It is always superior to utilize some mathematics to help quantify the behavior of a system or the distribution in a system to be more particular to our case. The Gaussian curve (or bell curve) is used in a variety of areas to statistically quantify the shape of the distribution graph. Not all distributions of measured values in a system are truly a Gaussian distribution, however, it is widely accepted to make the assumption of a Gaussian distribution because, often the shape of the measured data points seem to fill a bell curve shape as the number of data points increases. The importance of using statistics, particularly distribution either Gaussian, Piossen, etc. is the shape, whether sharp or wide, gives a graphical (and analytical) measurement of the experimenter’s precision through the variance of the distribution away from the mean (and related, the standard devation). Now, I’m sure you’re wondering how does this even matter? Suppose that ‘horror’ was a measurable quantity, either by measuring its constituent parts and deducing the “value” of horror, or just directly measuring horror value. If we had no way to measure the value of horror, then it would be impossible for us to place it into a genre, and preclude other from the horror genre. It is mostly likely that measuring horror is measured by its constituent parts (the requirements for horror, like Noel Carrolls, necessary condition of a monster) on some rating scale of 1-5 perhaps and if the sum of all constituent pieces is above some certain threshold value, then the work can be considered a work of horror. Now using this methodology there would be for, each value of horror and number of works that have that value, and if we made a histogram plot, where on the x-axis we had discrete bin values of say 3,4,5..15, and then the y-axis would be the number of works that have X bin value. (See below)
fig 1.1
It is the fact, that because we can say there is some ‘mean’ to what a horror work is and that a large number of totally horror works are that mean value, then we can find a distribution around the mean value like in figure 1.1 where the mean value is the tallest bar in the center. Noel Carroll put some strong restriction on what it means to be a work of horror, and whether or not the work can art-horrify an audience, while further philosophers like Freeland, have expanded Carroll’s work and loosen the reins of art-horrifying it and broadened the idea by saying a work can art-terrify an audience. Now, this is the roughest approximation, and most analogyish statement. Suppose, using Carroll’s art-horror, Freeland’s art-terror, and combine this with the idea of horror following a normal distribution with a standard deviation. One standard deviation away from the mean incorporates ~60% of all works, lets define the standard deviation where =value 1-5 of each rated part, and TCarroll= is threshold of allowed works by Carroll’s definition and requirements. Similarly, for Freeland we define where TFreeland is the threshold of allowed works by Freeland definition and 2σ would incorporate ~95% of all horror works. Now this is really mathy-nerd-analogy and not really solid, but it gets the right ideas moving about. When analyzing and measuring a film or work, there is often times a lot of cross talk between genres, this is due to the distribution of each type of genre having overlapping edges (See Below)
fig 1.2
The idea of overlapping distribution lead me to the idea of horror existing in the positive quadrant of a 3- dimensional space where, the x-axis is the real axis (the amount of realism in the work) the y-axis is the uncanny axis (the amount of uncanny things in the work) and the z-axis being the marvelous axis (the amount of super-natural things in the work). Using the three orthogonal axis, the R-axis (real), the U-axis (uncanny), and the M-axis (marvelous) we develop a space where, Fantasy, Drama, and Action are 2-D planes defined by the combination of the orthogonal axis. (see below)
fig 1.3
Where horror follows some 3-d distribution in that space where some works are closer to the Fantasy plane, some closer to drama plane, and some are closer to action plane. If we reduce our view to the Fantasy plane, then using the ideas of Todorov, with the pure fantastic, the fantastic marvelous, and the fantastic uncanny, there is a simple linear model that follows. Suppose we have the M-axis, where the y-axis normally is, and the U-axis where the x-axis normally is, then we can define a line of the pure fantastic. (see below)
Fig 1.4
Where the pure fantasy line is defined as YPure Fantastic = , where
And wi & wj are the weights of how persuasive each event Ei & Ej are the value of the event that reveals if it is uncanny, or supernatural, if the sum of the Marvelous events, are equal to the sum of the uncanny events, then the work lies on the pure fantastic line, and follows Todorovs descriptions of fiction. In the three dimensional space in fig 1.3 the pure fantastic line can be generalized to a 3-d line with an equal rotation from every axis. These math ideas aren’t actually models based on collected data, but rather math analogies that help flesh out ideas present in class when covering and working through the different aspects of what really makes up a horror work.
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