The Digital Secret of the Moving Image

First, I analyze the five conditions that constitute Noël Carroll’s definition of the moving image, and I argue that the third condition – the typetemplate-performance condition – raises a problem concerning the relationship between the cinematic type and the digital type. Solving this problem allows us to explain away the other conditions introduced by Carroll, and to give a simpler formulation of the definition of the moving image. Then, I compare this new definition to a similar amendment of Carroll’s definition proposed by Trevor Ponech. Finally, I test my definition by considering two issues that all attempts to define the moving image have to deal with: the historical issue and the depiction issue.

yet neither Ingarden nor Cavell specify what ontological category things like 'visible music' or 'moving image of skepticism' should belong to.
On the other hand, Walter Benjamin provides us with a useful insight for an ontological characterization of cinema, suggesting that a key feature of cinematic works is their 'technical reproducibility. ' 3 Still, Benjamin aims to highlight social and cultural consequences of technical reproducibility rather than to investigate its ontological underpinnings.
In the history of the attempts to define or characterize cinema, Noël Carroll was, it appears, the first scholar who made the dependence of definition on the ontological question explicit. 4 Carroll's definition of what he prefers to call 'the moving image' includes an insightful ontological account of cinema. But I believe that the connection between ontology and the definition of the moving image requires further investigation.
With this aim in mind, I shall start by introducing the five conditions that constitute Carroll's definition of the moving image. Some of these conditions treat the moving image as a particular display, while others treat it as a type, a nonparticular entity that can be instantiated by particulars (II). The latter conditions raise an ontological puzzle when the moving image is a digital movie. In this case, the moving image as a type is instantiated by a digital encoding which in turn is a type; therefore, the digital encoding of a digital movie enigmatically ends up being both a type and a token. Solving a puzzle of this sort leads us to conceive of the moving image as a type that specifies a spatiotemporal distribution of pixels (III). I shall argue that this new definition can autonomously take into account all those specifically cinematic features which Carroll accounted for by means of his five conditions (IV, V, VI, VII, and VIII). Finally, I shall investigate the key notions of pixel and type in more depth, thereby establishing to what extent an account of the moving image as a type involves an account of cinema as a Platonic form of art (IX and X).

II. CARROLL'S DEFINITION OF THE MOVING IMAGE
Carroll addresses the problem of definition by describing five conditions an entity x must satisfy in order to qualify as a moving image: (1) 'x is a detached display. ' 5 More specifically, the cinematic display consists of a 'visual array' , and it is 'detached' since it provides the spectator with The Digital Secret of the Moving Image 3 Walter Benjamin, 'Das Kunstwerk im Zeitalter seiner technischen Reproduzierbarkeit' , in Schriften (Frankfurt: Suhrkamp, 1955), 431-69. 4 Noël Carroll, Theorizing the Moving Image (New York: Cambridge University Press, 1996). 5 Ibid., 70. the visual experience of a space which is not connected to her body. 6 The space S presented by the display does not allow the spectator to orient her body with respect to S through an experienced connection between S and her body. The display provides the spectator with a perspective on a space, but this perspective is reduced to a 'disembodied viewpoint.' 7 Through the display, the spectator experiences a space that is not her space.
(2) 'x belongs to the class of things from which the impression of movement is technically possible. ' 8 That is to say, the cinematic display is technically produced in such a way that it can provide the spectator with a visual experience of movement.
(3) 'Performance tokens of x are generated by a template that is a token. ' 9 In claiming that x has tokens, Carroll is presupposing that x is a type, a nonparticular entity that can be instantiated by particulars. Furthermore, Carroll calls 'templates' those particulars that instantiate x in virtue of their being objects (for example, film print, videotape, DVD, computer file), while he calls 'performance tokens' those particulars that instantiate x in virtue of their being events -namely, screenings.
(4) 'Performance tokens of x are not artworks in their own right.' 10 That is, the screening of a movie, unlike the execution of a symphony or the staging of a play, is not artistically evaluable in its own right. What one can artistically assess is nothing but the movie as a type.
(5) 'x is […] two-dimensional. ' 11 That is, the visual array constituting the cinematic display is just a flat surface.
In a later work, Carroll strengthens his definition by arguing that the five necessary conditions are also jointly sufficient. 12 In the previous account, Carroll characterized the conditions as necessary but not jointly sufficient, since he did not intend to include among the moving images some artefacts (such as flip books and the zoetrope) that nonetheless satisfy all the necessary conditions. Yet, in the new account, Carroll changes his mind, thereby treating those artefacts as So, x is a moving image if and only if (1) x is a detached display or a series thereof; (2) x belongs to the class of things from which the promotion of the impression of movement is technically possible; (3) performance tokens of x are generated by templates that are themselves tokens; (4) performance tokens of x are not artworks in their own right; and (5) x is two-dimensional. Notice that each of these five conditions is alleged to be necessary and to be conjointly sufficient. 13 It is worth noting that conditions (3) and (4) are ontological requirements that establish what kind of entity a moving image is, while conditions (1), (2), and (5) rather specify what further features an entity of that kind must possess in order to be a moving image. Let us call the former type-conditions and the latter display-conditions.
Carroll's definition has been criticized both as too essentialist by Trevor Ponech and as not essentialist enough by Thomas Wartenberg. Still, both such criticisms focus mainly on display-conditions rather than on type-conditions. Ponech focuses on condition (1) and argues that the essence of the moving image can be made explicit by revealing the structure of its displays. 14 Wartenberg focuses on condition (5) by arguing that the requirement of two-dimensionality makes the nature of the moving image strongly dependent on our current historical context in which technologies for the production of holographic movies are still not available. 15 Unlike Ponech and Wartenberg, I shall criticize Carroll's definition by focusing on type-conditions and their relationship to display-conditions. For this purpose, I start by questioning whether the term x really refers to the same kind of entity in these two groups of conditions.
On the one hand, in display-conditions, x seems to refer precisely to a display, that is, a two-dimensional visual array that portrays a detached space, and may trigger the impression of movement. On the other hand, in conditions (3) and (4) x designates the moving image as a type having templates and performances as its tokens. Yet the display, as a visual array, should be a particular entity, whereas the type, as such, is a non-particular entity. 16 How can the putative moving image x be both particular and non-particular? Of course, it cannot. Since the type unquestionably is a non-particular, the only way to reconcile the moving image as type with the cinematic display is to conceive of the display as the last step in the instantiation of the type. In other words, the display should not be identified with the moving image as such, but rather with the instance of the moving image that Carroll calls 'performance token. ' Thus, we can rephrase Carroll's definition by claiming that the moving image is a type that can be instantiated by a display that should be (1) detached; (2) capable of triggering the impression of movement; (3) produced by means of a template; (4) non-artistically-evaluable as such; and (5) two-dimensional.
Nevertheless, once we turn to the special case of the digital moving image, then Carroll's definition, even in such different guise, raises a puzzle, which I will focus on in the following section.

III. THE PUZZLE OF THE DIGITAL TYPE
Carroll claims that the main difference between theatre and cinema is that 'the play performance is generated by an interpretation that is a type, whereas the performance of the motion picture is generated by a template that is a token' . 17 Furthermore, in his 1996 book, he claims that the cinematic template 'is a film print, but it might also be a videotape, a laser disk, or a computer program ' . 18 And, in his 2008 book, he specifies that the cinematic template 'was a film print, but in recent decades it might be a videotape, a laser disk, a DVD, or an instantiated computer program ' . 19 I see Carroll's adding of the adjective 'instantiated' to the term 'computer program' as the clue to a peeping puzzle. If the cinematic template is a computer program, as Carroll writes in 1996, then the evidence that a computer program is a type which is made of digital symbols contradicts Carroll's claim that the cinematic template is a token. In his 2008 book, Carroll tries to avoid such contradiction by specifying that, in the digital case, the cinematic template is not a computer program but an instantiated computer program. Yet, in the latter case, a new puzzle pops up.
Consider a moving image whose template is an instantiated computer program or, better yet, an instantiated digital file, which consists of traces or circuits. Such a concrete particular is both the template token of a cinematic type C (that is, the moving image as type) and the token of a digital type D (that is, the file as sequence of digits). We thus have two types at play. Are those 17 Carroll, Theorizing the Moving Image, 70. 18 Ibid., 67, my emphasis. 19 Carroll, Philosophy of Motion Pictures, 66, my emphasis.

Enrico Terrone
Estetika: The Central European Journal of Aesthetics, LI/VII, 2014, No. 1, 00-00 C and D the same type or two different types? In the latter case, what exactly is the relation between C and D?
At a first sight, C and D seem to be completely different types. As pointed out by Nicholas Wolterstorff and Julian Dodd, the cinematic type C specifies what visual qualities ought to be instantiated by showings. 20 By contrast, the digital type D specifies a sequence of digital symbols, so that D is not instantiated by visual showings but rather by physical representations of this sequence of symbols.
Still, C and D are related to one another, since D specifies the sequence of symbols that allows C to be instantiated by a visual array. A token of D, if coupled with an appropriate device capable of translating the digital symbols into chromatic values, behaves as a cinematic template whereby C is instantiated by a showing.
To sum up, the shift from an analog template to a digital template involves a change in the instantiation of the moving image. In the analog case, the whole instantiation required a two-stage process: first, the moving image was embodied by a template; second, the template was used to generate a screening. In the digital case, the structure of instantiation is more complicated. The moving image is not directly embodied by a physical template, but rather encoded by a digital template which is in turn a type -the digital type. The sequence of symbols specified by such digital type is embodied by a physical particular (made of traces or circuits) which is finally used to generate a screening. Therefore, in the digital case, the whole instantiation of the moving image requires a three-stage process: first, the cinematic type is encoded by a digital type; second, such a digital type is embodied by a physical particular; third, such a particular is used to generate a screening.
The mediation of the digital type D between the cinematic type C and its final showing allows us to understand exactly what C itself is. The structure of C, indeed, has to be such that it can be encoded by means of the structure of D.
In the digital type D, symbols are placeholders for light values, which correspond to chromatic qualities. I will call such values pixels. A pixel, so understood, is not the digital encoding of a light value but the light value itself.
Furthermore, D is structured in a temporal series of frames, each of which is made of a spatial distribution of pixels. Since the structure of D is aimed to encode According to Wolterstorff, the moving image is a type instantiated by 'an occurrence of a sequence of illuminated colour-patterns (counting black and white as colours)' . According to Dodd, 'a film, after all, is just a type whose tokens are datable, locatable showings' . the constitutive features of C, should we infer that C consists of a temporal series of frames which are made of spatial distributions of pixels?
Such a question presents us with a dilemma: either a cinematic type C cannot be wholly encoded by a digital type D, or C should have constitutive features that can all be encoded by D. Choosing the first option amounts to claiming that there are movies that cannot be digitally encoded, but this claim seems to contradict our practices concerning movies and their appreciation. For example, the practice of digital restoration of early films would no longer make any sense if old analog films had constitutive features that could not be encoded by the structure of the digital type. 21 Thus, we are left with the second option. Since the only features that can be encoded by the digital type concern temporal series of frames and spatial distributions of pixels, choosing the second horn of the dilemma amounts to acknowledging that the cinematic type is wholly characterized by temporal series of frames and spatial distributions of pixels. Here is the new definition of cinema.
The moving image is nothing but a type specifying a temporal series of frames that are made of spatial distributions of pixels. In short, the moving image is a type that specifies a spatiotemporal distribution of pixels.

IV. RETHINKING THE MOVING IMAGE
The digital encoding of a moving image is not a token template, that is, a concrete particular. It is rather an abstract notational structure that reveals the ontological structure of the moving image as a type. With respect to concrete templates like film strips or videotapes, indeed, the digital encoding has an epistemological advantage, that is, it makes the ontological structure of the moving image explicit.
In this sense, technology reveals the essence.
The unpacking of Carroll's condition (3), which concerns the cinematic types and its tokens, leads us to a thorough definition of the moving image. But what about the other four conditions of Carroll's definition? How can they be traced back to the ontological structure that is made explicit by the digital type?
As we have seen, conditions (1), (2), and (5) are display-conditions in which x refers to the display that instantiate the moving image, whereas conditions (3) 21 Scholars like Rodowick or Aumont suggest that analog movies have features that digital movies necessarily lack. I cannot analyse their arguments in this article, so I limit myself to observing that endorsing such arguments, in the current era in which almost all cinema is becoming digital, amounts to claiming that a relevant portion of the history of cinema is about to disappear. I do not believe so. Digital technology currently guarantees high definition in such a way that it is hard to see how even very fine texture could not be and (4) are type-conditions in which x refers to the moving image as a type that can be instantiated by displays. Addressing the puzzle of the digital type has led us to develop condition (3) so as to define the moving image as a type that specifies a spatiotemporal distribution of pixels, which can be instantiated by displays.
Still, according to Carroll's other conditions, the display that instantiates the moving image has further necessary features: (1) it is detached; (2) it is capable of producing the impression of movement; (4) it is not artistically evaluable; and (5) it is two-dimensional. In the following sections, I shall argue that all these features of the display can be taken into account in terms of the cinematic type introduced in condition (3). More specifically, I shall consider detachment in section V, impression of movement in section VI, two-dimensionality in section VII, and non-evaluability in section VIII.

V. DETACHMENT
Condition (1) of Carroll's definition states that the cinematic display is detached, that is, in watching the display, the spectator experiences things that are not localizable in the spatiotemporal system that has her body as its centre. In other words, the moving image supports an experience that allows the spectator to recognize what there is, but not where she is with regard to what there is.
Indeed, a particular showing of a moving image is not necessarily detached.
I can use my web-cam as a mirror while shaving. In this case I can recognize where I am with regard to the displayed scene. The display is necessarily detached only if it is considered as a token of the moving image as a type. Treating the display as a token requires that the scene displayed can be shown in a multiplicity of different spaces, without any special connection to the spectators who inhabit those spaces. If we conceive of the display as a token, then it does not matter whether I can shave by looking at my web-cam. From this perspective, the current display of my web-cam is just the token of a type that can be displayed in a multiplicity of other circumstances. What matters is that the generic spectator of a showing of the moving image produced by my web-cam cannot shave by looking at it. In this sense the cinematic display is detached in virtue of its being the token of a type.
Since the repeatability of the moving image as a type allows this image to be replicated in several different spaces, the displayed space cannot have any special connection to the bodies placed in all those spaces. Repeatability necessarily breaks the spatial connection between the displayed space and the space of the audience. If we consider the display as a particular event, nothing prevents the displayed space from being connected to the space that the beholder The Digital Secret of the Moving Image inhabits. What makes the displayed space necessarily detached is the repeatability of the moving image as a type. The only token that is connected to the spectator's own space is arguably the particular display that instantiates the moving image during its production, as in a web-cam used as a mirror. But if the display is considered as any token of an existing moving image, then it is necessarily detached from the space of the spectator.
From this perspective, all the 'prosthetic devices' 22 (for example, mirrors, microscopes, telescopes) that Carroll attempts to distinguish from the moving image by means of the detached display condition can be distinguished much more simply by considering that they do not have a type-token ontological structure. Mirrors, as well as other glass-based prosthetic devices, cannot be repeated. They are nothing but visible particulars. They are not tokens of types that specify visual features. There is no type of which several mirrors, being displays, are all tokens. Any mirror displays only its own space. The basic ontological difference between mirrors and moving images is that the former are just particulars whereas the latter are tokens of types. The fact that moving images are detached display whereas mirrors are not simply follows from such a difference.

VI. IMPRESSION OF MOVEMENT
In formulating condition (2), Carroll considers the spectator's disposition to believe that what the display presents might move, instead of giving the mere impression of movement, because he wants to take into account works such as Marker's La jetée, Frampton's Poetic Justice, and Snow's One Second in Montreal, made, partly or wholly, by still images. According to Carroll, these works are different from a mere slide show because spectators of the former can legitimately expect (at least at the first viewing) that sooner or later there will be some movement in the pictures. As Carroll puts it, 'it is always justifiable to entertain the possibility that the image might move' . 23 I also argue that this condition can derive from the structure of the cinematic type that the digital encoding makes explicit. 'To entertain the possibility that the image might move' is indeed 'always justifiable' because the moving image as a type consists of a series of frames whose temporal rate is capable of affording the impression of movement to our perceptual system. The epistemological possibility (we know that there could be movement) is based upon an ontological possibility (the type consists of a series of frames, so it is capable of affording the impression of movement to us). Paintings and photographs cannot move 22 Carroll, Theorizing the Moving Image, 57. 23 Carroll, Philosophy of Motion Pictures, 60.

Enrico Terrone
Estetika: The Central European Journal of Aesthetics, LI/VII, 2014, No. 1, 00-00 since they consist of a spatial distribution of coloured points, whereas the moving image can move (and spectators believe it can) since it consists of a spatiotemporal distribution of coloured points.
In short, the movie's content can move since the movie not only occupies a surface, but also has duration. The moving image does not consist of a series of frames because it can move: it can move because it consists of a series of frames.
That is why 'movement is a permanent possibility in cinema. ' 24 Even in the cases in which the moving image does not really move, it might move, because the cinematic type carries this possibility in its structure. Still, if the moving image ultimately is a spatiotemporal distribution of pixels, how can we distinguish moving images from slide shows? Slide shows are also constituted by series of frames, that is, spatiotemporal distributions of pixels. How do they differ from moving images? I argue that slide shows belong to an ontological category that is between still images and moving images. More specifically, the slide show provides us with an experience that is akin to the experience of still images, but rests upon an ontological structure that is akin to the structure of moving images.
The difference between the slide show and the moving image is basically a matter of frame rate. Below a certain threshold rate R1, the series of frames is experienced as a series of still images. Above a certain threshold rate R2, the series of frames is experienced as a moving image (likewise, a series of musical notes can be heard as a continuous melody only if such notes are played at a rate that is above a certain threshold). In between R1 and R2, the series of frame is experienced as a jerky image, that is, an image that is no longer still but not yet moving.
In spite of lacking the possibility of the impression of movement, slide shows exhibit a distinctive temporal mood. Like moving images, and unlike mere books of images, slide shows can be synchronized with sounds. Yet the frame rate of a slide show, unlike that of a moving image, is not necessarily established by the maker or by the practice, but can be up to the presenter. 27 To sum up, Carroll's conditions (1) and (2), which describe the relation between the cinematic display and the experience of the spectator, can be explained in terms of structural features of the moving image as a type. Cinematic displays afford detachment and impression of movement to the spectator because they are tokens of the moving image, which is a type constituted by a series of frames made of pixels. Detachment and impression of movement are phenomenal and epistemic consequences of the ontological structure of the cinematic type, as well as being transparent and drinkable are phenomenal and epistemic consequences of the chemical structure of water.

VII. TWO-DIMENSIONALITY
Carroll introduces the requirement of two-dimensionality in order to exclude 'moving sculptures of the sort that are exemplified by the moving figurines on various antique clocks' from the domain of the moving image. 28 This sort of moving sculpture is akin to the moving image to the extent that they both present a detached space in which we can see movement. Furthermore, they have both multiple instances that are produced from a template.
Still, moving sculptures are three dimensional whereas moving images are twodimensional. 29 The requirement of two-dimensionality is thus sufficient to exclude moving sculptures from the cinematic domain. On the other hand, Carroll acknowledges that this requirement is not sufficient to cleave the moving image from theatre. That is because 'there is, in fact, theater that is two-dimensional, for example the shadow-puppet shows of Bali, Java, and China' . 30 27 A quite impressive example of a slide show whose frame rate is up to the performer can be found in the so-called 'Kodak Carousel scene' of the TV series Mad Men (Season 1, episode 13; the scene is available on YouTube with the title 'Mad Men -The Carousel'). 28 Carroll, Philosophy of Motion Pictures, 72. 29 By claiming that moving images are two-dimensional, Carroll means that their screenings take place on flat surfaces. Of course, what is seen by spectators in such two-dimensional surfaces can (and usually does) consist of three-dimensional scenes. 30 Ibid., 73. In order to cleave motion pictures from shadow-puppet shows, Carroll exploits his condition (3) -namely, the type-template-performance condition. But his solution raises a question that he does not explicitly consider. What about a shadow-puppet show made by means of a moving sculpture? Since this sort of shadow-puppet show satisfies both the two-dimensionality requirement and the type requirement, we should conclude -against our intuitions -that it is a moving image. Thus, the moving sculpture has not really been explained away by the two-dimensionality condition. If we use moving sculptures in a shadowpuppet show, the problem pops up again.

First, if you want to preserve the intuition according to which 'still movies' like
Letter to Jane are moving images, then you should accept into the domain of the moving image any object-generated image that might exhibit movement.
Such a domain, which in Gaut's account is already immense, is further extended.
Even the shadow on the wall, which is generated by my table, is a moving image, since my table might move, and therefore its shadow might move.
Second, in spite of our shared understandings, in Gaut's account cinema is no longer something that was invented towards the end of the twentieth century, but rather something almost as old as the wheel or the knife. From such a perspective, to treat the Lumière Brothers as the inventors of cinema would be as wrong as to treat Gutenberg as the inventor of writing. Indeed, I agree that it is arguable whether the Lumière Brothers really invented cinema. In cinema museums, you can find many screening devices made in the nineteenth century that somehow anticipate the Lumières' Cinématographe. Yet I do not know of any cinema museum in which shadows of tables are exhibited as examples of cinema.
In this sense, Gaut's ontology of cinema is too hospitable, even to the point of contradicting established practices, intuitions, and judgements concerning cinema.
If you want to avoid such a slippery slope towards too hospitable an ontology of cinema, you should find a safer way than Carroll's to prevent moving sculptures from counting as moving images. For this purpose, it is worth setting Carroll's condition (5) (the two-dimensionality requirement) aside, and looking once again to his condition (3), that is, to the structure of the moving image as a type. Moving sculptures differ from motion pictures because they have different structures at the type level. The type of the moving sculpture is not made of a spatiotemporal distribution of visual qualities; rather it includes properties such as height, weight, and chemical composition. The moving sculpture is excluded from the cinematic domain because of the different ontological structure of its type, not because of its three-dimensionality.
Such a difference in ontological structure also explains why the moving image, which is just made of visual (and possibly auditory) qualities, provides us with the impression of movement, whereas the moving sculpture, which has further physical and chemical features, provides us with true movement. Furthermore, the distinctive ontological structure of the moving image as a type allows us to take into account the possibility of holography, whose affinity with the moving image is suggested by Carroll himself: 'Imagine that we could project a scene of mortal combat in the Coliseum three-dimensionally with the audience seated around the virtual arena like ancient Romans. Would not such a spectacle be rightfully categorized as a moving image?' 33 33 Carroll, Philosophy of Motion Pictures, 73. We need a criterion to distinguish holographic screenings, which our intuition is prone to consider as moving images, from moving sculptures, which we aim to exclude from the cinematic domain. The two-dimensionality condition fails to support this distinction, since Carroll is forced to exclude both moving sculpture and holography from the cinematic domain. But if we pose as a criterion the ontological structure of the type, then we can treat holograms as peculiar cinematic types whose frames are three-dimensional distributions of pixels, instead of two-dimensional ones like in ordinary movies. In this way, we can substantially exclude from the cinematic domain only the moving sculptures, whose types are not spatiotemporal distributions of pixels at all, while preserving the cinematic nature of holograms in spite of their three-dimensionality. In short, the ontological structure of types explains why the hologram is not different from the moving image whereas the moving sculpture is. 34

VIII. NON-EVALUABILITY
Carroll's condition (4) claims that cinematic tokens lack artistic value. I argue that such lack follows from the fact that all you need in order to instantiate a moving image is already specified by the corresponding type, and no further contributions are required. You only need to instantiate the visual (and auditory) patterns constituting a moving image as a type, that is, the patterns established by the makers of the image. Such instantiation can be done with merely automatic processes, in which there is no room for human intentionality and creativity, and, a fortiori, for artistic value. By virtue of the cinematic type's ontological structure, once the makers of a moving image constitute it as a type, the subsequent displays will be just a matter of automatic technical processes.
On the other hand, theatrical performance is an interpretation that involves intentional acts. The reason for the sharp difference between cinema and theatre lies precisely in the structure of the type. The theatrical work as a type is just a written text, so in principle it cannot specify all the perceptible properties that should constitute an experienceable instance of the work. In order to turn such a text into a theatrical production you need some creative act of interpretation.
By contrast, the cinematic type, as a spatiotemporal distribution of visual qualities, specifies all the relevant experienceable features that constitute an instance of the moving image, leaving no room for interpretation and preventing the screening of a moving image, unlike the presentation of a theatrical performance, from being evaluated as a work of art in its own right. Shadow-puppet shows of any kind also differ substantially from moving images since the former are not individuated by discrete spatiotemporal distributions of frames and pixels but by continuous spatiotemporal distributions of light and darkness.
The structure of the cinematic type, conceived as a spatiotemporal distribution of pixels, is such that, at the token level, it only remains to make those distributions accessible to the viewers. Of course, we can distinguish between better or worse screenings. But a normative distinction of this kind only concerns technical procedures. Some displays may correctly instantiate the visual pattern specified by the type (as in high definition copies and high quality projectors), while others may have poor quality (as with VHS copies or old and worn projectors). But the difference between a good and a bad screening of a moving image is not a matter of interpretation at all, let alone of artistic value. It is only a matter of technical approximation to the visual appearance wholly specified by the moving image as a type.

IX. PIXELS
So far, I have argued that the moving image is a type specifying a spatiotemporal distribution of pixels. In these final sections, I shall focus on the fact that not only digital movies but moving images in general are types specifying spatiotemporal distributions of pixels. For this purpose, I shall analyse in more depth the key notions of pixel and type.
According to Ponech, pixels are particular points of light: '"Pixel" usually denotes "picture element". I use it in a slightly adjusted but related technical sense. By "pixels" I intend points of light. This usage converges with descriptions of movie images as constructed from separate regions varying independently in spectral distribution. At a basic level of physical description, visual displays are composed of pixels. ' 35 Pixels, so understood, are constitutive elements of both digital and analog displays. The only difference is that the points of lights constituting a digital display are arrayed in a grid whereas in analog displays they are not. In the latter case, indeed, the spatial distribution of pixels matches the irregularbut nevertheless discrete -distribution of individual grains on the film strip.
The cinematic display is essentially discrete, that is, consisting of particular points of lights separated by temporal and spatial interstices. Discreteness is sharply exhibited by the digital display, whose pixels are regularly distributed in a grid. Discreteness also characterizes analog displays, whose pixels are separated by spatial interstices in spite of the lack of a regular grid, since every frame consists of individual grains of colour. Furthermore, both analog and digital pixels belong to frames that are separated from each other by temporal interstices, since analog and digital projectors both show a limited number of frames per second, and since the film of analog projectors alternately blocks and reveals light. 35 Ponech, 'Substance of Cinema' ,. The limit of Ponech's account is the conception of the pixel as a particular point of light. The pixel, so understood, can only concern a particular display, that is, a particular showing of a moving image. It follows that any new showing involves a completely new series of pixels on the screen. Therefore, Ponech's characterization of the moving image in terms of pixels cannot take into account the moving image as a repeatable work that can be instantiated by a multiplicity of showings. If the moving image is made of pixels that are no more than particulars, then there is no appropriate way to relate the screening of Behind the Candelabra that I watched in London to another screening of the same movie that took place in Los Angeles.
Therefore, I agree with Ponech that pixels are 'the substance of cinema' , 36 but I argue that in order to take repeatability of cinematic works into account we should conceive of the pixel not as a particular point of light but rather as a value of light which can be instantiated by a multiplicity of particular points of light.
If all of this is right, both digital and analog moving images are types that specify pixels. The only difference is in the way in which the cinematic type specifies the pixels that should be instantiated by displays. In the analog case, pixels are implicitly specified by means of concrete templates, as, for example, reels of celluloid that allow us to instantiate roughly the same spatiotemporal distribution of light values at each showing of a given moving image. By contrast, in the digital case pixels, can be explicitly specified as light values, because the template is no longer a concrete object but a series of numbers denoting light values.
In a similar vein, Gaut accounts for digital cinema by conceiving of the pixel as a discrete unit that measures 'the light intensity […] as a discrete integer' . 37 Yet he challenges the claim that, in digital pictures, the pixel is a 'minimal denotative unit' by claiming that 'the parts of a pixel denote the parts of the area of the object that the pixel denotes.
[…] The denotation relation still holds at the sub-pixel level. The parts of a pixel do denote, unlike the parts of a word.' 38 That is to say, if we look closely at a pixel on the screen, then we can see a small coloured area denoted in turn by its coloured parts.
I contend that Gaut's argument is wrong, since what we really see in looking closely at the screen is not the pixel itself but the particular spot of light that instantiates the light value constituting the pixel. This spot of light is seen as a small coloured area having coloured parts, but the pixel instantiated by this token is a light value having no parts at all. By claiming that in digital pictures the pixel is not a minimal denotative unit, Gaut seems to mistake the ontological nature of the pixel with the empirical fact that the particular spots of light instantiating pixels are not usually recognized by viewers as minimal denotative units. But, in digital pictures, the pixel is a minimal denotative unit since it is not a particular spot of light but rather a light value that denotes the light intensity in a precise spatiotemporal location.
In challenging the claim that in digital pictures the pixel is a minimal unit, Gaut also argues: The digital photograph is not […] different from a traditional photograph. For the latter is comprised of sometimes billions of individual grains […] In this respect there is also an array of picture elements in the traditional photograph, albeit one with vastly more elements than is usual in digital photographs, and which are not arrayed in a grid. Keep on enlarging such a photograph, and in the end one will see individual grains, from which the object is not recognizable, even though the grains denote parts of the object. 39 Still, those considerations do not necessarily show that pixels are not minimal denotative units. Rather, they seem to show that traditional photographic pictures also have minimal denotative units, grains, which play the role of pixels, in spite of the lack of a notation capable of representing them. Let us consider, in this sense, the example proposed by Gaut: 'This is the lesson of Michelangelo Antonioni's Blow-Up (1966): as Thomas, the photographer played by David Hemmings, keeps enlarging the image that he thinks shows a murder, the grains of film become more prominent and it becomes impossible in the end to tell what they denote. ' 40 If, as Gaut writes, 'the grains become more prominent' , then the grain must not to be identified with the area it occupies on the paper (or on the screen, if we move from the photographic example to a hypothetical cinematic counterpart of it). An area that becomes more prominent is no longer the same area. The grain has rather to be identified with a light value, which could be instantiated by more or less prominent areas on the paper (or on the screen). Conceiving of the moving image as a normative type allows us to take into account an indispensable aspect of our cultural practices, that is, the fact that we usually assess not only cinematic works ('this is a good movie, that is a bad one') but also instantiations of these works ('this is a faithful screening, that is a flawed one'). Carroll's condition (4) points out that the former is an artistic assessment whereas the latter is rather a technical assessment. Still, they both are assessments which rest upon some form of normativity. More specifically, the artistic assessment rests upon some standard of taste, whereas the technical assessment rests upon the work itself, understood as a normative type that establishes the standard for its correct screenings.

Moreover, in developing the
According to Wolterstorff and Dodd, treating a type as normative obliges us to treat this type as a Platonic universal. Therefore, movies or symphonies, as normative types, are 'abstract, fixed, unchanging, and eternally existent entities' . 42 Yet David Davies challenges the claim that conceiving of moving images as normative types commits us to such a counterintuitive Platonic view, according to which movies are not created but discovered. 43 He argues that we can conceive of the moving image as a normative type by considering the Wittgensteinian account of normativity developed by Robert Brandom: 'a pragmatist conception of norms -a notion of primitive correctnesses of performance implicit in practice that precede and are presupposed by their explicit formulation in rules and principles' . 44 In such an account of normative types, what establishes whether a particular display D is a correct instance, a flawed instance, or a non-instance of a given cinematic work W is not an explicit list of light values residing in the abstract space The Digital Secret of the Moving Image 41 of the universals where they are grasped and made normative by the filmmaker.
Instead, the status of D as an instance of W depends upon an implicit negotiation between two parties: what the filmmaker specifies in making his or her work W public in a given cultural context, and the practices that implicitly establish which displays are fully qualified to play the experiential role in the appreciation of W.
According to Davies, there are no explicit rules of correctness for the instantiation of a given moving image W. Practices sanction conditions of appreciation of W, and cinematic displays are technically assessed with respect to the role they play in appreciation of W, but nothing more.
I agree with Davies that normativity of the moving image as a type rests upon cultural practices rather than upon some abstract, fixed, unchanging, and eternal entity. Yet I think that, in this respect, digital cinema requires special treatment, since digital technology allows us to produce instances of a given image (regardless of its being static or moving) which are all 'phenomenally identical in respect of color, shape, and size'. 45 That is because digital technology provides us with a sort of notation whereby we can represent an image W by means of a script S of discrete symbols that denote the points of light constituting W. Thus, in order to instantiate W, we only need some device capable of translating the discrete symbols constituting S into the points of light constituting W. If these devices are properly functioning, then all instances of W produced by coupling such devices with S are phenomenally identical.
In principle, digital cinema enables the filmmaker to establish once and for all the only way in which correct instances of her work should appear. Specifying a moving image W by means of a digital script, indeed, amounts to unequivocally establishing the appearance of any correct instance of W. In this way, the standard of correctness for the instances of W is no longer implicit in practice, but is made explicit by means of the digital script. As a thought experiment, we can even conceive of special digital devices (perhaps embedded in mobile phones) with which movie-goers can check whether the movie they are watching is shown correctly. Such devices could measure light values on the screen and compare them with the original light values approved by the filmmaker and stored in some online database.
If all of this is right, should we conclude that digital technology turns moving images into everlasting Platonic entities? I do not think so. Digital technology is something that was created in the context of our cultural practices. For this 45 John Zeimbekis, 'Digital Pictures, Sampling, and Vagueness: The Ontology of Digital Pictures' , Journal of Aesthetics and Art Criticism 70 (2012): 51. It is worth noting that, according to Zeimbekis, the digital encoding of pictures is a notational schema, but is not a full-fledged Goodmanian notational system since it lacks Goodman's semantic requirement of finite differentiation. Nevertheless, digital technology seems capable of supporting what we could call a Platonic practice, that is, a way of univocally establishing the appearance of a work that no longer depends on metaphysical virtues but rather on technical devices. Such devices are a necessary condition for the rise of a Platonic practice but not a sufficient one. Agreement is also required. Therefore, cinema can become a Platonic practice, namely, Platonic cinema, only if practitioners agree that all correct screenings of a moving image W ought to be phenomenally identical by complying with the pixels specified once and for all by the maker of W.
Currently, we have a technique allowing for Platonic cinema, but we do not yet have a practice establishing Platonic cinema as the cinematic medium in force.
In spite of the fact that digital technology enables us to make moving images explicit in terms of unique series of pixels, we keep relying on the implicit normativity of cultural practices in order to constitute movies as spatiotemporal distributions of light values. Yet if we want to be sure of transmitting not just instances but correct instances of our movies to future generations, then Platonic cinema, which our technology already enables in principle, is the right way forward.