The Bartlett Faculty of the Built Environment
In 'Space', the object - or architecture - is generated by a cumulative process of information (geometrical transformations, visual sequences, sound structure…) directly related to the psychological and physiological user’s frames. Each interaction transforms the visible environment in a dynamic, elastic and multidirectional imaginary space. The relationship between the object-space system (geometrical and phenomenological determinate) and the body-mental projection system (subjective view /aural decoded data ) induces new modes of perception strictly connected to the inner spatial geometry and its physical reflecting (aural and lighting) phenomena.
Sound as well light reveals cryptic information about the space via echo and reverberations. Those non linear physical process articulate the space along a dynamic and continuous medium and the geometrical space suggested by echo and reverberation not longer deals with Euclidean but with Multidimensional spaces. In this work, the conception of 'Space' explores structurally and visually the dynamic process engaged in a huge architectural volume (the Byzantine Saint Mark’s basilica in Venice) by reflections of the acoustic rays produced by a polyphonic song and the following transcription of reflections phenomena into geometric parameters and shapes.
This process enhances how the same acoustic phenomena distorts the architectural space creating “ghost-spaces”. These “unreal” spaces will exist even beyond the physical limits of real architecture. As a consequence this doubling process will destroy the spatial identity (perceptive level) as well as the centrality role of the subject (existential level). The space and the Ego will dissolve into a new geometrical and psychological pattern, mutable, dynamic and elastic.
In space, the image of an object or architecture is built through the accumulation of information (geometrical, visual, aural). The strength of this process is such to create spaces which are imaginary, elastic and open to saundry directions; spaces existing beyond those really perceived and geometrically described by the Euclidean systems of geometry.
Our perceptive apparata have such a degree of sensitivity to be able to grasp, for example, small variations in light and sound, and, on the basis of these variations, elaborate a mental image of space, translating data such as volume and strength, brightness or reverberation period into parameters of distance, extension and depth.
Sound and light, perhaps due to their unsubstantiality, are, in fact, able to reach the essence of a space that is revealed through the reflexion of its light and sound. This paper explores the mechanisms — both physical and psychological — through which these reflexions induce our mental apparatus to deform the real image of a space, and analyses how and why these transformations generate imaginary architectures existing beyond the boundaries of the real ones.
Geometry as frozen music 
Music and light are partly a matter of solid geometry, in the sense that sounds and rays of light propagate according to definite geometrical patterns. Athanasius Kircher during the 17th century wrote that “(…) sound is a geometrical emanation of its source,” stating, in other words, that the Euclidean theories were at the heart of the acoustic phenomena, and that it was possible to plot (through bundles of radial straight lines) the route taken by sound waves.
Left: Athanasius Kircher, Musurgia Universalis (1650), tome II, fol. 264, Iconismus XV. Middle: Athanasius Kircher, Musurgia Universali (1650)s, tome II, fol. 303. Iconismus XVII. Right: Athanasius Kircher, optical studies.
Another reason for investigating musical sound in terms of architectural geometry “has to do with the spaces within which sounds are produced and heard. A basilica, legislative chamber or concert hall, designed to reinforce and clarify musical and spoken sound, can be thought as an enlarged version of a musical instrument’s resonator, or even of the human voice box. “Architectural acoustics” is a modern discipline, but the subject itself goes back into antiquity. The Greeks and Romans built indoor theatres for music known as “odeia”. The spaces presumably sought to channel and amplify the performers’ music and speech. As to outdoor structures, where the audiences were usually much larger, Vitruvius discusses the use of strategically placed sound resonators or boosters (Vitruvius, De Architectura, 5.5.1). Presumably when speakers and singers sounded those pitches, their notes were amplified or perhaps transmitted to a different part of the audience. The 16th century, while almost always quoting Vitruvius, embarked on its own elaborations of these ideas. The French natural philosopher and musical theorist Marin Mersenne   begins his treatise Harmonicorum Libri (1636) with a short illustrated essay on architectural acoustics, maintaining that “sonic rays” (radios sonoros) are projected in conical form. The rays bounce off inclined planes and can be mapped onto screens using reflectors shaped like half-ellipses or parabolas. The reflectors focus and project sounds by locating the speaker or player at one ellipse’s two foci. Additionally, Kircher’s Musurgia Universalis (1650) is a landmark in the history of acoustic theory. He is particularly concerned with echoes and reverberations, writing about caves and classical buildings where strange, elaborated echoes can be heard, and about how echoes may be bounced onward for long periods of time. Kircher also reinforces the analogies, so common in the late Renaissance period, between music and light. According to him, sound — especially musical sound — is the ape of the light: sonus lucis simia est. He diagrams the geometries of the linea actionis phonicae, the line of ray of “phonic action”. For Kircher, acoustics — like optics —is a matter of spherical and conic sections. Following this method in its essence, we will start by considering the acoustic geometry of a wide volume like the one of a Byzantine church, St. Mark’s in Venice. Built in the 10th century, the church is of the Greek-cross plan, with transepts of the same length and vaults of the same height, ideally tending towards a circular space. Moreover, the whole church typology seems to repeat, almost in a fractal fashion, the same basic circularity, traceable (in decreasing scale) in the domes, vaults, apses, and even in the columns themselves.
Left: Venice and St. Mark’s basin. Middle: Interior of the basilica with the two choirs. Right: Basilica Plan
The sections also display in quantity what the ratio is among the radia of the respective circumferences that, following Fibonacci’s sequence, draw a parallel with the cochlis progression of the human aural apparatus . There is, therefore, in St. Mark’s basilica, the intangible but consistant presence of an acoustic design, at times conscious, at times unconscious, that certainly influenced the centuries-old development of this building. The church, in fact, for the characteristics of its geometrical space and the kind of material covering it, behaves like a huge sounding box, amplifying the resonance of sounds, and extending the period of their echo. During the 16th century, composers like Giovanni Gabrieli   and Claudio Monteverdi wrote the “Sonatas in Echo” which, exploiting the peculiar acoustics of the basilica, produced sophisticated effects of sound distorsion, such as the protraction of the echo, or the harmonic overlapping of a note with the reverberation of the previous one. In those same years, the practice of the salmi spezzati (‘divided or split psalms’) was introduced, which consists of arranging the choir on two different lofts, opposing one another from the two sides of the nave. Whereas the choir’s splitting, in the field of acoustic phenomena, doubles the echo’s depth, the same phenomenon, in the field of sound perception, manifests itself in the image of an elastic space, deep, dilated beyond the visual spacial boundaries of the church. Hearing the echo of a sound expanding from side to side is as if the image of the basilica, with its columns and mosaics, transformed slowly into something similar to the sonority of the hollow belly of a grotto. Particular sounds, exalted by the acoustics of the building, have the power of evoking, so to speak, the idea of a space exceedingly wide, accelerating our imagination in a race towards infinity.
Euclidean Patterns in Aural Phenomena
The “Sonatas in Echo” imitate an acoustic phenomenon — i.e. the echo — that works through definite physical mechanisms which follow (Marsenne and Kircher) geometrical Euclidean patterns. But how do these mechanisms work exactly, and how can they, in the last resort, lead to the distortion of spacial perception? Let’s move in time and space, and imagine ourselves walking down into the tube, hearing a train arrive from a distance. Thinking we understand from which side of the corridor the train is coming, we are surprised to find that the sound heard from the left actually comes from the train arriving from the right. The reflection inside the tunnel “deceives” our perception, driving it to represent the existence of a train where no train actually exists, and the deception lasts till our sight is able to verify the real train as it arrives
Reflected standing waves. The moment of overlapping is called interference, and it represents the sum of the single wave fronts.
opposite our expectation. The walls, like mirrors, reflect the sound rays, projecting their real source — the train — beyond the wall, giving us the impression that the sound is coming from an “imaginary” train (or a “ghost” train) that exists only by virtue of the reflecting wall. In Euclidean geometry, this phenomenon is well represented by conic reversal projections, and the example of the train in the tube demonstrates how Kircher’s acoustic geometry can faithfully represent the reality of sound phenomena. Going back to St. Mark’s, let’s consider the acoustic geometry of the basilica’s internal space; that is, let’s imagine placing the sound sources on the pulpits where the Salmi Spezzati were performed and leaving the spread of sound rays to trace their reflections along the basilica walls. Some reflections will cover the space of the church tens of times before reaching the listener located under the central dome. With every reflection, the geometrical space transfers to the incident wave part of its geometrical features, modifying the internal composition of its frequencies. The modified sound wave conveys to the listener the sound characteristics of the space that contained it during all the reflections. Considering, in the specific, the route of some acoustic rays, it is apparent how they travel far and wide through the whole space of the basilica, connecting different and opposing points of the church. Each of these points transfers to the wave its geometrical features which the sound moves elsewhere, reflection after reflection. The sound, acting as a sort of dynamic spatial memory, manages to connect images otherwise scattered at the time of their perception.
Preliminary studies of the propagation of acoustic rays in volumes with circular vaults. The drawing introduces the idea of a surface (top centre) that is moved away and distorted by the sound reflections.
An acoustic image is, therefore, characterized as the completely absorbing experience of a space, because it is capable of giving back to the observers, the moment they hear it, the interaction of a sound with the space that contained it, reflection after reflection. (…) A sound reflected and sent back from wall to wall saturates the internal volume of the basilica, and prolongs the impulse for many seconds. Going back to our example, a listener located under the central dome perceives the sound coming from each direction, reflected by the walls and floor, with decreasing volume and reverberation period. Cognitive psychology tells us that our sensory apparatus places a sound source (also invisible ones) farther away, the smaller it is in terms of sound volume. With the progressive decrease of the reverberation, the listener himself, although able to see the orchestra playing beside him, is instinctively lead to imagine it moving away, beyond the basilica’s walls, beyond those walls which, like mirrors, reflect both the sound and its source. Extending the example, it is as if the whole space of the church dilates beyond St. Mark’s, to the extent of reaching St. George island. Sound has therefore the power of deforming spacial perception, making space assume geometrical configurations that are complex and not linear, configurations of “ghost” spaces extending beyond the physiological boundaries of our sensory perception.
Acoustic geometry studies. A bundle of sound straight lines emitted by a punctiform source is reflected by the walls of a cubic environment, projecting the reflected source on a plane symmetrical to the original source. Below: a study of the projection of a sound ray, oblique to all the Cartesian axes xyz. Right: Preliminary studies of the representation of reflected sources. The resulting sonic space takes on the features of a cloud of points gathering in limited areas in the space surrounding St. Mark's.
Geometry of Acoustic Perception.
Towards a geometry of imaginary.
Sound sources emit standing waves which expand in all directions, and saturate the acoustic volume of the basilica. At the outset, this paper will take into consideration two sources, placed on the pulpits inside St. Mark's, where the choir singers used to sit. The geometrical procedure used to trace the sound rays consists of a straight line - incident on a surface - having the same angle as the reflected one, both on the plane and in space. As displayed in these diagrams, some reflections travel the church's length hundreds of times before finally reaching the listener, positioned under the central dome. A few rays seem to "get lost" in an endless series of reflections, as if they were trapped inside the resonance chamber of the north and south transepts. The procedure only includes the calculation of 5 rays, placed in each square meter of the basilica, reaching a total of 3,800 reflections covering the whole angle of the source. From physics, we know that the angle of incidence is equal to the angle of reflection, and the sound straight lines are arranged on symmetrical axial planes. Consequently, the real source is mirrored on the symmetrical straight line and moved beyond the surface at a distance d, which is proportional to the space existing between the listener and that surface. It is then evident that, as the number of reflections increases, the imaginary sources - those which are perceived as real - apparently move away from the listener, reaching a considerable distance that we can quantify, by means of geometry, as being equal to the sum of the single segments travelled by each acoustic ray. If we apply this method to all sound rays and try to represent on a Cartesian plane all of the reflected sources (the red points in the final render and the letter “S” in the CAD studies), we are able to observe how they form "cloud"-like clusters, almost creating a force field within which the golden surface is passively distorted. It is as if the sound produced by a source and the reflection coming from the walls had "fluidized" the church's surface, progressively expanding it in a hazy and rarefied space.
Each geometrical projection establishes, through the sound rays, a biunique correspondence between the Cartesian space and the acoustic space. As already mentioned, a few rays get lost in the basilica's gaps, only reaching the surface after thousands of reflections and with a sound intensity close to null. Since the physiology of our aural apparatus allows us to pick up only the sounds above a certain threshold , many projections - theoretically possible - actually become pointless in terms of phenomenology, since they are impossible to decipher in images. To prevent transforming our imagination into an a-priori geometrical product , it is necessary to set a limit beyond which the task of the reflexive projections can be considered concluded. At this point, an extremely fascinating horizon opens before us, because the Cartesian unit that could once describe the basilica's physical space, if considered in terms of sound, becomes a discontinuous system of presence and absence. We find ourselves poised between a literal translation of Euclidean space and the beginning of the indeterminate realm of permanent transiency. The sonic space, originating from the lucid and crystal Cartesian geometry, evolves into an existential condition of suspension, forcing the subject into a state of aesthetic passiveness.
The Realm of Antithesis.
Contradiction in Perceptive Processes.
A sound’s echo dilates — during the period of its reflexions — a space already existing in the sight of the observer. As a consequence, the observers find themselves between, so to speak, two contradictory realms: an “objective” realm, connected to the sense of sight and conditioned by perspective; an “imaginary” realm created by echo and sound reflexions. From the geometric viewpoint, perspective and sound reflexion behave in ways as opposite as the spaces they generate. Perspective tends to compress differences in distance on the line of the horizon; on the contrary, sound reflexion phenomena prolong the geometrical space in many directions, extending it beyond the horizon of the visible. The situation that comes into being represent a paradox — from both the Cartesian (two contradictory linear projections) and a psychological point of view. The doubling of space, in fact, triggers a process of internal division: it is as if our cognitive apparatus has to process contradictory data, albeit sensing their common origin . Moreover, anthropologically speaking, the sense of belonging to a space is based on the univocal identification of all the sensory data gravitating around that particular environment. The very principles of logic and Euclidean geometry are known as principles of identity and non-contradiction; in the specific of our example, this means that being in a place excludes being at the same time in another. .This study, however, demonstrates how some constructions, due to their geometry, compel the observer to experience the simultaneous existence of many spaces, causing a feeling of disorientation foreboding the loss of identity.
Antithesis and Rewriting.
Like Kant, in his Critique of Judgement , we understand the ‘sublime’ as the aesthetic value created by the perception of something measureless and immeasurable that generates within us an ambivalent frame of mind. It is exactly the perception of a space shown as limited by our sight, but proven to be immensely vast to our hearing which is ambivalent in this case. On the one hand, we are disappointed because the visual image cannot embrace the sweep of our aural image; on the other hand, we are fulfilled because our consciousness is driven to raise to the idea of an infinity suggested by this boundless acoustic space. The disappointment our imagination suffers the pleasure experienced by our reason, because boundless spaces have the power to evoke inside us — through sound — the idea of a superior infinity. In this sense, the initial phenomenological dissociation is then recomposed in a dynamic feeling able to transform the subject’s physical smallness into a final awareness of spiritual greatness. In other words, becoming aware of the fact that the real sublime is not in the architecture we are looking at — with its twofold and ambiguous space  — but in ourselves, we convert the initial regard for the geometrical objects into a final regard for the subjects, i.e. for the supersensitive and qualified beings that we are. St. Mark’s space, like the space of any wide, resonant geometry, is called sublime because it uplifts imagination so that it might represent those cases in which the mind is able to “feel the sublimeness of its destination” . Initially depressive, the feeling of the sublime becomes exaltation, and our anguish turns into an active enthusiasm, able to project us beyond the immediacy of the phenomenon, beyond the confines of the geometrical space, and into the experience of pure space.
First CAD model for the display of reflected sources (S letters). The light coloured nurbs represent the way the sources arrange themselves in space, showing the forces that determine the arrangement and justifying the subsequent distortion of the golden surface (light brown).
Geometry as Frozen Music:
·  George, L. Hersey, Architecture and Geometry in the Age of the Baroque, The University of Chicago Press, Chicago and London, 2000. See chapter 2: “Frozen music”, pp. 22-52.
·  George, L. Hersey, The Monumental Impulse. Architecture’s Biological Roots, Cambridge, Mass. London, 1999. See chapter 9: “The Biology of Architectural Reproduction”, pp. 167-70.
·  Tipler P.A., Invito alla fisica, Zanichelli, Bologna 1997. See cap 15-17.
·  Helmut A.Muller, Principles and Application of Room Acoustic, Lothar Cremer, Bhonn 1994. See 1.1-4.
· Otto Demus, The Church of San Marco in Venice : History, Architecture, Sculpture, with a Contribution by Ferdinando Forlati. Dumbarton Oaks Research Library and Collection, Trustees for Harvard University , Washington, 1960.
·  I. Fenlon, “Strangers in Paradise: Dutchmen in Venice in 1525,” in Music and Culture in Late Renaissance Italy, Oxford, 2002, pp 36-8.
· , “Architectural Spaces for Music: Jacopo Sansovino and Adrian Willaert at St Mark’s,” published in Early Music History, Cambridge University Press 2004, Vol. 23, pp. 153-84.
·  Jeffrey Kurtzman and Linda Maria Koldau, “Trombe, Trombe d'argento, Trombe squarciate, Tromboni, and Pifferi in Venetian Processions and Ceremonies of the Sixteenth and Seventeenth Centuries,” in Journal of Seventeenth-Century Music, Vol. 8.1, the University of Illinois, 2002. see chapter 17: “Matteo Pagano's Woodcut of a Ducal procession 1556-59.” The original xylograph 1556-59) are preserved in the Museo Correr in Venice.
·  Angelo, Gardano, Canto, concerti di Andrea et di Giovanni Gabrieli etc. In Venetia: appresso Angelo Giordano, 1587.
·  Giovanni, Gabrieli, Sacrae Symphoniae, liber secundus, senis 7-19. Tam vocibus, quam instrumentis. Editio Nova etc.Venetiae: Aere Bartholomei Magni, 1615.
·  Marin Mersenne, Harmonie Universelle, Contenant la Théorie et la Pratique de la Musique, transl Chapman, R.E., Martinus Nijhoff, The Hague, Netherlands 1957.
·  AAVV,The New Grove Dictionary of Music and Musicians, 2nd Edition, ed. Stanley Sadie , McMillan, 2000.
·  Michael John Gorman,: The Angel and the Compass: Athanasius Kircher's Geographical Project, Stanford University Press 2002.
Geometry of Acoustic Perception.
·  Mannel, Robert, The Perceptual and Auditory Implications of Parametric Scaling in Synthetic Speech, Unpublished Ph.D. Dissertation, CITTA', Macquarie University, 1994.
·  Suzuki Aae, James Kozloski, and John D. Crawford, "Temporal Encoding for Auditory Computation: Physiology of Primary Afferent Neurons in Sound-Producing," in The Journal of Neuroscience, July 15, Washington, 2002.
·  Abbagnano, Nicola, Giovanni Foriero, Filosofi e Filosofie nella Storia, Edizioni Paravia, Torino, 1992. See Vol. II, pg. 228-33.
·  Cremaschi, S., L'Autonomia Spirituale. La teoria della Mente e delle Passioni in Spinoza, Vita e Pensiero, Milano 1979, See the introduction, pg. XV-XXIII, and chapter 3, pg. 89-94.
The Realm of Antithesis:
·  Durand, Gilbert, Les structures anthropologiques de l'imaginaire : introduction à l'archétypologie générale, 11e éd. Paris : Dunod , c1992. See the introduction “Convergent Method and Psychologist Methodology”, pp33-41.
·  Casey, E. S., Getting Back into Place. Bloomington, Indiana University Press, 1993. See pp. 256-289
·  Rapoport, A., A Critical Look at the Concept `Place', National Geographic Journal of India, 1994, 40, pp 4-19.
·  Boschetti, M., Staying in Place: Farm Homes and Family Heritage, Housing and Society, 1993, 10, pp 1-16.
· Casey, E. S. (1997). The Fate of Place: A Philosophical History, Berkeley: University of California Press.
·  Merleau‑Ponty, The Phenomenology of Perception, Humanities Press, New York, 1962.
·  Heidegger, M., Being and Time, Harper & Row, New York 1962.
Anthitesis and Rewriting:
·  L. Pareyson, The Aesthetic in Kant, London Press, London, 1976.
·  R.Assunto, L’estetica di Emmanuel Kant, Loescher, Torino 1998.
·  B. Foltz, Inhabiting the Earth: Heidegger, Environmental Ethics, and the Psychology of Perception. New York: Humanities Press(1995). See Chapter V, pp. 156-178.
·  Immanuel Kant, Critique of Judgement, transl. James Creed Meredith, Duquesne, 1790.
·  Immanuel Kant, Critique of Pure Reason, translated by Norman Kemp Smith and with a new preface by Howard Caygill, Palgrave Macmillan, 1929.
 These notions involve what, with a bow to Friedrich von Shelling, can be called “frozen music,” music that is somehow there but not audible, music whose sounds have been crystallized into the form of measurable visible spaces and solids. The musical ratios are simultaneously geometric relationships, so that the thing that “freezes” music into architecture is geometry .
 The upper part of the basilica is covered with mosaics laid with the Byzantine technique of hot fusion. Siliceous material was melted and laid in rectangular shapes; while the paste was still red-hot, a gold leaf was applied. After cooling, it was covered by another layer of melted glass to prevent the gold oxidation. Whereas the glassy paste behaves as a perfect mirror to both sound and light, the arrangement of the tesserae creates a rough surface which slightly reduces the wave front intensity, without affecting the composition of its frequencies ,.
 Laura Moretti wrote an interesting article  about the origin of the salmi spezzati pholyphony. In his travel notes, the Flemish Arent Willemsz offers detailed descriptions of the liturgical ceremonies in St. Mark’s basilica during the time of his stay in Venice in 1525. In his account of Vespers, Willelmsz writes: “There is a bench, preciously made, which is placed squarely in the middle of the choir. Here the precentors are sitting, and they alternate with one another, two together alternately intoning the psalms, very pleasantly and magnificently. And they sing splendidly, partly simple song (simplesanck), and partly fabridoen (falsobordone) on the other side; this is altogether very beautiful and magnificient to hear and to see” .
 Some studies   demonstrate how, for evolution reasons, our aural apparatus is adjusted to better perceive small differences in sound. Thus, we are more sensitive, both consciously and subconsciously, towards "background sounds," rather than sounds featuring high and distinctive frequencies. In the specific case of this paper, this observation confirms that even almost inaudible reverberations play a key role in the perception of sound phenomena.
 I am partly referring to Spinoza's concept of Geometrical Ethics  . In his Ethics, Spinoza states that human nature tends to identify itself with the necessary and rational order of the whole: a geometrical order whose rules organize the whole universe, both sensible and psychological. Referring to man, Spinoza says that our species is a natural phenomenon following nature's general laws, which can be researched with mathematical objectivity: "I shall consider human actions and desires in exactly the same manner - Spinoza writes - as though I were concerned with lines, planes, and solids." (Ethics, III, "Preface").
 The most illustrious example is possibly the church of Santa Maria in San Satiro, Milan. A space apparently as long as the church’s nave is actually 2 m long. Bramante’s optical illusion is obtained by physically compressing the intercolumnation’s space, according to the geometrical rules of perspective shortening.
 One significant dimension of life is the human experience of place, which is the major focus of phenomenological work in environment-behaviour research . In philosophy, Casey  has written two book-length accounts that argue for place as the central ontological structure founding human experience: "place, by virtue of its unencompassability by anything other than itself, is at once the limit and the condition of all that exists...[P]lace serves as the condition of all existing things...To be is to be in place".
Drawing on Merleau-Ponty , Casey emphasizes that place is the central ontological structure of being-in-the-world, partly because of our existence as embodied beings. We are "bound by body to be in place" (1994, p. 104); thus, for example, the very physical form of the human body immediately regularizes our world in terms of here-there, near-far, up-down, above-below, and right-left. Similarly, the pre-cognitive intelligence of the body expressed through action--what Merleau-Ponty called "body subject" — embodies the person in a pre-reflective stratum of taken-for-granted bodily gestures, movements, and routines, which is not self-contradictory in nature .
 A central focus of phenomenology is the way people exist in relation to their world. In Being and Time, Heidegger  argues that, in conventional philosophy and psychology, the relationship between person and world has been reduced to either an idealist or realist perspective. In the idealist view, the world is a function of a person who acts on the world through consciousness and, therefore, actively knows and shapes his or her world. By contrast, the realist view sees the person as a function of the world, in that the world acts on the person and he or she reacts. Heidegger claimed that both perspectives are out of touch with the nature of human life because they assume a separation and directional relationship between person and world that does not exist in the world of actual lived experience. Instead, Heidegger argued that people do not exist apart from the world but, rather, are intimately caught up and immersed in it. There is, in other words, an "undissolvable and coherent unity" between people and the world. This situation — always given, never escapable — is what Heidegger called Dasein, or being-in-the-world. It is impossible to ask whether people make the world, or the world makes people because both always exist together, and can only be correctly interpreted in terms of the holistic and non-contradictory relationship, being-in-world .
 Kant’s treatment of the Sublime comes under the more general framework of the reflective judgements, i.e. those judgements in which “given the particular you need to find the universal” (C.G., Intr., IV, pp 18-19). In other words, the determinative judgements are cognitive or scientific, as studied in the Critique of Pure Reason; i.e., those judgements that “scientifically” determine the objects of sensible intuition (phenomena) by means of universal a-priori Forms (space, time and the 12 categories). Reflective judgements are, instead, aesthetic judgements, that merely reflect on a pre-existing object by means of determinative judgements, and merely apprehend it through our universal need for purposiveness and harmony . I would like to underline the use Kant makes of the term ‘Reflexion,’ which for him takes the technical meaning of an operation through which specific representations (geometrical, visual, and aural) relate to our mental faculties and principles with the aim of singling out among them a possible agreement (concept of purposiveness). In Kant’s thought, this agreement always exists within the logic principles of identity and non-contradiction, under the assumption that a phenomenon will always provide univocal data (the image of a tree, of the mountains, etc.). In our specific case, the visual and aural phenomena of the same basilica (noumena) are to such an extent discordant that they destroy the Kantian a-priori Form of Space: the sight/hearing dissociation therefore destroys that (a-priori and necessary) representation of space which, according to Kant, is the foundation of all intuitions bonding us to the external evironment. This separation within the Noumenon (thing in-itself) opens the way to a weak version of the principle of identity itself, which can be considered as an identity of the parts, rather than an identity of the whole.
 An assessment on part of the subject that, however, does not imply the depreciation of the sensible world, no matter how contradictory and antinomic it is.
 Kant, C.G., Intr.,V, pp, 35-9.