Language of the Stars: A Discourse on the Theory of the Light Changes of Eclipsing Variables

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Whenever we study the properties of any celestial body - be it a planet or a star - all information we wish to gain can reach us through two different channels: their gravitational attraction, and their light. Gravitational interaction between our Earth and its celestial neighbours is, however, measurable only at distances of the order of the dimensions of our solar system; and the only means of communication with the realm of the stars are their nimble-footed photons reaching us - with appropriate time-lag - across the intervening gaps of space. As long as a star is single and emits constant light, it does not constitute a very revealing source of information.

A spectrometry of its light can disclose, to be sure, the temperature colour, or ionization of the star's semi-transparent outer layers, their chemical composition, and prevalent pressure through Stark effect or magnetic field Zeeman effect , it can disclose even some information about its absolute luminosity or rate of spin. It cannot, however, tell us anything about what we should like to know most - namely, the mass or size i.

JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Astronomy Astrophysics and Astroparticles. Buy eBook. Buy Hardcover. The term act is borrowed from theater, but it does not imply a break in the action. Instead, it is a convenient unit whose size is between the whole film and the scene in which certain story functions occur.

The first act is the setup , and this is the portion of the story where listeners, readers, or viewers are introduced to the protagonist and other main characters, to their goals, and to the setting in which the story will take place. The third is the development , where the narrative typically broadens and may divide into different threads led by different characters. Finally, there is the climax , where the protagonist confronts obstacles to achieve the new goal, or the old goal by a different route. Two other small regions are optional bookend-like structures and are nested within the last and the first acts.

At the end of the climax, there is often an epilogue , where the diegetic movie world order is restored and loose ends from subplots are resolved. In addition, I have suggested that at the beginning of the setup there is often a prologue devoted to a more superficial introduction of the setting and the protagonist but before her goals are introduced Cutting, The prologue and epilogue roughly act symmetrically, bringing the viewer into and out of the story see also Cohn, Where did this four-part structure come from?

Thompson suggested that it has been part of feature-length movies for a long time. But the existence of a four-part structure is likely much older than movies. I would claim that it has been endemic in many cultures for a long time. Perhaps most convincing in this domain is the work by Labov and Waletzky , who showed that spontaneous life stories elicited from inner-city individuals without formal education tend to have four parts: an orientation section where the setting and the protagonist are introduced , a complication section where an inciting incident launches the beginning of the action , an evaluation section which is generally focused on a result , and a resolution where an outcome resolves the complication.

Thus, I assume that a general narrative form of stories was in place in our culture at the end of the 19th century, ready to be adopted by the first feature-length films of the second decade of the 20th century and then beyond. That form entails at least three, but usually four, acts of roughly equal length.

Why equal length? The reason is unclear, but Bordwell , p. Early projectionists had to rewind each reel before showing the next. Perhaps filmmakers quickly learned that, to keep audiences engaged, they had to organize plot structure so that last-seen events on one reel were sufficiently engrossing to sustain interest until the next reel began. Cutting and Candan broached several issues about movies in relation to the other major arts, to culture, and to evolution. The first is that most classic art forms have been with us for a very long time.

The origins of music, dance, sculpture, and painting are lost in our prehistory; theater and architecture are thousands of years old; and, although full-flowered literature had to await the printing press, it is embedded in a poetic oral tradition that is also many thousands of years old. The recent development of this art form and the intense public interest it has sustained offer an intriguing possibility for studying human cognition.

Although we clearly did not evolve to watch movies, it is highly likely that movies have evolved in part to fit better within our cognitive and affective preferences and capacities. But these whole-film measures are coarse and fail to take into account narrative structure. My intention in this article is to track those changes as they apply to the structure of movies as the narrative unfolds.

To be sure, no psychological data are gathered here; only psychologically relevant physical measures on huge and lengthy stimuli that have heretofore been largely ignored are covered. In particular, I am interested in changes in syuzhets and how they have been shaped jointly by fabulas and by our cognitive and affective systems. Previously, I demonstrated that a four-part narrative structure of the fabula has implications for syuzhet Cutting, I explored the variations in a dozen aspects of film style as they are distributed along the length of movies.

These included shot duration; shot transition types cuts, dissolves, fades, and the like ; shot scale; motion; music; luminance; character introduction; conversations; action shots; and across-shot changes in location, characters, and time. Interestingly, each component aligned fairly well with one of the stimulus dimensions.

Thus, there is some convergence between a three-dimensional notion of pace and the three dimensions that are most orthogonal in the analysis of film style as it saturates whole movies. The focus of this article is to address the historical changes in pace through film style measures of shot duration, motion, and emotion. Cutting, DeLong, and Nothelfer studied of these films from to for other purposes, and Cutting, DeLong, Brunick, Iricinschi, and Candan added 10 more from with still other goals.

I next reduced these feature-length movies to the that were shorter than 2. This length criterion made them better candidates for having a theoretical structure proposed by Thompson : four roughly equal-length sequential acts — setup, complication, development, and climax. Longer movies may have five or even six acts, often with more than one development section.

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For this article, the 10 longer movies were replaced with 10 others of appropriate lengths and generally equal popularity from their same release year, bringing the sample temporarily back up to For this article, in addition to the 10 replacement films, I added 50 more movies — 10 from and 10 each from , , , and — yielding a total of movies. Like the others, the newly selected movies were among the most popular of their release year on IMDb.

Those from before are silent movies. I added the silent films to complete the investigation of feature-length movies in hopes of finding patterns in them that might be precursors to those of later films. Most are dramas, comedies, action films, or adventure films, with some animations, crime films, fantasies, musicals, mysteries, science fiction movies, war movies, and westerns as indicated by their first genre mention on the IMDb. Although Cutting, DeLong and Brunick and Cutting provided some analyses of genre differences, none are pursued here.

All films are listed in the filmography below. More importantly, I look at the changes in the temporal dynamics across release years with an eye toward revealing the evolution of movie pace and how film style has become enmeshed with narrative progression. Previously, among others, I analyzed these variables Cutting, but was unconcerned with historical changes in pace. After this, the values within like bins could be averaged across movies and a general pattern discerned.

Individual movies can show strikingly different patterns on any given measure. Thus, this type of data is quite noisy and requires pooling results over many films. For later analyses in this article, the movies were divided into 4 groups — the 30 silent films from , , and , the 60 early sound films from , , , , , and , the 60 midsample films from , , , , , and , and the 60 more contemporary films from , , , , , and Cuts and Shot Durations.

These values are much higher than my students and I would accept. Thus, we tackled the task of finding all transitions cuts, wipes, dissolves, and fades by manually going through the digital versions of each movie frame by frame. Shot durations were determined in several steps. First, we found the number of the first frame of each new shot in each movie, cross-checking to assure ourselves that we found almost all transitions, and recorded results on a spreadsheet.

The transitional frame number for dissolves and other noninstantaneous transitions fades and wipes was taken as its judged midpoint, thus beginning a new shot. The number of transitions that fell within each of the equal-duration bins was then determined across the length of that movie. In this manner, each bin had between 0 transitions found in at least 1 bin in 89 different movies where it was aligned with a long take , the term for a long-duration shot and as many as 80 found in 1 bin in the analysis of Avengers: Age of Ultron , a nearly 2.

These means were then rescaled back to the overall mean shot duration across all movies 7. The average shot duration for the silent films was 7. The movie-length patterns of shot duration in seconds, left panel , of the extent of motion middle panel , and of relative luminance right panel across popular English-language movies released from to The lengths of the movies were normalized so that each measure was assessed across equal-duration bins, and those values were normalized within each movie before averaging across them.

Shot duration converted back to seconds , flicker motion converted back to mean correlations of eight-bit pixel values across frames , and luminance converted back to the mean pixel value per frame are three roughly orthogonal measures of film style Cutting, The data of each panel are also separated by vertical lines that suggest four narrative divisions see Thompson, : the setup roughly bins 1—25 , the complication bins 26—50 , the development bins 51—75 , and the climax bins 76— Also noted are a prologue initial and variable number of bins of the setup and an epilogue a variable number of bins at the end of the climax , optional units that do not appear in every film.

A take is another name for a shot. The term long shot is reserved for a wide-angle shot, not a long-duration shot. Thus, I have investigated the easiest to measure — flicker motion or flicker noise , the change in pixel values without regard to the patterns of form that change over time and space. I then adjusted the gamma of each pixel value to accord with human visual sensitivity, keeping them within the 0— range. Shot averages were then assigned to the bin in which the shot began and, if that shot stretched across the next bin, to that second bin as well. Finally, as before, like-bin values were then averaged across movies.

All pixels were averaged within a frame and then averaged within a shot. Again, shot means were assigned to the appropriate bin, normalized within each movie, and averages taken across like bins. As I have done previously Cutting, , I fit polynomial functions to the bins of mean data. The sequence of these bins will be broken into 4 equal-length regions acts , following the suggestion by Thompson that movie narratives generally consist of 4 roughly equal-length sections — the setup here assumed to correspond to bins 1—25 , the complication bins 26—50 , the development bins 51—75 , and the climax bins 76— Polynomials, with their inherently curved nature, make sense in this context because there is variation in the length of the acts in a given movie.

Polynomial curves should accommodate these differences when averaging over the slightly different-length acts of different movies. Nonetheless, using polynomials to fit data can lack the appropriate conservativeness in statistical analysis. This is because high-parameter count models easily lead to false-positive results. One solution to overfitting is to prefer simpler models to those that are more complex and that do not reliably produce better fits by a strict criterion.

I will take such a result as a first confirmation of a reliable result. A second approach to model comparison is to penalize model complexity models that have more parameters. For example, using adjusted R 2 values is one way to handle this problem in regression situations, a procedure I follow here. Unfortunately, this method is widely agreed to underestimate overfitting Stauffer, , p. Moreover, across the plenum of multivariate analyses, there is debate about how much penalty should be levied.

A third solution, and one preferred in machine learning and elsewhere, is cross-validation see, for example, Browne, , sometimes called within-sample prediction. That is, one splits the data into two groups, runs the analysis on the first dataset called the training set , and then uses the model form and its parameter values in a parameter-free assessment of the other set the test set.

If both fits are comparable and statistically reliable, this can be called a replication. If the fit to the test data does not yield a reliable result, then the first results are said to be due to overfitting. In practice, it is good to do this procedure many times, so, in the cross-validation analyses performed here, I randomly split the data in half 10, times, then take the averages across all training and all test fits. Of importance in this context is whether the test set mean R 2 value is statistically reliable. Because after a cross-validation run the training results are parameterless, the comparison between the training means and the test data means affords a two-sample correlation test on which a t value can be calculated.

In this article, I will accept results across the bins only if the polynomial fit is confirmed in both ways, 7 although some interesting situations arise and are worth discussing when the polynomial fits are not corroborated by cross-validation. Finally, I will display the data in a manner that reveals both its variability and its underlying trends.

Within that region, I will show a candidate higher-order polynomial that failed cross-validation as a line in a contrasting color. Because the focus of this article is on the dynamic patterns across the length of movies, I will try to determine when they first arose in the history of popular feature-length cinema. To do this, I will start with the movies from the sound era to establish general patterns, then work backward through time in divisions within this sample, and finally consider those of the silent era to see how these patterns may have developed.

Studies 1—3 will begin by exploring the global patterns across the whole of the sound-era sample; studies 4—6 will address the different eras of sound film —, —, and — for each of the dimensions; and studies 7 and 8 will consider their possible roots in silent movies — Again, the three dimensions investigated here are the mean shot durations measured by transition density, the mean amount of flicker motion as measured by interframe correlations, and the mean luminance across all frames of shots in the sound movies released from to Again, these are related to the film studies notion of pace, and they are the pertinent film-style variables to consider because, through componential analysis, Cutting found them to align with three orthogonal stimulus dimensions encompassing perhaps all of the various correlated dimensions of film style.

The left panel of Fig. It presents the mean pattern of shot durations across the duration-normalized time bins for the movies. Thus, one can be quite confident that this polynomial is a reasonable representation of the trend underlying the data. In the left panel , the sequence of bins is also broken into 4 equal-length regions, following the suggestion by Thompson : the setup again, roughly bins 1—25 , the complication bins 26—50 , the development bins 51—75 , and the climax bins 76— The two optional subsections also leave their marks on shot duration.

The end of the climax often contains an epilogue where a new diegetic film-world order is established and loose ends are tied up Thompson, , and the beginning of the setup often contains a prologue in which the setting, the time period, and the protagonist are introduced Cutting, Notice two striking features within the four acts, both of which make narrative sense. Cutting also reported that the shot durations in the development were slightly longer than those in the complication, but in this expanded sample, this difference, although present, is not reliable.

Visual inspection suggests that the decline in shot durations starts earlier, before the end of the complication, nullifying the possible result. As noted above, I have divided the movies into four eras — silent — , early — , middle — , and near-contemporary — This result presages evolutionary trends and is sufficiently important to pursue in study 4. The middle panel of Fig. Again, several striking patterns are apparent that make narrative sense. A bit less obvious is the reduction of the confidence interval at the beginning of the prologue. The reason for this will become clearer in study 5.

This result is pursued in study 5. Finally, the right panel of Fig. There are two striking trends across this luminance profile. Less obvious, but similar to the pattern in the left panel of Fig. This effect will be pursued in study 6. The psychological import of the overall pattern of the results of study 1 stems from the relationship between cuts and eye movements.

Smith , reported that cuts are generally associated with later eye movements. Viewers typically saccade back in the direction of the center of the screen. It suggests that movie viewers should be particularly attentive during the climax, driven by the content of the narrative. Similarly, the increase in cut frequency across the prologue into the remainder of the setup could serve to increase eye movements and possibly attention, bringing the viewer into the plot.

Symmetrically, the decreasing pace and eye movement demands of the epilogue should help bring the viewer back out. This, too, suggests that engagement in the movie may be greatest during the middle of the climax. Further, and more speculatively, motion has been shown to affect the perception of the passage of time Brown, , dilating it making it seem longer at short durations.

This might give the viewer a sense of increased processing speed, which can be associated with positive affect and well-being Pronin, Finally, consider the nadir of the luminance function. It occurs at the end of the development section, when events seem to be most stacked against the protagonist in trying to achieve her goals. In luminance terms, this is literally true; epilogues are often the brightest sequence of a movie.

Thus, and again, film style has appeared to mesh with the pacing goals of filmmakers. How effective this manipulation is for the viewer is unknown, but it seems to be an appropriate adjunct to the content of the narrative. Demonstrating these three congruences — the yoking of the aspects of pace and film style to the progression of narrative events — was exactly the intent of Cutting Here, these results expand those to a broader corpus and time frame.

However, the main goal of this research effort is to trace when these congruences arose. With these expanded overall dynamic patterns in place, I now focus on trying to determine when they arose. Will these same higher-order polynomials be found in the patterns of all movies across the century-wide sample?

Movies from to As shown in the right panel of Fig. The two major features of the general results in the left panel of Fig. Variations in mean shot duration in seconds across the duration-normalized films of three different eras of popular movies. The extents of the vertical axes show equal variance in the data across the three panels. The statistical lines and regions of the middle and right panels are as they were in Fig. Vertical lines in all panels separate the bins into the four narrative sections, as in Fig.

Thus, the pattern for the more recent movies matches quite well the average pattern of the movies from to Of course, the former are contained within the latter, but, among other things, this result suggests that the overall pattern, if not pervasive across time, may at least have bin regions that are not too discrepant from those shown in the left panel of Fig.

Thus, the patterns of the middle and right panels of Fig. Two features in the pattern of the middle sample movies differ from that of the latter films.

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These are captured in the decrease in polynomials from sixth order to fourth order. In short, the pattern is less articulated. For example, the lengthening of shots in the epilogue is not nearly so marked as in the later movies, suggesting less contrast between the action of the typical climax and the calm of the typical epilogue. In addition, the decline in shot duration is extended from the complication through to the point in the climax where the epilogue weakly turns toward longer-duration shots.

This suggests that stylistically there is a bit more anticipation of action in the complication of movies of this era than in those that are more contemporary. In other words, the pattern of shot durations in movies from to is generally similar, but not identical, to those from to The overall later form is nascent but not fully present in the midsample movies. There is no reliable pattern among the shot durations of the earliest sound movies. Thus, the stylistic patterns of shot durations seen in the left panel of Fig. As seen in the right panel of Fig.

The mean flicker motion variation across the duration-normalized movies in three different eras of popular movies. The extents of the vertical axes show equal variances in the three datasets. Again, the statistical lines and regions of the middle and right panels are as they were in Fig. Vertical lines in all panels separate the bins into four narrative sections. The difference in results between the larger group of sound movies and the more recent subset is again one of polynomial rank — sixth order for the movies and fifth order for the 60 more recent ones.

A comparison of the middle panel of Fig. This suggests that the newer movies are much more likely to start with greater motion than older ones, likely explaining the tightening of the confidence interval in the middle panel of Fig. The style of contemporary movies seems better geared to engross the viewer earlier in the film, bringing her into the narrative. The motion results of the middle-era movies are quite different, as shown in the middle panel of Fig. Here we have a drop in polynomial fit from fifth-order to second-order, showing less articulation in the data.

Nonetheless, gone in the fit to the midsample movie data are the systematic decreases in motion in both the prologue and the epilogue. The expansion of the confidence interval in the epilogue suggests that movies differ in whether their motion retards at this point or not. The only residual effect is the increase in motion in the development and through the climax. The pattern of motion results for the oldest sound movies is shown in the right panel of Fig. As there was for shot durations of this movie era, there is no reliable pattern here for motion. Thus, as with shot durations, it is clear that the general pattern of motion in movies emerged relatively slowly and became more articulated across the century.

The right panel of Fig. The mean luminance variation across the duration-normalized movies in three different eras of popular movies. The extents of the vertical axes show equal variance in the three datasets. Again, the statistical line and regions of the left panel are as they were in Fig. The pattern for the more recent movies has a polynomial fit of the same order as the entire group of sound movies. A comparison of the right panels of Figs. Again, the most prominent result is the progression across the complication and development of increasing darkness, matching the increasing narrative difficulty for the protagonist, followed by the striking rise in luminance as things turn out well.

Again, film style corroborates narrative form. Thus, and again, there is a hint of a trend in these data similar to that found in later films. Shown in the left panel of Fig. It seems possible that the hint of a linear trend over the whole film may be a precursor to the future linear trends over just the complication and the development.

Nonetheless, it also appears that the full-blown pattern of luminance shown in the right panel of Fig. Perhaps nascent forms of these trends in shot duration, motion, and luminance can be found in silent movies. To be sure, direct comparison of sound movies and silent movies in this context is difficult. These affect the distribution of shot durations.

Although the mean duration of intertitle shots in this sample 7. In other words, it is much more likely for live action shots to be very long or quite short in duration. Unsurprisingly, luminance is also affected title slides are dark and so is motion ideally there is no motion in a title slide, although a bit of jitter is quite common. In addition, the distribution of the intertitles is not uniform throughout the length of the movie. Compositionally, there are two types of intertitles — dialogue titles and expositional titles see Salt, The former occur within scenes and were rare before about ; the latter typically introduce scenes and began to appear incrementally in about , often with text surrounded by artistically illustrated scroll patterns.

Although dialogue intertitles are long gone from sound movies, expositional intertitles have not completely disappeared. For example, they can be found in Goodfellas and Avengers: Age of Ultron and are often present in the films of Quentin Tarantino Cartmell, Intertitles also had a special status in early filmmaking; scriptwriters and intertitle writers were rarely the same person, and there was even one Academy Award in given for title writing Cartmell, In addition, intertitles were not simply add-ons after the movie was shot; they were embedded in the design of the film at its conception.

But again, for my purposes, intertitles are a nuisance. They play havoc with each of the analyses that I have undertaken and may disrupt the psychological effects that film style patterns might afford. Nonetheless, in hopes of finding some patterns that are useful to compare with the sound films, I analyzed the silent movies in two ways — first with the intertitles considered as regular shots and second with the intertitles stripped out and the remaining shots abutted as if the former did not exist.

Shot Durations. These results are shown in the top left panel of Fig. To be sure, the long prologue shots are often associated with complex and often multiple intertitles, and the long epilogue shots are also often similar intertitles projecting events of the narrative future. In the 30 silent movies of this sample, there are no reliable patterns of shot duration, motion, or luminance that survive cross-validation, regardless of whether the shots of intertitles are included in the analysis.

However, the pattern of shot durations and luminance with intertitles and motion without intertitles showed statistically reliable polynomial fits, but these failed cross-validation. Nonetheless, one should be cautious inferring too much here. The silent era data are very noisy, sufficiently so that there was no reliable difference in shot duration patterns for the silent vs.

Motion and Luminance. As shown in the upper middle panel of Fig. This is perhaps not surprising, because in this analysis the silent movies include intertitles. The lower panels of Fig. One might claim that the lack of patterns in the data for silent movies with and without their intertitles is caused by mixing movies with different act structure — some with three equal-length acts and some with four.

Although this is entirely possible, the beginnings of the setups and the ends of the climaxes should align in both cases, and yet there is no evidence in the data shown in Fig. As a recap, let me proceed through the sequential narrative structure of movies and outline the changes in film style, when they occurred. I will also suggest possible psychological reasons for them and give examples from particular movies from this sample along the way. The prologue and the setup. Shots are relatively long in duration; they are wide shots people fill relatively little of the screen ; they are occasionally coupled with dissolves rather than cuts; they may jump across time and place; they are covered with nondiegetic background music; they typically show few conversations; and they are often covered with title credits Cutting, The latter might seem to account for much of this structure, but all of these features except being covered with title credits which began in this sample in existed in the early live action shots of movies in the two decades before, when opening credits were title cards printed lettering, typically in black on white.

In the silent era, and even into the s and s A Tale of Two Cities , ; Mutiny on the Bounty , ; Foreign Correspondent , , introductory narrative information about time and place was typically carried by one or more expository intertitles.

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Thus, long-duration live action shots were not used. These often include pans and tracking shots of the initial settings of the narrative. The purpose of the structure of prologue shots appears to be to bring the viewer down into the narrative. Often this is literally true; in The Hunt for Red October , for example, we first hover over a digital globe that rotates, first showing the United States and then Russia, and then in live action we look down on snowcapped mountains near Murmansk. In MASH , we first look down on a helicopter flying over the mountains of Korea the stand-in for Vietnam before then looking up as it lands.

In East of Eden , we look down on the Monterey, California, coastline. Such shots create an atmosphere and inform the viewer about the locations and time periods of the narrative. Background music also helps create calm, or anxiety, or whatever emotion is appropriate to the situation Kalinak, There then follows an almost seamless glide into the setup and the narrative proper.

Shot durations shorten but not too rapidly, and motion diminishes, but in contemporary movies again not too fast. The exogenous demands for eye movements will increase as the shot-reverse shot technique alternately showing the characters conversing takes over. The modal pace of the movie becomes established — the average shot duration during a conversation is typically about the average shot duration of the movies — as we learn about the goals of the characters and their circumstances.

Near the end of the setup, an inciting incident often derails these goals, and a new plan of action needs to be formulated. Complication and Development. Neither shot duration nor motion has any distinctive patterns in the complication and development sections. Nonetheless, changes have taken place in film style that affect these narrative sections. The decreases in shot duration in this range affect exogenous eye movements and are likely to increase attentional demands on the viewer.

The mean amount of motion also increases steadily from the silent era to the present, and this, too, is likely to affect eye movements and attention, particularly in our current era of intensified continuity Bordwell, The major signal of dynamic change in the complication and development is in lighting, measured as overall frame luminance. Each of the four movie eras investigated here show some evidence of a decline in luminance across these sections.

The evidence was weak in the silent movies, weak and nondiscriminating for the early sound movies the decline covers the setup and climax as well , and nascent for the midsample films, but it finally crystallized in the more contemporary films. The rationale for this darkening of cinematic images appears to be connected to the travails of the protagonist as she is thwarted in her plans to achieve her goal.

Indeed, the term used for the end of the development is the darkest moment Bordwell, ; Keating, ; Smith, Interestingly, until recently Cutting, , there was no evidence that this was literally true.