In our recent paper (Cutting, DeLong, & Nothelfer, “Attention and the evolution of Hollywood film”, Psychological Science, 2010, 21, 440-447; henceforth AEHF), we were interested in the shot structure in a reasonable sample of films across 70 years and in how that structure has changed. Our main conclusion was that the pattern of shots in more contemporary movies has come to match better the large-scale structure of human attention. In particular, a cut between shots forces the reallocation of attentional resources to the new scene or to the new vantage point, and the pattern of the length of those shots reflects natural tendencies of how attention ebbs and flows over as much as an hour and more. The structure of both attention and, more and more often, contemporary film appears to follow a 1/f pattern, sometimes called pink noise.
The 1/f pattern can be thought of as a simultaneous combination of many transverse, nonsynchronous waves whose up and down-ness, or amplitude (power is proportional to the square of the amplitude), is fixed by their wavelength (or the reciprocal of frequency, hence 1/f). Thus, the big (up and down) waves are also long waves (in time); smaller waves are shorter waves and proportionately so. For example, a relatively big wave
Blogged science reporting vs. science
Popular representations of science often skew things, and occasionally they simply get things wrong. Indeed, there were a number of howlers that appeared in the blogosphere about our research. As evidence, all one need do is to check out the title of the first popular piece on our work (https://www.newscientist.com/article/mg20527483.900-solved-the-mathematics-of-the-hollywood-blockbuster.html). Fortunately, the article’s content was more reasonable and more accurately reflected what we
Now Barry Salt has joined the mix, and we are quite happy with his comment on AEHF. Among all possible responses, one can ask for nothing better than to be “usefully provocative.” Against the misrepresentation by others, rightly notes that we did not try to account for the box office success of movies. We didn’t even focus on the highest grossing movies, or attempt to
Historical near parallels: Changes in ASL and in power spectra
Clearly, shot lengths have become shorter over the course of the 20th century and into the 21st. Salt updates his past data with an elegant graph in his commentary. In AEHF, we found that, since about 1950 or so, films have increasingly adopted a shot structure that approaches a 1/f pattern (pink noise). One might think these two are related – and indeed they are correlated. But there is no causal
Salt (Moving into Pictures, 2006) was first to note that the shot distributions of most films tend to follow a lognormal distribution and generalizing this he produced two new graphs in his commentary, one for Catherine the Great (1934) and one for Derailed (2002). In showing these graphs Salt is concerned about is what psychologists call a floor effect. That is, the average duration of shots may have decreased to
What lognormality means is that if one took the logarithm of every value in the distribution and then replotted the data, the distribution would look normal – like a bell-shaped curve, more or less. Shown below are the log-scaled distributions for four films from our sample, two from 1935 and two from 2005:
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Despite 70 years, fairly dramatic differences in ASL, and the great differences in number of shots per film, all four distributions look generally the same. The important point is that log-scaled shot-length distributions for films look normal and that normal distributions have no real floor (the logarithm of zero is undefined). Likely, as shot lengths in films get shorter, shots measured in fractions of seconds (not just seconds) will continue
Our analysis in AEHF started by normalizing the shot distribution of each film. That is, the mean is set to zero (subtracting the ASL from each shot length) and the standard deviation is set to one (dividing the value above by the standard deviation of the shots in the whole film). This creates what is called a unit normal distribution, and it is a standard statistical procedure when comparing the shapes
Thus, diminished ASLs cannot cause our power spectra results; ASL is factored out before the analysis is done. Also, we found no evidence in the changes in film distributions in our film sample as ASL diminishes, and we also renormalized the distributions before our analysis. Moreover, as counterexamples, consider The 39 Steps (1935) with an ASL of 10.8 s and a slope of .93 (1.0 is the slope for a 1/f
Nonetheless, Salt rightly notes our power spectra results are still correlated with ASLs for our sample of films. It is just that neither has caused the other. One should then ask: What has caused the change in power spectra over the last 50 years or so? Our guess in AEHF was that there has been a kind of cultural transmission among filmmakers about what seems to work in shot composition and
Also, in discussion of the differences between Catherine the Great and Derailed, Salt also reported the Lag-1 autocorrelations for the two films (about .12 and .20, respectively) and suggested these would make a difference, perhaps contributing to what we found in our power spectra. These lag correlations map the length relations between Shots 1 & 2, 2 & 3, 3 & 4, and so forth along the length of the film.
Basic film units: Shots, scenes, and beyond
In AEHF we looked at shot structure across films without regard to scene structure. In his essay “Speeding up and slowing down” (https://www.cinemetrics.lv/salt_speeding_up_down.php), Salt performed a moving average analysis of ASLs in several films, particularly Ride Lonesome (1959). He found, not surprisingly, that different scenes in a given film have different ASLs. In a moving average window this creates a wavy pattern on a larger scale
That is, the Fourier and power analysis that we performed (doggedly and mechanically) looked for waves in the shot-length sequences of each film, where those waves could be of 2, 4, 8, 16, 32, 64, 128, 256, 512 shots long and sometimes longer. Notice that these numbers form a progression in powers of 2. They do so in order that the measured waves be completely independent. These waves are assessed within
What we think is more striking about our AEHF results, however, is that there are such waves in film that are considerably larger than mean scene length. That is, for a 1/f pattern to emerge, there have to be waves of similar-length shots coursing through an entire film that are in the range of 256, 512, out to even 1024 shots apart. In contemporary films this can be in a range
In addition, Salt and others have highlighted our result that action films tend to approach a 1/f structure more than the other genres we explored (adventure, animation, comedy, drama films). It is by no means the case, however, that action films always have close to a 1/f shot-length profile. We recently analyzed the James Bond film Quantum of Solace (2008). Despite its 1.71 ASL (trimming out the glossy credit sequence
In summary and in response to Salt, (1) our power analysis is causally unrelated to ASL even though the two have developed more or less in parallel over the last 50 years or so, (2) we find no evidence for the change in shot distributions in popular films in our sample across time; they are all lognormal to reasonable approximation, and (3) the ASL differences he found in scene-length structure are