Does quantum uncertainty have a place in everyday applied statistics?

Several months ago, Mike Betancourt and I wrote a discussion for the article, Can quantum probability provide a new direction for cognitive modeling?, by Emmanuel Pothos and Jerome Busemeyer, in Behavioral and Brain Sciences. We didn’t say much, but it was a milestone for me because, with this article, BBS became the 100th journal I’d published in.

Anyway, the full article with its 34 discussions just appeared in the journal. Here it is.

What surprised me, in reading the full discussion, was how supportive the commentary was. Given the topic of Pothos and Busemeyer’s article, I was expecting the discussions to range from gentle mockery to outright abuse. The discussion that Mike and I wrote was moderately encouraging, and I was expecting this to fall on the extreme positive end of the spectrum.

Actually, though, most of the discussions were positive, and only a couple were purely negative (those would be “Quantum models of cognition as Orwellian newspeak” by Michael Lee and Wolf Vanpaemel, and “Physics envy: Trying to fit a square peg into a round hole,” by James Shenteau and David Weiss). We expressed some vague skepticism but it’s hard for me to be really negative about the idea, given that classical probability theory is not actually correct, and we do indeed live in a quantum world (otherwise all our tables and chairs would fall apart, for one thing). I certainly see no logical reason why our models of probability and uncertainty should be restricted to the “Boltzmannian” simplification.

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