L'editoriale di (h)ortus


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Dopo quasi vent’anni di assenza – trascorsi, forse colpevolmente, a indagare architetture in luoghi più distanti del pianeta – sono ritornato a Urbino, alla ricerca non soltanto delle opere di Giancarlo De Carlo (e di tutti gli illustri architetti che lo hanno preceduto nella città di Federico da Montefeltro) ma anche della possibilità di fare un personalissimo punto sullo stato dell’architettura. Avevo sentito parlare da più parti del pessimo stato di conservazione degli Continua...

La città della postproduzione

Questo libro raccoglie una serie di saggi sulla postproduzione intesa sia quale condizione che connota oggi i territori europei, sia quale atteggiamento progettuale – realizzare non è più sufficiente e non è più centrale servono interventi altri, altre sovrascritture. Come nella prassi cinematografica, raramente la presa diretta esaurisce il momento di formalizzazione di un film: è necessario applicare un complesso di operazioni quali il doppiaggio, il montaggio, il missaggio che seguono la fase delle riprese e precedono la commercializzazione.
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Monocular vision as “conditio sine qua non” which is at the base of the reflection of flat mirrors

Paragraph 6
“Furthermore, [all this] is verified in this manner since the disposition of the eyes is constituted as if the one saw the other in the same instant, which is what happens since from the one and from the other the vision falls on a unique and same point between those [two] that are on the mirror.
If it does not occur in this way, it transpires that neither of these is aware of the other and that signifies that the rays of sight reflect themselves from one part and from the other.
From these things it results also that the reflection is at equal angles. There will be in fact a single and same angle because of the loss of one of the two rays on the mirror and because of the reflection of one of the two [rays ]parting from the mirror. [...]”
In this paragraph it is specified that the disposition of the eyes is constituted as if the one sees the other in the same instant on a single and same point between the two that one sees on the mirror. If this weren’t so, the eyes would each operate separately each for itself in such a way as to have a double reflection: one for each eye. Thus it is clear that the double reflection did not exist for the Ancients, as it does not exist for us, because this entailed, then as now, the visual alteration to which has been given the name ‘dyplopia’.
Therefore the fundamental notion which is at the base of vision remains certified: the cyclopic unity of sight, with the consequent co-incidence of the two optical axis in one principal visual axis. This unity, scientifically linked to the loss, in the reflection of the mirrors, of one of the two optical axis, becomes the “conditio sine qua non”, placed at the base of the Theory of Vision, and allows us to mark (Fig.7) a single eye O, or one sole pupil, instead of two.
Let us now proceed to analyze what are the motivations that justify the presence of the points Oo and O” that we have marked and what are the effective meanings that Ptolemy gives them.

The reflexion of the pupil, the principal optical axis, the double and opposite view, the necessity of a sign

Paragraph 16
“Since [the rays] proceed also perpendicularly from (the position of) sight to the mirror, the image will occur according to the dimension rendered of the established object in conformity to the gaze which is set straight forward. Each of these rays [orthogonal to the mirror], in fact, is seen on the perpendicular line which passes through the pupil. The rays in fact which transit through one who looks and which extend themselves towards the pupil parting from the origin, whose position is found within, at the center of the spherical globe, are all perpendicular to the surface of the pupil, which assumes the nature of a curved mirror, with a form of its own and configuration. For this reason we are able to know also the forms of things, exactly as the sight positions receive them which are, on one side and on the other, opposite.
When the reflection, which should occur from the objects to be observed to the pupils according to a direction and an opposition, is transferred to the mirrors, since it conserves the disposition that would be from the pupils to the objects themselves, there will be at this point the co-incidence also of the line which proceeds from the (position of) sight with the same ray which, in that case, there is between the pupil and the object to be observed.
Just as it occurs in the things which appear opposite from one part and from the other, when the gaze will fall at right angles onto the mirror and it reflects upon itself.
Thus there will be a sign of this [reflection ], in conformity to which occurs the appearance of the object, one only in the quantity and in the position, position which is that through which (the ray) arranges itself in a straight line perpendicularly to the mirror and to the pupil.
And consequently there will be a double and opposite view of the object in the dimension rendered and in characteristics: one which certainly goes from the (position of) sight to the thing which
appears, the other that goes instead from the thing that appears to the (position of) sight.”
This is the key paragraph, which constitutes a true turning point in the interpretation and in the scientific collocation of Ptolemy’s Optics within the outline of the history of Perspective. The sequence of the passages is as following.
Since the visual rays (Fig.7) can proceed also perpendicularly from the position of sight to the mirror (the ray OOo is perpendicular to the mirror), the image of the object to be observed will be in function of the gaze which is set straight forward in respect to the mirror. But each point of these orthogonal rays, thus including also that of the pupil, or better that which individuates the center of the pupil, as specified by Ptolemy, is seen on the perpendicular line which passes through the pupil orthogonally to the mirror. In other words, also the pupil, or the eye, must have a proper reflection, that is to say, a virtual correspondent of its own beyond the mirror on the orthogonal line to the mirror, passing through the pupil. One could not better grasp the importance of the rays orthogonal to the surface of a flat mirror if not through the reflection of the pupil itself. Being in front of a mirror, in fact, the real pupil indicates to us the exact position from where one perceives that given vision which we see in the mirror. But we immediately realize that the pupil is reflected onto the mirror upon the extension of the ray orthogonal from the pupil to the mirror, individuating the virtual pupil whose distance from the mirror, on the opposite side, is exactly as much as the distance of the real one from the mirror. We are able, therefore, to draw the corresponding virtual O” of O from the other part of the mirror, onto the orthogonal line through O to the mirror, so that O°O ”is equal to O°O.
But attention –again says Ptolemy-since the perpendicular line through the pupil to the mirror, or through the eye, intercepts the mirror, it reflects itself and returns on itself, returning upon itself, it is well that, in the point where the perpendicular line from the position of sight strikes the mirror, there should be a “sign”, a “nutus”, says the Latin, of the point of this reflection. This is the point “in conformity to which the apparition of the object occurs”; “a quo fit apparitio rei” says the Latin. But Ptolemy specifies again that this point must be “unus in numero et situ”, that would be to say “one only in quantity and in position”. The sign must be one only “in quantity” because the eyes, as we have seen, even though they are two and both appear in the mirror, they create just one single reflection of the image; it must be one only “in the position” because that point must be placed upon the mirror there where the perpendicular from the real pupil strikes the mirror. Thus the positioning of the point O° remains justified, in reference to which we have established our constructions.
The first, immediate conclusions which are deduced, once the drawings based on these indications have been made, consist of the fact that there are:
1) two eyes,the true one O and the virtual one O”;
2) two points, the true one A and the virtual one A”;
3) a single image A’ for both eyes and for both points.
It is easy, in fact, to realize that the true eye O sees the point A’ as if it were positioned in A” and that the virtual eye O” sees the same point A’ as if it were positioned in A.
Therefore the point A’, is an image twice.
To better illustrate what has been said up to now, let us observe (Fig.8) the two
cubes: the real one and the virtual one. We repeat: let us observe the ray from O orthogonal to the mirror. Upon the perpendicular OO°O” to the mirror is found the virtual pupil O”, which is opposite the first one, on the other side of the mirror and which is distant from the mirror exactly as much as the pupil O is distant from the same mirror.
The segments of the visual rays, which we have traced from the real pupil toward the image on the mirror, and their extension, onto the points of the virtual object, form a first pyramid with vertex O. The form which we have traced, or the reflected image, must therefore be understood as a straightforward image of the virtual object. Naturally it is this image, which is after all that perspective, that Ptolemy wants to develop. We will examine, in the paragraphs which follow, what is implied by the reflected image that is “associated” to the straightforward vision of the virtual object. The segments of the reflected rays, instead, which part from objective points in order to reach the images on the mirror, once prolonged starting from the mirror, converge beyond the mirror in the vertex O” of a second pyramid.
Summing up: for “a double and opposite view of the object in the dimension rendered and in characteristics” (the Latin says “aspectus rei duplex et diversus in proportione et virtute”), which generates or naturally implies, also two visual pyramids having vertices in the two points O and O”, we understand the reflected image that we have traced of the true object; this image coincides also with the straightforward image of the virtual object.
It is well to focus immediately our attention on the fact that during the Renaissance appeared, in a towering manner in Leonardo da Vinci, “two contrary pyramids”, when he says: “Perspective, in dealing with distances, makes use of two opposite pyramids, one of which has its apex in the eye and the base as distant as the horizon. The other has the base towards the eye and the apex on the horizon. Now, the first includes the (visible) universe, embracing all the mass of the objects that lie in front of the eye; as it might be a vast landscape seen through a very small opening; for the more remote the objects are from the eye, the greater number can be seen through the opening, and thus the pyramid is constructed with the base on the horizon and the apex in the eye, as has been said. The second pyramid is extended to a spot which is smaller in proportion as it is farther from the eye; and this second perspective (pyramid) results from the first.”
But let us again pause for a moment upon the fact that Ptolemy felt the necessity to put that sign, or rather that “nutus”, there where the ray orthogonal through the pupil to the mirror is fractured upon the mirror itself. Though the Latin text presents evident interpretative difficulties and is not easy reading, as Lejeune himself affirms, it stands out in any case and is immediately evident that here are introduced two great concepts, which are at the base of the science of Renaissance perspective. Ptolemy’s ‘nutus’ is none other than the tangible ‘sign’ of the ‘hole’ which Brunelleschi made on his first panel, that is to say, the “centric point”of Alberti, while the orthogonal ray, which goes from the pupil to the mirror, is none other than the “centric ray”, again of Alberti.
For a long time I have been in search of further clarifications of this “sign”. Every effort has been futile. In the Latin text which Lejeune quotes later I have not found any reference to that “nutus”.
In the end, after having attentively reread several times the paragraphs which precede the Sixteenth as well as those which follow it, my attention fell upon the Latin text which goes from “<secundum id quod pretaxavimus ...” up to “... penes rem vere videndam ad prope>”, which is quoted in Lejeune twice. It is in fact part of Paragraph 1 and of the entire following Paragraph 13, as well as of the entire Paragraph 60. In this text,which goes from “<secundum id quod pretaxavimus...” up to “...penes rem vere videndam ad prope>” there is a phrase, which had caught my attention: “et conservat hanc metam cum eo quod ex utrisque apparet”, which translated signifies “and conserve this meta (destination point) with that which from both [the conformations] appears”. I was unable to find any connection of this phrase in Lejeune with the texts which immediately follow or precede the Paragraphs 1 and 13; in the same way I was unable to find any connection of the same phrase with the texts which immediately follow or precede the paragraph 60.
I maintain that the entire passage, which goes from “<secundum id quod pretaxavimus...” up to “...penes rem vere videndam ad prope>” must be placed immediately after the Paragraph 16, where it constitutes, as we will now see, the missing link. Let us give it the name Paragraph 16a and let us read it attentively in continuity with the text preceding it.

The associated image, the virtual object, the “meta” or the principal point, the ascertainment of the virtual, apparent “forma”, the straightforward and the reverse.

Paragraph 16a
“(And consequently there will be a double and opposite view of the object in the dimension rendered and in characteristics: one which certainly goes from the (position of) sight to the thing which appears, the other that goes instead from the thing that appears to the (position of) sight, in conformity with that which we have discussed before, where it was said that the images of things erected upon the mirrors at right angles, are seen according to straight lines without folds and appear positioned on the same side towards which the objects move.
In conformity to the scientific concept, in fact, that within the mirror we perceive that which appears in a straight line, and consequently we come to know the position of the object to be seen, we proceed in this manner also for the finding of the position of the virtual, apparent form, since the associated image is seen straightforward, according to the one and the other conformation, which is to say of the conformation of the object placed in front (of the position of sight) and of that which really appears, and conserves this meta (destination point) with that which from both (conformations) appear, as if all (the points) were seen according to an opposite position in respect to the side of its own apparent position. Therefore a straight quantity appears straight. At pre-established distances then, when a true image will be found on a straight line and the object will be arranged at right angles to the mirrors, it is necessary that that which appears of one side
is found at the same time in conformity to both (the views) on a single straight line.
And if a same segment will appear erect to the surface of a mirror and its apparition will be found on a straight line, again it will be seen erect upon the same surface, so that there is no distinction between this one and the entire extension, as if the objects to be observed were arranged in real places, naturally those which are arranged according to that which regards the mirrors in conformity to the things that are seen and to their forms, after having maintained, for each of the two positions, the meta (destination point) of that which appears in the object to be observed correctly according to the proximity.”
In order to better understand the text we should once again observe (Fig. 8) the two eyes, the two cubes and their image traced upon the mirror, which we will call the “associated object” (in Latin ‘res congregata’). The scientific theory of tracing upon the mirrors enables us:
1) to see the original cube as if it were placed straightforward, though opposite, in front of the observer;
2) to proceed in “the finding of the position of the virtual, apparent form” (the Latin says “cognitione loci forme non vere apparentis” where “non vere” has been translated as ‘virtual’).
This concerns two cardinal arguments which we will now analyze.
Let us begin by specifying that the original point of view O sees straightforward the image associated with the virtual object. In this operation of straightforward positioning, the associated image conserves “this meta” (destination point) (“hanc metam” says the Latin), which will be necessary to indicate on the mirror by means of “a sign” (the Latin “nutus ”), to which the image will remain anchored in its double correspondence to two objects: the real one and the virtual one. Through the orthogonal visual ray, (Fig. 9) which goes from the pupil to the mirror and which corresponds to Alberti’s centric ray, or to our principal ray, pass all of the planes of the reflection: in our case the four planes OO°Ta-a, OO°Tb-b, OO°Tc-c, OO°Td-d, which are perpendicular to the mirror and contain both the original visual rays and the refracted segments. Whereas, it is towards the “meta” (destination point) which is the point O°, that all of the images tend and flow as into a “pivot” or into a “vanishing point”, as well as the portions of the images, of the straight objective lines orthogonal to the mirror, placed both on this side and on the other side of it, since they have the virtual extension on the opposite side. Upon these images of straight lines (Fig.10) are also found all of the associated images of the objective points and of the respective virtual opposite ones. By placing us in front of the traced form, Ptolemy thus places us in front of this “meta” (destination point), which corresponds exactly –I repeat– to the famous hole in Brunelleschi’s panel, to be put “...in that place where upon the eye struck” (as told by Manetti), as well as the “centric point” of Leon Battista Alberti, that is our ‘principal point’, to say it in modern terms, of all the orthogonal lines to the picture plane. This vanishing point also constitutes the “pivot” to which are linked the two images: the reflected one (or specular) and the straightforward one (or perspective) of the virtual cube.
Let us continue for another moment to focus our attention upon the meaning of the “associated” image, in which coincide that reflected one and that straightforward one of the virtual object. Let us begin by making evident the three principal fundamentals that one may draw from this paragraph:
1) the images of straight lines, or portions of the same lines, erected upon the flat mirrors, are seen (Fig.10) according to straight lines without bending (“videntur secundum rectitudinem sine proclivitate”, says the Latin): such a very important factor implies that these images are not curved or arched;
2) the images of straight lines, or portions of the same lines, erected upon flat mirrors, “appear positioned on the same side towards which the objects move” (“apparent translate ad eandem partem ad quam res moventur”, says the Latin), that is why, for example, if one has the sequence 1, 3, 4, 5 etcetera, which begins to part from the mirror, this sequence will have to part in this same exact order also from the opposite side beyond the mirror;
3) based on the order of the rectilinear sequence one can find the position of the apparent “not true” object, that is to say the “virtual” object (the Latin says, “ita procedimus et in cognitione loci forme non vere apparentis”).
Let us explain by means of examples that which this implies. If we have (Fig. 11) the number 4, represented by simple lines and simple points, one can immediately draw its reverse, or viceversa, if we have its reverse, one can immediately draw its obverse with only the correspondence now described: this is the simple law of symmetry. Applying this same concept to the mirror, we will have, (Fig.12) for example, that the real points Tc, A, B etcetera, on one side, will be set on the opposite side always in the order Tc, A”, B”, starting from the mirror: a phenomenon which generates the turning over of the sequence and therefore the reversal of the square, with the inversion of the respective arrows. From the simple reduction onto a plane (Fig.13) of the spatial summary it is possible to further verify the facility with which one can obtain one or the
other of the two squares once the first one is fixed.
Therefore it is easy, if not immediate, to find the position of the virtual, apparent form or, vice versa, to return to that objective one.





 
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