uncertainty concerns our lack of knowledge about the state of the system that determines question outcomes. In QP theory, there is a deeper notion of uncertainty that arises when a cognitive system is in a superposition among different possible outcomes. Such a state is not consistent with *any* single possible outcome”

Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling*?. Behavioral and Brain Sciences*, 36(03), 255-274.

Even better:

“There is one obvious similarity between cognitive science and quantum physics: both deal with observations that are fundamentally probabilistic. This similarity makes the use of QT in cognitive science plausible, as QT is specifically designed to deal with random variables. Here, we analyze the applicability of QT in opinion-polling, and compare it to psychophysical judgments.”

Khrennikov, A., Basieva, I., Dzhafarov, E. N., & Busemeyer, J. R. (2014). Quantum Models for Psychological Measurements: An Unsolved Problem. *PLoS One*, *9*(10).

It may sound as if this idea of describing attitudes or reasoning in terms of quantum theory for the reasons given is natural, even necessary. After all, whatever the biological mechanisms underlying cognitive processes, experiments on cognition can’t get very far if they are limited to what can be explained by neurobiology. So we have to measure beliefs, attitudes and similar mental states and processes by asking participants questions, and the outcome is fundamentally probabilistic. Also, there is something like the uncertainty principle at play, in that measurements will always involve uncertainty (including exactly *what *is being measured).

There’s one little problem: there’s nothing special about the mathematics used in quantum mechanics (in fact, the mathematical formalisms of quantum mechanics is incompatible with special relativity, so field theories like quantum electrodynamics rely on a rather fundamentally different mathematical framework). It’s true that quantum mechanics utilizes some unique notation, called Dirac notation, that one can now find strewn across papers on mathematical psychology, cognitive science, social psychology, etc. It’s also true that this notation was developed specifically for use in quantum physics. But were there alternative mathematical formalisms prior to Dirac’s creation? Sure. Is Dirac notation superior? That depends: “Mathematicians tend to despise Dirac notation, because it can prevent them from making important distinctions, but physicists love it, because they are always forgetting that such distinctions exist and the notation liberates them from having to remember.” (N. David Mermin). I hated Dirac notation because I was already quite familiar with the more powerful and more widely use notation for complex vector spaces, matrices, Hilbert space, and the other concepts that Dirac notation is used to represent (systems in quantum mechanics are represented by vectors in Hilbert space; if you don’t know what that means don’t worry about it). The new notation encouraged things which I had been repeatedly warned in textbooks and by professors never to do (e.g., writing a vector as a row) because such notational violations can make mathematical operations produce incorrect results, confuse coefficients with their variables, and in general result in a mess. However, because quantum mechanics doesn’t require the full power of abstract algebras and functional spaces physicists can get by without the kind of rigor mathematicians demand. The problem is that this notation was developed specifically to fit the kinds of measurement outcomes and experiments of quantum mechanics, not simply uncertainty, superposition, probabilistic outcomes, etc.

In fact, the statement that both “cognitive science and quantum physics…deal with observations that are fundamentally probabilistic” is idiotic. Statistical mechanics is “fundamentally probabilistic”, and so is (surprise!) probability theory. The only thing special about probability in quantum mechanics is that they can’t be calculated directly but are derived from wave amplitudes (things can get more complicated, but probability is still probability). There isn’t some quantum normal distribution. Quantum mechanics still makes use of the familiar ol’ bell-shaped curves used for well over a hundred years. Hilbert space, so fundamental to quantum mechanics (quantum states “exist” in this space), was developed by a mathematician for mathematics and continues to be used by mathematicians.

So what is behind the papers cited below as examples of this trend? Psychologists trying to act as though they’re doing physics and the trendiness of “quantum weirdness”, i.e., a desire to be just as hardcore and cool as theoretical physicists. And here are some of the pointless results from this physics envy (you have to love the *prima facie *ridiculousness of the paper arguing that the “mental lexicon” displays quantum-like “spooky-action-at-a-distance”) :

Aerts, D. (2009). Quantum structure in cognition. *Journal of Mathematical Psychology*, *53*(5), 314-348.

Aerts, D., Broekaert, J., & Gabora, L. (2011). A case for applying an abstracted quantum formalism to cognition. *New Ideas in Psychology*, *29*(2), 136-146.

Ashtiani, M., & Azgomi, M. A. (2015). A survey of quantum-like approaches to decision making and cognition. *Mathematical Social Sciences*, *75*, 49-80.

De Barros, J. A. (2012). Quantum-like model of behavioral response computation using neural oscillators. *Biosystems*, *110*(3), 171-182.

Bruza, P., Kitto, K., Nelson, D., & McEvoy, C. (2009). Is there something quantum-like about the human mental lexicon?. *Journal of Mathematical Psychology*, *53*(5), 362-377.

Busemeyer, J. R., & Bruza, P. D. (2012). *Quantum Models of Cognition and Decision*. Cambridge University Press.

Khrennikov, A., Basieva, I., Dzhafarov, E. N., & Busemeyer, J. R. (2014). Quantum Models for Psychological Measurements: An Unsolved Problem. *PLoS One*, *9*(10).

Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling*?. Behavioral and Brain Sciences*, 36(03), 255-274.

Pothos, E. M., Busemeyer, J. R., & Trueblood, J. S. (2013). A quantum geometric model of similarity. *Psychological review*, *120*(3), 679.

Wang, Z., Busemeyer, J. R., Atmanspacher, H., & Pothos, E. M. (2013). The potential of using quantum theory to build models of cognition. *Topics in Cognitive Science*, *5*(4), 672-688.

Wang, Z., Solloway, T., Shiffrin, R. M., & Busemeyer, J. R. (2014). Context effects produced by question orders reveal quantum nature of human judgments. *Proceedings of the National Academy of Sciences*, *111*(26), 9431-9436.

Reblogged this on Mind to Multiverse and commented:

I promise I won’t continue to do this, but I just want to ensure that the “millions and millions” of non-existent readers know that I have started another blog and that this one has a new central theme.

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