We can give a direct argument for why 2-category theory should be relevant for quantum theory. Suppose we have a quantum system with a finite-dimensional Hilbert space, seen as an object in the category Hilb of finite-dimensional Hilbert spaces. Then if a projector-valued measurement takes place, future dynamics can be different depending on which of the n possible measurement results occurred. We now effectively have n independent copies of our state space, conveniently described as an object in Hilb, the n-fold Cartesian product of the category of finite-dimensional Hilbert spaces.  A categorical setting in which to study the measurement process must therefore include both Hilb and Hilb, since these give our mathematical context before and after the measurement takes place; and since they are themselves categories, the correct setting in which to study them will be a 2-category. The 2-category 2Hilb is then a natural choice, since up to equivalence, its objects are precisely the categories of the form Hilb.

James Vicary, Higher Quantum Theory



The twenty-eighth episode of the show, which was first uploaded June 14, 2009. Here are some relevant links, as is our way.

In case you don’t remember or weren’t aware of that Disney “scandal”…




Bear in mind, all though this has a good chance of being exactly true, it does come from the website of a film (not documentary) that is based on the idea. 


1957: James Vicary first tested subliminal messages on unsuspecting movie theater audiences. At the time, technology only supported 24 fps (frames per second), which was well within the human mind’s capacity to consciously perceive, which in turn, disqualified them as ‘subliminal’ and his studies were dismissed by the CIA. As far as the American public knew, they had no further belief in subliminal suggestion.

Subliminal messages

While researching Subliminal message, I have come across one experiement many times. The infamous “Eat Popcorn/Drink Coke” study by James Vicary in the 1950s. Vicary’s goal was to make people want popcorn and coke by flashing “eat popcorn” and “drink Coke” very briefly on a screen during a movie. Vicary claimed that the sales of popcorn went up by 57.5% and the sales of Coke rose by 18.1%. The impact of his study was in the spread of the common knowledge of subliminal messaging, as months after his study was conducted, 41% of respondents of the survey had heard of the term subliminal advertising. By the 1980s, over 80% of the surveyed were aware of the term, and 70% believed that it was effective.